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Synthese (2011) 182:181–183 DOI 10.1007/s11229-009-9664-z

Synthese special issue: representing philosophy Colin Allen · Tony Beavers

Received: 3 July 2009 / Accepted: 3 July 2009 / Published online: 6 October 2009 © Springer Science+Business Media B.V. 2009

The disciplinary output of philosophers has exceeded the comprehension of any single individual for a couple of hundred years now. Today even the largest philosophy departments cannot claim to cover the entire discipline. The traditional solution to the problem of attaining an overview of the profession as a whole, of “representing philosophy,” has been to print encyclopedias, dictionaries, handbooks, and indexes of philosophy. Encyclopedias promised the most comprehensive coverage, and for Anglophone readers, the publication of Macmillan’s The Encyclopedia of Philosophy in 1967 was a landmark effort in that direction. It took another thirty years for other encyclopedias of philosophy to be produced that attempted to cover even more unmanageable amounts of published literature. By this time, futurists inspired by the amazing growth of the World Wide Web (WWW) were already predicting the demise of the traditional book and its replacement by on-line publication in ever-increasing volumes. Whatever happens to traditional books, it is clear that digital technologies have changed the terrain in which all academic disciplines operate. The development of computers and philosophy have been intertwined from the beginning of computing, and philosophical ideas—such as the application of logic and formal ontology (in a sense that is now fully co-opted by computer scientists) to the organization of information—continue to be a driving force in the development of the WWW. Philosophers have also spearheaded numerous digital projects, and by the mid 1990s they were among the first humanities scholars to recognize the potential of the WWW for organizing their discipline. The advent of the Web has clearly

C. Allen · T. Beavers (B) Department of Philosophy and Religion, The University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, USA e-mail: [email protected] C. Allen e-mail: [email protected]

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reinvigorated the motivation of philosophers to build authoritative overviews of their entire discipline, and it has provided the tools to reinvent the encyclopedia as a dynamic reference work, capable of responding to new ideas and scholarship much more quickly than a traditional print encyclopedia ever could. The Stanford Encyclopedia of Philosophy is an archetype, predating the Wikipedia and its cousin, the peer-reviewed Nupedia by half a decade. But new digital methods also make it possible to go beyond encyclopedias to other forms of representation of philosophical content, and several such projects are nascent. This special issue of Synthese discusses the conceptual, ontological, technological, ethical, political, and professional dimensions of attempts to represent the entire discipline of philosophy. One of our goals with this issue was to collect in one place several of the leading projects in digital philosophy so that the profession can begin to discern and debate what might be the best practices for the representation of philosophy in the 21st century. The papers herein describe and reflect upon the promise and perils of attempts to represent the discipline, ranging from encyclopedias to formal data structures (e.g., formal ontologies and new forms of logic), search engines, and graphical methods for visualizing relationships among philosophical ideas and philosophers. Attempts to codify the discipline raise questions about the boundaries of philosophy, the legitimacy of specifying a canonical set of topics, texts, authors, and the possibility of capturing adequately the relationships among them. All representations of the discipline necessarily emphasize some ideas over others, even to the point of excluding some of them entirely. All philosophers should therefore be worried about the effects that prominent representations of the field might have on the shape of philosophy itself, especially since students and scholars may tend to favor the pursuit of questions and topics that are featured in the most visible or accessible resources. Some forms of representation also risk turning the rich dynamics of the discipline into something all too static. Furthermore, many philosophers are skeptical about the potential of digital methods for extracting meaningful representations of the discipline from the voluminous output of professional philosophers. These challenges and questions are addressed in a variety of ways by the papers in this special issue. The first three papers explore the use of “ontologies” with slightly different understandings of that term. Pierre Grenon and Barry Smith describe PhilO, a formal ontology of philosophy, which they describe as “a theory of the kinds of entities found in the philosophical domain and of their interrelations”. Their ontology is designed to be maximally useful for formal, machine reasoning and for compatibility with formal ontologies of other domains besides philosophy. Because of the care required to define terms explicitly and to axiomatize their relations, they envisage an “arduous long-term endeavor” by experts to build and maintain the ontology. In contrast, in their contribution to this issue, Cameron Buckner, Mathias Niepert, and Colin Allen describe the Indiana Philosophy Ontology (InPhO) project, which uses automatic methods and a small amount of expert feedback to create what they call “a dynamic computational ontology” for the discipline of philosophy. In accepting looser requirements than are placed on formal ontology, Buckner et al. aim to produce tools that can be highly automated but have significant utility for specific projects in digital philosophy – especially, but not limited to, the Stanford Encyclopedia of Philosophy. A third application of computational ontology to the representation of

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philosophy is described in the paper by Michele Pasin and Enrico Motta, who introduce their PhiloSurfical project. The goals of Pasin and Motta are explicitly pedagogical, seeking to provide a framework in which students may explore a key philosophical text (Wittgenstein’s Tractatus is their example) through a formal ontology which aims to capture the expert knowledge of a specific teacher. The different aims and methods of these three projects lead to different ways of organizing philosophical material into types of objects. Undoubtedly these papers are capable of seeding a debate about the appropriateness of these and other ways of organizing philosophical representations for the various purposes in which they are intended to be deployed. The fourth paper in this issue is by Christopher Menzel, who takes a broader look at developments in logic for the WWW. First-order logic has long been taken as the best tool in the philosopher’s toolbox for representing philosophical ideas and arguments. Yet, as Menzel points out, first-order logic reflects certain metaphysical assumptions from its Fregean heritage and is thus not a philosophically neutral tool. Interestingly, there have been parallel developments among philosophers seeking a more flexible representational tool for philosophy and among computer scientists who need to deal with the fact that the same information can appear in multiple formats on the WWW. Menzel, who has been among the leading developers of “Common Logic” for the Web, describes the evolution of logic on the WWW and tracks its relationship to the underlying semantical and metaphysical issues in philosophy. The last two papers in this issue describe attempts to represent philosophy as it is practiced. David Morrow and Chris Sula, originators of the Phylosophy Project, argue for a “naturalized metaphilosophy” – the data-driven investigation of the social interactions among philosophers and the spread of their ideas. They describe sources of data and ways of visualizing the networks in which philosophers participate, and they argue that their naturalized approach to the social aspects of philosophy is complementary to, not a replacement for, the argument-driven analyses which underlie most philosophers’ self-conception of their activity. The final paper in the issue is by Anthony Beavers, who describes the third iteration of his Noesis search engine for philosophy, current plans for its development, and the practical utility of enhancing its search capabilities with new affordances provided by machine-readable ontologies of the discipline. Beavers argues that Noesis fills a gap between general purpose search engines, such as Google, and site-specific ones, such as the Stanford Encyclopedia’s internal search engine. As a consequence, Noesis seems well positioned to supply philosophers with comprehensive access to all aspects of philosophy, tying together everything from departmental and individual faculty websites, to online journals, professional associations and encyclopedias. Beavers argues that Noesis will make it possible to gather evidence to test claims about the discipline as a whole, potentially reducing our dependence on the necessarily idiosyncratic views of self-appointed gatekeepers. In sum, this special issue of Synthese demonstrates that philosophers are creatively using the computational tools and digital resources to manage, provide access to, and learn from the ever-increasing amount of activities and texts produced by the profession. In doing so, they are finding new ways to represent philosophy. We hope that these contributions will stimulate, challenge, and inspire other philosophers to build even better tools for furthering our own self-understanding.

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Synthese (2011) 182:185–204 DOI 10.1007/s11229-009-9658-x

Foundations of an ontology of philosophy Pierre Grenon · Barry Smith

Received: 28 August 2008 / Accepted: 11 March 2009 / Published online: 10 October 2009 © Springer Science+Business Media B.V. 2009

Abstract We describe an ontology of philosophy that is designed to aid navigation through philosophical literature, including literature in the form of encyclopedia articles and textbooks and in both printed and digital forms. The ontology is designed also to serve integration and structuring of data pertaining to the philosophical literature, and in the long term also to support reasoning about the provenance and contents of such literature, by providing a representation of the philosophical domain that is oriented around what philosophical literature is about. Keywords

Ontology · Philosophy

We take philosophy to be a field of human activity which leads to the creation of entities of a certain special kind: philosophical entities, including philosophical concepts, theories, doctrines, arguments, and methodologies. For our purposes here, what makes these entities philosophical is the fact that they are results or outcomes of philosophical activity. What makes such activity philosophical is something which, for our present purposes, can be seen as being primitive and thus undefined. Thus, we will not enter the debate as to what distinguishes philosophical entities from other entities of similar kinds (for example scientific ones). We merely assume that philosophical activity defines a domain in which we find philosophical entities, and we devote our attention to the question of what kinds of philosophical entities there are and how they are interrelated. The development of ontologies on the part of natural scientists and of knowledge system engineers has become common practice. The results of their work are used as P. Grenon Department of Philosophy, University of Geneva, Geneva, Switzerland B. Smith (B) Department of Philosophy, SUNY at Buffalo, Buffalo, NY, USA e-mail: [email protected]

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the basis of controlled vocabularies for the annotation of data and information in very many fields. They serve to make this data more easily retrievable, combinable, and susceptible to automatic reasoning. In what follows we apply analogous techniques to the domain of philosophy. Philosophical creations are entities of the sort that are documented publicly in philosophical literature, and they are themselves subject to further philosophizing. Philosophy itself is not the sum total of philosophical writings. Rather it is the process which leads inter alia to the creation of such writings through the creation and study of entities of various sorts. Hence an ontology of philosophy is neither merely nor even primarily a theory of philosophical language or terminology. Rather, an ontology of philosophy is a theory of the kinds of entities found in the philosophical domain and of their interrelations. The distinctive feature of PhilO, the ontology we present in draft form below, comes from the methodology used to obtain it. Many ontologies in the field of information science are obtained from the semi-automatic application of natural language processing techniques to large corpora of texts. PhilO, in contrast, is itself the product of a philosophical methodology. The result is, to be sure, rather humble as a work of meta-philosophy. This has to do with a number of methodological principles which we will explain in due course. In particular, it is not to be seen as the product of any fixed doctrine. It is, instead, merely a suggested starting point for what we anticipate will be an arduous long-term endeavor. It is to be viewed also as being in every respect revisable. The creation of ontology artifacts to serve retrieval and processing of data is an infant discipline, and in this, as in other domains, we are still learning how best to proceed. All ontologies in non-trivial domains will remain forever works-in-progress, and this is true, too, of the PhilO ontology. What we present here is only a portion of a complete ontology of philosophy (more precisely: it is an ontology that covers the entire domain of philosophy but only in first approximation and only at a general level). Our aims are as follows: (i) to present a methodology for building ontologies that is inspired by a certain philosophical method (which we believe is generalizable to ontologies of other types and in other domains); and (ii) to identify the questions which would need to be addressed in order to further enhance the ontology presented.

1 Why an ontology of philosophy? The products of philosophical activity are nowadays contained in publications, books, articles, and collections thereof, and to some degree also in videos and other media. They are contained also in documents whose purpose is to summarize, such as textbooks, dictionaries, encyclopedias and collections of abstracts. Increasingly, in philosophy as elsewhere, problems are caused by the fact that there is a large and growing mass of documents and other materials which one needs to sift through in order to find philosophical contributions of given sorts. On the other hand this mass of material is increasingly becoming available in easily searchable forms in on-line repositories of various sorts. Bibliographical databases such as the Philosopher’s Index are being used as aids to help in organizing and

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structuring such resources in such way as to make them more easily navigable. This includes a list of subject terms used to describe or annotate bibliographical entries modeled on lists such as the Library of Congress Subject Headings created by librarians. The more a search in the database can rely on such lists of keywords, the greater its likelihood of being successful; this is the rationale behind using such lists. But there is a significant shortfall where searches cannot be performed on the basis of matching strings identical to those which appear in the lists of keywords. The same applies to searching for information in a printed volume by using an index, and it applies even when using online resources such as the Stanford Encyclopedia of Philosophy, for example through its table of contents, since such resources impose no control over the terminologies used by the authors of their separate entries. Increasingly, however, the keywords used in browsing through and more or less efficiently retrieving content from such resources are being compiled into so-called controlled vocabularies (controlled by the editors of the corresponding resource on behalf of the relevant disciplinary community). There are two major types of such vocabularies in the philosophical domain: Unstructured thesauri, which are lists of terms with a low degree of informal organization. For example (Broughton 1998) consists primarily of two lists; a list of names of persons frequently mentioned in the Philosopher’s Index (for example Aristotle, Le´sniewski and Spinoza), and a list of so-called ‘descriptors’, which are terms encountered in the database of bibliographical entries (for example ‘About’, ‘Abstract’, ‘Cigarettes’, ‘Entailment’, ‘Fictionalism’, ‘Moral proof’, ‘New Zealand’, and so on). Structured thesauri, which are lists of terms with some organization, primarily of a hierarchical sort. For example (Berman 2001), which is based on the Library of Congress classification, is similar in content to (Broughton 1998), but differs in that its terms are organized into families and ordered (into ‘narrower’ and ‘broader’ terms) according to levels of generality. The notion of generality involved here is however still somewhat idiosyncratic, and defies straightforward logical definition. Thus, for example, ‘Beauty’ is seen as being a narrower term than ‘Aesthetics’. This does not mean that beauty is a subkind or instance of aesthetics; rather it means that documents dealing with the concept beauty are intended to be included by the compilers of this resource among the documents dealing with aesthetics. While unstructured thesauri are useful, for example in indicating coverage of bibliographic resources via enumeration, they do not convey any further information pertaining to the meanings of the terms they list. Moreover, they typically contain large numbers of terms which do not seem properly to belong to the domain in question. Thus although there may be a number of philosophical publications addressing issues related to cigarettes and smoking, it is unclear whether representations of these items ought to belong to an ontology of philosophy more strictly conceived. Similarly, among frequently named persons we find not only philosophers but also artists, writers, and historical figures. The relation of the latter to the field of philosophy may be obscure, but this does not mean that we should restrict ourselves to a purely

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institutional approach to populating an ontology of philosophers of the sort which inspired, for example, the Philosophy Family Tree (Tree n.d.). For there are also those borderline cases of authors who have produced philosophical writing through works that do not fit the academic standards, such as Musil philosophizing by writing novels (Mulligan 2001). This shows that we cannot rely on term lists only, but must incorporate also further means for detailing relevance to philosophy in some explicit way. Structured thesauri carry further information, in particular they loosely indicate certain forms of non-hiearchical relationships between their terms (as when saying that the term ‘philosopher’ is a term ‘related to’ or ‘associated with’ the term ‘philosophy’). One shortcoming of such artifacts is that they do not specify further the non-hierachical relationship between their terms. Yet, as already noted, a more fundamental concern derives from the origin of the mentioned resources in the realm of library science. For the information they contain pertains not to the meanings of the included terms, but rather to the documents which these terms are used to index. The relation captured by thesauri in the subordination of ‘Beauty’ to ‘Aesthetics’ is something along the lines of: beauty is a concept used in works in the philosophical field of aesthetics. Thesauri are blind to the structural relations that obtain between the referents of the terms they list, but it is precisely this sort of structure that interests us here.

2 A philosophical approach to ontology building Ontologies as information artifacts are constructed nowadays in many disciplines (Watson n.d.), and methodologies differ as to the sources used and the role of machine vs. human intervention. There is then a fundamental distinction, among ontologies in information science, between those that are handcrafted and those generated via natural language processing techniques. The latter are in practice created semi-automatically, since the process of ontology extraction requires validation by human editors if it is to yield usable content. The most successful approach to the building of ontologies seems however still to be one which relies entirely on human input. This is so, for example, of the Gene Ontology and of the other biomedical ontologies now being heavily applied in clinical and translational research (Smith et al. 2007; Rubin et al. 2008). Increasingly, too, the latter are relying on an approach rooted in part in the acceptance of the need to take seriously insights of logicians and philosophers for example on the role and nature of definitions and on issues of meaning and reference (Smith 2003). Such insights, too, can help in the avoidance of the use–mention and other confusions still standard in many ontological engineering circles (Smith 2004; Ceusters and Smith 2007). There is a simple rationale for using a philosophical approach to ontology elaboration in whatever one’s chosen domain. It is that, through careful examination and logical analysis, and careful attention to potential ambiguities and to the category mistakes and mistakes of use and mention that have plagued ontology construction in many information, library, and computer science circles thus far, we can reach more accurate and consistent representations of the domain at issue and of the relations which obtain between the represented entities. The resultant representations are also

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of a sort that makes them more readily able to support logical reasoning. This same motivation for using a philosophical approach to ontology elaboration speaks also in favor of ontologies created manually from the start, not least because post hoc review of the product of automated language processing is a task which, in our experience, rarely leads to outcomes which are structurally sound. Automated techniques yield networks of ‘associated’ terms which are thought to be more or less closely related; they yield what are called ‘lexical networks’. But such artifacts are no more insightful when it comes to representing the structure of a domain than are the sort of thesauri which relate terms according to their putative co-occurrence in an indexed document. Terminological and lexical information based on co-occurrence links are useful for certain retrieval purposes, but they typically do not rest on a well-founded representation of the corresponding target domain, and so they do not provide an account of how entities in that domain are interrelated. One further problem pointing to the limitations of lexical approaches is that of the lack of interoperability. This is because, even where one and the same term appears in a plurality of such systems, there is no guarantee that it will be similarly handled. One important quality criterion on ontologies, however, is that ontologies should as far as possible embrace a principle of modularity (leading to convergence on a single ontology for each domain) and that ontologies for neighboring domains should work well together (Smith 2008). The philosophical approach we advocate rests on a view of ontologies as consisting of representations of the entities in the domain of reality to which the ontology relates. Only on the basis of representations of this sort, we believe, will it be possible to make coherent progress in linking together different terminology systems (for example in different languages).

3 Guiding principles Our methodological approach is perhaps best summarized by a number of guiding principles for ontology building.

3.1 Realism Ontology, as we conceive it, is concerned with providing an account of the entities existing within a given domain of reality, where ‘reality’ is here understood in the broadest possible sense, to include for example not only molecules and planets but also works of literature, laws, and historical epochs. The objects of the ontological inquiry into a domain D are first-order entities in the domain D, rather than concepts in the minds of people (experts, in particular) who study D, or terms used (by experts, in particular) to refer to D and its components (Grenon 2008). Concepts and terms may, though, perfectly well form the subject matter of ontologies addressing psychological or linguistic domains; then, however, they are first-order entities in their own right. In the domain of philosophy, of course, many of the entities which our ontology is intended to help categorize are concepts.

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3.2 Relevance and modularity Before we can embark on the construction of an ontology of philosophy, we need to establish what sorts of entities and relations exist in the philosophical domain. This is problematic in part because many of these entities fall under kinds which are contextual specializations of more generic kinds, and pinpointing the differentia for the more specialized kinds is one important part of the ontology enterprise. Thus for example the kind philosophical concept and the kind philosophical theory are objects of enquiry the parties to which are themselves using concepts and theories which are philosophical in nature. To draw out the implications of this apparent self-referentiality is far from trivial. Establishing what sorts of entities and relations exist in the philosophical domain is problematic also because there are entities that may not be specific to the domain of philosophy but appear only under a certain guise in this domain. For example Bertrand Russell was a philosopher at certain intervals in his life, but he was not born a philosopher. He was also a father, an Englishman and many other things that are beyond the purview of an ontology of philosophy. Philosophers are all those persons who are involved in some way in the domain of philosophy. But they do not form a natural kind. To be a philosopher is what is sometimes called a role and typically demands a relational account (for example in terms of the participation of role-bearers in certain activities) (Trautwein and Grenon 2003; Arp and Smith 2008). To ease our problems with such questions we adopt two fundamental principles: The principle of relevance: we are interested in entities or features of entities which belong exclusively to our selected domain. For example we are interested in Bertrand Russell’s philosophical activity and productions and not in his biography as a political activist. Also we are interested in philosophical concepts, not in concepts as such. The principle of modularity: we assume that our ontology of philosophy is to be integrated into a larger body of interoperable ontologies pertaining to other, neighboring domains, for example, culture, politics, science, history, literature, and theology. It is in this larger embedding system that categories such as person, for example, would be found, thereby enabling us to attach to Bertrand Russell his personal features. This allows us also to make provision for fitting our ontology of philosophy under a more general umbrella ontology in which the generic features of concepts could be accounted for and in which also distinctions such as that between concepts and theories could be made in a more robust fashion. While the principle of relevance is used to select elements to include in the ontology of philosophy, the principle of modularity is there to allow room for elements that will allow us, in the future, to complete and embed the representations in this ontology into a broader system. This might for example allow extension of the framework to incorporate linkages between properly philosophical entities and entities of a geographical, historical or biographical nature.

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3.3 Maximally opportunistic use of resources In the main, our method is to proceed from ground-level analysis of the alleged entities in a given domain (for example, the philosopher Bertrand Russell, the concept of definite description or the axiom of reducibility) to the elaboration of a system of kinds of entities and their relations. The question we face now is: which sources and resources we should use for this purpose. This is not a simple question, because resources may differ not only in quality and comprehensiveness, but also in the sorts of biases they impose (for example Western vs. non-Western, analytical vs. Continental, and so forth). For the purpose of initial term selection there is some value in artifacts such as thesauri. The task of sketching an ontology can partly be seen as one of sifting through the lists of philosophical entities which such thesauri in their ramshackle way represent, and assigning them to coherent categories organized hierarchically by type and subtype. This is not, however, a fully satisfactory strategy because such lists fail to account for the nature of philosophy as a complex domain in which the different sorts of entities are related together by ontologically important sorts of relations (for example, parthood, precedence, influence). We may also draw on sources such as textbooks and articles for term selection. Unfortunately these, too, differ in the way they recognize alleged entities in the domain of philosophy and in the way they partition the domain of philosophy itself—since philosophers, the authors of the works in question, precisely disagree on such matters. Here, moreover, there is the problem of factual accuracy and also doctrinal neutrality, so that the question arises as to what sources can be trusted and to what degree. These considerations suggest a combination of an empirical approach, starting from a variety of established lists of relevant entities in the form of abstracts repositories and textbook indices in the domain of philosophy, and a more global classificatory approach to the domain—based on logical principles that are as far as possible neutral as between different points of view—the latter to be used as a means of ensuring consistency and coherence of the ontology structure.

3.4 Philosophical neutrality Initially we rely on those sources that are commonly recognized as authoritative. In many domains, such as those of the sciences or engineering, ontologists consult experts from whom they elicit knowledge about the domain. One could argue that this procedure is compromised in our present case, given the conceptual and controversial character of philosophy. But an ontology of philosophy does not have to engage with or resolve philosophical disputes. Rather, it is concerned with what entities there are in the domain of philosophy and thus also with what entities philosophical debates are concerned with. Thus an ontology of philosophy has to be guided by a principle of neutrality regarding its content in order to make room for all philosophical views, the latter themselves, together with the associated disputes, being treated as entities in their own right. The driving force behind the adoption of an unbiased perspective

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on philosophy is at bottom to ensure the adequacy of our representation for mundane purposes such as information retrieval. 3.5 Revisability of the representation One of the problematic aspects of many engineered ontologies is that they are static artifacts. This has to do with the fact that they need to be used in robust software applications to meet well-defined goals and requirements of a purely technical nature. They are not easily modified nor amended, sometimes because they are tailored to be used by specific systems and sometimes also because systems which are hard to update are tailored to them. We can see an analogous phenomenon also at the level of library artifacts such as thesauri and classification systems. The list of subject headings used by the Library of Congress, for example, has remained fundamentally unchanged for more than a century, and thus still shows considerable influence of nineteenth-century scholarship in the United States. Problems arising from such legacy phenomena give rise to short term ad hoc solutions when unforeseen situations are encountered (for example the need to classify books on hitherto unknown topics). As ontologies have become increasingly adopted by systems requiring frequent updates, new ways have had to be found to design them so that they are more easily extended and revised. The reasons to allow for ontology change turn not only on the fact that our knowledge is growing and being constantly subjected to correction, but also on the fact that the world is changing. The changes affect not only the world of information artifacts, which some ontology terms will be used to describe, but also the world that is represented in these artifacts. Ontologies rest on accounts of reality which are based on expert knowledge, but not only can knowledge of reality (in particular that of experts) evolve, so also can reality itself. This is true, too, in a domain such as philosophy. One objection which may be made against our approach is that the needed philosophical neutrality of the representation is betrayed by our adoption of what amounts, in effect, to a principle of realism as concerns the entities that populate the domain of the ontology we are constructing. Perhaps it is a philosophically biased position which regards (philosophical) concepts, theories, disputes, and so forth as entities. But this is the sort of bias that comes with the territory. Ontologies are representations of entities and of the relations between them. What we should beware of doing is building into our ontology controversial relations between the concepts which the ontology treats (for example that beauty is a kind of good). On the other hand, where claims are controversial, it must be possible to represent the distinction between doctrines which embrace these claims and doctrines which deny them. 4 The big picture The first thing we need to do in building an ontology of philosophy is to delimit the domain. The most generic claim behind our choice is that philosophy is an activity carried out by human beings, and that the main output of this activity is entities of certain sorts: philosophical entities. We believe that the thesis that philosophy is an

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activity carried out by human beings is uncontroversial. But even if we are wrong, a combination of our principles of modularity and revisability will allow a broader category of entities to be recognized as the substrate for the role of philosopher (for example including non-human agents, such as software systems, as authors of philosophical ideas). Another potential problem has to do with how we view the outputs of the activity of philosophizing. For example, is producing a philosophical argument a case of creation or discovery? We leave open such questions by employing a correspondingly general reading of ‘output’. The approach we have sketched so far leads us to identify three main features characterizing the domain of philosophy. In the first place there are philosophical entities which may belong to various categories (for example of concepts, theories, arguments, methods). In the second place there is philosophy itself, which is an entity dependent on certain activities performed by philosophers. We can then easily see that philosophy is a field divided into subfields (for example metaphysics, philosophy of science, aesthetics, and so forth). Finally, we can see that there are philosophers. We have said already that philosophers do not form a natural kind, but it is nonetheless also not only possible but traditional to divide philosophers into various groups according to more or less robust criteria (for example community of thought, tradition, nationality or period of principal activity). For the purpose of representing the domain of philosophy and philosophical activity in the form of an ontology, we are concerned not with the nature of philosophy as such, but rather with the distinctions and interrelations between the categories identified in the foregoing. It will matter to us, when mapping (as in: drawing a map of) the philosophical domain that there are at least three main polarities for such an ontology—philosophers, philosophical entities, and the field that is covered by these entities (what these entities are about). But we can leave open the question of the precise nature of these entities themselves. Whatever the answers to such questions might be, our claim is that the distinctions and interrelations between these three groups of entities will be preserved (no field is a philosopher, no philosopher is a philosophical entity, and no philosophical entity is a field). 4.1 Philosophical entities Philosophical entities are those entities which live their life within the philosophical domain of reality. They do not come in one kind only. Some are more simple, some more complex, and we can distinguish part-whole relations between philosophical entities of certain sorts, as for example between the concept of space and a theory of space. Such relations will themselves be of different kinds, so that we have not only different degrees but also different kinds of complexity. A cursory survey of philosophical activities suggests the following preliminary list of kinds of philosophical entities: – – –

concept (for example the concept of form) proposition (for example that forms exist) theory (for example Plato’s theory of forms)

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argument (for example Plato’s Third Man argument) method (for example the dialectic method as practiced by Plato).

Philosophical concepts are as near as we shall come to basic units of philosophical activities. Philosophical propositions are in first approximation made of concepts. And theories are made of propositions. There are also a number of roles that some of these objects may take on, for example, with respect to argumentation, the role of an axiom, hypothesis, theorem or conclusion. Arguments are of course primarily logical entities, but they can be philosophical in two ways: firstly when their object is philosophical and secondly when they follow argumentation patterns which are properly philosophical. This may be the case when arguments contain propositions whose support is philosophical in nature (for example appeals to intuition). Methods, too, are not in and of themselves philosophical, but there are philosophical methods (for example introspection, phenomenological analysis, argumentation, conceptual analysis, and so on), which will fall within the coverage domain of philosophical ontology as here conceived.

4.2 Philosophical fields and philosophers Philosophy, the field of activity, is a particular entity. It can be broken down into branches, its subfields. There is also a way of partitioning the field of philosophy in order to do justice to the fact that there is philosophy that is the philosophy of some philosopher. We make room for this partition in two ways. Consider young Immanuel, mesmerized by the beauty of a pebble in the garden and wondering whether the hidden face of the pebble exists. Immanuel is here philosophizing, though he does not yet know that he will grow up to be the great philosopher Immanuel Kant, who will be remembered for only one part of his lifelong philosophizing activity. He does not suspect, either, that out of this already impoverished portion of the whole, some subportion will be more or less digested by generations of philosophers to come, who will produce the philosophical entity called ‘Kantian philosophy’. There is Kant’s philosophizing and his philosophy; there are some congeries of theories that are an output of this activity, and there are various sequelae of this output. Since philosophy is also occupied with itself, there are two specific kinds of reflective exercise concerned with Kant’s philosophy. There is, on the one hand, philosophical historiography concerned with the philosophizing activity of Kant himself, from pebble to death. And on the other hand, there is Kantian philosophy, a developing creature with a life of its own. The first is concerned with a subfield of philosophy in which Kant himself was the main, if not the only player; the second is concerned with a theory or family of theories and, thus, with philosophical entities in our sense. Entities like the philosophy of Kant (in the first sense distinguished above) are not prime examples of philosophical fields; they are in fact very special cases. More interesting to the ontology of philosophy for us here are such portions of philosophy as are concerned with knowledge (epistemology) or with science (philosophy of science) or even with Kant’s writings (Kantian exegesis). These are distinctions among philosophical fields according to the topic with which the philosophizing activity is

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195 Instances

Philosophical Entity Philosophical Concept

Concept of form

Philosophical Proposition

Forms exist

Philosophical Argument

Third man argument

Philosophical Theory

Plato’s theory of forms

Philosophical Method

Dialectic method

Philosophical Field

Metaphysics

Person (philosopher)

Plato

Group of persons (group of philosophers)

Realist about forms

Fig. 1 The main kinds of entities in the domain of philosophy and examples of their instances

concerned. Such topical distinctions form the more robust and bona fide distinctions among subfields of philosophy. It is traditional to speak of philosophy as having a variety of branches or subdisciplines. Although there is a handful of examples of a very generic nature on which everybody seems to agree (metaphysics, ethics, political philosophy, philosophy of science, and so on), it is a quite obscure matter to recognize how philosophy is divided and by what principles. In Sect. 6 we will propose systematic criteria for dividing philosophy into subfields. We will also see how some of these criteria can be applied in the classification of philosophical entities of other sorts, including philosophers themselves. Classifying philosophers is warranted not only because philosophers are sources of philosophical entities—and thus of philosophy and its subfields—but also because their works, as well as to some extent they themselves, are subjects of further philosophizing. Thus there are not only ethicists and metaphysicians, but also Aristotle scholars and Hegel exegetes as well as philosophers of sport and philosophers of engineering. This does not mean that philosophers form kinds; rather they enter into, or form, groups. Thus Kant is not an instance of a putative philosopher–kind, not least because he wasn’t born a philosopher, however early he might have started philosophizing. Kant, like Plato, belongs to the group of people who are philosophers. This in turn means that he engaged in philosophical activity. Philosophical fields are niches for philosophers to produce philosophical entities, and these entities in turn may serve as tools (inputs) for further philosophizing. Figure 1 sums up in visual form the big picture that emerges from the foregoing discussion. The main kinds of entities in which we are interested in the philosophical domain are branches of philosophy, philosophers and groups of philosophers (in so far as they bring about and deal with philosophical entities), and philosophical entities themselves.

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5 Classificatory distinctions Subfields of philosophy, philosophers and groups of philosophers, and philosophical entities (concepts, theories, and so on) are the main kinds of entities we find in the philosophical domain. But of course it is possible, and indeed traditional, not only to arrange philosophy into subfields, but also to arrange philosophers into subgroups and, finally, to divide philosophical entities, concepts in particular, into a variety of kinds. Thus philosophy is divided into branches addressing specific topics, following specific methods or adhering to specific perspectives. Philosophers are often classified on the basis of the historical period during which they lived but also according to the country in which they were born or in which they were active as philosophers and the languages in which they spoke or wrote. Philosophical entities are in turn attached to these divisions, as the concept of nous is an example of an ancient Greek philosophical concept and the concept of transcendental ego is an example of a German idealist concept. These divisions do not however yield clear cut and systematic distinctions. In order to systematize the divisions in question we appeal to our principle of modularity. There is, in the first place, a backbone classification which corresponds to the main categorial distinctions we have made in the foregoing (into concepts, theories, and so forth), together with a subdivision of philosophy itself which follows the traditional topic-oriented division (into ethics, aesthetics, and so forth). In addition, we make provision for a number of modules providing further dimensions onto which to project this backbone structure. Suppose for example that we have an ordered list of periods of time. It is deceptively simple to segment philosophy as a whole as well as many of its subfields and groups of philosophers to produce a corresponding set of timedetermined divisions: twentieth-century ethics, nineteenth-century Aristotelians, and so forth. And what can be done with time can be done with many other aspects of philosophical activity and its actors, including geographical location, nationality, and cultural, linguistic or religious background. Although a formal approach allows systematization of such divisions along combinatoric lines, it is unclear to what extent the results are coherent reflections of genuine divisions in the underlying domain. Consider for example what German philosophy is or what a German philosopher is. Do such terms refer to a geographical, a geopolitical or a linguistic division? When does Germany start and end historically? Is Kant a Prussian or a German philosopher, and is he somehow less German than Heidegger or Habermas? And if the feature in question is linguistic, then is Roman Ingarden a German philosopher by this light, and is Hume (as in many German philosophical reference works) an English philosopher? Smaller and smaller divisions are easily defined combinatorially. The challenge, however, is to see whether such divisions are actually significant for carving up the domain at its joints, and this is hard work, as is shown for example by the discussions of the meaning of ‘Austrian philosophy’ in (Simons 2004, pp. 145–146) and of the complexity of the underlying reality in (Mulligan 1997). It would be the work of many disciplines (sociology, history, philosophy itself) to evaluate these divisions for tenability. It is in any event an enormous enterprise (see for example Holenstein 2004). What we are interested in here is the power of formal ontology in generating

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and manipulating such divisions. The question of which of them has a counterpart in reality is an empirical matter and hence a question that has to be answered by other means. 6 Formalization PhilO is a formal ontology of the philosophical domain. Formalization is useful on many counts. Not least because it is one step towards making the product of an ontological investigation readily available to computer processing, but also for explanatory purposes in virtue of the clarity of expression it provides. For our purposes here we adopt the resources of classical first-order predicate logic (with identity) and use the usual symbols for logical constants (in particular, ‘→’ for material implication). We use concatenations of large and small capital letters for names of individual constants (for example Philosophy but also PhilosophicalField) and the letters of the end of the Latin alphabet for variables ranging over individuals. Predicates will be italicized strings of letters of the alphabet (for example disjoint but also instanceOf ). Finally, we omit external universal quantifiers. 6.1 Top level categories An ontology is first and foremost a theory of entities, their kinds and their interrelations. We need now to put in place the formalism allowing us to sketch such a theory for philosophical entities. 6.1.1 Instantiation of a kind and subsumption between kinds The first relation that occurs in an ontology is that between a kind and the entities that fall under this kind. This is the relation of instantiation (here dubbed instanceOf ) holding, for example, between philosophy and the kind philosophical field or between Immanuel Kant and the kind person. As illustration, we will write the latter formally: instanceOf (Kant, Person). We will leave open the question of the features of the relation of instantiation, but we will treat all entities, both particulars and kinds, as individuals in our domain, following the strategy outlined in (Smith 2005) and applied to the domain of geography in (Grenon and Smith 2004) and to the domain of biology in (Smith et al. 2005). An ontology arranges kinds into classificatory trees or ‘taxonomies’. Taxonomies are ordered by a relation subcategoryOf between categories. Thus the second relation that occurs in an ontology is the relation of subsumption between kinds which holds, for example, between the kind philosophical concept and the kind philosophical entity. The relation of subsumption among kinds can be defined in the following way: subcategor yOf (x,y) ≡de f ∀z(instanceOf (z,x) → instanceOf (z,y)) We will use disjoint to express the relation between two or more kinds when they share no instances.

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We can now register what we have said in our informal discussion above: instance Of (Philosophy, PhilosophicalField) disjoint(Person, GroupOfPersons, PhilosophicalField, Philosophical Object) subcategoryOf (Concept, PhilosophicalObject) subcategoryOf (Proposition, PhilosophicalObject) subcategoryOf (Theory, PhilosophicalObject) subcategoryOf (Argument, PhilosophicalObject) subcategoryOf (Method, PhilosophicalObject) disjoint(Concept, Proposition, Theory, Argument, Method) Not all hierarchical structures in an ontology are subsumption trees. For categories can be also organized, for example, according to how their instances relate through the relation of parthood (partonomies). More generally, the relations there are between instances of kinds will allow for defining various relations between these kinds (Smith et al. 2005).

6.2 Domain relations We have already alluded to a number of ontological relations in the domain of philosophy. For lack of room, we will only draw a formal characterization of a small number of them (Table 1). This is already sufficient to go a long way in representing the domain of philosophy and we hope also that it will indicate the right direction for extending this preliminary account.

6.2.1 Subsumption among fields We use subfieldOf for the relation between two fields when the first is more specific than the second as, for example, between metaphysics and philosophy (formally: subfieldOf (Metaphysics, Philosophy)). This relation satisfies the following axioms (it is between fields, asymmetric, and transitive):

Table 1 Examples of binary relations used in PhilO

Entries in the first column indicate the domain; entries in the first row indicate the range of the corresponding relation

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sub f ieldOf (x, y) → (instanceOf (x, PhilosophicalField) ∧ instanceOf (y, PhilosophicalField)) ¬ (sub f ieldOf (x, y) ∧ sub f ieldOf (y,x)) (sub f ieldOf (x,y) ∧ sub f ieldOf (y,z)) → sub f ieldOf (x,z) 6.2.2 Subsumption among concepts We use subconceptOf as the relation between two concepts when the first is a specialization of the second. We mean moreover that the specialization is definitional and not subject to philosophical debate, thus, in particular, not theory dependent. For example, the concept of feminine beauty is a sub-concept of that of beauty (formally: subconceptOf (FeminineBeauty,Beauty)). But also the concept of space in aesthetics is a sub-concept of the concept of space in philosophy simpliciter. However, the concept of beauty is not a sub-concept of the concept of good, nor is the concept of person a sub-concept of the concept of material object, irrespectively of whether beauty is good or a kind of good or of whether persons are material objects. subconceptOf is a relation between concepts that is asymmetric, and transitive: subconceptOf (x,y) → (instanceOf(x, PhilosophicalConcept) ∧ instanceOf(x, PhilosophicalConcept)) ¬ (subconcept O f (x,y) ∧ subconceptOf (y,x)) (subconceptOf (x,y) ∧ subconceptOf (y,z)) → subconceptOf (x,z) 6.2.3 Group membership and subsumption among groups of philosophers We use memberOf for the relation between a person and a group (as between Kant and the group of all philosophers, which we will write formally: memberOf (Kant, Philosopher)). All groups in the domain of the PhilO ontology will be sub-groups of the group of all philosophers. We use subgroupOf for the relation between two groups of philosophers (more generally: between groups of persons) when the first is a group included in the second. The Cynics formed a group of philosophers in the here intended sense. The relation memberOf is asymmetric: ¬ (member Of (x,y) ∧ member Of (y,x)) We can define subgroupOf as follows: subgr oupOf (x,y) ≡de f ∀z(member Of (z,x) → member Of (z,y)) 6.2.4 Relation of an entity to a philosophical field We use inField as a generic relation between a philosophical entity and a philosophical field when the entity is one that belongs to that field as, for example, the concept of beauty belongs to the field of aesthetics: inField(Beauty, Aesthetics).

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in Field(x,y) → (instanceO f (x, PhilosophicalEntity) ∧ instanceOf (x, PhilosophicalField)) We keep this relation generic for the purpose of this presentation but of course what it is for a philosophical entity to belong to a field comes in many flavors, not least because philosophical entities themselves come in different kinds. Compare for example the relation between the concept of beauty and the field of aesthetics to the relation between the concept of space and the field of aesthetics and compare them both to the relation between Kant’s theory of aesthetics and the field of aesthetics. All philosophical entities in a field are entities in any superfield of that field. (sub f ieldOf (x,y) ∧ in Field(z,x)) → in Field(z,y) Moreover, all philosophical entities are objects in at least one field, even if this be only the field of philosophy. instanceO f (x, PhilosophicalEntity) → ∃y in Field(x,y) 6.2.5 Activity of a philosopher or group thereof in a field We use activeInField for the relation between a philosopher and a philosophical field in which the philosopher in question has been or is active as for example, Kant has been active in the field of aesthetics: activeInField(Kant, Aesthetics). Use of this relation allows for registering contributions by a person to a philosophical field. It is generic in the sense that it does not specifically relate to the contribution itself. Moreover, being active in a given field transfers to any superfield of that field. (sub f ieldOf (x,y) ∧ activeI n Field(z,x)) → activeI n Field(z,y) We can remark that if a person is active in any philosophical field, she is ipso facto a philosopher. (activeI n Field(x,y) ∧ instanceOf (y, PhilosophicalField)) → member Of (x, Philosopher) Generalizing that notion, we can also relate a group of philosophers and a philosophical field of their activity. For example, ethicists are those philosophers active in the field of ethics. We have a variety of options available as to how to represent such relations. For the sake of simplicity, we will allow expressions such as ‘activeInField(Ethicist, Ethics)’. In order to have a finer grained representation, one could introduce variants of activeInField, one for individual philosophers and one for groups. 6.2.6 Work on philosophical entities We use workedOn as the relation between a philosopher and a philosophical entity. This is a generic relation between person (here: a philosopher) and a philosophical

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entity which may be a concept, theory, argument or belong to any kind of philosophical entities. This is for example the relation between Kant and the concept of transcendental ego or Kant and the theory of transcendental aesthetics: workedOn(Kant, TranscendentalAesthetics). Here too we could refine the representation by introducing variants in order to account in particular for the variety of ways in which the workedOn relation between a philosopher and some philosophical entity can obtain. It would seem that the most important relation between philosophers and concepts is a relation of creation. Indeed, philosophy as an activity is in large part the creation of concepts. But philosophy is also a public matter and there are thorny issues as to the metaphysical nature of concepts themselves. This poses problems for the introduction of a creation relation (and variants, see Smith and Grenon 2004) for instance because it is often indeterminate whether a given concept should be described as having been created anew by a given philosopher or, rather, appropriated or rediscovered. For these and similar reasons we confine ourselves here to documenting the relation of working on. We can tie together work on philosophical entities and activity in philosophical fields in the following way, which expands on the earlier claim that philosophers are those persons active in philosophical fields: (wor ked On(x,y) ∧ in Field(y,z)) → activeI n Field(x,z) activeI n Field(x,y) → ∃z(wor ked On(x,z) ∧ in Field(z,y))

6.3 Further classificatory elements In addition to the categories and relations we find in the domain of philosophy, it is possible to carve out further distinctions for example among entities such as fields, philosophers, and objects. We will here only sketch how this may be done in modular fashion. Suppose we have a dimension such as time along which we wish to segment a number of philosophical fields. We can then map the one onto the other in the obvious way, creating terms such as ‘twentieth century philosophy’, ‘nineteenth century metaphysics’, ‘eighteenth century ethics’, and so forth. Now, imagine we do the same with another dimension such as one that lists cultural or national groupings. We can easily combine these in order to produce a more complex segmentation. Such a process can be reiterated indefinitely up to a level at which we reach very specific segments. This process is illustrated in Fig. 2. As already noted, such systematic segmentation might produce segments which are not all equally interesting from a philosophical standpoint or from the standpoint of history of philosophy. However, deciding to which degree the delineation of a given segment is relevant, insightful or valuable belongs to a level of analysis more detailed and more empirically oriented than that attempted here. PhilO, ultimately, must absorb this more detailed level. The preliminary version of the ontology presented here is however important, since it allows this more profound kind of segmentation to take place.

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Europe Ancient Period Greece 3rd Century BCE

Metaphysics

European Metaphysics

Ancient Metaphysics

Ancient European Metaphysics

Greek Metaphysics

Ancient Greek Metaphysics

3rd Century BCE Metaphysics

3rd Century BCE European Metaphysics subfieldOf

3rd Century BCE Greek Metaphysics

in during

Fig. 2 Metaphysics segmented along geographical and temporal axes with the resultant crosssegmentations

Figure 3 below provides an overview of the types of information whose representation is supported by PhilO already in its preliminary form presented here.

7 Conclusions and future work We have here presented a preliminary version of the central part of the PhilO ontology. In virtue of the methodological approach guiding its elaboration this preliminary version is just a step towards a fuller treatment of the whole domain of philosophy. Because of the modularity of our approach, we can take for granted that much relevant material from neighboring ontologies—for example from the domain of geopolitical ontology, ontology of persons, of activities, of publications and so on—could be associated with PhilO as supplementary modules. One line of future work would then be to link up the elements presented here to such external modules, eliciting in particular significant cross-ontology relations and adding further axioms to fit. But there is also much work to be done on the PhilO ontology itself. We have indicated in several places simplifications and approximations. In particular, we have only provided a sketch of the formalization of a selected fragment of the relations which would be needed in a full ontology of philosophy. In several cases, we have indicated desirable specializations or generalizations of both categories and relations. Once the catalogue has been augmented there will follow the arduous task of axiomatizing in a more detailed and serious fashion. Finally, the purpose of an ontology is to provide the

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Forms exist Concept of form

Metaphysician

workedOn

Plato

Third man argument Theory of forms

Ancient philosopher

Dialectic method Ancient Greek philosopher

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memberOf Realist about forms

subgroupOf activeInField

Fig. 3 Plato and some of the entities surrounding him in the domain of philosophy

elements for the representation of a domain. The ultimate test of its validity will be in its usefulness to this purpose in annotating philosophical resources on a broad scale and in demonstrating pragmatic benefits which can be gained therefrom, in philosophy as in other domains. Acknowledgements This paper is based on work supported by the Philosophy Documentation Center in Charlottesville, Virginia—www.pdcnet.org.

References Arp, R., & Smith, B. (2008). Function, role, and disposition in basic formal ontology. In Proceedings of bio-ontologies workshop (ISMB 2008) (pp. 45–48). http://bio-ontologies.org.uk/download/ Bio-Ontologies2008.pdf Berman, B. L. (Ed.). (2001). Library of Congress subject headings in philosophy: A thesaurus. Philosophy Documentation Center. Broughton, K. M. (Ed.). (1998). The Philosopher’s Index thesaurus. Philosophy Documentation Center. Ceusters, W., & Smith, B. (2007). Referent tracking for digital rights management. International Journal of Metadata, Semantics and Ontologies, 2(1), 45–53. Grenon, P. (2008). A primer on knowledge representation and ontological engineering. In K. Munn & B. Smith (Eds.), Applied ontology. An introduction (pp. 57–81). Frankfurt/Lancaster: Ontos. Grenon, P., & Smith, B. (2004). SNAP and SPAN: Towards dynamic spatial ontology. Spatial Cognition and Computation, 4(1), 69–103. Holenstein, E. (2004). Philosophie-Altas: Orte und Wege des Denkens. Zurich: Ammann Verlag. Mulligan, K. (1997). Sur l’histoire de l’approche analytique de l’histoire de la philosophie: de Bolzano et Brentano à Bennett et Barnes. In J.-M. Vienne (Ed.), Philosophie analytique et histoire de la philosophie (pp. 61–103). Paris: Vrin. Mulligan, K. (2001). De la philosophie autrichienne et de sa place. In J.-P. Cometti & K. Mulligan (Eds.), La Philosophie autrichienne de Bolzano à Musil (pp. 8–25). Paris: Vrin.

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Philosophy Family Tree. Last accessed July 14, (2008). https://webspace.utexas.edu/deverj/personal/ philtree/philtree.html Rubin, D. L., Shah, N. H., & Noy, N. F. (2008). Biomedical ontologies: A functional review. Briefings in Bioinformatics, 9, 75–90. Simons, P. (2004). The Anglo–Austrian analytic axis. In P. Simons (Ed.), Philosophy and logic in Central Europe from Bolzano to Tarski: Selected essays (pp. 143–158). Dordrecht: Kluwer. Smith, B. (2003). Ontology. In L. Floridi (Ed.), Blackwell guide to the philosophy of computing and information (pp. 155–166). Oxford: Blackwell. Smith, B. (2004). Beyond concepts, or: Ontology as reality representation. In A. Varzi & L. Vieu (Eds.), Formal ontology and information systems. Proceedings of the Third International Conference (FOIS 2004) (pp. 73–84). Amsterdam: IOS Press. Smith, B. (2005). Against fantology. In J. C. Marek & M. E. Reicher (Eds.), Experience and analysis (pp. 153–170). Vienna: HPT&ÖBV. Smith, B. (2008). Ontology (Science). In C. Eschenbach, & M. Gruninger (Eds.), Formal ontology in information systems. Proceedings of the Fifth International Conference (FOIS 2008) (pp. 21–35). Amsterdam: IOS Press. Smith, B., Ashburner, M., Rosse, C., Bard, J., Bug, W., Ceusters, W., et al. (2007). The OBO foundry: Coordinated evolution of ontologies to support biomedical data integration. Nature Biotechnology, 25(11), 1251–1255. Smith, B., Ceusters, W., Klagges, B., Khler, J., Kumar, A., Lomax, J., et al. (2005). Relations in biomedical ontologies. Genome Biology, 6(5), R46. Smith, B., & Grenon, P. (2004). The cornucopia of formal-ontological relations. Dialectica, 58(3), 279–296. Trautwein, M., & P. Grenon (2003). Roles: One dead armadillo on Wordnet’s speedway to ontology. In P. Sojka, K. Pala, P. Smrž, C. Fellbaum, & P. Vossen (Eds.), Proceedings of the Second International Wordnet Conference (GWC 2004) (pp. 314–346). Brno, Czech Republic: Masaryk University. Watson Semantic Web Search Engine. Last accessed July 16, (2008). http://watson.kmi.open.ac.uk/ WatsonWUI/

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Synthese (2011) 182:205–233 DOI 10.1007/s11229-009-9659-9

From encyclopedia to ontology: toward dynamic representation of the discipline of philosophy Cameron Buckner · Mathias Niepert · Colin Allen

Received: 10 January 2009 / Accepted: 2 June 2009 / Published online: 16 March 2010 © Springer Science+Business Media B.V. 2010

Abstract The application of digital humanities techniques to philosophy is changing the way scholars approach the discipline. This paper seeks to open a discussion about the difficulties, methods, opportunities, and dangers of creating and utilizing a formal representation of the discipline of philosophy. We review our current project, the Indiana Philosophy Ontology (InPhO) project, which uses a combination of automated methods and expert feedback to create a dynamic computational ontology for the discipline of philosophy. We argue that our distributed, expert-based approach to modeling the discipline carries substantial practical and philosophical benefits over alternatives. We also discuss challenges facing our project (and any other similar project) as well as the future directions for digital philosophy afforded by formal modeling. Keywords Ontology · Taxonomy · Encyclopedias · Metaphilosophy · Digital philosophy · Semantic web 1 Introduction Encyclopedias have always occupied a precarious position in academia. On the one hand they taxonomize human knowledge and provide valuable entry points for scholars C. Buckner (B) Department of Philosophy, Indiana University, 1033 E. Third St., Sycamore Hall 026, Bloomington, IN, 47405-7005, USA e-mail: [email protected] M. Niepert KR & KM Research Group, Department of Computer Science, Universitaet Mannheim, B6, 26, Raum B 1.20, 68159 Mannheim, Germany C. Allen Department of History and Philosophy of Science/Cognitive Science, Indiana University, 1011 East Third Street, Bloomington, IN 47405, USA

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and students into the intellectual worlds of academic disciplines, covering their subject matters in more breadth and detail than could any single person or even any reasonably-sized university department. On the other hand, they carry a risk of congealing knowledge into a cold and quickly-obsolete imitation of living scholarship, stultifying the thought of beginners who might be better off wrestling with multiple, recent perspectives than the predigested orthodoxy of a designated expert. The tension in being encyclopedic is especially acute today, given the recent explosion in the number of universities, scholars, and academic publications. While the explosion has made faithful and succinct summarization even more elusive, encyclopedias have perhaps never been more relevant. If we wish to prevent disciplines from disintegrating into collections of highly-technical cottage industries in which specialists speak only amongst themselves, the development and maintenance of reference works offering accessible, up-to-date summaries is imperative.1 Fortunately, the advent of the digital humanities has brought a rich new arsenal of strategies to help us respond intelligently to the academic avalanche. The development of dynamic reference works such as online encyclopedias has brought some relief, as these publications are more responsive to new work than was possible with traditional printing methods. Different editorial models have been created for dynamic reference works, from Wikipedia’s open authorship and editorship to the Stanford Encyclopedia of Philosophy’s more traditional editorial policies of selected editors reviewing the work of invited authors. Even though the availability of online encyclopedias does, in principle, make the latest scholarship more accessible, the relatively unsophisticated capacities of search engines and their users make it likely that the full potential of digital encyclopedias is far from being realized.2 In short, scholars and students don’t just need the reference works—they also need the means to search and navigate them effectively. To preserve the utility of encyclopedias as they grow, we must also improve our ability to represent their contents in meaningful ways accessible to novice and expert alike. The dynamic nature and increased scale of digital reference works, however, render traditional editorial methods of gathering and organizing metacontent (indices, cross-references, tables of contents) so resource-intensive and inefficient as to be practically inapplicable. This is especially true for projects with limited staff and resources, common consequences of adherence to the ideals of open access. To address these problems adequately, 1 For a discussion of the impact of this explosion on the discipline of philosophy in particular, see Rescher (2007). Rescher believes that one effect the explosion has had on the discipline of philosophy has been to reduce the relevance of the “Great Man” approach to its history—to hold that the agenda of philosophy is determined by a “dominant elite” and that if one follows the work of the several greats of the time, one captures everything of import. Rather, Rescher thinks we should instead recognize that “philosophical innovation today is generally not the response to the preponderant effort of pace-setting individuals but a genuinely collective effort that is best characterized in statistical terms.” 2 For an overview of the ineffectiveness of search, see for example Holscher and Strube (2000). Their unsurprising finding is that the initial searches of novices and subsequent corrections of their search string are largely ineffective. More interestingly, their research also suggests that neither expertise in the content domain nor expertise in web search are alone sufficient to produce a high success rate on common searching tasks; rather, a high success rate is only achieved by users with both high web experience and high domain knowledge. Thus the paradox of accessibility for digital reference works: those users most in need of the information that encyclopedias offer are the least able to find it.

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more sophisticated techniques of generating metacontent from large, asynchronouslyupdated textual corpora are required. These issues should be addressed with the help of domain experts and not merely by technologists working according to their own ideas of what scholars might need. The best practices require technological expertise to design the formal representations and domain expertise to capture the semantic content of corpora. Decisions here should not be made lightly, as choices in the process of representation embody substantive commitments about the nature of the subject which, if widely-adopted, may come to affect the trajectory of the discipline itself. 2 The Indiana Philosophy Ontology project This paper seeks to open a discussion about the difficulties, methods, opportunities, and dangers of creating and utilizing a formal representation of the discipline of philosophy. We review our current project at Indiana University, the Indiana Philosophy Ontology (InPhO)3 project. We are developing an ontology for the Stanford Encyclopedia of Philosophy (SEP),4 an online, open access, dynamic reference work. The ontology should also be suitable for deployment in other digital philosophy applications.5 Our approach to representing the discipline derives from what computer and information scientists call “formal ontology.” However, we will avoid using this term because some researchers sensitive to Husserl’s distinction between “formal ontology” and “material ontology” prefer to reserve the former for a stricter kind of ontology than is satisfied by some aspects of our approach (Poli 1995; and see 6.2 below). Instead, we prefer to refer to our representation as a “computational ontology” and “dynamic ontology.” We speak of ‘ontology’ in the information science sense of the term, rather than the metaphysical sense which may be more familiar to some readers. In information science, ‘computational ontology’ denotes a formally-encoded specification of the concepts relevant to a subject domain (including their properties and relations between them) and a hierarchical classification of those concepts into categories and subcategories (Noy and McGuinness 2001; Gruber 1993, 2008).6 The purpose of such 3 http://inpho.cogs.indiana.edu/. 4 http://plato.stanford.edu/. 5 For example, the InPhO is to be integrated with the Noesis philosophy search engine (http://noesis. evansville.edu/) and the InPhO interface itself already provides for ontology-guided search in the SEP, Noesis, and Google Scholar (see Fig. 4). 6 Put more precisely, we take a computational ontology to be a directed acyclic graph where nodes represent concepts and the links between concepts represent the taxonomic “isa” relation (e.g. in the graph where ‘Wine → Red Wine → Brunello di Montalcino, everything that “is a” instance of Brunello di Montalcino “is a” instance of Red Wine, and everything that “is a” instance of Red Wine “is a” instance of Wine (we are less strict as to whether this subsumption relation must hold in all contexts of discourse—see Sect. 6.2). A knowledge base is an ontology that has been populated with individuals; mathematically, knowledge bases contain another kind of link denoting the “instance of” taxonomic relation, and a new kind of node denoting individuals (with the restriction that no individual can have any children). Thus we may populate our toy ontology with an individual, ‘Campogiovanni Brunello’, which is an instance of the concept Brunello di Montalcino. A computational ontology will also contain declarations for a number of non-taxonomic relations, which can either hold between individuals and constants (properties) or between two (or more) individuals (relations). Instances of these non-taxonomic relations may also be encoded in the process of

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an ontology is to assist humans and automatic agents in understanding the contents of the domain (especially in terms of properties, relations, and subsumption/inheritance relationships which hold between the domain’s types) and to allow data generated in one project to be interoperable with others.

2.1 Some nuts and bolts: the SEP and why it needs an ontology The SEP is the first attempt by academics of any discipline to organize their own professional subject matter by collaboratively writing, publishing, and maintaining a dynamically-updated reference work entirely on the web. Articles are submitted by more than 1,300 volunteer authors and asynchronously updated to reflect the latest in scholarship. As of May 2009, those authors have submitted over 1,100 entries (with an additional 300+ currently on commission) containing almost 13 million words. Everything submitted by the authors is in turn reviewed by one or more of the approximately 115 volunteer subject editors before publication on the web (a critical difference between the SEP’s approach and, for example, wiki-style approaches). As a result, the SEP is both authoritative and comprehensive. Consistently topping the GoogleTM search lists for philosophical concepts and thinkers, the SEP has emerged as the most visible and popular online reference work for the discipline of philosophy, as evidenced by its averaging almost 600,000 entry downloads per week. Since its inception, a major goal of the SEP has been to keep the encyclopedia available without charge both to scholars and the public. This goal has so far been satisfied through the volunteer efforts of many field experts, grants from federal and other sources, and a major fundraising effort involving the international community of librarians. The innovative nature of the work, however, brings with it a host of new difficulties not faced by traditional encyclopedias. It is increasingly impractical, for instance, to have editorial staff manually manage cross-references, tables of contents, search keywords, and other metacontent due to the asynchronous submission and revision of articles. There is also a pressure to minimize the editorial burden placed on volunteer contributors, who cannot be expected to constantly monitor the massive, ever-changing contents of the SEP and update metadata themselves. These challenges, coupled with the desire to preserve free, open access to the encyclopedia, create a strong drive to develop automated and semi-automated information-management tools which can be integrated into the editorial workflow of the encyclopedia. The development of an ontology for the domain of philosophy is central to the success of these tools.

Footnote 6 continued ontology population. For example, a knowledge base might record the property ‘alcohol_content (Campogiovanni Brunello, 7%)’ and the relation ‘pairs_with (Campogiovanni Brunello, Parmigiano Reggiano)’. Finally, a computational ontology may also contain a number of inference rules and axioms that can be used to reason about objects in the domain (e.g. infer the presence of certain relations on the basis of others, enforce consistency and default properties, and so forth).

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2.2 The InPhO: a dynamic ontology In the design, implementation, and long-term deployment of computational ontologies, knowledge modelers face several enduring challenges. For one, computational ontologies have often been designed without sufficient logical rigor, which may come with pragmatic costs in terms of the expressive power, clarity, and interoperability of the scheme (Guarino 1995; Smith 2006; Arp, this volume). The economics of ontology design is also a problem, generally requiring significant time from scholars speciallytrained in both the target domain and the principles and methods of computational ontology design (hereafter, “double experts”). Obsolescence looms large, as change in the problem domain or our understanding of it can render all that design effort useless, in the best case requiring more time from double experts to manually evolve the ontology (Flouris et al. 2006; Ceusters and Smith 2006) and in the worst cases taking a project back to the drawing board. One broad response to these challenges, emphasized by the “formal ontologists,” is to attempt to produce a “once and for all” description of the underlying reality of the subject domains, and to link the types of those subject domains into a standardized upper-level ontology describing the most basic, enduring features of reality. While this approach can hope to minimize the amount of change needed in future iterations, when change is called for it is usually performed manually. Another approach might be characterized by the phrase “dynamic ontology.” On this approach, more effort is placed on automating as much of the design and evolution process as possible rather than on attempting to produce a final description in the initial stages of a project. Dynamic ontology has a slightly different problem space than other approaches. For one, forgoing the use of double experts is a double-edged sword; while dynamic ontology can aspire to be more economical than alternatives, it must be more creative in its methods of obtaining data for the purposes of ontology construction and population. Automatic processing of heterogeneous sources of data (frequently of different degrees of reliability) is typically required, and problems of data inconsistency and validation loom large. Automated methods of ontology evolution should be, like the more traditional, manual methods, both flexible and conservative: they should preserve as much of the previous iteration as possible without leading to inconsistency. In addition, while many projects can aspire to ontologies that are useful for a wide array of other applications, dynamic ontologists can hope that their automated methods of ontology design will generalize as well. Many of the automated metadata management tools available today operate primarily on term co-occurrence statistics. Term co-occurrence approaches attempt to recover semantic information about terms from the textual context in which they appear (whether it be sentence, paragraph, or entire document). As anyone who has used a search engine can attest, however, co-occurrence information alone is often not enough to intelligently infer semantic relevance. Even standard methods of augmenting co-occurrence methods—such as utilizing user searching and linking behavior, as in Google’s PageRankTM algorithm—do not reach the standards of reliability or transparency one desires in an academic reference work (Hinman 2005). The problem of automatically identifying semantic relevance is deep and abiding in computer science, and we do not expect a general solution which meets our reliability criteria anytime soon.

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Rather than searching for a fully-automated solution to our metadata needs, we seek to utilize the SEP’s most valuable resource—regular access to domain experts in philosophy. Our approach to dynamic ontology begins with a small amount of initial manual ontology construction. Once the initial structure is in place, a variety of automated methods are used to structure feedback solicitation forms and deploy that feedback in data validation, ontology population, and the semi-automatic extension of its taxonomic structure. Our hope is that by managing our access to domain experts as efficiently as possible, and by distributing feedback solicitation throughout the SEP’s normal workflow, we can minimize or even eliminate the need for expensive double experts. Once we have created an ontology for the discipline and populated it with individuals corresponding to SEP keywords (created a knowledge base), semantic relationships between terms can be read off of the ontology by humans or automatic agents through the taxonomic and non-taxonomic links it records between them, thus addressing the SEP’s metadata needs.7 3 The engineering task The engineering task facing our project is to efficiently and economically produce, populate, and maintain a dynamic ontology for the domain of philosophy. As such, we have created a process to semi-automatically generate a formal representation of the tools, products, attributes, and activities of the philosopher, with special emphasis on the category of philosophical ideas.8 The InPhO contains information about philosophical ideas and positions, an extensive array of biographical data about philosophers, citation information on the documents they read and produce, information about the organizations in which they participate, and much more (Fig. 1). 3.1 Related projects With any technical project, it is worth reviewing other endeavors in the neighborhood. First, we note that we have been unable to locate any relevant ontologies of philosophical ideas in the standard ontology databases (Protégé databases, DAML, Ontolingua, Swoogle, for example); and, in general, there seems to be little work 7 This approach has a further semantic advantage over mere co-occurrence approaches in that the semantic

relationships come marked with taxonomic and non-taxonomic types. The semantic types here will include taxonomic relations (e.g. “more general”, “less general”) and non-taxonomic relations (e.g. “teacher of”, “wrote”, “defended”, “had_profession”). There are several additional reasons why one might desire an ontological approach to the problem of similarity noted in Noy and McGuinness (2001). For one, it allows domain assumptions to be made explicit and rendered in a form more conducive to analysis and critique. This may be especially useful for a large encyclopedias like the SEP—for if the ontology is generated through a combination of co-occurrence methods and author feedback, then any bias observed explicitly in the ontology is likely present implicitly in the SEP itself. Making such biases explicit (especially overemphasis or underemphasis) provides SEP editors with useful information when commissioning future entries. Secondly, coding the information in a formal language like OWL (Web Ontology Language) allows it to be reused and exported to other projects and purposes. Finally, having a comprehensive, machine-readable, open-access knowledge base about philosophers and philosophical ideas is of interest in its own right. 8 The scope of “philosophers” here ranges over professional academic philosophers in the Western tradition.

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Fig. 1 Protégé screen shot showing InPhO categories with sample instances

done on ontologies of ideas. Rather, most ontologies focus on more stable taxonomic structures (especially on types of physical objects or positions in social hierarchies), and few focus on the classification of abstract objects. This is to be expected, as the classificatory structure of abstract entities is much more likely to be unstable, vague, and controversial. One relevant project is the philosophy family tree9 maintained by Josh Dever. It uses genealogy software to record philosophers and their dissertation advisors—in some cases, all the way back to Leibniz. Dever has graciously allowed us to use his data to enhance our ontology, and we have incorporated its information into our current version. In addition, the Phylo project (Sula and Morrow, this issue) is collecting a large database of information about dissertations accepted by philosophy PhD programs in North America.10 We intend to collaborate and share data with the Phylo project in the future. The other project most directly relevant to our own is the PhiloSURFical project11 (Pasin & Motta, this issue). Pasin’s research concerns the creation of an ontology which can be used to “describe philosophical resources, and allow an easy contentdriven navigation of them.” Pasin’s approach is explicitly driven by pedagogical goals, especially the desire to formally annotate philosophical texts and take a learner on a “guided tour” of the text’s logical structure. The current draft of Pasin’s ontology, 9 https://webspace.utexas.edu/deverj/personal/philtree/philtree.html. 10 http://phylo.info/. 11 http://philosurfical.open.ac.uk/index.html, and see also Pasin et al. (2007) and his essay in this issue.

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however, lacks the primary structure we require for our Information Retrieval (IR) needs: a decomposition of encyclopedia keywords along subdisciplinary lines, grouping together concepts and positions by mutual relevance. Our differing interests limit the degree of overlap while maximizing the possibility of future productive collaborations. In particular, we are enticed by the idea of offering a learner a “guided tour” through the contents of the SEP as part of the SEP’s envisioned conceptual and semantic navigation interface. The richest sources of information for our project have been two excellent annotated bibliographies maintained by SEP editors. David Chalmers has created a superb bibliographical taxonomy for the specialization of philosophy of mind.12 In addition, there is an excellent philosophy of science bibliography maintained at the University of Pittsburgh (created by Rob Clifton, John Earman, and John Norton).13 With the permission of the authors, both were incorporated with appropriate modifications into the ontology. Finally, Wikipedia is increasingly adding more classificatory structure to its encyclopedia, and its various “table of contents” features contain extensive classification of philosophical ideas and positions. However, as is often observed, Wikipedia’s peersupported nature—which brings with it the persistent possibility of inaccurate information, malicious manipulation of controversial entries, and vandalism—makes it unsuitable for academic referencing purposes.14 Our approach treats metadata derived from Wikipedia as a valuable source of unverified input, which is then passed to domain experts for validation before being incorporated into our representation. It is also worth noting that Larry Sanger, the estranged co-founder of Wikipedia, has announced the development of a new reference work called Citizendium,15 which adopts a much more expert-centered approach, and the new Scholarpedia16 is also trying to find ways of harnessing expert review to manage distributed authorship. 3.2 Guiding principles For those unfamiliar with the process of ontology design, it is worth noting three pieces of accepted wisdom that have been stated succinctly by Noy and McGuinness (2001):

12 http://consc.net/biblio.html. David Chalmers and David Bourget are currently developing an extension of this taxonomy to cover all areas of philosophy, called Philpapers, the beta version of which has just been released (see http://consc.net/taxonomy.html). 13 http://philsci-archive.pitt.edu/view/subjects/. 14 See, for example, Jaschik (2007). But see also Giles (2005), who argued that Wikipedia, while error-

prone, is not much worse off than Encyclopedia Britannica. In this debate, it is important to note that errors in Wikipedia are often self-promotion or intentional vandalism and are thus often more fantastic and malicious than those of traditional encyclopedias like Britannica. Finally, Wikipedia’s lack of archiving features for citation purposes is also problematic. Wikipedia should perhaps not be faulted for these shortcomings; while it is a goal of the SEP to be academically-citeable, it is not clear that it is ever a good idea to cite a domain-general encyclopedia (like Britannica) in academic contexts for anything but a survey of common opinion. 15 See http://www.citizendium.org/. See also Sanger (2008). 16 http://www.scholarpedia.org/.

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(1) There is no one correct way to model a domain—there are always viable alternatives. The best solution almost always depends on the application that you have in mind and the extensions that you anticipate. (2) Ontology development is necessarily an iterative process. (3) Concepts in the ontology should be close to objects (physical or logical) and relationships in your domain of interest. These are most likely to be nouns (objects) or verbs (relationships) in sentences that describe your domain. 3.3 The categories Our ontology currently contains six basic categories: Thinker, Document, Organization, Nationality, Profession, and Idea. The “Thinker”, “Profession”, and “Nationality” categories possess little classificatory structure and only contain as instances lists of philosophers, nationalities, and professions obtained by various sources (primarily by “slurping” data from the sources described above, as well as by allowing authors/editors to manually insert missing individuals). In order to maximize data interoperability, top-level concepts have been mapped into standard ontologies where possible. The Thinker category has been mapped into the W3C class FOAF::person (augmented with the additional biographical property slots).17 The hierarchical structure and properties of “Document” categories are adapted from the AKT Reference Ontology,18 and the “Organization” category was taken (with appropriate augmentation and pruning) from the Protégé ontology library.19 3.4 Dual ontology for ideas Perhaps the most noteworthy aspect of our approach is its classification of ideas according to semantic inheritance relationships holding between the contents of ideas rather than more formal inheritance relationships observed in their types (e.g. social or structural roles). For example, the most straightforward ontological decomposition of the category philosophical idea might break it down into various social or structural roles—for example, philosophical idea → {position, concept, problem, distinction, argument, . . . }, problem → {dilemma, trilemma, paradox, . . .}, distinction → {bipartite distinction, tripartite distinction, continuum }, and so on (see also Grenon & Smith, this issue). However, this categorization—though useful for some purposes—would not answer to the metadata needs of the SEP. For one, this “social/structural” decomposition would likely be too shallow. We have several thousand concepts and need a rich classificatory structure which can separate them into meaningful clusters for the purposes of cross-referencing and semantic navigation. Moreover, we prefer a decomposition focusing on taxonomic structure that is as stable and non-controversial as possible, and thus would be familiar to most of the SEP’s authors and editors. No widely-accepted 17 http://xmlns.com/foaf/spec/#term_Person. 18 http://www.aktors.org/publications/ontology/. 19 http://protegewiki.stanford.edu/index.php/Protege_Ontology_Library.

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social/structural decomposition of philosophical ideas currently exists, so one would have to be engineered. For these reasons, we chose to focus instead on a decomposition classifying ideas according to their locations in the semantic space of the discipline. Thus, our category philosophical idea breaks down into idea about epistemology, idea about metaphysics, idea about ethics, idea about logic, idea about philosophy of mind, and so on. (Note that hereafter, the “idea_about…” prefix is omitted from all category names, and should be implicitly assumed to avoid confusion.) Information about the “idea type” is nonetheless useful for inferential purposes. For example, knowing whether an idea is of the type position or of the type distinction can constrain the types of relationships philosophers can have to it. The InPhO thus represents this information as non-taxonomic relations (e.g. ‘is_idea_type(connectionism, position)’). 3.4.1 Experts for finer structure For the initial draft of our ontology, we directly solicited taxonomic schemes from editors of the SEP. Instead of imposing a single conceptual structure or set of design principles on all subdisciplinary areas in the encyclopedia (for example, by trying to force general philosophical divisions like realism/anti-realism or subjectivism/objectivism onto political philosophy as well as metaphysics), the remainder of the idea category’s initial build has been shaped by soliciting subdisciplinary taxonomies from area experts. By choosing not to normalize organizing principles across subdisciplines, we grant experts more freedom to provide their best conceptualization of the target domain. A benefit of this approach is that the information is current and likely to be highly semantically relevant, and most likely to lead to objective, comprehensive, and elegant representations of the subject matter (Sanger 2008). There are drawbacks, of course: individual experts are likely to be highly influenced by their own particular interests,20 and hence their taxonomic representation of ideas in a particular subject area may be biased—for example by devoting disproportionate resources to certain areas while being overly sparse in others (Fig. 2). Another important aspect of ontology design concerns the drawing of a line between categories and individuals. For instance, should connectionism be considered an instance of the category philosophy of artificial intelligence, or should it be treated as a subcategory with instances of its own? Such questions are always present in ontology design, but there can be no right answers without considering the intended applications. We have been guided by a rough rule of thumb that we should approximate a one-to-one correspondence between the most specific titles of SEP articles and individuals in the ontology; thus, whether connectionism will be a category or individual will depend on the amount of treatment it receives in the current version of the SEP. It is also an important feature of our design that the ontology is revisable, and items treated as individuals in one iteration may be treated as categories in the next. For example, though connectionism may initially be made an individual, as the 20 To see our attempt to address this worry, see Sect. 6.1 below.

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Fig. 2 View of InPhO interface showing subcategory structure

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encyclopedia adds more entries in cognitive science, it may become appropriate to treat it instead as a category (“ideas about connectionism”) with instances of its own such as parallel processing, backpropagation, distributed representation, and so on. Another issue is that some concepts and individuals may not naturally belong in a single unique location in the ontology, being multiply classified by experts and/or automated methods. While most ontology languages permit multiple inheritance, rampant multiple classification erodes the classificatory utility of the ontology and increases the computational complexity of population (see next section). We have attempted to finesse this issue by limiting concepts to a single appearance per subdiscipline while adding “semantic crosslinks” to the ontology. These crosslinks capture the relatedness of ideas deemed mutually relevant by feedback or automated methods yet which have been manually classified by experts in distant areas of the ontology. The inferred semantic information is important for editorial needs such as cross-referencing, as well as for readers who may wish to follow leads into related topics. Considering the reachability of concepts via semantic links also allows us to prune redundant arcs from the ontology and classify individuals in optimal locations during population (Niepert et al. 2008). We believe that cross-links can be relatively sparse yet still provide these advantages, and additional computational complexity is minimized because our reasoning always begins with a significant amount of the ontological structure already in place. Such cross-links can compensate for the categorization of a concept in a location which does not accurately reflect its importance in the SEP. An idea which has been categorized by experts at a low level of specificity which does not reflect its corresponding term’s greater presence in the corpora will preserve its high degree of connectedness by having a large number of semantic crosslinks. For example, philosophy of cognitive science was placed under philosophy of psychology by a domain expert, but, given that the former phrase occurs in a wider range of SEP articles than the latter, our semi-automated methods classified it at a higher level of generality and inferred many crosslinks to topics in other parts of the structure such as theories of mental content, artificial intelligence, consciousness and intentionality, and the intentional stance. Semantic crosslinks allow us to capture the relevance of philosophy of cognitive science to these otherwise distant nodes without directly contradicting the expert’s taxonomy (Fig. 3). 3.4.2 Properties (non-taxonomic relations) We sought to include all salient properties and relations in our ontology which could possibly be inferred by semi-automated means. In general, an ontology with more properties and relations is better than one with fewer, as it increases the scope of the knowledge base and the chances of bootstrapping via intra-ontology inference. The drive to map out every possible property or relation, however, should be balanced against the ability to populate those properties or relations (whether through automated or manual means), lest large swathes of the ontology remain unpopulated over the long term—a situation which can often perplex users and discourage participation. Table 1 below contains a list of the initial property list for our ontology organized by domain and range.

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Fig. 3 View of InPhO interface showing crosslinks (@) from philosophy of cognitive science to other topics. SEP thinker icons to the left of terms indicate links to Stanford Encyclopedia articles, while the ‘SEP’, ‘Noesis’, ‘Scholar’ links provide direct access to the search engines using a query that is composed of that term plus its superordinate category

3.5 Populating the InPhO using expert feedback Population (also called annotation) is the process by which individuals are classified according to an ontology’s taxonomic structure and values are supplied for those individuals’ non-taxonomic properties and relations (“slots”). Semi-automated population of the InPhO’s taxonomic and non-taxonomic relations takes place through the solicitation of expert feedback as part of the SEP’s document submission process. When SEP authors submit a document for publication, their feedback is solicited in a three-stage process. First, statistical measures such as the widely used “tf-idf” measure (term frequency–inverse document frequency) and n-gram models (conditional probability within the corpus of a word given the previous n words) are run over their document to infer terms and names of possible significance which occur in the

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Table 1 Initial property list Thinker → Thinker Relations

Thinker Properties

Teacher_of

Born_on

Influenced

Died_on

Criticized

Spoke_language

Defended

Nationality (Thinker → Nationality)

Dissertation_Advisor_of

Profession (Thinker → Profession)

Discoursed_with

Alias

Thinker → Document Relations

Idea Properties

Wrote

Idea_type (concept, position, etc.)

Edited

Thinker → Organization Relations Member_of

Thinker → Idea Relations

Studied_at

Worked_on (problem) Created_view

Document → Document Relations

Attacked_view

Published_in (article → journal/book)

Espoused_view Aware_of

Idea → Idea Relations Opposed_to

Document → Idea Relations

Commits_to (idea1 commits one to idea2)

Discusses Ternary and Quaternary Relations Disagreed_with(X, Y, Z): ThinkerX disagreed with ThinkerY on IdeaZ Appointed_at(W, X, Y, Z): ThinkerX was appointed at OrganizationY during time duration Y-Z

document; authors are presented with a list of such terms and asked whether their document really discusses them or they occur in it only incidentally (“Is your article about connectionism?”). Second, the authors are asked to evaluate the relatedness (on a five-point scale from ‘totally unrelated’ to ‘highly related’) and generality (‘more general’, ‘less general’, ‘both’, and ‘incomparable’) of terms they selected in the first stage to other terms highly ranked by our statistical methods as candidate hyponyms (of lesser generality) or hypernyms (of greater generality) to those target terms (Fig. 4). Once we have obtained this feedback, the task is to use it to populate the ontology by classifying in its hierarchy terms which occur in the document. This is accomplished by representing the expert feedback as a series of facts in first-order predicate calculus21 and using non-monotonic inference techniques to infer the classifications induced by the feedback.22 Currently, we use this method only to classify idea instances according to the existing ontology structure, but with appropriate feedback it could be extended 21 For example, if the author indicates that connectionism is highly related and more specific than philosophy of mind, we represent these facts as “highly_related(connectionism, philosophy of mind)” and “more_specific(connectionism, philosophy of mind)”. 22 We describe this task and the advantages of our approach in more detail in Niepert et al. (2008).

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Fig. 4 The idea feedback interface

to build (partially or completely) the idea ontology’s taxonomic structure itself. We intend to explore this extension, but we do not expect its results to be as reliable as the more modest method already implemented.23 Finally, experts are shown a third feedback page where they are asked to evaluate the non-taxonomic relations inferred by our automated methods (see Niepert et al. 2007). We currently import non-taxonomic relations from unvalidated sources like Wikipedia, and statistical methods such as hidden Markov models and conditional random fields are being developed to infer relationships obtaining between terms occurring in the document. Authors and editors will be asked to confirm or falsify these hypotheses about non-taxonomic relations between individuals in the knowledge base, and their feedback will be used to construct training sets to further augment the statistical hypothesis-generation techniques. This three-step feedback-harnessing strategy demonstrates how we hope to achieve a higher degree of reliability than pure co-occurrence and unsupervised wiki-style approaches. Our database will be separated into “clean” and “unclean” portions. The “unclean” portion consists of information inferred by taxonomic methods or gathered from other external sources (such as from Internet crawls and user search traces). The “clean” portion consists of information either gathered directly from experts (such 23 See Sect. 5.3 and Niepert et al. (2008) for ideas about how this could be accomplished.

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as the taxonomic decompositions recovered from the annotated bibliographies) or approved by experts through the feedback-elicitation process. The threat of inaccuracy is addressed by assuring that only the clean parts of our database are used to infer the knowledge base and thus feature in cross-referencing, navigation, and other implementations viewable by the SEP’s users. An advantage of our expert-supervised approach to ontology population is that it provides ample quality-control while still allowing for the possibility of novel discovery. Our co-occurrence statistics have turned up a number of connections that might easily have been overlooked by area experts. To take one example, the methods ranked anaphor as one of the highest hypernym candidates for propositional attitudes. Though two of the authors of this article are philosophers of mind, we initially thought this connection was due to error. A quick SEP search revealed, however, that the ranking could be explained by the fact that anaphoric sentences pose a challenge to the Fregean theory of propositional attitudes. This interesting connection would likely not be discovered by novices; and though experts might not think of the connection off the tops of their heads, they can easily uncover its validity with a cursory inspection of the relevant SEP articles. A key challenge facing philosophers in the digital age is to discover how best to use computers to support our understanding of the discipline. As should be clear by now, we do not expect our text processing tools to write a compelling philosophy paper any time soon. Rather, we recognize what has long been true: that humans and computers work better together than either do in isolation. With careful collaboration, reliable representations of the discipline can be created facilitating a wide range of future tasks in digital philosophy (several discussed below). Keeping future tasks such as the design of visually-effective conceptual and thematic navigation tools in mind, we have tried not to “overfit” our methods and ontology to the present needs of the editorial staff of the SEP.

3.6 Raw materials—exploitable semantic structure In this section we describe five sources of exploitable semantic structure utilized in the course of our project. It may be read as a series of hints to any other projects seeking to design an ontology and statistical text processing tools for their reference works. 1. The SEP’s editorial structure: The richest source of large-scale classificatory structure available to us was the editorial structure of the SEP. Editorial oversight of the encyclopedia is divided into twenty subject areas corresponding to widelyrecognized academic subdisciplines of philosophy (logic, ethics, metaphysics, philosophy of action, and so on). Within most of these subject areas, each article is under the jurisdiction of one subject editor, with the articles in a given subject area subdivided between several subject editors. We could infer a considerable portion of the large-scale classification of ideas by noting the editorial jurisdiction under which the articles about those concepts fell. (It is important to note, however, that the editorial structure of the SEP is partly a matter of administrative convenience and contingency.)

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2. Current cross-references: Another rich source of information on semantic relevance is provided by the current cross-references of articles, which have all been hand-coded by editors and contributors. Such information can be taken as objective feedback and incorporated into future, semi-automated cross-references and used to instruct future sets of cross-references as they are dynamically updated. 3. Article citations: The citations of SEP articles can also be used to infer relevance of articles (and thereby derivatively to the concepts the articles are about) under the assumption that semantically-related articles will tend to cite the same influential papers. 4. Article titles: The article titles were the biggest gift provided by the structure of the SEP. Article titles, by unspoken convention, have largely been kept spartan and neatly-correlated with concepts or philosophers that the article is about. This makes it easy to build a one-to-one correspondence between individuals in the ontology and articles in the SEP. Though our current draft of the InPhO only operates at a level of specificity corresponding to that of subjects of whole articles, we eventually hope to incorporate more specific ideas and terms by moving to the level of article sub-sections or even paragraphs. If we do so, section sub-headings will also be very useful in recovering more specific information about the themes of passages. 5. User search traces: The final useful source of information to be explored is user search traces. This information becomes significant on the assumption that users tend to search for semantically-relevant topics in the same session, although there are reasons for skepticism about this assumption. Nevertheless, we believe that looking for convergence of searching behavior among different users can also be used to improve our cross-referencing system. 4 Challenges The following section presents a summary of challenges we encountered in the course of designing and implementing our ontology, which may also confront similar projects. Each section contains a summary of the difficulty, presents our current solution, and briefly theorizes about the origin and scope of the difficulty. 4.1 Problematic category names In constructing the ontology, we found that many seemingly straightforward category names provided by experts were difficult to adapt to the constraints of our statistical methods (which operate using semantically significant keywords and their co-occurrence statistics). Below is a list of types of category names which proved troublesome. 4.1.1 “Grab bag” category names Examples “Other Psychophysical Theories,” “General Issues in Philosophy of Science,” “Topics in Feminism”

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The most common problematic category names were those which seemed to be “grab bag” categories. A “grab bag” category here is understood as one which groups together possibly heterogeneous elements which are “leftovers” from more significant sibling decompositions; in other words, the category name itself occurs rarely (if at all) in the SEP, and its significance derives from a mutual exclusion relation to its more significant siblings. This sort of problem arose throughout the ontology, but we may focus on a useful case study which emerged in the metaphysics of mind. In one expert-solicited taxonomy for the philosophy of mind, for example, metaphysics of mind decomposes into the subcategories {materialism and dualism, functionalism, and other psychophysical theories}. This decomposition makes intuitive sense; views on materialism and dualism form one closely-related way to conceive of issues in the metaphysics of mind, various ideas related to functionalism comprise another broad way to tackle the subject, and finally there are other less popular but still significant psychophysical views which do not clearly fall into the other two categories. The name “other psychophysical theories,” however, is somewhat useless to methods which rely on co-occurrence statistics. The frequency of such categories in the taxonomies supplied by experts suggests to us that, rather than simply demonstrating a lack of a label due to ‘laziness’, they seem to be doing some real classificatory work. Unfortunately, it isn’t clear how to replace these categories with something more informative and statistically tractable, even when they are considered on a case-by-case basis. The problem is not crippling for our methods where the grab bag category decomposes into more meaningful subcategories; where they do not, however, we have excluded them from the current build of the ontology.24 4.1.2 “Philosophy of X” vs. “X” Examples “Philosophy of Connectionism” vs. “Connectionism”, “Philosophy of Cognitive Science” vs. “Cognitive Science,” etc. In numerous places in the expert-supplied taxonomies, we also noticed that category names sometimes included a “philosophy of” prefix and sometimes did not; examples include “artificial intelligence” vs. “philosophy of artificial intelligence,” “connectionism” vs. “philosophy of connectionism,” and so on. As knowledge modelers, we then must ask ourselves: does each member of the pair of labels denote the same category? In the context of philosophy and as far as the co-occurrence methods are concerned, the answer frequently seems to be “yes.” When we determined this to be the case, the “philosophy of” prefix was discarded, but not when it was obvious that the two denoted robustly different entities (e.g., “philosophy of logic” vs. “logic”). 24 We are interested in exploring means to help the automated methods manipulate the category name in the same methods that humans do, perhaps by a kind of exclusion rule with its sibling categories. In this case, then, we might make “Other Psychophysical Theories” significant to the IR methods by translating it to a category comprised of the keywords “Psychophysical,” “Theory”, and “Metaphysics of Mind” and exclude the keywords “Materialism”, “dualism”, and “functionalism.”

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4.1.3 Category names containing prepositions: “and”, “in”, “of” Examples “Language and Society,” “Reference and Denotation,” “Materialism and Dualism,” “Consciousness and Qualia,” “Consciousness in Physics,” “Cosmology of Physics” Again, our methods must interpret the contents of the ontology in terms of keywords and co-occurrence statistics. Where possible, therefore, it is best to translate category names involving keywords joined by prepositions into keywords joined by union or intersection; in other words, for each category name of the form “Keyword1 <preposition> Keyword2,” we should decide whether both Keyword1 AND Keyword2 must be required for a phrase to be deemed relevant to the category, or whether either Keyword1 OR Keyword2 may individually be relevant. In general, “in” and “of” signify contexts in which both terms should be required, and this is represented by the intersection of the categories of ideas about each keyword; we use automatic scripts to replace these with the intersection symbol. “And,” however, was ambiguous throughout the ontology, and no principled translation rules could be developed without surveying the contents placed in that category by the experts. “(Ideas about) Materialism and Dualism” for instance, expresses the union of the category of ideas about materialism with the category of ideas about dualism, whereas “(Ideas about) Consciousness and Physics” expresses the category of ideas in the intersection of the categories of ideas about each keyword. There seems to be no way to mitigate this ambiguity at this stage of our project without having a human operator manually disambiguate after surveying the contents of the category. 4.1.4 Subconcepts involving anaphor or omitted adjectives Examples “Mental content → theories of content” Such decompositions are easily intelligible to humans, but it is difficult to automatically resolve (or even notice) the anaphor in the above example. Without resolving this problem, the automated methods may conclude that the children of “theories of content” are relevant not just to “mental content”, but also to linguistic content, intentional content, teleological content, and so on. The only solution to this problem seems to be to prohibit such anaphor in the ontology and carefully ferret out any possible anaphoric or ambiguous category names. 4.2 Change and evolution of the ontology As our ontology is populated over time, we may predict that the manually-coded classificatory structure will become increasingly obsolete. In particular, as some areas of philosophy become increasingly neglected and others become more fertile, some categories may shrink (as, for example, articles are deleted or radically edited) while growth in others (as a result of new articles being commissioned and added) may

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result in clusters which are larger than optimal for our metadata needs. Even more drastic changes to the idea category may be required by intellectual sea changes, such as those caused by the advent of new technologies (e.g. computers), the discovery of new scientific theories (e.g. quantum mechanics), or the growth or decline of broad philosophical movements (e.g. logical positivism). There seems to be no way around the conclusion that large-scale paradigm shifts in philosophy will require fresh re-conceptualizations of the field from the top down. Rather than being fatalistic, however, we can note the advantages of the “dynamic ontology” approach to these issues, for which ontology evolution can be seen as a natural extension of the initial process of ontology creation and population. First, re-conceptualizations which result from large-scale paradigm shifts may not have to be coded entirely from scratch; much of the old ontology may be reincorporated or used as inspiration where relevant, and metrics about the unsuitability of the obsolete ontology may guide the creation of the new one. Second, smaller changes to the ontology are tractable by modest semi-automatic means. For example, we will be able to automatically detect when some categories become too large, and then use automated methods to divide the contents of the category into two or three more closely-related clusters; human users may then be prompted to provide category names for these newly-created clusters by surveying their automatically-populated contents. Similarly, categories which become defunct as a result of article deletion or radical editing of articles may be detected and pruned from the ontology. A further advantage of managing change in any formal setting is the possibility of comprehensively tracking changes within the discipline over time. Versions of the ontology are currently saved and archived monthly, and intellectual trends can be studied with precise metrics. This should be an enticing prospect for academics in a number of different areas interested in the change of ideas and socially-accepted conceptualizations, from metaphilosophy to history to social network theory. 4.3 Author/Editor compliance Another worry centers on the issue of author/editor compliance: why should volunteer authors and editors be willing to provide all the necessary feedback? Though we admit that this is a challenge, we feel that numerous incentives encourage SEP authors to supply feedback. First, we can note that the metadata production is currently completed manually in a time-consuming manner—authors or editors provide cross-references using the labor-intensive and imperfect method of searching through the SEP. By contrast, the feedback form conveniently presents authors with a thorough list of candidate cross-references ranked by relevance.25 Second, the authors are submitting their articles as a matter of professional service and to increase their profile as an expert on a given issue; the augmentation of their article’s metadata (and of the success of the SEP in general) increases the accessibility and visibility of their articles. 25 This provides an advantage over the approach of Kim et al. (2007) which provides technological facilitation for human construction of a philosophy ontology, but does not automate the processes for discovering the semantically significant relationships among philosophical objects.

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Finally, we have designed the feedback forms to be as ergonomic as possible, and the amount of feedback we need from any one author is minimal—thus the process should not place undue demands on any one author’s time and attention. 5 The pies in the sky 5.1 Semantic and thematic navigation In Sect. 2, we mentioned that ontologies should be of use to humans as well as software agents; perhaps the most important way the structure of the InPhO might be used to make the SEP’s content more accessible to its human browsers involves the creation of a system for semantic and conceptual navigation. In such a system, an information visualization interface would allow browsers to navigate the SEP by visually following semantic relationships between the SEP’s ideas, thinkers, documents, and organizations. An envisioned user interface with the system is described as follows: A user will search for some specific keyword; a graph will then be displayed with the closest keyword contained by the ontology displayed in the center; the graph will be populated with a number of other related keywords linked to the search keyword, where the links are labeled with the relationship recorded in the ontology; the user can browse this structure, recenter it, and repopulate it; and each time the user clicks on one of the concept bubbles, a small window will be displayed showing the first few lines of the SEP article most correlated with that keyword. Moreover, the user can control the type of links displayed by checking various options, such as focusing on philosopher → philosopher relationships, idea → idea relationships, etc (Fig. 5). Such a system would facilitate interaction with the encyclopedia for expert and novice users alike. Experts could see the “big picture” of an idea or philosopher in a glance, capturing a large amount of information in an efficient manner, and novices could surf through the encyclopedia’s content by following paths hewn by an expertlevel understanding of the domain. Students engaged in research could instantly see which other topics are importantly related to their current search item, and the semantic labels of those links would tell them not only which other items are related to their current search but also how. We have made some exploratory progress in this direction using several visualization packages.26 While there are a number of existing visualization applications with an impressive set of customization features, we would prefer to eventually develop our own visualization tools designed especially for ontology-guided navigation of dynamic reference works (Crampes and Ranwez 2000). Plans for such a system have been developed, and the InPhO project has recently been awarded a continuing NEH grant which will allow us to develop these applications. We believe that just as sci26 We have made some initial experiments using the java-based package JUNG—http://jung.sourceforge.

net/, and for an analysis of JUNG’s capabilities, see O’Madadhain et al. (2005). We have also developed test applications using the Exhibit and Prefuse visualization tools (http://www.simile-widgets.org/exhibit/ and http://prefuse.org/, respectively. A page displaying our visualization experiments can be viewed at http:// inpho.cogs.indiana.edu/viswidgets.

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Fig. 5 Mock up of navigation interface using ontology structure and contents

entific visualization has become an important area of research for the sciences, philosophy visualization should be an important topic for philosophers. What can be visualized, and what visual metaphors guide our comprehension of philosophy? These are questions whose answers affect the development of philosophy as a discipline in the digital age. 5.2 Exploration of the amount of semantic structure retrievable from co-occurrence data How much semantic information about terms is recoverable from co-occurrence information alone, and how much, instead, can only be recovered by agents possessing human perceptual apparatus, physical or causal interaction with the subject domain, memory, emotions, human cognitive dispositions, neural architecture, and so on? Despite great advances in the last few years on both co-occurrence models and other models of semantic structure, and on language learning and semantic memory, no general answer to this question is currently known. One advantage of our project is that it would provide a means by which this question could be explored in the domain of philosophy. As our text processing methods are implemented and tweaked over time, we may be able draw generalizations as to which items or areas they handle comparatively well and which comparatively poorly. Moreover, the ontology and the SEP’s corpus would provide a playground for new

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statistical text processing methods and cognitive models to explore these questions in a live domain. 5.3 Inferring large sections of the InPhO dynamically Thus far, we have discussed two ways in which the InPhO is a dynamic ontology: the dynamic population of instances and the dynamic extension of the ontology’s category structure when sections become too large. An alluring future direction which could make the InPhO even more dynamic involves the use of more ambitious automated reasoning techniques to infer large sections of the ontology’s taxonomic structure using semi-automated means. Of the many possible methods and techniques in which could be used to achieve this goal, there are two distinct but related approaches here we would like to pursue. The first involves “relaxing” some of the rules in our answer set programs such that instead of producing a single ontology, they produce a large space of possible ontologies which are consistent with a general theory of ontologies (satisfying acyclicity and other constraints) and current feedback. A metric would then be applied to rank these possible ontologies according to their suitability, likely using a mathematical measure of the degree to which each ontology fits the predictions of relatedness and generality derived from the co-occurrence statistics. Another approach uses Markov Logic Networks (Richardson and Domingos 2006), which combine first-order knowledge bases with probabilistic (Bayesian) networks. This method would provide a probabilistic ranking of the populated ontologies through the assignment of weights obtained directly from the statistical generality and relevance scores. A significant difference between these two approaches is that in the latter the populated ontologies are ranked directly as part of its inductive reasoning method, while in the former the rankings are computed as an independent, post-processing step. We hope to compare the two methods and determine which best serves the needs of dynamic reference works. 6 Philosophical issues and doubts Before concluding, we move to address three families of worries and objections to our approach we have encountered. 6.1 What is the relationship between the InPhO and metaphilosophy? Some readers may be skeptical of our statistical approach, supposing that we are engaged in a very dubious metaphilosophical methodology: to be arguing that because two terms frequently co-occur in the SEP, they ought to be seen as mutually relevant. We want to make clear that we do not take the InPhO to show how philosophy ought to be organized. Such an ideal conceptualization is neither recoverable by currentlyavailable automated means nor required for our purposes. Even human experts in metaphilosophy would be hard-pressed to produce a comprehensive decomposition of the conceptual space of philosophical ideas, and no doubt any such scheme would be

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the subject of controversy. However, we have real and pressing information management needs, and, for the purpose of meeting those needs, having an imperfect formal representation of the structure of the field is better than having none at all. Despite this caveat, we argue that the InPhO can play a non-trivial role in metaphilosophy. A common sort of distinction may be useful here in explaining this role. Let us call a metaphilosophical position descriptively adequate if it portrays the discipline as it is currently practiced in such a way as to support practical applications. Let us call a metaphilosophical position normatively adequate if it outlines the best way to arrive at philosophical truth, provides philosophy with a firm epistemological grounding, or otherwise describes how philosophy ought to be organized to maximize our chances of progress. While we do not defend the InPhO’s normative adequacy, we believe that the collaborative, distributed, and empirical approach used to construct it makes it more likely than standard alternatives to produce a representation of the discipline which is descriptively adequate. Traditional methods for obtaining a description of the intellectual space of the discipline take the form of a less than a handful of philosophers testing each other’s intuitions about ways to organize the content of the discipline. There are many reasons to be skeptical about this approach. First, there is the matter of individual bias; philosophers are likely to feel that the particular issues they work on are the most important. Second, the learning histories and intellectual trajectories which shape one’s metaphilosophical standpoint are idiosyncratic and politically charged. Third, the expert’s drive for simplicity and elegance comes at a cost: it may tempt philosophers to artificially impose a normalized structure on distant areas of philosophy. Fourth, once settled on an approach or a set of organizing principles, overconfidence and confirmation biases may set in, leading the philosopher to feel the chosen approach is appropriate in diverse settings. And finally, given the explosion in the number of significant philosophical publications mentioned in the introduction, it is unlikely that even a reasonably-sized subset of extremely well-read philosophers would be sufficiently qualified in all areas of philosophy to produce a thorough conceptualization.27 Viewed against these challenges, our semi-automated approach may be thought to possess significant empirical advantages over this traditional method. Granted, our reliance on expert conceptualizations for the InPhO’s basic framework renders us vulnerable to some of these worries—but we do not ask experts to represent anything outside of their own area of specialization. Furthermore, our feedback system is deployed with redundancy in mind. We propose the same hypotheses to multiple experts in the feedback process, and the nonmonotonicity of our logic programming methods allows us to flexibly respond to expert disagreement (Niepert et al. 2008). Our 27 We might look, for example, at the top-level classification scheme of the Routledge Encyclopedia of Philosophy (http://www.rep.routledge.com/signpost-articles). One may object to philosophy of psychology falling under philosophy of mind rather than (also) philosophy of science; one may object to the article on African Religion coming under the heading of African Philosophy rather than World Religions (showing a Eurasian bias). Our purpose here is not to point any fingers at the REP, for similar concerns could be raised about classifications in the InPhO; we would, however, like to raise a question about how such disputes are best settled. We believe that they are better settled by looking at statistical properties of philosophical texts and soliciting feedback from multiple experts rather than by asking a one or two experts their opinion of the best classification.

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hope is that this will afford the InPhO a degree of intersubjectivity. We also note that basing our relevance and generality estimates on the actual text of the SEP provides an independent and perhaps more objective window on the structure of the discipline than does the impressions of the authors and editors of those articles. We record not just what philosophers think they are writing about, but also study statistical properties of their actual output. For example, an author may think the central ideas of their article are X and Y, but if they spend five pages dealing with objections pertaining to Z (that the author would perhaps prefer to ignore), this is potentially significant information that should be taken into account when deciding what the text is actually about (information which can, of course, still be deemed irrelevant by the community of experts in the feedback process). Thus while it remains to be proven that our method produces a more accurate descriptive metaphilosophical framework, there are a number of good reasons to suppose it will. Furthermore, while we agree that there is little reason to suppose that the InPhO presents a normatively adequate metaphilosophy, the InPhO may be useful in the search for one. While foundationalist approaches to metaphilosophy may recommend sweeping away the debris and starting again from first principles, iterative approaches require a descriptively adequate picture of the current state of affairs. If our goal in metaphilosophy is to assess the suitability of the current way of conceptualizing the intellectual space of the discipline (which includes assigning relative importance to various ideas, positions, problems, and areas of philosophy), a formal representation may prove more amenable to analysis than an informal one. A last word on this issue: while we do not defend the InPhO’s normative adequacy, we do retain a keen interest in the suitability of our ontology’s specific structure and conceptualization scheme, especially as it is evaluated by its users (novice and expert alike). We welcome further additions to the metacontent structure we have inferred, including extensions of the existing ontology as well as alternative, mutually inconsistent classification schemes. Our metadata management and visualization methods are likely to be more effective with the help of multiple ontologies, and so we welcome suggestions—and even contributions of alternative ontologies from readers who find themselves dissatisfied with ours.

6.2 Is the InPhO properly called an ‘ontology’? In presenting this material, several critics have lamented our terminology. This criticism has come from at least two different directions. The first line of criticism comes from those who believe the word ‘ontology’ has been stretched too far from its original metaphysical roots, feeling that it is more misleading than useful when referring to a formal data representation rather than an actual hierarchy of being. This group of critics—which has included at least one lexically-conscious information scientist, as well as philosophers—tends to object to the use the term has acquired in the computer and information sciences in general. Another, more focused line of objection has come from those who prefer to reserve the use of the term for a particular kind of a formal representation used in the overarching project of the semantic web. These critics tend to focus on our idea category,

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indicating that the kind of semantic taxonomy expressed there is somehow not properly described as ontological. There are a number of things one might note here: it isn’t clear how the semantic divisions we focus on will enhance automated reasoning, or how the category of philosophical ideas will plug into higher-level ontologies to ensure interoperability (e.g., SUMO, Pease et al. 2002). Or, relatedly, one might worry about the social and dynamic nature of the conceptualizations we elicit through the feedback process, as domain ontologies in the semantic web are supposed to be authoritative descriptions of the types of entities in a domain suitable for a wide array of purposes (Smith 2003). The most serious form of this last worry centers on the semantics of the isa relation. The isa class subsumption relation is often presumed to hold in a context-general way and capture “purely ontological” relations; if it is true that “A isa B”, then any A in any context should by its nature be a B. Because our idea category is organized primarily by contingent semantic relationships holding only in the context of certain philosophical discussions, its isa links may fail to hold domain-generally and may conflate taxonomic and non-taxonomic relations.28 For example, the set of “ideas about connectionism” may be a subset of “ideas about philosophy of mind” in the context of philosophy, but not in the context of computer science or network theory. We concede this last point; the classifications under the idea category will likely not hold domain-generally. For these divisions, we propose that the isa relation be understood to express conditional subsumption: A isa B, but only in the context of C, …, Z, B’s ancestors. Let us call this conditional subsumption relationship ‘isa*’.29 Rather than supposing that this prevents the InPhO from being a proper ontology, we think the move from isa to isa* helps capture precisely the sort of information required for our metadata needs. We believe that this sort of conditional, hierarchically-structured knowledge is important in modeling the ability of philosophical experts to say which topics are most relevant to the examination of particular ideas in particular scholarly contexts. One might worry that the isa* relation will have a mysterious semantics or that it might harm data interoperability. While dealing with isa* relations will be more involved than dealing with good old isa, the previous paragraph gives the relation a straightforward technical semantics. As for determining data interoperability, the simplest schemes rely on matching types to one another across diverse representations in a one-to-one correspondence, often with the help of upper-level ontologies; let us call this “context-independent interoperability”. More sophisticated methods for determining interoperability are possible, however, which might for example compare contextual features of the two data representations (in this case, the two candidate types’ ancestors) to determine the their compatibility. For example, we may determine that data are not interoperable between two isa* ontologies if “philosophy of cognitive science” is a child of “philosophy of mind” in one ontology and “philosophy of science” in another. Finally, we note that only the idea category of the InPhO is structured around isa*. The rest of the data in our knowledge base should approach the 28 For related problems faced by projects attempting to convert the Wordnet’s hypernym/hyponym taxonomy into an ontology, see Trautwein and Grenon (2004) and Oltramari et al. (2002). 29 For a related approach, see Stuckenschmidt (2006).

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ideal of context-independent interoperability, and all of the subcategories of the idea category can be discarded in the process of translation if needed. In other words, the thousands of idea keywords can simply be treated as instances of the class philosophical idea, and their properties and relationships to instances of other categories should be as close to the ideal of context-independence as is realized in other standardized ontologies. While these observations clarify the issue, it may remain a point of dispute whether a representation based on the isa* relation is properly called an ontology. Our general response to the terminological worries of this section is to acknowledge the need to regiment language for purposes of clarity and precision, but note that all we mean by “ontology” and “dynamic ontology” is precisely what we say in Sect. 2 above. To the second line of response, we can also reply that the type of authoritative, domaingeneral, “final answer” description often sought by semantic web researchers would not prove responsive to the SEP’s full range of metadata needs (for the reasons why, the reader may glance back at the discussion of the “social/structural” option in Sect. 3.4). Though we would be reluctant to give up the word “ontology” entirely, readers sufficiently bothered by this issue may call the idea section of the InPhO what they like—we place no special importance on its terminological status.

6.3 Stagnation, self-confirmation, and bias One of the general doubts we have faced when explaining our project goes something like this (to preempt critics from seizing upon a tempting pun): “You aren’t engaged in a taxonomy of ideas, but rather a taxidermy of ideas. Philosophy is by its nature a fluid, ongoing conversation with rules always in flux, and to attempt to tie it to some conceptualization scheme or another is to destroy the essence of dialectic inquiry, reducing it to something sterile and irrelevant.” In response to this concern, we can agree that philosophy is in flux but deny that attempts to represent the current state of this flux are necessarily inadequate or stultifying to the discipline. Encyclopedias have not had this effect, because philosophers and their students have always regarded what they contain as subject to challenge and revision. There is no reason to expect that other attempts to represent philosophy will be treated any differently. Furthermore, the dynamic methods used to generate, populate, and evolve the InPhO over time should render it reasonably responsive to the ongoing dialectic of the discipline. Secondly, one may argue that there is a broader bias in either the content of the SEP itself and/or the fundamental design principles behind the ontology. For example, one might accuse the SEP or InPhO of a pro-scientific bias, an anti-Continental bias, a pro-Western bias, a sexist bias, and so on. Furthermore, one might think that not only is the SEP and/or the metaphilosophical picture expressed in the InPhO biased or inaccurate, but giving it wide exposure is also likely to only exacerbate the problem. For instance, once the ontology has been deployed and comes to influence the way that cross-references, tables of contents, and navigational tools are designed and used in a widely-viewed reference work, it makes it more likely that “metacontent inertia” will set in, strengthening the current biases of the SEP in future versions. Moreover, it seems that most of the methods proposed to change and evaluate the ontology are

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not independent of interaction with that ontology; experts may be influenced by their constant interactions with it, and users who learn from interaction with the visualization tools are likely to accept its conclusions and confirm them in future sessions (as expressed in search traces). Our central response to these worries is that we are only aiming to model the way that the discipline (as practiced by certain experts in the roughly Western, analytic tradition) currently sees itself. If there is a bias in this viewpoint or in the SEP itself, we think that formally modeling it may actually shine a light on it and spur reform. Furthermore, the act of constructing an ontology using data drawn from the SEP can help reveal imbalances in its coverage, or areas that are not sufficiently sub-divided into specialized topics. Analysis of the statistical properties of the entries and the generality of the terms they contain can help ensure uniformity of treatment across the discipline. After all, it isn’t like philosophers to allow standards or accepted truths to stifle such progress; in fact, the history of philosophy shows that stating something precisely and making it widely available is instead an invitation to more intelligent critique. Given the contentious nature of philosophy and its practitioners, therefore, it seems more likely to these authors that codifying philosophy’s self-conceptualizations will enhance metaphilosophical critique rather than nullify it. 7 Conclusion In brief, just as human understanding of everything, from geometry to the human genome, has been enhanced by developing new ways of representing it, so the discipline of philosophy also stands to gain much in being represented in explicit, formal, and computationally-tractable ways. We have argued here for the advantages of a dynamic approach to representing the discipline of philosophy. The near future of representing the discipline proves to be exciting, as many other approaches are possible, and it is largely an empirical question which will turn out to have the best combination of advantages and disadvantages for particular applications. Acknowledgments This research has been funded by Indiana University under the grant “New Frontiers in the Arts and Humanities” and by Digital Humanities Start-up Grant HD-50203-07 from the National Endowment for the Humanities. We also wish to thank the members of the Experimental Epistemology Laboratory for helpful comments on earlier versions of this document.

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Synthese (2011) 182:235–267 DOI 10.1007/s11229-009-9660-3

Ontological requirements for annotation and navigation of philosophical resources Michele Pasin · Enrico Motta

Received: 6 July 2008 / Accepted: 22 January 2009 / Published online: 29 September 2009 © Springer Science+Business Media B.V. 2009

Abstract In this article, we describe an ontology aimed at the representation of the relevant entities and relations in the philosophical world. We will guide the reader through our modeling choices, so to highlight the ontology’s practical purpose: to enable an annotation of philosophical resources which is capable of supporting pedagogical navigation mechanisms. The ontology covers all the aspects of philosophy, thus including characterizations of entities such as people, events, documents, and ideas. In particular, here we will present a detailed exposition of the entities belonging to the idea branch of the ontology, for they have a crucial role in the world of philosophy. Moreover, as an example of the type of applications made possible by the ontology we will introduce PhiloSurfical, a prototype tool we created to navigate contextually a classic work in twentieth century philosophy, Wittgenstein’s Tractatus Logico-Philosophicus. We discuss the potential usage of such navigation mechanisms in educational and scholarly contexts, which aim to enhance the learning process through the serendipitous discovery of relevant resources. Keywords Ontology · Philosophy · Digital narratives · Knowledge representation · Semantic web · CIDOC · Tractatus Logico-Philosophicus 1 Introduction The Semantic Web augments the web with a layer of data, called metadata, which formally describes information. The idea here is to develop a large-scale repository of

M. Pasin (B) · E. Motta Knowledge Media Institute, Open University, Milton Keynes, UK e-mail: [email protected] E. Motta e-mail: [email protected]

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formally characterized resources, over which intelligent agents would perform various kinds of operations for the user (Berners-Lee et al. 2001). As part of this effort, our research focuses on the definition of the appropriate metadata which could be used to describe philosophical resources. In particular, the approach we are taking is further characterized by the fact that we want to make use of such metadata in a pedagogical scenario. This set of descriptors, codified in an ontology (a formalized conceptual organization to support the encoding of metadata) (Noy and McGuinness 2001), can then be used to provide intelligent mechanisms for selecting and navigating through learning materials. Moreover, by linking metadata to relevant explanatory and exegetical materials, we will give students additional means for contextualizing philosophical resources. In general terms, the pedagogical principle inspiring us reflects the idea of an ‘invisible guide’, able to support ‘smart’ navigation by discovering interesting connections between metadata and philosophical resources. This approach can be implemented in three steps. First, we let experts (e.g. philosophy teachers) represent part of their knowledge using the ontology—i.e. they instantiate the ontology using contents related to a philosophical subject of choice. For instance, in the context of annotating Wittgenstein’s Tractatus, an expert may instantiate the generic notion of school-of-thought with the concept of “logical atomism”. Second, our experts annotate learning resources using the metadata just created—i.e. they formally associate one or more instances to a learning resource. For example, they may associate “logical atomism” with a specific statement in the Tractatus. Third, we construct algorithms which, by drawing on the ontological categories and the experts’ annotations, can organize dynamically the presentation of learning resources. For example, by bringing in other resources related to schools of thought that oppose “logical atomism”. In other words, resources can be viewed according to a specific perspective, which can be historical, theoretical, geographical , etc. This results in a series of navigation mechanisms for students to explore such resources in an unsupervised manner. In a nutshell, the ontology-based annotation would bring ‘authoritative structure’ to learners’ autonomous explorative activities. In this scenario, the ontology is similar to an invisible map that helps students moving through learning resources by means of pre-defined learning pathways. As discussed elsewhere (Mulholland et al. 2004), it is important to remember that the underlying assumption of this approach is that the ontology-based system is not supposed to provide a specific answer to the questions a learner or researcher may pose to it; instead, its goal is to facilitate the discovery of related (and possibly unknown) resources where the answer can be found. This is achieved by making transparent a number of coherence principles typical of the philosophical discourse (e.g. a historical evolution of a school of thought, the theoretical implications of an argument, etc.). Given these premises, we can describe the research work presented in this article as an attempt to construct a formal meta-language that allows the categorization of philosophical subjects. In defining this meta-language, we have taken inspiration from concepts that are commonly used for characterizing philosophical scholarship. For example, we included in the ontology notions such as philosophical system, argument and school of thought. This does not mean that we are prescribing a particular

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usage of these concepts; different authors can in fact characterize the same philosophy in different ways. This important aspect may be clarified through an example. Our ontology strictly defines a philosophical-system as a type of object which can have the property part-ofschool-of-thought (cf. Sect. 3.5.3), but it does not specify any philosophical-system in particular. Annotators and domain experts are expected to do this—and quite surely, they will do it with a great degree of subjectivity. For example, in a Wittgensteinian context some will consider “the philosophy of the first Wittgenstein” and “the philosophy of the second Wittgenstein” as separate instances of philosophical-system, while others could find the distinction quite unreasonable and instead define a single instance of philosophical-system, which represents “Wittgenstein’s philosophy” as a whole. What we are pointing out here is that the ontology supports both interpretations. This is a consequence of the fact that we gave our representations (classes and relations) a high level of generality i.e. we wanted them to be as re-usable as possible, especially among annotators having different philosophical views. The main advantage of this approach is that even when two authors’ interpretations are radically different, if the underlying meta-language is the same, we can still create connections between the alternative models. Of course, we are not claiming that there can be only one ontology for this purpose. And indeed our work has been driven by a very specific objective, i.e. the creation of navigation mechanisms which are pedagogically interesting and computationally feasible. Other philosophical ontologies with different modeling choices and rationales are likely to be created in the future. In such cases, ontology-mapping techniques (Kalfoglou and Schorlemmer 2003) could be investigated so to guarantee interoperability among heterogeneous models. The rest of the article is organized as follows: the next paragraph (1.1) gives a few technical notes which will facilitate readers in understanding the rest of this article. Section 2 summarizes a number of ontological requirements and the generic approach we used to satisfy them. Section 3 focuses on the description of the classes and relations representing philosophical ideas. Section 4 introduces PhiloSurfical, a prototype tool exemplifying the use of ontology-based navigation mechanisms within a pedagogical scenario. Finally, Sect. 5 contains some references to related projects.

1.1 Technical notes From the implementation point of view, the ontology (which at the time of writing counts 348 classes) is formalized by using the Operational Conceptual Modelling Language (OCML) (Motta 1999), which provides rich support for both specification and reference. Import/export mechanisms from OCML to other languages, such as OWL (W3C 2004) and Ontolingua (Farquhar et al. 1996), ensure interoperability with knowledge representation standards.1 1 The latest version of the ontology can be found online at http://www.philosurfical.open.ac.uk/ontology/.

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In the rest of the article, when examples from the ontology are provided, we use the OCML syntax for describing classes, instances and rules. In order to facilitate the reading of this article we used different fonts depending on whether we refer to classes in the ontology (e.g. event) or properties associated to them (e.g. has-duration). Instances are always double quoted (e.g. “the concept of will”). In the figures, classes are oval-shaped, rounded rectangles stand for instances and arrows represent relations. In particular, if not labelled otherwise, dashed arrows stand for the instance-of relation, while solid arrows stand for the subclass-of relation. As a final remark, we invite the reader who is not familiar with the knowledge representation approach and terminology to consult the relevant literature, since such an understanding is crucial in order to fully comprehend our work. In fact, we must remember that although ontologies have their roots in philosophy, their computational equivalents have raised a number of research problems which were previously unseen in philosophy (Zúñiga 2001). Unfortunately, a discussion of such issues would exceed the scope of this article. Readers may find a good introduction to the topic in the course on ontological engineering by Riichiro Mizoguchi (Mizoguchi 2004)). 2 Philosophy as a domain for knowledge representation 2.1 Domain analysis In order to identify an initial set of ontology requirements, we used various informal knowledge acquisition techniques.2 Mainly they consisted of discussions with domain experts, analyses of the implicit curricula formalized in philosophical textbooks, consultation of traditional encyclopedias and online philosophy directories. Then we also carried out a more formal knowledge acquisition experiment:3 a group of domain experts (lecturers and Ph.D. students) were involved in a card-sorting task (Rugg and Mcgeorge 2005) aimed at identifying some mechanisms practitioners employ for classifying philosophical entities (especially abstract entities, i.e. ideas). In general, these results led us to conclude that a suitable semantic model should provide support for representing: (a) historical events, that is, events which are inherently time-dependent (e.g. the publication of a book, or an author’s subscription to a viewpoint); (b) generic uncertainty, since often we are talking about facts which cannot be located exactly in the time and space dimension (e.g. the birth of Heraclitus); (c) information objects, and especially language-based information objects, as they are the traditionally preferred medium philosophical contents are expressed with; (d) interpretation events, intended as the process of attributing an abstract content to an information object (e.g. when we say that ‘Aristotle’s fourth book of the Metaphysics states an ontological principle’); 2 A good overview of the various techniques available can be found at http://www.epistemics.co.uk/Notes/ 63-0-0.htm 3 We intend to make available all the results of the experiment in the near future, in a separate publication.

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(e) coexistence of contradictory information, which is a direct consequence of D (e.g. when people claim different or opposing views on the same subject); (f) viewpoints, and other non-material entities (‘philosophical ideas’), for they are the objects philosophers are usually involved with, in their everyday practices; (g) varying granularity: this feature refers to the fact that philosophers normally (re)define the questions and ideas which lie at the centre of their work. As a result, the conceptions of two philosophers can have very little in common, if not at a meta-level. Thus, our model should be capable of overcoming the difficulties imposed by the ‘radicalism’ of philosophical conceptions. This means providing facilities to properly describe a philosophy, considered in both its singularity and within an historical perspective. For example, being able to express the historical contiguity of ‘Aristotle’s distinction of the four causes’ with ‘Hume’s radical skepticism regarding the cause notion’, although the two conceptions, taken singularly, do not have much in common with respect to the definition of the ‘cause’ notion.

2.2 Overview of the ontology The main feature characterizing our ontological approach is the decision to employ the CIDOC Conceptual Reference Model (Doerr 2003) as a starting point for our formalizations. The CIDOC-CRM ontology started out as an attempt of the committee of the International Council of Museums (ICOM) to achieve semantic interoperability for museum data. Since 1996, the formal model has improved considerably till becoming in 2006 an ISO standard (Crofts et al. 2005). It is now (version 4.2) in a very stable form, and contains 75 classes and 108 properties, both arranged in multiple is-a hierarchies. The choice of using CIDOC-CRM was motivated by two reasons. First, because of its widely recognized status as a standard for modeling cultural heritage data. In fact, by reusing and extending an existing and internationally recognized ontology, we will give our users more chances to benefit from the emerging Semantic Web infrastructure. Second, for its extensive event-centered design. This design rationale, in fact, appeared to be appropriate also when trying to organize the history of philosophy. Even if it is common to see it as an history of ideas, stressing the importance of the theoretical (i.e. meta-historical) dimension, we believe this cannot be examined without an adequate consideration of the historical dimension, that is, a history of the events related (directly or indirectly) to those ideas. Thus, with reference to the domain analysis described above, we can say that point A is directly addressed by CIDOC’s generic modeling approach. As an example, in Fig. 1, we can see a typical event-centered instantiation of the PhiloSurfical ontology. The persistent-item class, which is one of the five classes composing CIDOC’s top layer (together with time-specification, dimension, place and temporal-entity) subsumes thing and actor. The two branches of the ontology departing from them can have various instances, which are related by taking part (in various ways) to the same event (“1933-Prague-meeting”).

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Fig. 1 A typical event-based modeling in CIDOC

This kind of modeling, in the context of the PhiloSurfical tool (cf. Sect. 4), is extremely useful because of the multiple navigational pathways it can support (e.g. imagine a ‘lateral’ step taking us to another event having the same topic, or to another topic treated during the same event, etc.). Please note that in the figure, some relations (e.g. has-worked-for) are graphical shortcuts for the actual and lengthier formalization of the relevant event (e.g. an event instance stating that an actor worked for an institution at some point in time, etc.). As already pointed out in previous publications (Pasin and Motta 2007; Pasin et al. 2007), we decided to integrate the event-based CIDOC reference model with formalizations from other ontologies, because they provide facilities that are relevant to the points C, D and E we have highlighted earlier during the domain analysis. For example, we included a time-reasoning library implementing the well-known Allen specifications (Allen 1984); we included knowledge about the domain of publications from the AKT reference ontology (AKT 2002) and knowledge about information objects from the related module of the Dolce foundational ontology (Gangemi et al. 2002). Finally, a large portion of the ontology consists of new concepts and relations, mostly aimed at the description of philosophical events and ideas. The events having more relevance with respect to the philosophical domain are the following: (1) the temporal entities regarding events related to the academic life and to the life of philosophers. Among this group of events, we have births and deaths of philosophers (e.g. the death of Socrates), production of physical objects (e.g. Pascal’s construction of the arithmetic machine), journeys performed during their lives (e.g. Wittgenstein’s trip to Norway), production of publications (e.g. the publication of the first English version of Kant’s “Critique of practical

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Fig. 2 The intellectual activities branch

reason” in 1836), social-gatherings, conferences, joining of groups (e.g. when Aristotle joined the Academy of Plato, or when Heidegger joined the Nazi party). (2) The temporal entities related to the production and modification of philosophical ideas. These types of events are gathered under the class intellectual-activity (see Fig. 2). Among them, we can find conceptual-creation (event modeling the creation of conceptual entities such as ideas and information objects); idea-modification (events reflecting the changing of one or more ideas within the context of a view, e.g. the evolution of the meaning of “libido” in the work of Sigmund Freud); theory-transposition (class modeling the special case when a theory is taken out of a context and reused within another one, e.g. “Spencer’s evolutionism”, which extends “Darwin’s evolutionism” from biology to metaphysics), etc. (3) The temporal entities representing philosophical historical periods, i.e. macroevents (in CIDOC, such entities are subsumed by a class named period) characterized by an intrinsic reference to a specific group of people or a school of thought. The important classes here are intellectual movement (e.g. the “enlightenment”) and philosophical movement (e.g. “logical positivism”, interpreted as an event). The formal framework used for representing the characteristics of these entities has been previously discussed (Pasin and Motta 2007) under the title ‘pattern #1: is rationalism a school of thought or an event?’ The other major section which we extended CIDOC with is the one departing from the philosophical-idea class, which is located in the conceptual-object branch of the ontology (according to CIDOC, this is where all abstract entities are).

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In relation to the initial domain analysis, these formalizations satisfy the requirements described in points F and G. In Sect. 3, we concentrate the discussion on this branch of the ontology. 2.3 Support for alternative interpretations It is important to remember that only classes and relations are what remains unchangeable in our system, i.e. that is where lies the ontological commitment4 we demand from anybody using the ontology. On the contrary, the instantiation of our classes with elements specific to a single philosophy is a process which relies entirely on a user’s private understanding of that philosophy. As already discussed in Sect. 1, this feature allows annotators to use our meta-language with a great degree of freedom. As a result, the interpretations of philosophical subjects they create can be very different from each other. The only downside, in such cases, is that the results of incompatible instantiations are not handled easily by computers, thus requesting a manual integration. In order to provide a solution to this problem, the ontology features a mechanism by which we can construct alternative and possibly competing interpretations of the same entity, in such a way that the computer ‘knows’ how to handle each interpretation as an alternative view on a common topic. This mechanism becomes useful, for example, when we want to have multiple annotators working simultaneously within a single ontology-based environment (i.e. because we are interested in highlighting with precision how the various people’s interpretations differ). The interpretation class, a subtype of event, is meant to abstract the act of interpreting something, intended as the process by which we attribute a meaning to an object (cf. also Fig. 3). In ontological terms, this translates to associating an instance of propositional-content (i.e. the idea representing the interpretation) to any other instance of the ontology (i.e. theinterpreted-thing). Of course, since an interpretation is also an event, it inherits various properties which capture useful information such as the author of the interpretation (carried-out-by property), the time it was made (has-time-specification property), etc. For example, in our Wittgenstein-related knowledge base, we can have the following instance (see also Sect. 4.1): (def-instance interpretation-001 conceptinterpretation ((interprets a-posteriori-by-wittgenstein) (has-related-concept experience-by-wittgenstein prop-of-science-concept) (has-opposite-concept a-priori-by-wittgenstein laws-of-logic-concept) (is-equivalent-to form-prop-science-concept) 4 Ontological commitments can be defined as “agreements to use the shared vocabulary in a coherent and

consistent manner” (Gruber 1993).

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Fig. 3 Reification of ideas through the interpretation class

(is-related-to-idea mesh-metaphor fate-science-analogy) (carried-out-by michele-pasin) (has-time-specification 10-dec-08)) In this case, we are describing the properties of the concept of “a-posteriori by Wittgenstein” in such a way that these descriptions will be associated only to a specific user (i.e. the value of the property carried-out-by) and time (i.e. the value of the property has-time-specification). This is possible because the concept-interpretation class (a further specification of idea-interpretation) possesses all the properties normally used for describing an instance of concept: for example, has-related-concept, has-opposite-concept, is-equivalent-to, etc. (cf. Sect. 3.7). The result of this ‘reification’ mechanism is that we can have different descriptions of the same concept (and, in general, of any idea5 ) coexisting within the same knowledge base. In other terms, we are providing support for concurring and possibly contradictory information management. In future versions of our work, this feature is likely to be further developed with more a complex mechanism to retrieve, for example, contrasting interpretations, or letting users navigate through alternative views of the same ideas. Finally, as represented graphically in Fig. 3, notice how the ontology allows also separating the name of an idea (through the appellation class) from the idea itself (an instance of philosophical-idea). For space reasons, we will not describe 5 In fact, by using a similar approach we created also other subtypes of interpretation, so to match all the

remaining subtypes of philosophical-idea.

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this feature here, but let us underline that it is a mechanism provided by CIDOCCRM. In particular, within our philosophical context, this can be useful for describing multiple linguistic translations of the same idea. 3 A formal model for describing philosophical ideas The ontological approach presented in the previous sections accounts mainly for the factual and temporal dimensions of the philosophical domain (e.g. we modelled entities such as people, events or documents). We must now investigate another dimension that is eminently philosophical, i.e. the theoretical one, the realm of philosophical ideas. Where should one start in order to formalize the types of abstract entities discussed in philosophy? This seems a really puzzling question, and probably totally nonsensical to some. Such a slippery and debated domain, in fact, appears to challenge any stable formalization, and defeat any meaning-agreement process. On the other hand, modern day digital phenomena such as the incredible growth of available information or the increasing need for interoperability standards call for a solution which, although inevitably partial and non-definitive, can bring many more advantages than no solution at all. As claimed by the authors of a recent project for the indexing of the Stanford Encyclopedia of Philosophy (Niepert et al. 2007): “while no single ontology can possibly capture the full richness and interrelatedness of philosophical ideas, we are operating on the principle that having (at least) one ontology is better than none.” In the light of this simple but important reflection, we have attempted to model commonly used philosophical concepts without taking any particular philosophical position, that is, for what is possible, trying to remain “outside” specific philosophical stances. Not doing so would have caused a multiplication of ontologies and definitions, each of them reflecting the world according to a single thinker. Our approach, which can be related to a constructivist epistemology (Bachelard 1938), sees every philosophy as a system of interrelated conceptual entities which make sense of the world. From this perspective, we can say that such entities are all abstract (non-physical), since they are ‘what we use’ to refer to the physical world. The main consequence of this perspective is that even a common concept like “fire”, which would be normally instantiated as a physical entity, in our model becomes an instance of a concept (which is possibly related to a physical entity). In fact, the notion of fire, as any other notion, is socially constructed (Vygotsky 1978) and often explicitly defined by a viewpoint (e.g. the “Newtonian physics”, or the “philosophy of Heraclitus”). The fact that a generic agent happens to be more or less explicitly aware of this viewpoint, in all its aspects and subtleties, constitutes another issue and does not disprove the existence of it. For us, the problem to tackle is therefore the individuation of the types of nonphysical-objects playing a role in the construction of viewpoints, and, more broadly, having a recognizable function in the process of interaction and succession of viewpoints within the whole history of thought. As previously discussed (cf. Sect. 1),

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Fig. 4 The main classes of the philosophical-idea branch

the pragmatic requirements of creating a model which is at the same time vastly reusable and useful for creating pedagogical learning pathways have driven much of the formalizations presented below. In total, we identified eight main types of philosophical ideas (see Fig. 4). The following sections discuss them in greater details.

3.1 Argument-entity With the argument-entity class, we decided to group together two sets of related classes: argument and argument-part (see Fig. 5). The first one is the reification of the argumentation class (which is a subtype of event), as it ‘freezes’ an actual argumentation between two or more thinkers into an abstract idea (i.e. an entity outside space and time). In previous versions of the ontology, we also named it ‘argumentative-knot’. In fact, it refers to famous focal points of the philosophical argumentation, where all the main argumentative threads converge and meet. These knots usually originate with one author, and subsequently recalled and reused (maybe in different domains or for different purposes) by other authors. So, for example, we can have the “third-man argument” of Plato, the Cartesian “cogito-ergo-sum” or the Kantian “transcendental deduction”. An important property of this class is uses-method, whose range is argumentative-method (a subclass of abstract-method), because through it we can specify, for example, a deductive-argument, an inductive-argument or an abductive-argument. The second subclass of argument-entity is instead argument-part, which precisely serves to map out all the argumentative steps of a standpoint. For the moment, we only defined assumption, demonstration, conclusion and

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Fig. 5 Argument and argument-part

hypothesis (a subclass of assumption specifically referring to argumentations based on experimental evidence). It is important to note that this is only a simplified classification of the entities that can possibly build up an argument. In the future, other work from the argumentation community (Kirschner et al. 2003) could be brought in, so to represent at a finer granularity the different argument structures.

3.2 Problem-area In order to give an account of the distinctive features of fields of study, we decided to use as a starting point a problem-centered approach. This means that we tended to see the activity of philosophers as essentially an ongoing process of specifying and giving solutions to problems. Consequently, we consider any recognized area of study, of whatever type or dimensions, as a problem-area. In its simplest version, a problem-area is composed by a set of problems linked by different relational schemas, but in general, tying around a main theme. This theme, in our ontology, can be represented through a problem (has-central-problem property) or thanks to a thesis functioning as a criteria (has-criteria property). For example, “psychology”, when treated as a problem-area, can gather problems tied to the “mind-definition” problem, to the problem of “relating human behaviour to brain activities”, or to the thesis that “brain and mind can be investigated with the methods of natural sciences”. Other features of problem areas are that they can be related-to each other (e.g. “mathematics” and “philosophy of mathematics”) and that they can be organized into simple hierarchies (e.g. “internet-ethics” is a sub-area of “ethics”).

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However, we realized soon that “psychology” has a role and significance in our world that goes beyond a mere problem-area. In a similar fashion, “ethics” or “cognitive science” would not be properly characterized only as instances of problem-area, for they also refer to theories or methods which have become intrinsically related to the definition of the area. Moreover, if we consider the history of thought, the topic and description of problem-areas have always been the subject of many debates: different views aspire at having the ultimate vision about what the central issues to look at are, or the right methods to take. In this respect, problem-areas are not very different from other ideas that can be defined by multiple views. For example, we can just consider how different was the sense given to “philosophy of language” by the first philosophy of Wittgenstein and the second one. In order to catch these subtle differences, we defined the class field-of-study as a problem-area that has been socially and historically recognized as separate from the others (and from being a mere agglomerate of problems). In the ontology, this is reflected by the fact that a field-of-study is not just specified by a criteria, but is defined-by a view. It is also characterized by the fact that it collects not only problems, but also ways to solve or tackle them (i.e. theories and methods). The distinguishing properties are therefore defined-by-view, has-exemplar-theory and has-methodology. (def-class Field-of-study (Problem-area) ((defined-by-view :type view) (has-exemplar-theory :type theory) (has-methodology :type method))) As an example, we show a possible formalization of an old fashioned field-ofstudy, “phrenology”. (def-instance phrenology field-of-study ((has-referred-author Franz-Gall) (defined-by-view phrenology-theory) (contains-problem what-is-personality what-is-character relation-personality-skull) (has-criteria skull-shape-determines-personality-thesis) (sub-area-of psychology) (related-to-area craniometry physiognomy) (has-methodology phrenological-analysis))) Finally, a last tricky issue regarding fields of study must be addressed. This does not emerge when treating relatively isolated entities such as “phrenology”, but it clearly is an issue if we consider, say, “physics”. In our everyday language and also in the organization of academic programs, we usually refer to “physics”, “psychology” or “philosophy of mind” as generic fields of study. What this means is not really clear. In fact, when we delve into them (or even more, if we ask a practitioner for clarification), we discover quickly that there are many “physics”, “psychologies” and “philosophies”, at least as many as the views defining them. From our ontological perspective, these would all be separate instance-candidates of the field-of-study class. However,

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Fig. 6 Generic and specific fields of study

we also need to represent the fact that they are all part of a more generic (and probably emptier in its meaning) field-of-study. Our solution to this problem (cf. Fig. 6 above) consists in the creation of a generic-field-of-study class, which has no defining view but the views defining the specific fields of study that are claimed to be part of it. In other words, we are formalizing the fact that generic-fields-of-study such as “physics” or “philosophy: can be defined only extensionally. So we have the following OCML rule: (def-rule generic-field-rule (defined-by-view ?GF ?V) if (generic-field-of-study ?GF) (has-sub-area ?GF ?F) (defined-by-view ?F ?V)) In the formula, the variables ?GF, ?V and ?F refer respectively to genericfield-of-study, view and field-of-study. Therefore, doing so we can maintain the interoperability between specific thinkers’ definitions of classic problem areas, and the generic but useful ways to refer to them. 3.3 Problem The problem class represents a very central notion in philosophy, since it is usually the point of departure of any investigation (which often culminates with the creation of a view). Examples at hand are many: we talk about the “mind-body” problem, the “alienation” problem or the “problem of the universals”. A key feature we can easily recognize is that a problem is always framed within a larger context which gives a more

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precise connotation to it. So, for example, Marx considered the “alienation problem” to be rooted in “economy”, while Searle treats the “mind-body problem” within the “philosophy of mind”. Therefore, the problem exists within a problem-area. Moreover, the context which makes us understand a problem is given also by the set of assumptions that justify its existence. Or better, by the views and arguments that define it (and, conversely, try to solve it). The remaining properties of problem, as shown below, relate them to other problems or to the view and arguments that tackle them. A special role is held by the property has-problem-type, which can have value “openproblem” (meaning a problem which does not have any solution), “multilemma” (a problem having or allowing multiple solutions), “dilemma” (a problem allowing two solutions only, but neither of the two being satisfactory) and “paradox” (a problem whose solutions seem equally plausible, but when considered together generate a contradiction). Essentially, these concepts describe a problem from the viewpoint of the number of solutions it has. We have modelled them as instances of the class problem-type (which is not in the philosophical-idea branch, but is instead a subclass of CIDOC’s type), since they do not appear to be ‘essential’ for the definition of a problem, but just accidentally related to the existence of any solution. In other words, a definitional-problem (see below) will always maintain its structure, regardless of being an “open-problem” (i.e. having no solutions) or a “multilemma” (i.e. having various solutions). From the analysis of the literature, we thought it was useful also to provide a classification of problems based on their morphology. That is, on their external structure, which can be sometimes related to their content, but is usually independent from it. In total, we identified six ‘morphological types’ of problems: (1) the existence-problem has usually the form “Does X exist?”; specializations are existence-as-concrete-problem (“Is X concrete/real?”) and existence-as-abstract-problem (“Is X abstract?”) (2) the definitional-problem has usually the form “What is X?”. Specializations are definitional-problem-essence (“what are the characteristic traits X has?”), definitional-problem-attribute (“what are the attributes X has?”) and composition-problem (“What is X composed of?”) (3) the functional-problem has usually the form “What is the function of X?”; the only specialization is purpose-problem (“What is the purpose of X?”) (4) the relational-problem has usually the form “What is the relation between X and Y?”; specializations are dependence-problem (“Are X and Y dependent?”), dependence-cause-problem (“Is X the cause of Y?”), dependence-effect-problem (“Is X the effect of Y?”), independence-problem (“Is X independent from Y?”), equality-problem (“Is X equal to Y?”) and difference-problem (“Is X different from Y?”). (5) the modality-problem is a problem about the degree of certainty X is likely to happen (or not). Specializations are necessity-problem (“is X necessary?”), possibility-problem (“is X possible?”), contingency-problem (“is X contingent?”) and impossibility-problem (“is X impossible?”)

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(6) the factual-problem has the form “how, in what way does X happen, or manifests itself?”. At the time of writing, we are instantiating these problem templates by filling the empty spaces in the question with instances of concept. For example: (def-instance what-is-virtue definitional-problem ((contains-concept virtue) (has-problem-type multilemma) (exists-in-area ethics) (related-to-problem what-is-value) (is-tackled-by-View Plato-philosophy Aristotlephilosophy stoic-philosophy) (linked-to-fact death-of-socrates))) A much more interesting solution would be instead letting any instance of philosophical-idea be filling those spaces. This would result in a powerful reification mechanism: e.g. we could define a problem about the relation between two other problems. Moreover, we are also investigating how to use these structures for producing inferences (e.g. from a relational-problem, we can create a path which links to the definitional-problems of the concepts related). These and other issues (such as how to classify problems according to their ‘contents’ e.g. “moral problem” or “epistemological problem”) will be investigated in future research.

3.4 Method Various ontologies introduce a class named ‘procedure’, with reference to any sequence-like specification. Similarly, a heuristic or method in philosophy is essentially defined as a series of steps leading from a problem towards its solution. Depending on whether the method suggests a practical activity, or an intellectual one, we classified instances as belonging to abstract-method or practical-method (see Fig. 7). The main types of abstract-method are logical-mathematicalmethod, rule-of-inference and argumentative-method. The first one subsumes algorithm and comprises instances such as “the quick-sorting algorithm”, Wittgenstein’s “truth-table method” or Leibniz’s “infinitesimal calculus”. The second class refers to rules that are used to justify the steps in a formal proof of the validity of a more complex argument. For example, we can have “modus ponens”, “hypothetical syllogism”, “conjunction”, “double-negation elimination”, etc. The class fallacy, instead, refers to invalid argumentative steps that may appear convincing at first glance because they closely resemble legitimate patterns of reasoning. For example, fallacies can be the “illicit major”, “affirming the consequent”, “denying the antecedent”, “affirming the alternative”, etc. Finally, the class argumentative-method categorizes famous and well-established argumentation styles, such as “deductive argument”, “argumentum a fortiori”, “argumentum ad hominem”, “argumentum ad populum”, etc.

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Fig. 7 The method branch of the ontology

The other branch of method, practical-method is divided into scientific-method and life-praxis. With the first class, we refer to any structured method to investigate reality, in a “scientific” manner (e.g. so to produce and test some explanatory hypotheses). Examples can be “Bacon’s scientific method” or “Galileo’s scientific method”. The second class instead is a method of life conduct, such as the Epicurean’s “ataraxia” (e.g. a description of conduct to follow in order to achieve the tranquility of the soul) or a practice of meditation in eastern philosophies.

3.5 View This is a generic class referring to propositions expressing a viewpoint, that is, propositions picturing a perspective on the world in the form of more or less structured interpretations of things and events. Examples of view are “solipsism”, “theory of evolution by natural selection”, “philosophy of Plato” or “a name has a meaning only in the context of a proposition” (i.e. Frege’s context principle). Due to their categorical attitude, views usually define concepts and, in general, create the context for the definition of other meanings too (e.g. problem-areas, problems, methods etc.). A number of properties connect views to the other philosophical-ideas: views can use other ideas, tackle problems, influence and support/contrast each other, and be-supported by arguments. Most of them seemed to reflect quite well the common sense understanding of philosophy, so we will not treat them one by one here. However, the feature we want to highlight here is how views can have varying granularities. From our analysis of the literature, we identified four possible kinds of view:

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Fig. 8 The view-types

school-of-thought, theory, philosophical-system and thesis (see Fig. 8). The main differences among them depend on the degree of generality they exhibit and the level of complexity they have. In Fig. 9, we can see a small example including different views and some relations they entertain with each other. In the following four paragraphs, we will examine them one by one. 3.5.1 Thesis A thesis is the least structured view, as sometimes it consists only of a standpoint in the form of a statement (i.e. an assertion). So, for example, in the context of Wittgenstein’s picture theory of language, a thesis can be the “independence of the state of things” (as recognized by Stenius (Stenius 1960)), which can be instantiated as follows: (def-instance independence-state-of-things thesis ((defines-concept state-of-things independence) (part-of-system wittgenstein-first-philosophy) (part-of-theory picture-theory-of-language) (has-string-description “State of things are independent of one another”))) The local properties of thesis are the part-of relations linking it to the other subclasses of view. Most of its properties are therefore inherited. However, not all theses have the same status: two subclasses, law and principle, refer respectively to theses with vast predictive power, especially in scientific areas (e.g. the “law of universal gravitation”), and to theses that play a fundamental

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Fig. 9 The view-types instantiation

role within a view, usually a philosophical one (e.g. a principle in medical ethics). Finally, if the principle is not demonstrable but self-evident, it becomes a self-evident-principle. For example: (def-instance principle-of-contradiction self-evidentprinciple ((defines-concept truth thought) (part-of-system aristotle-philosophy) (exists-in-area logic))) (has-string-description “One cannot say of something that it is and that it is not in the same respect and at the same time”) (appears-in Metaphysics-book-IV))) 3.5.2 Theory With the class theory, we refer to a systemic conceptual construction with a coherent and organic architecture. A theory explains a specific phenomenon (or a set of phenomena) and typically answers to an already existing problem. Examples can be Darwin’s “theory of evolution” or Quine’s “verification theory”. The first one is a scientific-theory, while the second is a philosophical-theory. The main difference between the two is that the last one is not necessarily hypothetical and therefore it does not need experimental verification (although it can be provided with it).

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The local slots of theory define the following properties: part-of-theory expresses the situation where theories are composed by other theories (e.g. Plato’s “theory of metempsychosis”, which is contained and dependent on the “theory of anamnesis”); part-of-school can be used to express that a theory is classified as part of a school of thought (e.g. when we say that the “picture theory of language” is a kind of “reductionism”); finally, part-of-system links a theory to an author’s philosophy (e.g. the “theory of eternal recurrence” is part of “Nietzsche’s philosophy”). Moreover, theories can define-methods (e.g. Wittgenstein’s “picture theory of language” defines the “truth tables method”), they exist within a specific problem-area (exists-in-area) and usually within them, we can easily identify a set of thesis (has-thesis). A philosophical-theory does not differ much in its formalization from its direct super-class, apart from the fact of having range branch-of-philosophy on the property exists-in-area. The same property, instead, would have value scientific-area in the case of a scientific-theory. Moreover, a scientific-theory can be further defined as having a more peculiar relationship to the facts it tries to explain, as it is usually required to be verified (proved) by them, and to be able to predict them too. 3.5.3 Philosophical-system A philosophical-system might appear as a theory, at first sight, but it differs from it essentially for its generality and breadth. That is, because it spans over various problem-area, while a theory is usually confined to one problem-area only. As a consequence, theories are usually part-of philosophical systems. We can therefore define a system as the set of a person’s views (which singularly taken, approach problems coming from different problem areas) which are consistently connected to each other, in such a way to form a unity. In a way, this class refers to what is normally called the ‘philosophy’ of a thinker. So, for example, we can have “Epicurean philosophy”, “Kantian philosophy” or “Hume’s philosophy”. We must remember, however, that this class does not correspond to the mere sum of an author’s theories: in fact, thinkers might produce more than one independent system, during their lifetime (e.g. the first philosophy of Wittgenstein, as opposed to the second one). Finally, we also recognized how a philosophical-system (although being inherently related to various problem-area) is often considered as representative of a school-of-thought (which, as explained in the next section, is instead usually related to a specific problem-area). In other words, it makes sense to say “the philosophy of Hume is scepticism”, even if, in such a case, we implicitly refer to only certain aspects of his philosophy (i.e. his epistemology). As this is a normal practice for scholars, we reckoned important also for our ontology users to be able to quickly classify philosophies using the part-of-school property, without having to specify the relevant theories or thesis. In order to prevent wrong generalizations (e.g. inferring that all the theories of Hume are “sceptical”), we use a set of purpose-built rules. Finally, other rules also guarantee the consistency between philosophical-systems and the theories composing them (e.g. if a theory defines a method or a concept, the philosophy comprising the theory is also considered to define them).

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3.5.4 School of thought This class refers to the set of theory-types, or generic standpoints, which in the history of thought have acquired a particular significance and, seemingly, a life on their own. They correspond to widely known conceptions or standardized intellectual trends that hint at typical ways to answer a problem (or a set of problems). Examples are “pacifism”, “animism”, “expansionism”, “empiricism” or “monism”. Sometimes they can be so abstract (as in the case of “monism”) that they do not imply anymore than a link to a specific problem or area, but refer only to the ‘formal features’ of the view they classify. For example, in the case of “monism”, what is implied is just ‘a view that admits only one principle as fundamental’. A school-of-thought, compared to the other views, is not as formalized and specific as a theory, and not as broad and systematic as a philosophical-system. Accordingly, in our model, we decided to limit its contents to instances of thesis. Because of this “generic” flavour, we often perceive the meaning of schools as being vague and abstract (e.g. when trying to specify what is “rationalism”). On the contrary, we noticed that this is not the case when we refer to (1) their “instantiation” within a problem area (e.g. the “ethical rationalism”) and (2) their specific “expression” within an author’s philosophy (e.g. the “rationalism of Kant”). These last two examples seemed to us quite important; therefore, we attempted to give an account of them also in the ontology. According to our analysis, the first case (“ethical rationalism”) relates to the fact that schools of thought often have a ‘contextualized’ version. That is, they assume a different and more specific meaning when associated to a specific problem-area. For example, “rationalism”, can be found in “epistemology”, in “ethics”, in “metaphysics” or in “philosophy of religion”. The interesting phenomenon, in this case, is that the contextualized versions do not always have much in common and sometimes are even surprisingly unrelated. For example, let us mention the different meanings of “cognitivism” in “psychology” and in “meta-ethics”. Therefore, in order to keep separated the meaning of generic schools of thought from their localized ones, we introduced the class contextualized-school-of-thought, which has the additional slot exists-in-area with range field-of-study. Instead, regarding the second case (the “rationalism of Kant”), we concluded that it refers to the fact that schools of thought are normally used as ‘classifiers’ of other views. We showed in a precedent paragraph how this relation is already captured by the part-of-school property of theory and philosophical-system. In a similar fashion, we created also the slot has-exemplar-theory, which refers to the theory that inspired the school-of-thought, and is likely to help in understanding its original sense.

3.6 Rhetorical figure With this class, we aimed at grouping figures of speech or statements embodying some rhetorical value; usually these objects of discourse are used for emphasis, for clarity or as a device in the philosophical argumentation. Many of these entities could also

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have fitted as subtypes of argument-part, since in most cases they play that role. However, since often they assume a singular significance in the history of thought (i.e. the “myth of the cave”), we decided to represent them separately, so that they could be treated (and re-used) as independent entities. We have defined three types of rhetorical-figure: metaphor, which subsumes myth and analogy; maxim-motto, and thought-experiment. All of them can be described by using the properties used-in-argument and used-inview. Examples of the first type is the aforementioned “myth of the cave”, or Hegel’s metaphor of the “night, in which all cows are black” (used in the argument against Schelling). Maxim-motto refers instead to famous and exemplar statements or expressions philosophers used to sum up their position. For example, Descartes’ “cogito ergo sum”, Hobbes’ “homo homini lupus” or the ancient maxim “ex nihilo nihil fit”. Finally, thought-experiment refers to mind-simulations used to prove a point: among them, we can remember Searle’s Chinese-room thought-experiment (used to attack strong AI), Putnam’s twin-earth thought-experiment (used to support “semantic externalism”) or David Chalmer’s “unconscious zombies” thought-experiment (used to attack “physicalism”).

3.7 Concept A concept is an atomic element (i.e. not further decomposed) in the ontology. Instances of concepts can be “ego”, “evolution” or “god”. In determining what is a concept, we are not interested in its cognitive and linguistic features (i.e. the fact that it carries one propositional content, or that it is expressible through one or two words), but mostly in its functional role within the economy of a philosophy or a theory. That is, we tend to see a concept as an element which is defined by a view as primitive, and which is in a net of relations with other concepts. According to a ‘philosophy of minimum commitment’, we have chosen not to formalize specific philosophical concepts as classes, but to provide means to create alternative interrelated nets of instances which could resemble (and could be exported as) a small taxonomy. Thus, the creation of a network of interrelated concepts relies totally on the annotator. We expect people to organize the knowledge associated with an author’s conception very differently, according to user needs, background and interests. A concept can be linked to other concepts through various relations: specialization and generalization (is-specialization-of and is-generalization-of properties); similarity of meaning (is-equivalent-to), e.g. for the concepts “inexpressible” and “ineffable” in Wittgenstein; antinomic contrast (has-opposite-concept), e.g. when two concepts are part of a dichotomy; generic semantic closeness (has-related-concept), e.g. when they concur in explaining the same phenomena; notional dependency (requires-concept), e.g. with concepts such as “buy” and “pay”; causation (causes-concept), e.g. with concepts such as “to kill” and “to die”. For example, the Wittgensteinian concept of “picture” could be defined as follows:

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(def-instance picture-by-first-wittgenstein concept ((has-common-name picture) (defined-by-view first-wittgenstein-philosophy) (is-specialization-of fact-by-first-wittgenstein) (is-generalization-of logical-picture-by-firstwittgenstein) (has-similar-meaning-as picture-by-hertz) (is-in-contrast-with) (is-in-relation-with isomorphism-by-first-wittgenstein form-of-representation-by-first-wittgenstein representing-relation-by-first-wittgenstein)))) Finally, the has-common-name property (whose range is idea-appellation) is used for separating the concept object from the name used to identify it (e.g. “picture” in English, “immagine” in Italian, “image” in French, etc.). Let us remind that CIDOC provides a useful facility to detach entities from their names, that is the appellation class (it is located in the persistent-item branch of the ontology). By instantiating this class, for example, we can define multiple names for the same place or for the same person. Analogously, we added also an idea-appellation class in order to support the separation of an idea-object from its names. This turned out to be quite a handy feature, because often there are no explicit properties stating the relationships between two instances of concept, but the fact that they have the same name. In Fig. 10, we can see an example of how the word “alienation” (which is an idea-appellation instance) could be referring to four different concepts. Each of them, in fact, is defined by a different view, categorized by different school-of-thought and typical of different problem-areas.

3.8 Distinction We have a distinction when two ideas or more stand out as particularly meaningful in their opposition. That is, the specificity of their sense is obtained or clarified by their being different, but complementary. For example, “Hume’s distinction between truth of reason and matters of fact”, “Aristotle’s distinction between essence and accident”, or “Frege’s distinction between extension and intension”. Together, the two concepts fill up a whole, with respect to a specific domain of reference, e.g. “epistemological” (regarding the limits of human knowledge) or “ontological” (regarding the structure of being). A distinction can have an arbitrary number of concepts (e.g. “Aristotle’s four types of causes”), but when comprising two concepts only, it is also called dichotomy. For example: (def-instance hume-fork dichotomy ((has-referred-author david-hume) (related-to-area epistemology) (related-to-problem what-can-we-know) (defined-by-view hume-philosophy) (contains-concept relation-of-ideas matter-of-fact)))

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Fig. 10 The four concepts behind the philosophical term “alienation”

4 Putting things together: the PhiloSurfical tool In this section, we describe the main features of PhiloSurfical6 , a prototype software that allows the navigation of a semantically enhanced version of Wittgenstein’s Tractatus Logico-Philosophicus (Wittgenstein 1922). By relying on the various levels of abstraction provided by the ontology, the software lets users browse the text and other associated resources in a contextual manner. For example, users can select all text instances which have been annotated with a specific concept, discover how this concept relates to other concepts in the philosophy of Wittgenstein and, in general, access data using the network of relations that have been formalized in the ontology (Fig. 11). This methodology, which has been previously defined as ontology-based navigation (Crampes and Ranwez 2000), can be further developed by means of an approach modelled on narratology (Chatman 1978). As already discussed in an earlier publication (Pasin and Motta 2005), following structuralist theorists we can sketch out the structure of a narrative as the union of a story (what is told) and a discourse (the ‘how’ of what is told, that is, the specific way in which the basic elements of a story are re-organized and conveyed to the listener, in order to create different effects). In our narratology-inspired approach, a formal ontology can be used to express the semantics of the different elements composing a story, so that it is also possible to formalize the way a discourse recomposes the same elements according to different criteria. So, for example, the same chosen set of ‘atomic’ philosophical events could be ordered following a historical perspective, a geographical one or even one based on the most relevant schools of thought. Similarly, the same set of philosophical ideas 6 The application is available online at http://philosurfical.open.ac.uk

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Fig. 11 Screenshot of the PhiloSurfical application

could be organized differently if investigated under a problem-centered perspective, a theory-centered one, or simply one based on their historical succession. In other words, our approach takes the notion of a ‘digital narrative’7 (Brooks 1997) and attempts to transpose it to the specific scenario made up of philosophical entities. Accordingly, with PhiloSurfical, we aimed at creating a virtual environment for exploring user-triggered digital narratives, which we also call learning pathways. Due to space limitations, we cannot give here a complete description of all the pathways made available in PhiloSurfical. In order to better understand the role and usage of the ontology within the software tool, we will instead focus on the construction of a Tractatus-related knowledge base and on the functioning of a specific type of learning pathways, the theoretical ones (cf. Table 1 below). 4.1 Creating a knowledge base for the Tractatus Although the ontology was created with the aim of facilitating data-exchange among distributed resource-providers, for bootstrapping purposes (as the availability of free and adequately encoded ‘philosophical’ data on the web is still limited), PhiloSurfical strongly relies on an internal knowledge base of our creation. Before going further, an important clarification has to be made. By instantiating the ontology with various Tractatus-related data, we inevitably created a ‘unified’ philosophical view of this text, in the sense that we had to privilege certain interpretations instead of others. Certainly, such a result is not representative of the reality, 7 Brooks defines it as a “system of specially stored and organized narrative elements which the computer

retrieves and assembles according to some expressed form of narration”.

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Table 1 The theoretical pathways available in PhiloSurfical Name (input type)

Description

Ideas having the same name (propositional-content)

This pathway retrieves ideas having the same name but a different meaning than the selected one. For example, starting from the concept of ‘fact’ in Wittgenstein, we would find out about other authors who used the word ‘fact’ in a different sense (such as Frege and Russell). Starting from a school of thought, this pathway retrieves a set of related schools of thought which are all specializations of the same generic one. This pathway is related to the formalization presented in Sect. 3.5.4: e.g., by focusing on ‘atomism’ we would be able to see the related contextual versions of it, such as ‘logical atomism’, ‘metaphysical atomism’, ‘social atomism’, etc. Starting from a view, this pathway is a recursive function showing information about other views that support/compete with the first one. For example, starting from ‘Wittgenstein’s theory of language’, we could go to ‘Russell’s theory of language’ (which opposes it), then to ‘Whitehead’s theory of logic’ (which supports Russell’s) etc. This pathway shows all the information an idea has been described with. This is a generic way to retrieve all the interpretations associated to an idea. This pathway takes a problem instance and retrieves information related to the competing views (theories, schools of thought, philosophies) that tackle that problem.

“Generic and specific schools of thought” (school-of-thought)

“Influences among related views” (view)

“Generic map of related ideas” (propositional-content)

“Problem-centric map of the attempts to solve a problem” (problem)

where the amount of critical literature on this influential text is just enormous. Thus, consistently with what was emphasized in Sect. 1, our views on the Tractatus have no pretension whatsoever to be representative of all the literature, or to be truer than others. In general, we just aimed at creating a pedagogical resource that could be used as an introduction to the Tractatus. Accordingly, we stopped refining the knowledge base as soon as we thought we had reached a critical mass of data, usable for testing our ‘learning pathways’ approach. It is also useful to point out that in this respect, our work differs radically from other digital editions of Wittgenstein’s works, e.g. Bazzocchi’s Tractatus (Bazzocchi 2007) or the famous Bergen edition of the Nachlass (Pichler 2002). Our aim was simply to test the quality of the ontology by instantiating it with real-world philosophical data. The other digital editions focus instead on creating a new version of a classic text, usually by taking advantage of various features of the digital medium. The key difference here is that our research interest concerns the modeling and integration of philosophical data in an open context like the Semantic Web. Within such a scenario, the Tractatus is for us just a ‘handy’ testbed for the instantiation

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of the ontology (first of all, because it is a highly structured text, thus simplifying the analytical task of dissecting it into meaningful units). On the contrary, the digital editions mentioned above do not make available the (implicit) semantic model used in building the application, that is, they do not present it in the form of an ontology that others can reuse, modify or employ for exchanging philosophical data. The creation of PhiloSurfical’s knowledge base is composed of three phases. (1) The transformation of the text itself into a semantic format. First, we downloaded the Gutenberg edition of the Tractatus8 , which corresponds to the English translation made by David Pears and Brian McGuinness in 1961. We then built a suitable parser to extract the different paragraph numbers and text, so to populate the relevant parts of the ontology (mainly, subclasses of information-objects representing text entities at various levels of abstraction). Moreover, we repeated this process with two other editions of the text, the translations made in 1922 by Charles Kay Ogden9 and the original German version10 . As a result, we created 1591 instances representing Tractatus sentences. (2) The annotation of the text’s paragraphs. For the annotation phase, we worked in collaboration with a Wittgenstein scholar, Andrea Bernardi. Essentially, we went through all of the text’s paragraphs with the purpose of extracting the keyconcepts they are dealing with. We then drew a map where it is possible to see the association of each concept to the paragraphs where it is mentioned. During this process, our philosophy expert also created some basic relations that contextualize the concepts with respect to one another, so to form links among them (inclusion, opposition, similarity…). Moreover, we annotated a number of specific relationships the concepts entertain with other types of philosophical entities (e.g. a theorybelongs to a school of thought, a theory defines a concept, an author belongs to a philosophical school, etc.). To conclude this process, we generated a layer of interpretation instances about the Tractatus (analogous to what described in Sect. 2.3). By using this method, we created a total of 639 instances representing interpretations of Tractatus sentences, 434 instances of philosophical ideas related to the text and 290 interpretations of the ideas. (3) The enlargement of the knowledge base through the addition of further philosophy-related instances. This was done automatically, mostly by ‘scraping’ the relevant information from websites in the public domain. Afterward, this data was evaluated and sometimes refined manually. In general, we imported data about famous philosophers (more than 7,000 instances of person), schools of thoughts (about 500 instances of school-of-thought), the secondary Wittgensteinian literature (about 100 instances of information-object) and philosophical dictionary entries (about 5,000 instances of information-object). 8 http://www.gutenberg.org/etext/5740 9 http://www.kfs.org/~jonathan/witt/tlph.html 10 http://www.tractatus.hochholzer.info/

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Fig. 12 Pathway representing the various attempts to solve a problem

4.2 Ontology-enabled pathways for learning A ‘pathway’ is essentially a way to retrieve different instances stored in the knowledge base and organize them into a coherent whole. We classified pathways according to the ontological type of their ‘entry point’ (i.e. the instance we start the pathway from), and, more generally, according to the types of the instances that are retrieved from the knowledge base. So, for example, by selecting instances of philosophical-idea, we would usually trigger a theoretical pathway; instead, if we selected instances of person, we would probably trigger a textual or historical pathway. From the point of view of a learner, such mechanisms can be used as follows. First of all, users select a content of interest as the starting point of a pathway (Fig. 12, ‘item in focus’ box). Learners may then click on one of the available choices appearing in the ‘pathways list’ panel (see Fig. 12, bottom-left). The pathways that are not available are dimmed out; the available ones, instead, come with a brief description explaining their meaning. Once triggered, the pathway’s results are shown as a list of interrelated entities (Fig. 12, ‘results’ panel). Here, a number of important relations among the pathway’s items are made explicit, so to highlight their significance in the philosophical discourse. Moreover, by clicking on any of these items, it is possible to put it ‘into focus’ and use it as the ‘starting point’ of new pathways. A ‘recent items’ panel is used to keep track of all the items selected since the beginning; also, from here it is possible to search for these topics elsewhere on the web (e.g. on philosophical portals, specialized search engines, etc.). For example, starting from the problem instance called “problem of the foundations of mathematics” we might select the ‘problem-centric map of the attempts to solve a problem’ pathway. As shown in Fig. 12, this type of query produces a list of concurrent view instances which have been classified as attempting to solve that problem. Each view is presented together with other useful information too (e.g. has-main-exponent,has-exemplar-theory, etc.).

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Fig. 13 Graphical view of a theoretical pathway about Frege

Furthermore, by clicking on the ‘see in a graph’ button learners can view the pathway’s results using a graphical visualization.For example, in Fig. 13, we can see the results of a theoretical pathway starting from the idea of “Frege’s conception of logic”. In this case the pathway selected is ‘generic map of related ideas’, which simply shows all information associated to an idea. Internally, PhiloSurfical represents pathways as abstract procedures applicable to any ontology-compliant data repository. For instance, in Fig. 14, we reproduced the algorithms behind the ‘influences among related views’ and the ‘problem-centric map of the attempts to solve a problem’ pathways (cf. also Table 1 above). In general, after a pathway is triggered, we scan the knowledge base for instances of interpretation mentioning the item which has been selected by the user. Subsequently, we analyze the interpretation instances retrieved for the purpose of finding information which is relevant to the specific pathway the user has selected. For example, in the case of ‘influences among related views’, we are interested in relations such as supports-view and opposes-view. If some results are found, we store them for the visualization phase. Of course, each pathway presents individual differences too: e.g. the ‘problem-centric map of the attempts to solve a problem’ pathway searches for relevant interpretation instances twice: first with a problem instance, second with a view instance; instead, ‘influences among related views’ is a function that calls itself recursively a predefined number of times, so to create a ‘nested’ map of related views.

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Fig. 14 Abstract representation of two pathways’ algorithm

Usually, the output of these algorithms is a very ‘concise’ representation of the final dataset we present to the user. For example, the results of a theoretical pathway involving different concepts related to the same author may omit the repetition of the is-author-of property. On the contrary, the data shown in the user interface need to explicitly mention all these relations. At the moment, this ‘explosion’ process is handled by two routines, depending on whether the results are presented in html or in the java-based graphical view. In future releases of PhiloSurfical, it is likely that we will add also other types of data visualizations. 5 Related work The most relevant (and to our knowledge unique) attempt to systematically formalize the philosophical domain is the one carried out in Niepert et al. (2007), as part of a larger project aimed at building a dynamic ontological-backbone for the online version of the Stanford Encyclopedia of Philosophy (SEP). Compared to our approach, this work is less focused on knowledge modeling and more targeted at finding useful information extraction techniques, which could benefit from the vast expert-reviewed SEP. For example, in their case the idea sub-branch of the ontology is populated according to “semantic relevance” of ideas (based on words co-occurrence), instead of trying to model a hierarchy of types. Therefore, we see the two approached as fundamentally complementary and likely to be used together in future work.

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As various publications suggest, the humanities computing community has recently been more interested in the usage of ontologies for facilitating data representation and exchange (Gábor et al. 2005; Vieira and Ciula 2007). In this context, the Discovery project (2008) stands out for its explicit goal of creating a Semantic Web infrastructure specifically for philosophers. From the ontological point of view, the authors plan to use a ‘network’ of ontologies (Nucci et al. 2007). This seems really promising, but unfortunately at the time of writing, there is still no publicly available ontology for the philosophical domain. We plan to investigate how our results compare with theirs as soon as they will make them available. Regarding the formalization of ideas (and especially philosophical ideas), we found no evidence of relevant work in the knowledge representation research literature. Although models such as Wordnet (Fellbaum 1998) and Cyc (Lenat and Guha 1990) have in their knowledge base philosophy-related concepts, they present them in hierarchies that are either too flat (e.g. everything is a subclass of “doctrine”) or not complex enough to support any navigation mechanism. The noteworthy exception here is the DnS module of Dolce (Gangemi and Mika 2003), which is “intended to provide a framework for representing contexts, methods, norms, theories, situations” and has strongly influenced us. However, our ontology appears to be much more specifically suited to represent philosophical entities, such as schools of thoughts or problems. In fact, such topics are only marginally treated by DnS, which focuses on the formalization of entities such as plans, laws and regulations (legal objects). Furthermore, our formalization of fields of studies (cf. Sect. 3.2) could be related to the various work done in digital libraries subjects’ classification. Although we come from a different perspective, we acknowledge that approaches such as the mereotopological one (Welty and Jenkins 1999) could be well suited also for the philosophical domain. We plan to investigate further this issue in future work. Finally, it is worth mentioning recent research aimed at facilitating the semantic navigation of digital resource repositories, for it complements our learning pathways approach. Faceted browsing systems usually provide generic architectures that aim at letting users explore potentially unfamiliar domains in a gradual and incremental manner. These approaches, inspired by faceted theory (Ranganathan 1990), have been tested in various humanities domains, such as classical music (Schraefel 2005), visual arts (Hildebrand et al. 2006), cultural heritage (Hyvonen et al. 2008) and literature (Nowviskie 2005). In general, by means of highly interactive visualization mechanisms which are controlled by the user’s selection of facets, the structure of a domain can be disclosed in a very intuitive manner. The main limitations of these systems, in our opinion, is linked to their very best feature. That is, being largely non-domain specific and allowing navigation based on ‘small’ and ‘incremental’ steps (i.e. selection of views/facets) the navigation mechanisms can hardly be tailored to specific learners’ needs. For instance, it would not be possible to construct a ‘view’ which organizes resources in a way that mimics, or at least supports, the traditional ways a discipline is presented or taught. In conclusion, our narrative inspired approach seems to be better targeted to an educational scenario. Acknowledgments This work has been carried out under a grant provided by the EU-funded Knowledge Web project. We would like to thank all the people who have provided feedback and support during the

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various stages of the research. In particular, Andrea Bernardi, Keith Frankish, Gordon Rugg, Marian Petre, Riichiro Mizoguchi and Martin Doerr.

References AKT. Reference ontology v.2—AKTive portal ontology v.2. (2002). http://d3e.open.ac.uk/akt/2002/ portal-ocml-v2.0/portal-ocml-v2.0-t.html. Allen, J. F. (1984). Towards a general theory of action and time. Artificial Intelligence, 23, 123–154. Bachelard, G. (1938). La formation de l’esprit scientifique. Bazzocchi, L. (2007). On butterfly’s feelers: Some examples of surfing on Wittgenstein’s Tractatus. Proceedings of the 30th International Ludwig Wittgenstein-Symposium. Berners-Lee, T., Hendler, J., & Lassila, O. (2001). The semantic web. Scientific American. Brooks, K. M. (1997). Do story agents use rocking chairs? The theory and implementation of one model for computational narrative. Fourth ACM multimedia conference. Chatman, S. (1978). Story and discourse. Ithaca: Cornell University Press. Crampes, M., & Ranwez, S. (2000). Ontology-supported and ontology-driven conceptual navigation on the world wide web. 11th ACM hypertext conference. Crofts, N., Doerr, M., Gill, T., Stead, S. & Stiff, M. (2005). CIDOC-CRM Version 4.2—Reference Document. Discovery project, official website. (2008). http://www.discovery-project.eu/. Doerr, M. (2003). The CIDOC conceptual reference module: An ontological approach to semantic interoperability of metadata. AI Magazine Archive, 24, 75–92. Farquhar, A., Fikes, R., & Rice, J. (1996). The ontolingua server: A tool for collaborative ontology construction. Stanford Knowledge Systems Laboratory Technical Report Fellbaum, C. (Ed.). (1998). WordNet: An electronic lexical database. Cambridge, MA: MIT Press. Gábor, Nagypál, Richard, Deswart, & Oosthoek, J. (2005). Applying the semantic web: The VICODI experience in creating visual contextualization. Literary and Linguisting Computing, 20, 327–349. Gangemi, A., & Mika, P. (2003). Understanding the semantic web through descriptions and situations. International conference on ontologies, databases and applications of semantics (ODBASE). Gangemi, A., Guarino, N., Masolo, C., Oltramari, A., & Schneider, L. (2002). Sweetening ontologies with DOLCE. 13th international conference on knowledge engineering and knowledge management (EKAW02). Gruber, T. (1993). In Guarino, N. & Poli, R. (Ed). Formal ontology in conceptual analysis and knowledge representation. Boston: Kulwer Academic Publishers. Hildebrand, M., van Ossenbruggen, J., & Hardman, L. (2006). /facet: A Browser for Heterogeneous Semantic Web Repositories. International Semantic Web Conference—ISWC2006. Hyvonen, E., Ruotsalo, T., Haggstrom, T., Salminen, M., Junnila, M., Virkkila, M., Haaramo, M., Kauppinen, T., Makela, E., & Viljanen, K. (2008). CultureSampo—Finnish culture on the semantic web. The vision and first results. In K. Robering (Ed.), Information technology for the virtual museum. Berlin: LIT Verlag. Kalfoglou, Y.,, & Schorlemmer, M. (2003). Ontology mapping: The state of the art. The Knowledge Engineering Review, 18, 1–31. Kirschner, P., Shum, S.B., & Carr, C. (2003). Visualizing argumentation: Software tools for collaborative and educational sense-making. London: Springer-Verlag. Lenat, D. B., & Guha, R.V. (1990). Building large knowledge-based systems: Representation and inference in the Cyc project. Boston, MA: Addison-Wesley. Mizoguchi, R. (2004). Tutorial on ontological engineering—part 3: Advanced course of ontological engineering. New Generation Computing, 22, 198–220. Motta, E. (1999). Reusable components for knowledge modelling—principles and case studies in parametric design problem solving. The Netherlands: IOS Press. Mulholland, P., Collins, T., & Zdrahal, Z. (2004). Story fountain: Intelligent support for story research and exploration. 9th international conference on intelligent user interface. Niepert, M., Buckner, C., & Allen, C. (2007). A dynamic ontology for a dynamic reference work. Joint conference on digital libraries (JDCL-07). Nowviskie, B. (2005). COLLEX: Semantic collections & exhibits for the remixable web. http://www. nines.org/about/Nowviskie-Collex.pdf.

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Synthese (2011) 182:269–295 DOI 10.1007/s11229-009-9661-2

Knowledge representation, the World Wide Web, and the evolution of logic Christopher Menzel

Received: 17 December 2008 / Accepted: 5 March 2009 / Published online: 15 October 2009 © Springer Science+Business Media B.V. 2009

Abstract It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable divide between concept and object. These presuppositions, taken at face value, reflect a significant metaphysical viewpoint, one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar “adaptations” to FOL— culminating in a standardized framework known as Common Logic—have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning upon information on World Wide Web. Keywords

Common logic · Semantic web · Knowledge representation

In most philosophical contexts for the last 50 years at least, logic has usually meant first-order logic (FOL) of some ilk, perhaps with modal or other intensional operators. This is of course a very good thing. FOL, with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical ideas and their logical

C. Menzel (B) Department of Philosophy, Texas A&M University, College Station, TX 77843, USA e-mail: [email protected]

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connections. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. Modern FOL (as well as higher-order logic) of course is typically traced back to Frege. Interestingly, even though Frege’s metaphysical and semantical views are in many respects out of favor, a number of prominent syntactic and semantical properties of FOL still reflect distinctly Fregean ideas, notably, that there is an inviolable divide between concept and object, between the meanings of predicates and the meanings of terms. Indeed, FOL seems to generalize this metaphysical division by segregating objects from functions from properties from relations and, moreover segregating relations and functions internally according to arity. These divisions, taken at face value, involve a significant metaphysical viewpoint, one that in fact can hinder or prejudice the representation of philosophical ideas and arguments. Some philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to accommodate more flexible metaphysical frameworks. In this paper, however, my purpose is to illustrate a parallel move toward metaphysical egalitarianism that has been driven by more practical considerations. Specifically, recent developments in the use of the World Wide Web (henceforth, the Web) for storing, sharing, and reasoning upon information have motivated a fairly dramatic step in the evolution of FOL—realized in a framework known as Common Logic (CL)—in which rigid metaphysical divisions are largely eliminated and, accordingly, significant changes have been made to the “traditional” presentation of first-order languages and their semantics. Perhaps all of these changes can also be found, at least piecemeal, within philosophy itself. The point of interest discussed in this paper will be the manner in which these changes were motivated independently in the practical encounter of FOL with the Web. It is to be emphasized that ‘evolution’ is to be understood here in a manner more or less analogous to its biological meaning: The evolution in question consists in a suite of adaptations of traditional FOL in response to pressures within a certain environment that enhance its survivability—i.e., its utility for potential users—within that environment. Thus, while I do in fact think a reasonable case can be made that the resulting species of FOL is in at least some respects both intuitively and theoretically superior to more traditional varieties (I will close by sketching a case), my primary concern here is to emphasize how this particular evolution was motivated by the use of logic in open networks like the Web. 1 Salient features of traditional first-order logic Because we will be discussing a certain evolution in FOL, it will be useful to begin with a brief summary several of its familiar features that are particularly important for purposes here. 1.1 Syntactic features • A tripartite lexicon: Over and above the usual array of logical constants (Boolean operators, quantifiers, and identity) and delimiters found in a (typical) traditional

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first-order language L , the class of primitive, nonlogical syntactic elements— collectively, the lexicon—of L comprises three categories including: (individual) constants (Cn), function symbols (Fn), and predicates (Pr). • Fixed syntactic adicity: Every function symbol and every predicate has a fixed, finite adicity that determines the number of arguments it can take to form a legitimate function term or atomic formula. Because constants can take no arguments, they have no adicity.1 An n-adic function symbol or predicate is also said to be an n-place function symbol or predicate. • Strict syntactic typing: No member of any syntactic category can play the syntactic role of the members of any other category. Specifically: • In an atomic formula, among lexical items, only an individual constant or function term can occur in argument position and only a predicate can occur in predicate position. In particular, a predicate cannot be predicated of itself. • In a function term, among lexical items, only an individual constant or function term can occur in argument position and only a function symbol can occur in function position. In particular, a function symbol cannot be applied to itself. • No predicate quantifiers: Variables can occur only where individual constants can occur in atomic formulas. Hence, in particular, quantified variables can occur only in argument position.

1.2 Semantic features Corresponding to these syntactic features are familiar semantic features of first-order interpretations: • A tripartite ontology: Every interpretation for a first-order language L consists of three semantic classes: a set D of individuals, a set of functions over D, and a set of relations over D to serve as the semantic values of the individual constants, function symbols, and predicates, respectively, of L . • Fixed semantic adicity: Every function and every relation has a fixed, finite adicity that determines the number of arguments it can apply to. (In particular, properties are simply 1-place relations.) n-adic function symbols signify n-adic (or n-place) functions on the domain of individuals, n-adic predicates signify n-adic relations. Individuals, having no functional or predicative “nature”, have no corresponding adicity. • Strict semantic typing: In an interpretation of a first-order language, the semantic values of constants (“individuals”) are of an entirely different type than the semantic values of function symbols and predicates.2 Consequently, no member of any semantic category can play the semantic role of any other category. Specifically:

1 Some approaches in fact treat constants (rather naturally) as 0-adic function symbols. 2 Viewed as sets of n-tuples, of course, functions can be seen as a type of relation, so the syntactic division

of function symbols and predicates may not be quite as absolute in the semantic domain.

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• Relations can only be exemplified by individuals (in particular, a property cannot exemplify itself); only relations can be exemplified. • Functions can only apply to individuals (in particular, a function cannot be applied to itself); only functions can be applied to anything. • No quantification over “higher order” entities: Quantifiers range only over individuals. Hence, given that semantic categories are disjoint, properties, relations, and functions lie entirely outside the range of the quantifiers. One must turn to second-order logic to quantify over relations or functions. Two additional semantic features characterize traditional first-order interpretations: • Extensionality: Functions and relations are understood extensionally. That is, functions are identical if they map the same arguments to the same values and relations are identical if they are true of the same objects. Typically, extensionality for functions and relations is ensured by defining them to be sets; an n-place relation is simply a set of n-tuples and an n-place function is simply a set of (n+1)-tuples satisfying a certain “functionality” condition that ensures that every function yields a unique value for any given argument.3 • Variable assignments: Variables are assigned individuals relative to a fixed interpretation for the constants, function symbols, and predicates. Truth is defined in terms of variable assignments. In the evolution of logic described in this paper, all of these features, syntactic and semantic, disappear. 1.3 Interpretations, satisfaction, and truth For the sake of clarity, we present a relatively standard notion of an interpretation for first-order languages which will be modified incrementally in accordance with corresponding modifications to the notion of a traditional first-order language. Since the culmination of an interpretation is a definition of truth for formulas, it is useful to add to the definition of a traditional first-order language L in Sect. 1.1 the definitions of terms and formula of L . (Quotation will only be used when it seems particularly helpful.) 1. Every individual constant and variable (of L ) is a term (of L ). 2. If τ1 , . . ., τn are terms and α is an n-place function symbol, then α (τ1 , . . ., τn ) is a term. 3. If τ1 , . . ., τn are terms and π is an n-place predicate, then π(τ1 , . . ., τn ) is an (atomic) formula. 4. If ϕ and ψ are formulas, so are ¬ϕ, (ϕ ∧ ψ), (ϕ ∨ ψ), (ϕ ⊃ ψ), and (ϕ ≡ ψ) are formulas. 5. If ϕ is a formula and ν a variable, then ∀νϕ and ∃νϕ are formulas. 6. Nothing else is a formula. 3 More exactly, the “functionality” condition that a 1-place function—conceived as a set of ordered pairs—

must meet is that, if a,b and a,c are members of f, then we must have b = c.

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Following common practice, all quantifiers except the first in a string of similar quantifiers will be dropped, i.e., ∀ν1 . . .νn ϕ and ∃ν1 . . .νn ϕ will be written in place of ∀ν1 . . .∀νn ϕ and ∃ν1 . . .∃νn ϕ. An interpretation for a first-order language L is a 4-tuple I = D, den, f ext, r ext , where D is, intuitively, the set of individuals of I and den, fext, and rext are functions that map the basic syntactic items in the lexicon of L to appropriate semantic values: specifically, den maps the constants Cn of L to individuals of I; fext maps the function symbols Fn of L to (extensional) functions from individuals to individuals; and rext maps the predicates Pr of L to (extensional) properties of, and relations among, individuals. A little more exactly: • den : Cn → D; • fext : Fn → { f | f : D n → D, for some n ∈ N+ }4 ; • rext : Pr → {r |r ⊆ D n , for some n ∈ N+ }. rext and fext are of course so constrained that the adicity of a predicate or function symbol must be identical to the adicity of its semantic value. Given an interpretation I of L , denotations for the terms of L , and satisfaction for the sentences of L in I, can be recursively defined in the familiar sort of way. Specifically, for a variable assignment s, let s be the usual extension5 of s to all the terms of L and, for variables ν, say that t is a ν-variant of s if t (μ) = s(μ), for all variables μ = ν. Then, for a given variable assignment s: • s satisfies π(τ1 , . . ., τn ) in I if and only if s (τ1 ), . . ., s (τn ) ∈ r ext (π ) • s satisfies ¬ϕ in I if and only if s does not satisfy ϕ; similarly for the other Boolean cases. • s satisfies ∀νϕ(∃νϕ) in I if and only every (some) ν-variant t of s satisfies ϕ in I. Truth in I is then defined in the usual way: A sentence ϕ of L is true in I if every variable assignment satisfies ϕ. I is said to be a model of a set S of sentences of L if every sentence in S is true in I. 2 Knowledge representation and open networks Computer networks are nearly as old as computers themselves. However, prior to the Internet—the infrastructure of the Web—such networks were all closed: only designated computers—within the same business or organization—were able to join and, typically, each network had strict control over the sorts of information would be exchanged on the network and in what forms. Perhaps the most significant feature of the Web is that it is open, indeed radically so. Unlike closed networks, the Internet is accessible to a huge segment of the world’s population, and to publish virtually any content, one needs only access to a Web server. 4 Where N+ is the set of positive integers and D 1 = D, D 2 = D × D, D 3 = D × D × D, etc. 5 Specifically, for constants κ, s (κ) = den(κ), for variables ν, s (ν) = s(ν), and for function terms   α(τ1 , . . ., τn ), s (α(τ1 , . . ., τn )) = f ext (α) s (τ1 ), . . ., s (τn ) . We are obviously being careless about

quotation here.

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From its earliest days, it was recognized that the radical openness of the Web presented a revolutionary way of thinking about information. Typically, in closed networks, the information that is available is closely controlled and monitored by the administrators of the network. The Web, by contrast, is “anarchic”; it has no administrators. Because there are so few hindrances to the publication of content, new information is constantly appearing on the Web, from the lightest entertainment news to cutting edge results in science, engineering, and medicine; from political rhetoric to pornography. Human users thrive in such a milieu; but the Web, like other computer networks, is also a medium of exchange for formalized information intended for use by software agents, with little or no human intervention. The question then becomes: How can formalized information be represented on the Web in such a way that it can be identified by interested agents (notably, software agents), reasoned upon, and integrated with related information? The problem of identifying relevant information is essentially the problem of search technology, and that continues to be addressed effectively by, most notably, Google. Suitable representation of information is the more challenging problem. Following a bit of relevant history, in the following sections we will describe four representational “adaptations” of traditional FOL that were motivated initially by developments in knowledge representation and the Web and more recently, and more urgently, by the rise of the so-called Semantic Web. We will then describe Common Logic, in which all of these adaptations are manifested in a single standardized framework. 2.1 Knowledge sharing and the O(n 2 ) problem Long before the rise of the Web it was recognized in the Artificial Intelligence (AI) community that well-defined, logic-based languages are extremely effective frameworks for representing information clearly, and in a way that is subject to machine processing. This recognition gave rise to the development of a wide variety of knowledge representation (KR) frameworks built upon first-order logic or some fragment thereof, for example, SNePS (Shapiro 2000), LOOM (MacGregor and Bates 1987), CLASSIC (Patel-Scheider et al. 1991), Ontolingua (Gruber 1992), CycL (Lenat and Guha 1991) not to mention any number of lesser known in-house systems. Because they are all logic-based, information represented in any such system possessed the clarity and rigor that is needed to ensure understanding by human agents, to enable the use of automated reasoning techniques to draw useful inferences from the information, and to integrate that information with related bodies of information—so long as that information was also expressed in that systems own notation. With the rise of these logic-based systems, the latter limitation became acute. If I am working on, say, a diabetes knowledge base in LOOM, and you already have an extensive knowledge base on the production of insulin by the pancreas in Ontolingua, I must have some sort of translator to be able to get your information into my system. And you’ll need one to get my information into yours. This leads to what has been called the “order n-squared” (O(n 2 )) problem. Suppose you wish to establish a collaborative

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Fig. 1 The O(n 2 ) problem

environment with, say, three other research groups, each of which uses a different KR system. To exchange information between these systems, 12 (42 − 4) translators will be needed, two for each pair of distinct systems. If you then wish add a further group into the environment that is using yet another system, then you will be forced to find or develop eight new translators for a total of twenty (52 − 5), as depicted in Fig. 1. More generally, then, in an environment with n distinct systems, the inclusion of a further system requires 2n new translators to enable complete communication between systems. The desire for a more efficient solution to the O(n 2 ) problem than the construction of piecemeal translators (among other motivations) led to the development of the Knowledge Interchange Format, or KIF, largely the work of Stanford University computer scientist Genesereth (1998). The idea behind KIF was simple: If there were a single “interlingua”, i.e., logic-based language capable of expressing everything that is expressible in any of the systems in a given environment, then, to exchange information between systems, instead of O(n 2 ) pairwise translators, one would only need O(n); specifically: for each system S, a translator from S to KIF and another from KIF to S. Thus, the addition of a new KR system into an environment of n systems + KIF requires only two new translators instead of 2n, as depicted in Fig. 2.

2.2 Pull technology and the rise of the open networks However, with the rise of open networks the scenario that gave rise to the O(n 2 ) problem began to appear increasingly “academic” and artificial, most notably in the context of the so-called Semantic Web. This project, involving many hundreds of people around the world, proposes to exploit the information-interchange protocols of the largest and most open of networks—the World Wide Web—in a more systematic and standardized way by having software systems exchange machine-readable information expressed in some logic-based representational notation or notations.

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Fig. 2 The KIF “Interlingua” solution to the O(n 2 )

The O(n 2 ) problem looks artificial in the context of the Semantic Web simply because it is essential to the architecture of the Web that it makes no presuppositions about the existence of the sorts of two-way connections that could, in the event of unclarity, disagreements, or other failures or disruptions of communication, be used to facilitate negotiations and agreements about content and its representation. Rather, the default presupposition of the Web is that there simply are no such connections and, indeed, that they might not even be possible. The reason for this is that, in regard to knowledge sharing, the Web is primarily a “pull” technology: users get only what they go out and actively retrieve. There is no easy way, and perhaps no way at all, within this architecture, to set up a two-way communication path between the composer of the information and the user of it; a path that could be used to negotiate an agreement. A basic fact about publishing information on the Web is that publisher has no control over, or even knowledge of, how, where, and how much of the published information will be used. The architectural model of the Web allows for content to be archived, for example, introducing arbitrary delays between publication and consumption, while mandating that the meaning of the archived information should not be lost. Thus, there is no way for a publisher and a consumer of some piece of information to come to any further agreements about mutually accepted notational conventions, which vocabulary to use, and so on. Clearly, however, the meaning intended by the publisher should be retained by the consumer to the fullest possible extent. Thus, just as one must use HTML in order for one’s published Web site to be seen by others, publishers of Web content must all cleave to a set of universally accepted logical conventions if their content is to be understood by others: a universally accepted standard language with a clearly defined syntax and a universally accepted semantics in the form of a model theory. Not just any semantics will do, however. In order not to limit the scope of publishable content, the semantics should not place on constraints on the expressibility of the standard language. Moreover, the semantics should be monotonic. Pull technology requires that published content C remain stable in all contexts. Hence, it is critical that the semantics of the language in which C is expressed guarantee that the addition

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of new information C ∗ to C have no effect on the logical properties of C itself. New content might of course contradict C, but it should not alter it—anything that one could infer from C prior to the addition of C ∗ should still be inferable after it is added. This is precisely the property of monotonicity. These consideration, suggest that a standardized framework for publishing content on the Web should be based upon full first-order logic. Not only is the syntax of FOL clear and standardizable and its semantics monotonic, but FOL is generally considered the benchmark for expressibility—it is at least as expressive as any standard KR language, but not so expressive that logical consequence fails to be recursively axiomatizable.

2.2.1 KIF again Although unneeded after all as an interlingua for solving the O(n 2 ) problem, KIF is based upon first-order logic and hence seems to be viable, standardizable framework for publishing Web content. Moreover, KIF’s actual syntax is especially conducive to use on the Internet, and is indeed one reason why it in fact has become widely used as a medium for expressing content among KR practitioners. KIF’s syntax was inspired by the programming language LISP—famous for its economical and elegantly simple syntax—and was designed so that all KIF expressions consist of ASCII characters; notably, instead of the usual quantifiers and connectives of Principia-style languages—∀, ∃, ¬, ∧, ∨, ⊃, ≡ —KIF used forall, exists, not, and, or, =>, and <=>. Also, like LISP, KIF adopted prefix rather than infix notation for its binary propositional operators. So, for example, Every boy kissed a girl in traditional syntax would be represented as ∀x(Boy(x)∃y(Girl(y) ⊃ Kissed(x,y))).

(1)

In KIF, by contrast, this is expressed as (forall (x) (=> (Boy x) (exists (y) (and (Girl y) (Kissed x y))))). (2) In doing so, KIF reflects the shift from pen, paper, and, ultimately, typeset publications as the primary media for authoring and communicating logical information to computer keyboards and computer networks via electronic protocols like email and mailing lists. It also represents an important start in a series a significant developments in the language and semantics of FOL motivated by the development of open networks.

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3 Four evolutionary adaptations of FOL The shift to an ASCII syntax was the least significant change influenced by the rise of computer and network technology. However, KIF also anticipated the first of four more significant “adaptations” of traditional FOL that were motivated by pressures arising from the development of the open networks. 3.1 Adaptation I: variable polyadicity In addition to the more superficial departure from traditional first-order syntax just noted, KIF also abandoned two of the salient features of traditional first-order logic noted above—viz., syntactic and semantic adicity—in order more effectively to integrate information found across different knowledge bases. Neither the predicates and function symbols of KIF nor their semantic counterparts have a fixed adicity. What this means semantically is that, in KIF, a relation can consist of ordered tuples of arbitrary finite length; similarly for functions, subject as before to an appropriate functionality condition to ensure a unique value for every argument sequence.6 The reason for this adaptation is simply that assumptions regarding the number of arguments that a property, relation, or function can take can vary widely from context to context. As a simple example, in one knowledge base, ‘Teacher’ might have only one argument, e.g., Teacher(Plato)

(3)

while in another it might take two: Teacher(Plato,Aristotle)

(4)

and in yet another—one that includes a time interval parameter indicating the period over which the Teacher relation holds between the first two arguments—three: Teacher(Plato,Aristotle,364-360BCE)

(5)

In traditional FOL, each of these contexts would have to be represented by a distinct predicate with special axioms relating that predicate to the others. Intuitively, however, there is simply one predicate capable of taking varying numbers of arguments depending on how many explicit qualifying “roles” one wishes to include in a statement about Plato’s teaching career. KIF, with its “variably polyadic” syntax, the same predicate can serve for all three contexts. Syntactically, then, to accommodate variable polyadicity more formally, the adicity condition on function symbols and predicates is removed and the grammar is modified accordingly. More exactly, the language L1 is defined to be the result of modifying the traditional first-order language L such that: 6 Specifically, if b and c are distinct individuals, then an extensional function f cannot contain both a1 , . . ., an , b and a1 , . . ., an , c , for all n ≥ 1.

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1. The members of Fn and Pr are not assigned a specific adicity; 2. If τ1 , . . ., τn are terms and α ∈ Fn, then α(τ1 , . . ., τn ) is a term of L1 ; and 3. If τ1 , . . ., τn are terms and π ∈ Pr , then π(τ1 , . . ., τn ) is an atomic formula of L1 . Semantically, the shift to variable polyadicity requires only that, in the definition of an interpretation above, (i) the now inapplicable constraint on fext and rext that the adicity of a predicate or function symbol must be identical to the adicity of its semantic value is removed and (ii) the ranges of their possible semantic values is broadened  appropriately. Specifically, where D ∗ is the set n∈N+ D n of all finite sequences (i.e., n-tuples, for arbitrary n) of members of D: • f ext : Fn → { f | f : D ∗ → D} • r ext : Pr → {r |r ⊆ D ∗ }. That is, the functions that interpret function symbols, and the relations that interpret predicates, are now themselves variably polyadic; that is, the functions in question are now total functions on the set of all finite sequences of individuals in the domain of the interpretation and the relations in question can now contain sequences of varying finite length. Notice that this change simplifies the descriptions both of the syntax and the truth conditions of the language; this kind of simplification by removal of constraints will be typical of the evolutionary changes we will describe. Variable polyadicity was not new with KIF. Kenny (1963), in particular, suggested it as the natural syntax for action sentences and a formal syntax and semantics of variably polyadic predicates was explicitly developed by Grandy (1976).7 However, there is no indication that Genesereth or any of other contributors to KIF were aware of any such work. Rather, along with its adoption of an ASCII-based syntax, KIF’s variable polyadicity was an adaptation motivated entirely by its intended role as a general interlingua for facilitating communication between networked knowledge bases using distinct KR frameworks. 3.1.1 Sequence variables: a useful complication KIF also introduced an novel extension to conventional FOL syntax, one which is a pragmatic necessity when predicates are allowed to become polyadic. Consider as an illustration the polyadic equality relation AllEqual, which is true when all its arguments are identical, for any number of arguments. How can this be described using first-order axioms? The case of two arguments can of course be expressed as ∀xy(AllEqual(x,y) ≡ x=y)

(6)

but this only handles one of the denumerably many possible cases. To handle the rest, an infinite set of axioms is needed: ∀xyz(AllEqual(x,y,z) ≡ (x=y) ∧ (x=z))

(7)

7 Grandy’s anadic logic is actually a variable-free algebraic logic, but it is easily converted into an equivalent

but more traditional first-order logic.

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∀xyzu(AllEqual(x,y,z,u) ≡ (x=y) ∧ (x=z) ∧ (x=u))

(8)

and so on. Axiom sets which assign intended meanings to variably polyadic predicates are almost always infinite in this way, and this poses a problem for those who seek to capture such meanings in a finite document. The KIF solution was to provide a new quantifier pattern which can, in effect, summarize infinite sets like this. This is done by adding a new category of name, which, in KIF, are called sequence variables. Formally, a sequence variable is simply a variable of a special distinguished kind that can be bound by a quantifier in the usual way, and can occur as an argument.8 KIF wrote these prefixed by the symbol ‘@’, but for purposes here ‘s’, ‘s1 ’, ‘s2 ’, … will simply be reserved for sequence variables. Semantically, given an interpretation I for a language with sequence variables, a variable assignment s assigns to each such variable a finite sequence of individuals in the domain D of I. The sequence formed by interpreting the various arguments of a function term and concatenating the results in order is the sequence that the corresponding function operates upon; similarly for predicates. More exactly, for individuals a and b and sequences S = c1 , . . ., cn and S = d1 , . . ., dm of individuals, let a b = a, b , a S = a, c1 , . . ., cn , S a = c1 , . . ., cn , a , and S S = c1 , . . ., cn , d1 , . . ., dm . Then, for function terms α, predicates π , and terms τ1 , . . ., τn : • s (α(τ1 , . . ., τn )) = f ext (α)(s (τ1 ) . . . s (τn )). • s satisfies π(τ1 , . . ., τn ) in I if and only if s (τ1 ) . . . s (τn ) ∈ r ext (π ).9 This additional machinery allows infinite collections of axioms that conform to regular recursive patterns to be described as one or two sentences. Our example above can be axiomatized fully by two simple sentences: ∀x(AllEqual(x)

(9)

∀s∀x∀y (AllEqual(x,y,s) ≡ ((x=y) ∧ AllEqual(x,s)))

(10)

For example, by (10), where ‘x’ is instantiated to ‘a’, ‘y’ to ‘b’ and ‘s’ to ‘c,d’, AllEqual(a,b,c,d)

(11)

a=b ∧ AllEqual(a,c,d).

(12)

is equivalent to

By the same token, the second conjunct of (12) is equivalent to a=c ∧ AllEqual(a,d),

(13)

8 In KIF sequence variables were restricted to occur only in the last argument position in any atomic sentence; this restriction has been relaxed in CL. 9 Note that, where τ , . . ., τ

n are all ordinary individual terms, s (τ1 ) . . . s (τn ) is just 1

s (τ1 ), . . ., s (τn ) , so the clause for atomic formulas here is a simply generalization of the original clause.

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whose second conjunct is equivalent to a=d ∧ AllEqual(a)

(14)

Putting these together, given both the axioms (9) and (10), (11) unpacks ultimately to a=b ∧ (a=c ∧ a=d)

(15)

as desired. This kind of recursive expansion to a “terminal” case is typical of the axiomatic style one learns to use when writing axioms with sequence variables. Programmers will note that it is closely similar to the style of recursive programming pioneered by LISP. Now, importantly, it must be noted that the addition of sequence variables increases the expressive power of our framework beyond that of FOL. Notably, it is easy to show that the result of adding sequence variables to L1 with the above semantics makes the corresponding logic non-compact,10 hence not first-order, and hence incapable of having a complete proof theory—a potentially serious blow to prospects of automated reasoning with respect to knowledge bases formulated with sequence variables. However, for the vast majority of practical purposes, as in the example (10) above, all that is needed are sentences in which all of the sequence variables are universally quantified with widest possible scope. And if the grammar of L1 + sequence variables is restricted accordingly, the resulting logic remains fully first-order.11 3.2 Adaptation II: relaxed typing—predicates and function symbols Further representational possibilities that can naturally arise on open networks bring the highly typed nature of traditional FOL into question as well. This was perhaps initially seen in the development of “frame-based” KR languages in which the traditional role of predicates in expressing properties was, in part at least, subsumed by what were essentially function symbols. In these systems, attributes are often thought 10 A logic is compact if an arbitrary set of sentences of the logic has a model if all of its finite subsets do. By a famous theorem of Lindström (1969), a logic is first-order only if it is compact. To see that a logic with sequence variables (absent any grammatical restrictions—see below) and the above semantics for them is not compact, let S be the set   ∃sP(s), ∀x1 ∼ P(x1 ), ∀x1 x2 ∼ P(x1 , x2 ), ∀x1 x2 x3 ∼ P(x1 , x2 , x3 ), . . . .

Clearly, every finite subset S∗ of S has a model but S itself does not, as its universally quantified sentences jointly entail that no finite sequence of individuals is in the relational extension of ‘P’, i.e., they jointly entail that ‘∃sP(s)’ is false. 11 Let L + be L + sequence variables where its grammar is so restricted. To see in particular that the logic 1 1 for L1+ is compact, note simply that every sentence ϕ of L1+ is logically equivalent to a set of sentences obtained by explicitly unpacking the quantified sequence variables of ϕ. (For example, the sentence ‘∀sP(s)

will be true in an interpretation I if and only if I is a model of the set {P(), ∀x1 P(x1 ), ∀x1 x2 P(x1 , x2 ), . . .}.) Since the logic for L1 is compact, every set of sequence-variable-free sentences of L1+ has a model if all of its finite subsets do. Hence, the same is true for any set S of sentences of L1+ , since we can unpack all of the sentences of S that contain sequence variables into sequence-variable-free sentences.

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of as functions on individuals (often called “slots” or “roles”) that yield “values” that, in a more traditional representation, would simply be a second argument to a predicate (see, e.g., the influential KL-ONE system of Brachman and Schmolze (1985)). This, in such a knowledge bases, ‘Teacher’ might indicate a function on individuals that returns, for a given argument, his or her (most influential, say) teacher, e.g.: Teacher(Aristotle) = Plato

(16)

instead of the more traditional sort of representation one might well find in another knowledge base: Teacher(Plato,Aristotle)

(4)

Traditional FOL, with its strict typing, does not permit the predicate ‘Teacher’ simultaneously to play the role of a function symbol. Hence, to merge a knowledge base containing (4) with one containing (16) using a traditional first-order language would require considering the character string ‘Teacher’ in (4) to be a distinct lexical item from the identical string in (16). However, if one relaxes the strict syntactic typing of traditional FOL—if, that is, one allows certain lexical items to be members of more than one lexical category—there is no need to do so. One can simply allow ‘Teacher’ to play both roles, to be both a predicate and a function symbol, a member of both Cn and Fn. More formally, let L2 be the result of modifying L1 by rejecting the strict syntactic typing of function symbols and predicates and allowing for the possibility that Fn and Rn have members in common and, hence, that one and the same symbol can play the syntactic roles of both function symbol and predicate. Note that allowing this sort of “cross-categoricity” does not require any change in the definition of a interpretation (as modified to accommodate variable polyadicity in the previous section). Rather, as members of both the class of predicates and the class of function symbols, cross-categorical lexical items like ‘Teacher’ are simply assigned two extensions in an interpretation: a relation extension qua predicate and a function extension qua function symbol. One then evaluates an expression containing an occurrence of the item according to the role of that occurrence. (4), in particular, turns out true just in case, for any objects a and b in the domain of discourse, a, b ∈ r ext(‘Teacher’) and (16) just in case fext(‘Teacher’)(b) = a (truth conditions whose equivalence can be enforced if desired simply by requiring that, for cross-categorical lexical items ε ∈ Fn ∩ Pr, f ext (ε) = r ext (ε)). Of course, this is not a theoretically profound modification. And it may at first sight appear that there is little practical difference between, on the hand, allowing cross-categorical predicates/function symbols and, on the other, proscribing cross-categoricity and, in lieu of that, introducing distinct but (for all practical purposes) orthographically indistinguishable items to occur in different lexical categories. The former, however, is a more natural generalization of variable polyadicity: just as a single, variably polyadic lexical item can take any number of arguments rather than a distinct lexical item for each adicity, so a single, cross-categorical lexical item can play distinct syntactic roles rather than a distinct lexical item for each role. This therefore avoids any need for two

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different usages of the same symbol—or orthographically identical but theoretically distinct symbols—to be negotiated and separated. We elaborate on the importance of this point in the context of the Web in the following section, which introduces a much more profound relaxation of strict typing than cross-categoricity between function symbols and predicates. 3.3 Adaptation III: complete cross-categoricity and “objectified” relations The breakdown of clear and inviolable boundaries between lexical types in the context of the Semantic Web extends well beyond function symbols and predicates to include terms as well. This turns out to have much deeper and more interesting syntactic and semantic implications. In many systems, the traditional semantic values of predicates—properties, relations, classes of (n-tuples of) individuals—are treated as “first class citizens”, i.e., as individuals. This is particularly common in Description Logics (see Baader et al. 2003) which grew out of earlier knowledge representation systems that were originally designed to capture hierarchies of classes. Generally speaking, in these systems, quantifiers range over both individuals and classes and one is able to ascribe properties and relations to both. Thus, in such a system, one might well be able to say both that Plato is the teacher of Aristotle and that the Teacher relation is the converse of the Student relation. A knowledge base—one that might result, say, from merging a historical database with a more general ontology of education—might therefore very naturally contain both Teacher(Plato,Aristotle)

(4)

ConverseOf(Teacher,Student)

(17)

and

Strict typing, of course, would prohibit this in a traditional first-order language. One way of dealing with this phenomenon, of course, is to move to a second-order language in which one distinguishes between first-order predicates that take individual constants and other first-order terms as arguments and second-order predicates that can take first-order predicates as arguments. There are, however, several problems with this. First, as is well-known, second-order validity is not axiomatizable, which means that one cannot make use of the wide array of first-order theorem provers that are available to support automated reasoning on information within a higher-order knowledge base. Second, just as one finds variation in adicity, a second-order framework would be forced to deal with variation in order as well. For instance, the predicates THING and ENTITY that are common in Web taxonomies and other knowledge bases are freely applied to items referring to individuals, classes, and relations alike. There is in general no practical way to attach a fixed order to a given predicate in a dynamic, anarchic environment like the Web. Best, therefore, if there were only one order to choose from. Hence, as far as possible, it is desirable (a) to remain first-order and,

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consequently, (b) to loosen traditional first-order syntactic and semantic restrictions as far as possible in response to representational pressures like the co-occurrence of sentences like (4) and (17). Accordingly, in this spirit, just as the examples of the previous section led us to relax the partitioning of predicates and function symbols, let us accommodate examples like (4) and (17), not by moving to a strictly typed second-order language, but by rejecting the strict syntactic typing of traditional first-order languages and relaxing the divide between predicates and individual constants. More exactly put, to accommodate both (4) and (17), lexical items like ‘Teacher’ can be considered completely cross-categorical, that is, to be members, not only of the classes Pr and Fn, but of the class Cn of individual constants as well. Let L3 be the result of so modifying L2 . 3.3.1 Complete cross-categoricity and the Web As in the previous section, theoretically such phenomena could be accommodated by retaining strict typing and thinking of the occurrences of ‘Teacher’ in (4) and (17) as occurrences of distinct but orthographically identical expressions, one a predicate, the other an individual constant that might be related logically somehow. But this is simply not reflected on the Web. A fundamental architectural assumptions of the Web concerns the notion of a Web identifier, referred to by the various acronyms ‘URL’, ‘URN’, and, more generally, ‘URI’ (see, e.g., W3C 1995, 2005). URIs are, essentially, names that, by means of rather baroque but well-defined syntactic conventions, encode enough information to make them globally univocal. The contast with traditional FOL, however, is rather striking. In traditional FOL, the choice of names has been viewed as essentially arbitrary and not a matter of the slightest logical or practical importance; indeed, in some well known theories—ZF set theory, for example—there are no names at all. But on the Web, names have an essential, and essentially public, role: their scope, once published, is the entire planet and the entire future. Indeed, names—URIs—are in a very real sense the fabric, the skeleton, of the Web. Whatever logic is implemented on the Web is merely infrastructure in support of this world-wide system of interrelated names. The primary semantic assumption concerning URIs (and ensured in practice by the conventions just noted) is that every occurrence of a URI denotes the same entity in any context, regardless of the logical type of that occurrence. This is, of course, by design, as a mechanism guaranteeing that names consistently have the same semantic values regardless of context and syntactic type is essential for the sort of integration and interoperability across multiple knowledge bases that the Semantic Web is meant to foster. In this milieu, how cross-categorical phenomena are dealt with is no longer arbitrary or inconsequential. To the contrary, current Web theory and practice call for complete cross-categoricity. 3.4 Adaptation IV: type-free intensionality The desire to express logical relations between relations, as in (17), is not the only way in which relations might be “objectified”—i.e., treated as individuals in their

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own right—in a knowledge base. The pervasive linguistic phenomenon of nominalization can generate examples of very natural examples of cross-categoricity (see, e.g., Chierchia and Turner 1988). Consider: Whenever John is running, he hates it.

(18)

As this example shows, a gerund like ‘running’ can play both adjectival and nominal roles very naturally, even within the same sentence. Such examples are naturally formalized in a language allowing predicates to be cross-categorized with constants; (18), in particular, is naturally formalized as ∀t(Time(t) ⊃ (running(John,t) ⊃ Hates(John,running,t))).

(19)

Semantically, to accommodate examples like (4), (17), and (19) that can be expressed in L3 , it would appear that no changes are required to the notion of interpretation developed for L2 (which, recall, simply involved modifying the original notion of an interpretation to accommodate variable polyadicity). Rather, members of Pr ∩ Cn simply have both a denotation (qua members of Cn) and a relational extension (qua members of Pr); members of Fn L ∪ Cn L have both a denotation and a function extension (qua members of Fn). However, once completely cross-categorical lexical items are allowed that can play all three central grammatical roles in our Web-oriented language, a variety of intuitively valid cross-categorical inferences involving identity and quantification very naturally arise that that cannot be supported without ensuring a tighter connection between denotations and extensions. This requires a semantic adaptation paralleling syntactic cross-categoricity. 3.4.1 Identity and type-freedom Consider the following intuitively valid argument: Being married is the same as being hitched. Elvis and Priscilla are married. Therefore, Elvis and Priscilla are hitched. (20) Formalized, this argument would appear to be a straightforward instance of the logical principle of the intersubstitutivity of identicals, viz., Married=Hitched, Married(Elvis,Priscilla) ∴ Hitched(Elvis,Priscilla) (21) But the argument is not valid in the semantics of the previous section as it stands, as nothing about the relations expressed by ‘Married’ and ‘Hitched’ follows from the fact that their denotations are identical; that is, more specifically, from den(‘Married’) = den(‘Hitched’) it does not follow that r ext (‘Married’) = r ext (‘Hitched’). Hence, it might in be the case that den(‘Elvis’), den(‘Priscilla’) ∈ r ext (‘Married’) but den(‘Elvis’), den(‘Priscilla’) ∈ / r ext (‘Hitched’). Clearly, this won’t do. Arguments of the above form involving property identities are natural and common, and

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are especially important for integrating diverse knowledge bases, where it is often the case that one and the same property is identified by different expressions. The difficulty here is that the syntactic changes of the preceding section were not truly reflected in the semantics. To permit completely cross-categorical terms is to abandon the strict syntactic typing of traditional first-order languages—it is to say in particular that one and the same item can simultaneously be a constant and a predicate. By contrast, the semantics above preserved the traditional distinction between semantic types and simply allowed the semantic value of a cross-categorical term to be flatly ambiguous, taking on a different semantic value for each type. This gives rise to a disconnect that generates the problem above. The solution is a semantics that mirrors the syntax in rejecting the strict typing of traditional FOL and embraces type-free relations and allows that one and the same semantic entity can be simultaneously be—or perhaps more accurately, play the roles of— an individual and a relation. That is, for lexical items ε ∈ Cn ∩ Pr that can occur in both argument and predicate position in atomic formulas, it is stipulated that den(ε) = r ext (ε)—and hence that the relation r ext (ε) is a fully-fledged individual among others the domain D of I. From den(‘Married’) = den(‘Hitched’) it then follows immediately that r ext (‘Married’) = r ext (‘Hitched’) and, hence, that if den(‘Elvis’), den(‘Priscilla’) ∈ r ext (‘Married’) then den(‘Elvis’), den (‘Priscilla’) ∈ r ext (‘Hitched’). But this move might raise some red flags. To objectify a property or relation, as the identity just noted implies, is to consider it to exist in the set D of individuals of an interpretation. Running, of course, is not the sort of thing that could itself ever be running. However, suppose, for example, there is a cross-categorical identity predicate in L and hence that there is an objectified identity relation I d ∈ D that it denotes. As noted in Sect. 1, typically, in traditional FOL, properties and relations just are their extensions, i.e., sets of (n-tuples of) individuals in D. So understood, Id is simply the set {a, a |a ∈ D} of pairs of members of D. But since I d ∈ D, it follows that I d, I d ∈ I d, violating the set theoretic axiom of foundation, which proscribes selfmembership and other, more general forms of non-wellfoundedness. More generally, in the semantics of FOL, there are, typically, no restrictions on what individuals can occur in the extensions of what predicates. Hence, absent specific restrictions—which would seem entirely ad hoc—the denotation of any cross-categorical predicate can end up being a member of itself. An obvious move here is simply to abandon the axiom of foundation and opt instead for conception of set that allows self-membership and other forms of non-wellfoundedness. Foreign as the suggestion might seem, the axiom of foundation is in fact entirely inessential to all applied mathematical purposes and, indeed, as the work of, notably, Aczel (1983) and Barwise and Moss (1996) have shown, set theories with anti-foundation axioms—i.e., axioms that posit the existence of non-wellfounded sets outright—turn out to have powerful applications in mathematics, theoretical computer science, and philosophy. But the philosophical assumptions underlying the Semantic Web’s vision of distributed but integrated knowledge bases suggests a more satisfying solution.

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3.4.2 Intensionality A declarative knowledge base is (among other things) an attempt to characterize a set of concepts as richly as possible (or, at least, as richly as necessary for the purposes at hand), typically by means of axioms of some ilk. One of the promises of the Semantic Web is that one will be able to draw upon existing knowledge bases to flesh out one’s desired set of concepts without having to do all the work from scratch. Intuitively, then, one begins with an informal set of concepts in mind and subsequently, and often incrementally, characterizes them with greater increasing rigor and precision. Typically, that is, the creators of a knowledge are that their axioms are incomplete and often in need of further refinement. On this understanding, concepts—functions and relations—are best understood intensionally, the extensionalism of traditional first-order semantics notwithstanding. A concept is initially identified and, in itself remains stable; it is only one’s understanding of it—expressed in particular in the axioms one adds about it in a growing, dynamic knowledge base—changes over time. Additionally, even when fully characterized, a concept’s extension can change over time simply in virtue of the dynamic nature of individuals—a person who was not a mother comes to have a child; a tree that had lacked leaves gains them; and so on. To accommodate this intuitive view of concepts—one that is ubiquitous in the Semantic Web community—the extensional conception of properties and relations is best abandoned: Functions, properties, and relations have extensions, but they are not themselves identical with those extensions. The major technical modification is that function and relation extensions are now assigned to functions- and relations-in-intension directly, rather then to the function symbols and predicates that denote them. Thus, on this view, Id is an element of one of the ordered pairs in its own extension, but, as it is not identical with that extension, or with any set, it does not violate foundation. More exactly, then, to accommodate intensionality in the notion of an interpretation I, separate sets F and R are introduced—the functions- and relations-in-intension of I, respectively—and the definition of the extension functions fext and rext is so altered that these functions apply to these new semantical entities directly rather than to function symbols and predicates: • f ext : F → { f | f : D ∗ → D} • r ext : R → {r |r ⊆ D ∗ } Intuitively, as indicated in the preceding section, a cross-categorical function symbol that is also a predicate denotes a function that is also a relation. Accordingly, no restrictions are placed on F and R that would prevent a function from simultaneously being a relation, i.e., there is no restriction to the effect that F ∩ R is nonempty. Similarly, since objectified functions and relations occur in D, there can also be overlap between F and D and R and D.12 Recall that fext and rext had been the mechanisms for supplying meanings for function symbols and predicates. Accordingly, the denotation function den is extended so 12 See Bealer (1982) and Menzel (1993) for more philosophical motivations for a type-free, intensional

semantics.

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that it subsumes this functionality by defining it on all lexical items generally, appropriately restricted so as to assign an entity of the appropriate sort to each item. More exactly, that is, den is now defined to be a function on Cn ∪ Fn ∪ Rn such that: den : Cn → D den : Fn → F den : Rn → R The definition of satisfaction for atomic formulas is now revised accordingly: For a given variable assignment s: • s satisfies π(τ1 , . . ., τn ) in I if and only if s (τ1 ) . . . s (τn ) ∈ r ext (den(π )). 3.4.3 Logical concerns In fact, an intensional conception of concepts not only comports better with KR practice, it is arguably theoretically preferable (or at least, more familiar) as well, the idea can be implemented semantically with no violation of the axiom of foundation. Id, in particular, viewed as a relation-in-intension rather than a set of ordered pairs, is no longer a member of a member of itself but rather simply a member of an ordered pair—viz., I d, I d —in its extension. As such, intuitively, Id bears the relation of identity—i.e., itself—to itself, but that is simply an instance of self-exemplification and involves no violation of any set theoretic principles. It might, however, raise a couple of logical concerns. The first has to do with cardinality. Given the principle that, for every subset of D ∗ is the extension of at least one relation, it follows that, for an interpretation I with domain D: There are as many relations as there are subsets of D ∗ .

(22)

If so, however, there are more relations than individuals. For by simple transfinite arithmetic, if m is the cardinality of D (recall that, by definition of an interpretation, D must be nonempty, so m > 0), the cardinality of D ∗ is at least m and, hence, by Cantor’s famous theorem (which still holds in non-wellfounded set theories), there are more than m subsets of D ∗ . Hence, by (22), there are more relations than there are elements of D. Hence, on pain of paradox, it is not possible to think of relations as individuals in the manner suggested. The argument is specious. There are, of course, more extensional relations over D than there are elements of D. However, first, there is no reason to accept the principle that, for every arbitrary set of individuals there is some intensional property they uniquely share in common. But even if this principle is true in some deep, metaphysical sense, nothing about the semantics above requires that all properties and relations be in D. To the contrary, in order to represent any piece of information that one is likely to want to include in a given knowledge base, there is no reason to assume that there are any more relations than those that can be named in one’s language L . That is, one needn’t assume there are any more relations than there are predicates of L . This leaves us free instead to assume, without any obvious cardinality problems, that

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among the objects in D are as many relations as there are cross-categorical lexical items of L . That one needn’t assume the existence of anything other than explicitly named relations is also what alleviates concerns over logical paradoxes like the intensional version of Russell’s paradox: given the property R of nonselfexmplification, it is easy to show that R both does and does not exemplify itself. However, Russell’s paradox, as well as all other logical paradoxes, can only arise in a formal framework in which it is possible to name or otherwise prove the existence of R or some similarly problematic entity.13 Lacking any such capacity, no threat of paradox looms for L and its semantics. 3.4.4 “Higher-order” quantification and its logical consequences It is a prominent feature of FOL that it supports existential generalization on argument places. This implies that the nominal occurrence of ‘running’ in (19) can be existentially generalized, yielding: ∃x[∀t(Time(t) ⊃ (running(John,t) ⊃ Hates(John,x,t)))]

(23)

that is, in English, There is something that John hates whenever he is running.

(24)

(24) is of course intuitively entailed by (18) and, fittingly, (23) is validly entailed by (19) on the semantics of the previous section. However, intuitively, (18) entails something stronger, namely, that what John hates when running is exactly that, viz., running. That is, intuitively, as with (21), the two occurrences of ‘running’, despite playing different syntactic roles, have the same semantic value. That is, it is possible to infer not only (24) from (18) but also something like: There is something that John hates whenever he is doing it,

(25)

where both occurrences of ‘running’ in (18) are generalized upon. Accordingly, it should be possible formally to infer a corresponding representation of (25) from (19) in which on both occurrences of ‘running’ are existentially generalized, e.g.: ∃F[∀t(Time(t) ⊃ (F(John,t) ⊃ Hates(John,F,t)))].

(26)

But this is currently not possible in our language as it stands, as variables are only allowed to occur in argument position. 13 Paradoxes in set theory, in particular, arise from overly promiscuous set existence principles like the so-called naïve comprehension schema which generates a set {x : ϕ} for every expressible condition ϕ. From this principle the existence of the Russell set of all nonselfmembered sets follows immediately from the condition x ∈ / x.

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Again, a knowledge base containing both (4) and (17) entails ConverseOf(Teacher,Student) ⊃ Teacher(Plato,Aristotle).

(27)

Hence, intuitively, Plato and Aristotle stand in a relation whose converse is the Student relation. Thus, as with the move from (19) to (26), it should be possible to generalize on both the nominal and predicative occurrences of ‘Teacher’ in (27): ∃F(ConverseOf(F,Student) ⊃ F(Plato,Aristotle)).

(28)

Relatedly, it should be possible to infer from (27) that Student(Aristotle,Plato).

(29)

And this of course follows directly if the converse relation is axiomatized in the obvious way: ∀F∀G(ConverseOf(F,G) ⊃ ∀x∀y(Fxy ⊃ Gyx))

(30)

All three of these examples can be accommodated syntactically in our type-free framework by means of a simple adaptation that allows variables themselves to be cross-categorical, that is, to occur, not only in argument position, but also in function and predicate position as well. With this adaptation, (26), (28), and (30) are all syntactically legal. A concomitant semantic adaptation ensures that the three inferences above are all valid. With the relaxation of traditional typing distinctions to allow both type-free lexical items and corresponding, type-free properties and relations, these cases require only two simple semantic tweaks. First, for a variable assignment s, the extension s is defined so that it applies not only to terms but to function symbols and predicates as well.14 The satisfaction clause for atomic formulas is then restated accordingly: • s satisfies ρ(τ1 , . . ., τn ) in I if and only if s (τ1 ) . . . s (τn ) ∈ s (ρ). With this modification, (26) can be shown to follow straightaway from (19), (28) from (27), and (29) from (27) and (30). 4 Common logic As can now be seen, a mix of cross-categorical and non-cross-categorical lexical items in a first-order language requires a rather finicky semantics. However, having recognized the need for cross-categoricity, it is arguable that a general logical framework for the Web should by default be fully type-free, that is, by default, there should be no syntactic and semantic typing whatsoever. This is the standpoint of Common Logic (ISO 14 More exactly: For κ ∈ Cn, s (κ) = den(κ), for α ∈ Fn, s (α) = f ext (α), for π ∈ Pr, s (π ) = r ext (π ), and for variables ν, s (ν) = s(ν). Then, recursively, for function terms β(τ1 , . . ., τn ), s (β(τ1 , . . ., τn )) = s (β)(s (τ1 ) . . . s (τn )).

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2007), a recent ISO standard for publishing and exchanging logic-based information on the Web that embodies all of the adaptations discussed above.15 4.1 Complete type freedom There are two reasons for full type-freedom in a logical framework for the Semantic Web. First, while authors can be expected to comply reasonably well with web-based syntactic standards if flouting them prevents them from achieving their desired ends— as can occur, for example, if one attempts to publish an HTML document lacking a proper header—one cannot realistically expect a logical knowledge base to comply with even long-standing and well known syntactic standards in logic, especially knowledge bases that might have multiple authors and that might have developed gradually over time. And indeed it is not uncommon to find knowledge bases in which any given lexical item is used indiscriminately to play two or even all three lexical roles traditionally divided among predicates, function symbols, and individual constants. Secondly, however, even if adherence to traditional syntactic structures could be enforced within knowledge bases, in an open network, there is simply no way to ensure that the same term is used only as a constant, predicate, or function symbol across knowledge bases. Hence, if knowledge bases are to be integrated—as is a major goal of the Semantic Web—the possibility of cross-categoricity must be allowed. But, because it is impossible in general to anticipate which lexical items might end up being crosscategorical, and because, in principle, any (nonlogical) item could, it makes sense simply to take all nonlogical lexical items to be cross-categorical. Complete typefreedom, that is, should be the default and typing restrictions should simply be tacked on as needed as the special case. The corresponding semantic thesis is that there is no longer any distinction made between individuals, functions, and relations. There are simply objects, first-class citizens: Just as any name can play any of the three major syntactic roles—argument, function symbol, predicate—so any object can play any of the three major semantic roles—individual, function, relation. 4.2 A fully type-free logic To capture the idea, the lexicon of a language is now defined to consist of nothing other than a single nonlogical lexical category N of names. Even the distinction between names and variables can go by the wayside, for on the Web, absent any sort of shared convention, there is no way to distinguish names from free variables. The simplest 15 Common Logic is a product of a fairly large working group that evolved from two projects to develop parallel ANSI standards for conceptual graphs (Sowa 1984) and KIF (Genesereth 1998). Eventually, those projects were merged into a single ISO project. Menzel and Hayes (2003) defined a very general model theory for a precursor to CL which Hayes (2003) used to define the semantics for the W3C languages RDF(S) and OWL. In addition to defining the general syntax and semantics for all CL dialects, the CL standard specifies three concrete dialects that are capable of expressing the full CL semantics: the Common Logic Interchange Format (CLIF), the Conceptual Graph Interchange Format (CGIF), and the XML-based notation for CL (XCL).

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way of dealing with this is simply for names to subsume the usual role of variable: like variables, they can all be quantified. Unquantified, names function as usual.16 As there is no finite bound on the number of quantifiers that can occur in a sentence, it must be assumed that NL is countably infinite. 4.2.1 CL grammar: a family of dialects A final, very important feature of CL is also motivated by the rise of KR languages: their use to represent information on the Web. The rise of many distinct KR languages with many different features led to many internecine conflicts over whose language was superior to whose. While these debates were sometimes based in matters of genuine substance, often as not disagreements were rooted in mere matters of form, such as the superiority of LISP-like languages over traditional languages in the Principia Mathematica style. While there may be practical advantages of one language over another in various contexts, at root KR languages are theoretically similar, if not identical. Rather than spawn yet another series of debates over form, early in the development of CL it was decided to express the syntax of CL languages (or dialects, in CL’s terminology) in purely abstract terms so as to encompass a boundless variety of concrete representation languages, from LISP-like languages to graphical languages and everything in between. Specifically, then, let N be a nonlogical lexicon. The members of N are called names, one of which, referred to as Id, is distinguished. The logical lexicon of every CL dialect will include a countable set of sequence variables, or sequence markers in CL’s terminology, and five connective types—conjunction, disjunction, implication, biconditional, and negation—and two quantifier types—existential and universal. A CL dialect (based on N) must meet the following conditions17 : 1. Every name is a term (of L ). 2. A term sequence is a finite sequence of terms or sequence markers. 3. A functional term consists of a term, called the operator (of the term), and a term sequence, called the argument sequence, the elements of which are called the arguments. 4. A sentence is either an atomic sentence, a Boolean sentence, or a quantified sentence. 5. An atomic sentence consists of a term, called the predicate (of the sentence), and a term sequence, called the argument sequence, the elements of which are called the arguments. 16 Note that, semantically, this will be equivalent to one of two standard approaches to free variables. On one treatment, free variables are implicitly universally quantified; on the other, free variables are, in effect, names, and the combination of an interpretation plus a variable assignment essentially yields the approach here. 17 In fact, CL dialects are defined more flexibly than this and encompass traditional, typed first-order dialects with fixed arities as well as type-free, arity-free dialects like CLIF. For purposes here, where the emphasis is on non-traditional adaptations (and for the sake of space), the less general definition above is used.

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6. A Boolean sentence has a unique connective type and a number of sentences, called the components (of the sentence). The number of components depends on the type: conjunctions (i.e., sentences whose connective type is conjunction) and disjunctions can have any number; implications and biconditionals must have exactly two; negations must have exactly one. 7. A quantified sentence has (i) a unique quantifier type, (ii) a finite, nonrepeating sequence of names and sequence markers, called the binding sequence (of the sentence) and (iii) a sentence, called the body. Variable bondage and freedom are understood as usual. As in Sect. 3.4.2, the extension functions fext and rext are taken to be functions on semantic objects directly, rather on lexical items. However, in the spirit of full type-freedom, there is no longer any distinction made between individuals, functions, and relations. There are simply objects, first-class citizens, each of which is assigned a function extension and a relation extension. Semantically, therefore, an interpretation I for L it taken to be a 4-tuple D, den, f ext, r ext , where den, more or less as before, is a function on the names of L and fext and rext are taken to be functions on all of D: • den : NL → D. • f ext : D → { f | f : D ∗ → D} • r ext : D → {r |r ⊆ D ∗ } Truth for the sentences of a CL dialect L in an interpretation I is defined in a natural way. Since there is no distinct class of variables, the concept of a variable assignment goes by the board.18 Instead, the definition of a ν-variant is altered and generalized so that it applies to interpretations directly. Specifically, for a sequence ν1 , . . ., νn of names or sequence markers, say that I∗ = D, den ∗ , f ext, r ext is a ν1 , . . ., νn -variant of I just in case den ∗ (μ) = den(μ) for every name or sequence marker μ distinct from the νi , i.e., just in case den ∗ differs from den at most in what it assigned to the names and sequence markers of ν1 , . . ., νn . Then denotation for terms generally and truth for sentences is defined as follows. 1. If ε ∈ NL , then d(ε) = den(ε). 2. If τ is a functional term and α its function term and τ1 , . . ., τn its argument sequence, then d(τ ) = d(α)(d(τ1 ), . . ., d(τn )). 3. If ϕ is an atomic sentence and π its predicate and τ1 , . . ., τn its argument sequence, then ϕ is true in I if and only if d(τ1 ), . . ., d(τn ) ∈ r ext (d)(π ). 4. If ϕ is a conjunction, then ϕ is true in I if and only all of its components are. Similarly for the remaining Boolean types. 5. If σ is quantified sentence whose type is universal (existential) whose binding sequence is ν1 , . . ., νn and whose body is ψ, then ϕ is true in I if and only if ψ is true in every (some) ν1 , . . ., νn -variant I∗ of I. 18 Variable assignments exist for largely contingent historical reasons, rather than theoretical ones, and are

frankly unnecessary in traditional FOL.

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Despite their syntactic freedom and apparently higher-order character, CL dialects without sequence variables (or with the syntactic restriction discussed at the end of Sect. 3.1.1) are entirely first-order and hence complete.19 5 A brief final judgment In this paper, I have traced a series of evolutionary adaptations of FOL motivated entirely by its use by knowledge engineers to represent and share information on the Web culminating in the development of Common Logic. While the primary goal in this paper has been to document this evolution, it is arguable, I think that CL’s syntactic and semantic egalitarianism better realizes the goal “topic neutrality” that a logic should ideally exemplify—understood, at least in part, as the idea that logic should as far as possible not itself embody any metaphysical presuppositions. Instead of retaining the traditional metaphysical divisions of FOL that reflect its Fregean origins, CL begins as it were with a single, metaphysically homogeneous domain in which, potentially, anything can play the traditional roles of object, property, relation, and function. Note that the effect of this is not to destroy traditional metaphysical divisions. Rather, it simply to refrain from building those divisions explicitly into one’s logic; instead, such divisions are left to the user to introduce and enforce axiomatically in an explicit metaphysical theory. CL’s relevance thus arguably extends beyond the knowledge engineering community to philosophy proper, as it gives philosophers a more flexible logical framework for the representation of philosophical content as well. Acknowledgements My sincerest thanks to my friend and collaborator Patrick Hayes for countless discussions over several years about the issues the led to the development of Common Logic and also for his help with this paper.

References Aczel, P. (1983). Non-well-founded sets. Stanford, CA: CSLI Publications. Baader, F., Calvanese, D., McGuinness, D., Narde, D., & Patel Schneider, P. (Eds.) (2003). The description logic handbook: Theory, implementation and applications. Cambridge: Cambridge University Press. Barwise, J., & Moss, L. (1996). Vicious circles: On the mathematics of non-wellfounded phenomena. Stanford, CA: CSLI Publications. Bealer, G. (1982). Quality and concept. Oxford: Oxford University Press. Brachman, R., & Schmolze, J. (1985). An overview of the KL-ONE knowledge representation system. Cognitive Science, 9, 171–216. 19 The easiest way to demonstrate this is simply to translate a CL dialect into a traditional first-order language as follows. Let L be a CL dialect. Let L ∗ be a traditional first-order language in which all the names of L are individual constants and which contains countably many predicates Holds1 , Holds2 , . . . and countably many predicates App1 , App2 , . . .. Then define a translation function ∗ from L to L ∗ as follows: For each name κ of L , let κ ∗ = κ; for every complex term α(τ1 , . . ., τn ) of L let α(τ1 , . . ., τn )∗ = Appn (α ∗ , τ1∗ , . . ., τn∗ ); and for every atomic formula π(τ1 , . . ., τn ) of L , let π(τ1 , . . ., τn )∗ = Holdsn (π ∗ , τ1∗ , . . ., τn∗ ). Boolean and quantified sentences are translated recursively in the obvious way. It is easy then to define a method for translating any interpretation I of L into a unique interpretation I∗ of L ∗ and show that a sentence ϕ of L is true in I iff ϕ ∗ is true under I∗ .

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Chierchia, G., & Turner, R. (1988). Semantics and property theory. Linguistics and Philosophy, 11, 261– 302. Genesereth, M. (1998). Knowledge interchange format. Draft proposed American National Standard (dpANS), NCITS.T2/98-004. Retrieved January 9, 2009 from http://logic.stanford.edu/kif/dpans. html. Grandy, R. E. (1976). Anadic logic and English. Synthese, 32, 395–402. Gruber, T. R. (1992). Ontolingua: A mechanism to support portable ontologies. Technical Report KSL 91-66. Stanford University, Knowledge Systems Laboratory. Hayes, P. (2003). RDF semantics. W3C Technical Report. Retrieved January 15, 2009 from the W3C web site: http://www.w3.org/TR/rdf-mt. ISO. (2007). Information technology—Common Logic (CL): A framework for a family of logic-based languages. International Standard ISO/IEC 24707, 1st edn., 2007-10-01. Retrieved January 9, 2009 from the ISO web site: http://standards.iso.org/ittf/PubliclyAvailableStandards/c039175_ISO_IEC_ 24707_2007(E).zip. Kenny, A. (1963). Action emotion and will. London: Routledge and Kegan Paul. Lenat, D., & Guha, R. V. (1991). The evolution of CycL, the Cyc representation language. ACM SIGART Bulletin, 2, 84–87. Lindström, P. (1969). On extensions of elementary logic. Theoria, 35, 1–11. MacGregor, R., & Bates, R. (1987). The LOOM knowledge representation language. Technical Report ISI/RS-87-188. USC/Information Sciences Institute. Menzel, C. (1993). The proper treatment of predication in fine-grained intensional logic. In J. E. Tomberlin (Ed.), Philosophical perspectives (Vol. 7, pp. 61–87). Atascadero: Ridgeview Publishing Company. Menzel, C., & Hayes, P. (2003). SCL: A logic standard for semantic integration. In A. Doan, A. Halevey, & N. Noy (Eds.), CEUR workshop proceedings: Semantic integration (Vol. 82). Available online at http://ceur-ws.org/Vol-82. Patel-Scheider, P., McGuinness, D., Brachman, R., & Resnick, L. (1991). The CLASSIC knowledge representation system: Guiding principles and implementation rationale. ACM SIGART Bulletin, 2, 108–113. Shapiro, S. C. (2000). SNePS: A logic for natural language understanding and commonsense reasoning. In L. M. Iwanska & S. C. Shapiro (Eds.), Natural language processing and knowledge representation: Language for knowledge and knowledge for language. Menlo Park, CA/Cambridge, MA: AAAI Press/MIT Press. Sowa, J. F. (1984). Conceptual structures: Information processing in mind and machine. Reading, MA: Addison-Wesley. W3C. (1995). RFC: 1808: Relative uniform resource locators (RFC 1808). Retrieved January 15, 2009 from the W3C web site: http://www.w3.org/Addressing/rfc1808.txt. W3C. (2005). RFC 3986: Uniform resource identifier (URI): Generic syntax. Retrieved January 15, 2009 from the W3C web site: http://labs.apache.org/webarch/uri/rfc/rfc3986.html.

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Synthese (2011) 182:297–313 DOI 10.1007/s11229-009-9662-1

Naturalized metaphilosophy David R. Morrow · Chris Alen Sula

Received: 6 January 2008 / Accepted: 30 November 2008 / Published online: 29 September 2009 © Springer Science+Business Media B.V. 2009

Abstract Traditional representations of philosophy have tended to prize the role of reason in the discipline. These accounts focus exclusively on ideas and arguments as animating forces in the field. But anecdotal evidence and more rigorous sociological studies suggest there is more going on in philosophy. In this article, we present two hypotheses about social factors in the field: that social factors influence the development of philosophy, and that status and reputation—and thus social influence—will tend to be awarded to philosophers who offer rationally compelling arguments for their views. In order to test these hypotheses, we need a more comprehensive grasp on the field than traditional representations afford. In particular, we need more substantial data about various social connections between philosophers. This investigation belongs to a naturalized metaphilosophy, an empirical study of the discipline itself, and it offers prospects for a fuller and more reliable understanding of philosophy. Keywords

Philosophy · Sociology · Networks · Reason · Naturalism

In addressing questions of how to represent philosophy, we should begin—in good philosophical fashion—by first asking what philosophy is. Historical answers have often prized the role of reason in addressing questions of existence, knowledge, and value. Thus, Plato recommends contemplation of the forms, Descartes’ meditator attempts to deduce self-evident truths from first principles, Spinoza discusses an activity carried out sub specie aeternitatis by a rational thinker who has removed all traces of subjectivity and individuality from his thought, and Kant describes philosophy as

D. R. Morrow · C. A. Sula (B) The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, NY 10016, USA e-mail: [email protected] D. R. Morrow e-mail: [email protected]

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the system of principles of pure reason. These metaphilosophies have tended to prize the role of reason in giving an account of the field. But for any such account, a curious puzzle arises: nearly all philosophers are influenced by other philosophers around them, and influence is not necessarily rational, warranted, or wise. Cohen (2000) provides a vivid illustration of the persistently social nature of philosophy in discussing the analytic/synthetic distinction in the twentieth century: people of my generation who studied philosophy at Harvard rather than at Oxford for the most part reject the analytic/synthetic distinction. And I can’t believe that this is an accident. That is, I can’t believe that Harvard just happened to be a place where both its leading thinker rejected that distinction and its graduate students, for independent reasons—merely, for example, in the independent light of reason itself—also came to reject it. And vice versa, of course, for Oxford. I believe, rather, that in each case students were especially impressed by reasons respectively for and against believing in the distinction, because in each case the reasons came with the added persuasiveness of personal presentation, personal relationship, and so forth. (p. 18) Anecdotes like Cohen’s are common in the published record of philosophy, especially in more informal settings such as book introductions, autobiographies, interviews, and correspondence. These confessions suggest that philosophy does not proceed purely through “rational” reflection; the social dimensions of the field may be as important— perhaps even more important, in some cases—than the exercise of our “rational” faculties. In order to understand how much, if at all, these social factors influence philosophy, we need a more comprehensive grasp on the field than traditional representations afford. Where traditional representations have focused almost exclusively on ideas and arguments, alternative representations might also consider what causes ideas and positions to emerge, why some gain philosophical currency over time and others lose credit, and how the commitments, questions, and boundaries of the field shift over time. Where traditional representations focus on what has been talked about in past and present philosophy, these alternatives might ask why or how those views have achieved or lost dominance. To answer these questions, we need more evidence about the practice of philosophy in the past and present. We need to develop and test hypotheses about the interaction between social and rational factors in the development of the field. This investigation belongs to naturalized metaphilosophy, an empirical study of the discipline itself. 1 Two models of representation Questions of how to represent philosophy depend, in part, on what the content and limits of the field are taken to be. From a rationalistic perspective, representing the discipline is a fairly straightforward task. Good philosophy is a success story, a triumph of human capacity in ascertaining the rational order of the universe, including ideal states of social, political, and moral affairs. In turn, good representations of philosophy should contain ideas and arguments that have survived the test of

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rational scrutiny. They should capture the cumulative knowledge we have obtained, and the more truths a representation contains, the better the representation. One could even argue there is some single best representation that reflects the most truths ascertained and endorses the least falsehoods. This austere representation could still mention “mistakes” in the history of philosophy if their errors or oversights would prove instructive or fruitful for further discoveries. But failures and lesser theories would be footnotes to a larger history of successful claims supported by decisive reasons. Alas. We don’t all agree—and rarely have—on which claims are recommended by right reason. If anything, present and past philosophy looks more like a history of disagreement, rather than convergence on certain claims. Maybe there is no determinate rational order guiding our work, or maybe we simply lack enough access to that order to sort the true claims from the false ones in any widely accepted manner. In either case, more recent philosophers have tended to regard their overall work as the search for good questions, rather than answers. As Russell (1912/1997) says in his popular introduction to the field, Philosophy is to be studied, not for the sake of any definite answers to its questions since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation… (p. 161) Against this pluralistic backdrop of speculation, the best representations of philosophy (and we had better assume there can be more than one) should take a value-neutral approach that does not bias one (now-admittedly) contentious position over any other. Good representations should simply catalog the important ideas of philosophy in the broadest and most charitable sense. This line of thought probably undergirds much of the encyclopedic efforts made by philosophers in the past few decades. Since Macmillan’s 1967 Encyclopedia of Philosophy, there has been a movement toward collectively authored volumes that treat individual topics in an allegedly balanced way. Contrary positions are presented with equal regard—or at least given their day in court for the benefit of novices, scholars of other (sub)disciplines, and experts alike. These audiences expect that in consulting the catalog, they are receiving an accurate, thorough, and undistorted representation of philosophy. But is such an expectation really fulfilled, and, to ask the prior question, is such an expectation even warranted? If rationalistic representations suffer empirical defeat at the hands of disagreement, encyclopedic models face a parallel problem from the limits and biases of human cognition. Decisions about the content of encyclopedias and the exposition of their topics are the choices of scholars, who, incidentally, have their own views to defend on the very topics they attempt to present in an unbiased fashion. Individuals may overcome bias in some cases, and decisions may improve if they are made by collectives rather than individuals. Still, as we discuss in Sect. 2, there are strong psychological tendencies that bias one towards arguments and evidence that support one’s own position and against positions and objections that do not. It is not unreasonable to think

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that these tendencies compromise the neutrality advertised by many encyclopedic representations of the field. Even if encyclopedists are successful in overcoming psychological biases, their model imposes an overly restrictive view of what information belongs in representations of philosophy. Encyclopedias present a time-slice view of the field: the ideas and arguments that are currently considered important for understanding the topic of any given entry. People show up incidentally as the vehicles of these ideas and arguments, but do not play any substantial role in explanation. As an example of this point, consider two answers to the question, Why did Kant disagree with Hume’s account of morality? One explanation might be that Hume and Kant both began with the same basic premises, but Hume made some mistake in drawing a sentimentalist conclusion from them, which Kant corrected (or vice versa, as you like). If so, there is nothing more to their disagreement than a simple logical error on the part of at least one author. Another answer might be that Kant (or Hume) supplied or assumed additional premises to derive his conclusions. This, too, could be explained purely in terms of the rational manipulation of ideas. But surely there is more to be said about the field. Why, for example, did specific premises or specific inferences seem sound to one philosopher, but not another? How did specific ideas earn their place in the canon, while others never attained such status? Among those that did find their way into the canon, what explains the ebb and flow of their credibility? These questions go beyond ideas and arguments to consider changes within the field as a whole. As such, they require diachronic representations of philosophy for their answers. In these representations, people will play a more substantial role. Consider why, for example, Confucianism, rather than Mohism, came to dominate Chinese thought. During Mozi’s lifetime, “his fame was as great as that of Confucius, and his teaching no less influential” (Fung 1948, p. 49). Chinese philosophy might have resembled Western philosophy much more closely than it does had the Mohists come to dominate the Confucians, rather than vice versa. Conversely, Western philosophy might have resembled Chinese philosophy more than it does if different schools of thought achieved cultural dominance in ancient Greece. In the Chinese case, it was not for obvious want of philosophical abilities that the Mohists are now found only in history books and the Confucians still play an important role in Chinese culture. To understand the rise of Confucianism—and likewise, perhaps, the rise of Platonism and Aristotelianism—we need to place the development of these philosophical schools in their social contexts. We suggest that the dominance and survival of some philosophical ideas at the cultural level is due, not only to their rational significance, but instead to factors such as influence, dissemination, conflict, and loyalty. With this observation in mind, we turn to the influence of social factors on the field and to the alternative representation of philosophy they suggest.

2 Social influence in philosophy If we abandon a fetishism of ideas, what might we include in our wider representations of philosophy? Let us begin with the simple observation that nearly all philosophers’ views are influenced by the views of those around them, either through actual

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interaction with one’s teachers, students, colleagues, and critics, or merely imagined dialogue with past figures and foes. In either case, one’s own philosophical ideas do not come purely from consulting reason, but instead depend on processes of training and enculturation in the field. Collins (1998) develops this point in The Sociology of Philosophies: A Global Theory of Intellectual Change to describe the personal ties—often conflictual—between major figures, which drive the field of philosophy. Collins distinguishes four senses of ‘school’, only some of which are relevant to understanding the development of philosophy. First, there may be “schools of thought,” or individuals who have similar modes of thought, but need not be personally connected—present-day Platonists have presumably not had contact with Plato. These taxonomic classifications can be rather vague and need to be studied through more tangible structures. Second, intellectual historians often use the word ‘school’ to demonstrate transmission of intellectual influence. As Collins points out, this “is not an explanation, in the sense of showing why, out of all the persons who could read or hear of an idea, a certain few become important…” (p. 65). Such an explanation depends on a rigorous study of the final two senses of ‘school’. One of these involves chains of personal relationships between teachers and pupils (vertical ties) and personal contacts between contemporaries (horizontal ties). Another consists of organizations, such as the Platonic Academy, the Aristotelian Lyceum, the Vienna Circle, or perhaps the Harvard Philosophy Department, where teaching and discussion take place and authority may be passed down through explicit succession. In these latter senses of the term, schools are engines of inquiry that steer the course of philosophy as a discipline. They are places (physical and social abstractions) where philosophers have developed their positions under the influence of others. As Cohen points out, two ideas may be equally (or nearly equally) compelling, and one’s decision about which to endorse may be made on nonrational grounds including the presentation of the idea or one’s personal relationship with its proponent. While it is hard to pinpoint the exact causes of a philosopher’s views and their relative contributions to his or her beliefs, we can observe rather striking trends of association between specific people, places, and ideas. Collins’ study of social networks across 2,000 years of Eastern and Western philosophy reveals that “The most notable philosophers are not organizational isolates but members of chains of teachers and students who are themselves known philosophers, and/or circles of significant contemporary intellectuals” (p. 65, emphasis Collins). As an illustration of the master–pupil tie, consider the importance of teachers in one’s own philosophical training. Most beginning students in the field do not have well-worked-out philosophical positions, but only develop them under the tutelage of more experienced figures, who have arrived at their own views through the very same process. One may, on occasion, seek out a particular teacher because of one’s antecedent philosophical interests. But where did those interests arise? Mostly likely, they have developed under the influence of earlier teachers and discussion with one’s peers, or perhaps from a chance encounter with one text rather than another. It is more plausible to explain philosophical development in terms of social influence than pure reason for the same reason Cohen suggests: two sets of equally rational inquirers may disagree about a certain claim (e.g., the analytic/synthetic distinction), where

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the primary difference between them is their members’ closer interaction with one proponent in the debate, rather than the other. We need not take these sociological claims to suggest some spooky social causation in order to understand how social ties influence philosophical practice. There are ordinary, well-documented psychological mechanisms by which individual philosophers’ social environments can affect their judgments. As Collins himself points out, these claims about the influence of groups can be brought down to earth in terms of familiar social interactions: “The history of philosophy is to a considerable extent the history of groups. Nothing abstract is meant here—nothing but groups of friends, discussion partners, close-knit circles that often have the characteristics of social movements” (p. 3). Although more empirical study is needed to determine the precise effects of various mechanisms on philosophical practice in particular, we hypothesize that two broad psychological mechanisms operate in tandem to influence the course of philosophy. The first mechanism is what social psychologists call “uniformity pressure,” which is a form of social pressure that induces members of a group to seek uniformity of opinion within the group (Kruglanski et al. 2006, pp. 88–89). Psychologists have observed uniformity pressure at work in enduring social groups, such as political parties and families, as well as ad hoc groups formed in experimental contexts. Such pressure makes itself felt through interaction with other group members, who are motivated by peer disagreement to eliminate discrepancies among group members in certain kinds of beliefs. Group members might seek to eliminate these discomfiting discrepancies through either a “change other” strategy, in which they try to bring others’ beliefs in line with their own, or a “change self” strategy, in which they change their own beliefs in order to match those of their fellows (Festinger 1950). The “change self” strategy might play an especially important role in shaping the views of newer students in an academic department who find themselves unable to match the argumentative abilities of higher-status faculty and more advanced students, all of whom have themselves been shaped by uniformity pressure already. The end result is a strong convergence, within social groups, on a set of shared beliefs. Although philosophers may be better than others at overcoming such biases, philosophical claims are precisely the kinds of claims for which uniformity pressure is strongest. Festinger cites the empirical testability of the beliefs in question as a major determinant of the strength of uniformity pressure. To use his example, an individual who forms a judgment that a particular object is fragile by smashing it with a hammer is unlikely to be swayed by another group member’s insistence that the object is unbreakable; but to the extent that the individual’s claims cannot be easily tested, as counterfactuals about complex social events cannot, that individual is more likely to depend on others’ agreement in deciding whether to hold fast to his or her opinion. Many philosophical claims, of course, fall nearer to the untestable pole of that continuum than not, and so we should expect even stronger uniformity pressure among philosophers than among some other disciplines. This may offset whatever cognitive advantages philosophers gain from their insistence on careful argumentation. This is not to say that philosophers will not tolerate disagreement in their ranks. As in any discipline, there are always prominent points of contention in philosophy. The point is rather that a known social psychological phenomenon predicts that

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philosophers who form stable social groups, such as within academic departments, will converge in some of their philosophical opinions. This convergence is enough to begin a process by which social interaction can shape the course of philosophy. Once social influence begins to affect individuals’ philosophical views, a second psychological tendency known as confirmation bias will often entrench that influence more deeply. Following Raymond Nickerson, we take “confirmation bias” to subsume several more specific psychological tendencies that lead individuals to seek and believe information that is consistent with their existing beliefs and to ignore, disbelieve, or to be more critical of information that is inconsistent with their existing beliefs (Nickerson 1998). Confirmation bias is so pervasive and so potent that Nickerson suggests, “If one were to attempt to identify a single problematic aspect of human reasoning that deserves attention above all others, the confirmation bias would have to be among the candidates for consideration” (p. 175). What makes confirmation bias so insidious, however, is that it operates unconsciously rather than through the deliberate distortion of evidence, and, according to some psychologists (Ditto et al. 1998; Fischer et al. 2005), it can sometimes arise from reasonable methods for allocating cognitive resources. We hypothesize that four mechanisms of confirmation bias, out of the many identified by Nickerson, are particularly relevant to philosophy. First, the “primacy effect” consists in individuals’ tendency to give more weight to information acquired earlier in an inquiry than information acquired later. Thus, formative philosophical experiences, which may be saturated by social influence, are likely to carry more weight than arguments encountered later, tilting the balance of reasons concerning contentious issues in one direction rather than another. Second, “motivated skepticism” involves a tendency to be more critical of information or arguments that challenge one’s beliefs than of information and arguments that confirm them. For instance, a patient is far more likely to ask for a second opinion or to entertain alternative hypotheses when a doctor informs her that she has cancer than when a doctor gives her a clean bill of health (Ditto and Lopez 1992). This tendency probably causes philosophers to devote more time and energy to rebutting arguments against their position than thinking critically about arguments for their position. Third, the “preferential treatment of evidence” involves giving more weight to belief-consistent evidence than belief-inconsistent evidence. This sometimes occurs just because people are more likely to notice or recall evidence that supports their beliefs than evidence that does not. It sometimes occurs because people are likely to interpret evidence in ways that support, rather than challenge, their beliefs, even when other individuals interpret the same evidence in the opposite way. Thus, philosophers are likely to give more weight to arguments and information that supports their views than to other arguments or information, perhaps simply because these are the arguments that come most frequently to mind. Fourth, “selective exposure” is the tendency to seek out information that confirms one’s beliefs rather than information that challenges it. This tendency may lead philosophers to devote more energy to finding or concocting arguments that support their own position and undermine others’ than they do seeking out objections to their own position. Of course, academia is structured to counteract confirmation bias, and philosophers in particular may be well suited to resisting it. None of this is meant to suggest that philosophers never seek out objections or that they fail to take objections seriously.

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Confronting objections is a central part of philosophical practice. But it is an empirical question whether professional philosophers avoid this ubiquitous psychological bias altogether. The point of invoking confirmation bias is only to show that there is a widespread and powerful psychological tendency that may cause philosophers to persevere in the beliefs that uniformity pressure may cause them to adopt within their social groups. Taken together, these psychological processes could explain how social factors influence individuals’ philosophical judgments. These applications of psychological theories to philosophical practice would, of course, need to be tested, and we should expect that the actual processes at work are more complicated. Nevertheless, these conjectures lay grounds for the hypothesis that social factors influence the development of philosophy. Testing these empirical claims is doing naturalized metaphilosophy— studying the discipline itself in an empirical fashion. In Sect. 5, we will propose more sophisticated forms of data collection and analysis to assist this effort. Before considering such methods, it will be useful to reflect on the view of the discipline implied by naturalized metaphilosophy. In particular, we will consider the role that reason plays in the practice of philosophy and the implications of naturalized metaphilosophy for the idea of progress in philosophy.

3 The role of reason Some may fear that naturalized metaphilosophy will deny reason any role in the practice of philosophy. If we can explain why philosophers adopt the philosophical positions they do by appealing to psychological and sociological factors, it may seem that they are not basing their positions on rational argument. This suggestion clashes with philosophers’ subjective understanding of what they are doing. Most philosophers take themselves to hold the philosophical positions that they do on the basis of rational argumentation. But if each individual philosopher adopts theories on the basis of reason alone, then sociological factors play no significant role in the field. We take as a provisional assumption that reason does play an important role in philosophy. “Reason,” as we understand it here, is a psychological capacity to engage in reasoning, where “reasoning” is “the cognitive activity of drawing inferences from given information” (Grafman and Goel 2002). Some types of inferences are more likely to yield true beliefs (given true premises) than others. Good reasoning involves using those, and only those, types of inferences. To say that “reason” or “reasoning” plays an important role in philosophy, then, is to say that philosophers are significantly more likely to accept a claim if (they believe that) it is supported by good reasoning based on true premises. We do not intend to exclude from naturalized metaphilosophy philosophers who are prone to more inflated notions of reason. The challenge for such philosophers is to craft a definition of reason suitable for empirical testing, without which it is impossible to determine empirically whether “reason” does play an important role in the field. One task of naturalized metaphilosophy in the immediate future, then, is to explain the connection between the social hypothesis put forward in the previous section and the hypothesis that reason, as defined above, plays an important role in determining

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which views philosophers adopt. In advance of empirical inquiry, there are reasons to think that some kinds of social influence coincide with philosophical reasoning. As Collins puts it, “intellectuals are oriented toward what they believe is the truth. They do not want to undermine their own truths, even though it is socially useful to have flawed truths which will keep their names alive in subsequent generations of creative workers” (p. 33). Philosophers constantly challenge one another to defend their claims through argumentation. Philosophers who hold fast to claims that cannot be rationally defended presumably invite the ridicule of their peers and the exclusion of their views from the philosophical mainstream. Contrapositively, it is reasonable to hypothesize that most philosophers who do rise to positions of social prominence within the field are those who excel at offering compelling arguments for their claims. To the extent that these individuals shape the social influence at work in the field, that influence will reinforce the effects of argumentation on others’ philosophical views, rather than run counter to it. Both of these processes—the marginalization of those who cannot rationally justify their claims and the exaltation of those who can—require that reason plays a prominent role in shaping the discipline. If empirical study shows these processes to be as important as they initially appear, then this study will help clarify the ways in which reason and social influence interact in philosophical practice. Naturalized metaphilosophy may be able to do more than just clarify this interaction; it may help us harness social factors for the good of the discipline. We can appreciate this point by way of a parallel discussion in the history and philosophy of science. As critics have pointed out, various social factors affect which hypotheses get proposed, how they are tested, and whether results received recognition. These factors include demographics (The Biology and Gender Study Group 1989; Hays-Gilpin and Whitley 1998; Hrdy 1981; Keller 1985; Lloyd 1993; Longino and Doell 1983; Spanier 1995); science funding, administration, and policy (Hull 1988; Kitcher 1990, 1993; Solomon 2001; Strevens 2003); institutional structures of reward (Keller 1983; Latour and Woolgar 1979/1986; Waring 1990); moral or political views; etc. Understanding the effects of these factors is a precondition for mitigating undesired bias in science. As Antony (1991) argues, “an empirical study of biases” is needed to “tell us something about the reliability and corrigibility of biases of various sorts. It may turn out that we can on this basis get something like a principled sorting of biases into good ones and bad ones, although it will be more likely that we’ll learn that even a ‘good’ bias can lead us astray in certain circumstances” (p. 216). Similarly, an empirical study of the social factors at work in philosophy may help to reveal which kinds of social influence resulted in interesting and original philosophical ideas, and which have led us down more frustrating or less fruitful paths. These observations about the beneficial or detrimental effects of various kinds of social influence would help to inform practical decisions about admission, employment, tenure and promotion, even publication and citation in the field. The claim here is not that naturalized metaphilosophy will reveal determinate principles that ought to govern our policies. Instead, the hope is that by understanding more fully the ways in which the field operates, we might in turn revise our practices to enhance argumentation in the field. Even if social influence is present in philosophy, it need not be deleterious. Philosophers can rely on reason to justify (or reject) beliefs that they have adopted primarily for social reasons, even if confirmation bias makes this difficult. By awarding

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opportunities for social influence to individuals at least partly in accordance with their good use of rational argument, social forces can enhance the role of reason in philosophy. Achieving a level of understanding sufficient to shape philosophical practice wisely will require careful empirical study, to which we turn in Sect. 5.

4 The possibility of progress Another fear raised by naturalized metaphilosophy is that the influence of social factors undermines the possibility of progress in philosophy. If philosophical theories rise and fall because of purely social factors, their dominance and decline may have more to do with fashion than with truth. The ruffled collars of Elizabethan gentry may be hard to find today, but this is for social reasons, not because fashion has “progressed” beyond “false” beliefs about the attractiveness of ruffled collars. If the explanations for the general rejection of the teleological argument for God’s existence are sociological or psychological, it might be similarly difficult to explain its rejection as “progress.” If we understand progress in philosophy to consist in coming to have more true beliefs and fewer false beliefs, there are three arguments for the claim that the influence of social factors will undermine progress. Two of these arguments come form the literature on scientific realism: Putnam’s (1978) metainductive argument (MI) and Sklar’s (1981) unborn hypothesis argument (UH). The third is more specific to the field of philosophy because it depends on the fact that philosophers return constantly to ancient, medieval, and early modern sources. MI takes as its starting point the observation that past scientific theories have been wrong in their fundamental posits about the world. It amasses cases of luminiferous ether, phlogiston, the four humours, and even Newtonian mechanics—all of which were leading candidates in their day yet subsequently rejected for newer theories— and then concludes that it is highly likely that our present theories will suffer the same defeat. According to MI, we have no reason, at any time, to believe that current science is correct, given that is has been incorrect in many past cases. As Putnam puts the objection, “just as no terms in the science of more than fifty (or whatever) years ago referred, so it will turn out that no term used now…refers” (p. 25). The appearance of progress throughout the history of science is merely illusion foisted upon a series of errors. There is, of course, a good Kuhnian explanation for why these views survived for as long as they did: each was regarded as authoritative during its day and passed down to successive generations of scientists in the course of their training in the discipline. In a parallel way, one might run MI on the naturalized view of the discipline we have proposed: Many past philosophical views are regarded today as crude, incorrect, oversimplified, and so on. They were believed, in large part, because of social factors, rather than the light of reason. Though some take this judgment to reflect philosophical progress—the approximation of truth in the limit of inquiry—the failure of these past cases should invite skepticism of, rather than inspire confidence in, our current philosophical views. We have every reason to believe that our current views are as erroneous as our past ones, and naturalized metaphilosophy explains our shifting allegiance to different ideas based on the pull of social factors. The difficulty posed by MI is even

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greater in the case of philosophy than it is in the case of science. At least scientists can point to greater technical success than their predecessors and can more easily explain their predecessors’ failures in terms of limited experimental abilities (Devitt 1991). Aside from marked improvements in formal logic, what technical results can modern philosophy boast over the eighteenth century? What tools of inquiry do we have, which Hume or Kant lacked, that better equip us to find the truth? Another line of objection takes a less devastating, but equally pessimistic view of social influence in philosophy, drawn from Sklar’s discussion of “unborn hypotheses.” Sklar worries that if unborn hypotheses (theories that have not seen the light of day) were to be born, it is likely that some would replace our current hypotheses, and by their lights, our current hypotheses would be wrong. “[W]hat credibility,” he asks, “can accrue to the victor in a battle for survival which, by historical accident and paucity of imagination, simply keeps nearly all of the competitors out of the arena?” (p. 20). Adapting UH for the present context, one might worry that certain philosophical ideas have gained (or lost) prominence only because their adherents (or opponents) have been well-connected, influential figures in the historical network of philosophers. Were others to occupy those nodes in the network, their ideas would have entered the arena, displacing the views we hold in the present to be correct, interesting, fruitful, etc. The common worry posed by MI and UH in this context is that naturalized metaphilosophy will reveal our current views to be massively erroneous or unimportant—or, to put the point more mildly, so highly contingent that our credence in them would be severely threatened. Those who think that philosophy is a purely rational enterprise carried out according to the normative requirements of reason will deny that our philosophical judgments are contingent on social factors. Rather than consigning philosophy to the flames, they will argue, we should sooner reject the naturalized metaphilosophy that called it into question. This line of argument, however, is highly irrational. It is an empirical question whether philosophy is a purely rational enterprise devoid of social influence, a question that can only be settled by empirical investigation. To avoid empirical evidence on the matter is to succumb to confirmation bias, or perhaps just to irrational wishful thinking, thereby undermining the claim that philosophy is a purely rational enterprise. If this claim is correct, the rationalist should welcome empirical evidence, for it will reveal a lack of social influence. If, however, there is evidence of social influence, we would do well to follow Bloor’s (1976/1971) advice on the sociology of science: It is quite possible to sweep this empirical observation [that scientific disputes are often social “priority disputes”] aside and declare it to be irrelevant to the true nature of science. Science as such, it may be said, develops according to the inner logic of scientific enquiry and these disputes are mere lapses, mere psychological intrusions into rational procedures. However a more naturalistic approach would simply take the facts as they are and invent a theory to explain them. (p. 22) Nothing inherent to the methodology of naturalized philosophy lends support to the skeptical threats of MI and UH. The rational path of inquiry is to gather whatever evidence is available and develop a theory to explain that evidence.

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As part of this task, philosophers must explain a curious phenomenon in the discipline concerning progress: Unlike the sciences, which focus on current research, philosophers routinely study, cite, and engage with theorists who were writing several centuries, if not millennia, earlier. These sources remain en vogue, presumably, because teachers continue to assign them to students as canonically important texts in the field. But the mere fact that a text is well regarded does not entail that its claims are true, so we are again presented with a case in which social influence possibly leads the field astray, thereby hampering philosophical progress. To put the point more finely, either philosophers turn to old sources because they think those sources contain enough true claims to be worth reading, even at the expense of reading contemporary philosophers; or they devote attention to old sources for reasons other than to gain true beliefs. Either interpretation threatens the possibility of progress. On the first interpretation, this phenomenon suggests that we have not come far enough since Plato and Aristotle to set them aside. How often do contemporary scientists invoke or grapple with Newton, much less Ptolemy or Archimedes, in their work? On the second interpretation, it suggests that philosophers are so consumed with a search for something besides truth that any progress we make, as we understand ‘progress’ here, would be almost coincidental. Rather than fueling this skeptical fire, naturalized metaphilosophy suggests that we need not worry about it. On the first horn of the dilemma—the one on which we return to Aristotle, for example, because we think Aristotle was right with respect to some claim—we may indeed believe that Aristotle’s claims were correct because of social factors involving in our training in the field. But it would be a genetic fallacy to suppose that, because social influence directs us to read him, we err in thinking that he was right about some claim. The process by which we acquire our beliefs about which texts contain important truths does not determine whether those texts do contain such truths. On the other horn of the dilemma—the one on which we return to Aristotle, say, for reasons other than truth—tracing the lines of social influence may help us discover which aspects of a text we find valuable over and above its possible truth. These criteria for evaluating theories may include parallel characteristics from the philosophy of science: consistency, whether a theory contradicts itself or other currently accepted theories; scope, the degree to which a theory extends beyond the particular domain it was initially designed to explain; simplicity; and fruitfulness of further research programs (Kuhn 1977). This metaknowledge about the discipline may be useful, upon reflection, for revising our present views of the field and making evaluations that better fit that reality. Naturalized metaphilosophy, as we suggested in the last section, may be able to provide us with tools to better decide what counts in making progress in the field and adjust decisions of awards, promotions, and honorable posts in light of that understanding. Far from calling philosophical progress into question, naturalized metaphilosophy may be able to explain and enhance that progress through its empirical investigations.

5 A research proposal in naturalized metaphilosophy In Sect. 2, we hypothesized that social factors influence the development of philosophy, and in Sects. 3 and 4, we hypothesized that positions of status and reputation—and

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Table 1 Some formal relationships and sources of documentation for them Type of relationship

Sources of documentation

Student/teacher relationships Advisor/advisee

Dissertation front matter

Classroom student/teacher

Various sourcesa

Peer/peer relationships Fellow students

Degree dates in dissertations, CVs, etc.b

Fellow faculty members

University catalogsc

In-print relationships Citation (i.e., who cites whom)

Publications

Acknowledgements

Publication front matter, footnotes, autobiographies

Editor/contributor

Anthologies/journals

a These can be very roughly inferred by comparing students’ dates of attendance in a program with the lists

of faculty teaching in the program at the time, narrowed according to the students’ and faculty members’ areas of interest b At some institutions, doctoral candidates traditionally include a CV at the end of their dissertation, which gives dates and institutions for undergraduate degrees. Some institutions’ alumni records also contain information about doctoral students’ undergraduate degree c University archives maintain copies of all annual or biannual university catalogs

thus social influence—will tend to be awarded to philosophers who offer rationally compelling arguments for their views. These hypotheses about the role of social influence in philosophy are speculative; their confirmation will require comprehensive data about the discipline that is not available in any existing representation. Such a test will require substantial data about relationships between philosophers, theoretical methods for extracting useful information from that data, and techniques for rendering those inclusions in cognitively salient ways. All three of these elements are currently available, but they have not yet been brought together in a form sufficient to evaluate our hypotheses.1 Investigating social influence in philosophy requires compiling data about the social relationships, both formal and informal, between philosophers. The availability of this data varies by era and geographical location. Since around 1880 in North America and longer in Europe, institutions have maintained useful records about personal connections between philosophers. The written record of the field stems back even further. Relationships of particular interest are explained in Table 1. The relationships people establish thorough correspondence, conference attendance, scholarship on the same topics, membership in the same professional associations, and mutual friends are less formal, though at least as important as these

1 At present, there are several projects that address portions of this task: Josh Dever’s Philosopher’s Family Tree (Dever 2008), David Chalmers’ Australasian Family Tree (Chalmers 2008), the Indiana Philosophy Ontology Project (Allen et al. 2008), various departmental placement pages (vid. Blatti 2008), and Phylo (Morrow and Sula 2008), which explores the historical network of individuals, institutions, and ideas in the history of philosophy.

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formal relationships. Informal relationships can sometimes be documented, though with greater difficulty and less regularity. Data on philosophers living and working before the late nineteenth century may prove more challenging. In many cases, institutional records do not exist, and written works are lost or inaccessible. However, Collins’ achievement in tracing relationships among Western and Eastern philosophers over two millennia does give some hope that relationships parallel to those listed in the table above can be established, even for very ancient figures. In part, this process relies on the role of experts in the field who have catalogued and examined the documents pertaining to individual philosophers, including where they lived, with whom they communicated, and what they wrote about. Moreover, several digitization projects, such as the Universal Digital Library and Google Books have made explicit commitments to preserving older texts and making them publicly accessible. The digital form of these materials can allow for automated extraction of keywords and references, which greatly simplifies the task of analyzing millennia of data from the field. In some cases, these methods, too, must be enhanced with the input of experts. An eighteenth century moral philosopher, for instance, may make reference to “the author of a treatise on moral sentiments,” without naming Francis Hutcheson or David Hume explicitly. This reference might escape a computer algorithm, but it would be transparent to any historian of ethics. Identifying which (pieces of which) materials are purely machine-readable from which require expert input could be made more efficient with filtering algorithms trained to recognize possible references and queue them for further analysis. Requests for input could also be distributed across a group of experts, with each contributing small but important pieces of data, thereby minimizing the amount of work required by any single expert.2 If technology-enhanced methods of data collection are successful, the vast amounts of information gathered will require analysis in ways that make them cognitively salient to interpreters who wish to evaluate our hypotheses. One particularly promising method of analysis lies in the “science of networks” (Barabási 2002; Buchanan 2002; Watts 2003), a burgeoning field of research that has its roots in the field of discrete mathematics known as graph theory. Each network is made up of a set of discrete elements (i.e., vertices, nodes, actors) and a set of connections (i.e., edges, links, relational ties) between them, both of which vary by discipline. In recent decades, studies have included populations and disease, chemicals and reactions, people and information, and publications and citations. Of particular interest for our purposes are social networks, which can be used to study decision making, belief systems, diffusion and adoption of innovations, coalition formation, and other phenomena (Wasserman and Faust 1994). Network analysis can yield information about individual actors, including their prominence and the roles they play as isolates, liaisons, bridges, etc.; pairs of actors, including distance and reachability; and group-level properties, including centralization, density, prestige, and recurring structural patterns (equivalence classes and blockmodels). Current work by network analysts includes the study of multiple relations, dynamic networks, and longitudinal network data.

2 Our own project, Phylo, makes wide use of this distributed input from experts, combined with automatic

methods of data collection and analysis.

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Fig. 1 Rosvall and Bergstrom’s map of the social sciences based on 1,431 journals and 217,287 citations. The nodes correspond to different subdisciplines. The direction and thickness of the edges correspond to the flow and number of citations between those subdisciplines. (Rosvall and Bergstrom 2007)

By now, the prospects for network analysis in testing our hypothesis should be clear: the science of networks can serve as a tool for studying empirical observations of the field in a rigorous fashion. As an example of this application, consider Rosvall and Bergstrom’s study (2007) of citation patterns in more than 1,400 social science journals during a single year. Using tools of network analysis, they generated a map of the social sciences showing the relative density of citations in disciplinary clusters of journals, as well as the weight and direction of citations between them (see Fig. 1). The resulting map of the social sciences reflects some of our intuitive understanding of these disciplines and their connections. But its empirical foundation provides a measure of accuracy and reliability that is lacking in the nonempirical work. Similar applications of network analysis to citations in philosophy, as well as other forms of data discussed above, could yield representations of the field that go beyond traditional models in the kinds of information they reveal and the empirical support they provide. Such representations give us a rigorous way of identifying prominent individuals, institutions, and ideas; discovering patterns and trends in the way that the field develops over time; locating important divisions within the discipline and points of contact between subdisciplines; and tracking demographic changes in the discipline. Good representations in naturalized metaphilosophy will strike a balance between uncovering important structural features of the discipline and excessive amounts of detail. Emerging technologies of information visualization have an important role to play in creating intuitive displays that convey the results of network analysis in accessible ways to human users.

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6 Conclusion At the heart of naturalized metaphilosophy lies a recognition that philosophy is an activity carried out by human beings—social creatures who, despite being able to carry out complicated chains of reasoning, are deeply influenced by their social context. Traditional representations cling to a myth of pure rationalism—the myth that arguments, and nothing else, drive the course of philosophy, according to their objective logical merit. If this were true, it would be possible to understand the history of philosophy strictly in terms of the arguments on which these representations focus, and it would be possible to identify the important arguments (and the individuals through whom they were articulated) from a neutral, encyclopedic standpoint. But casual observations like Cohen’s remark about the analytic/synthetic distinction and more rigorous empirical studies like Collins’ suggest that there is more going on in the discipline. Naturalized metaphilosophy extends this investigation to discover what other forces shape the development of philosophy. In defending this approach, we do not wish to advance social factors at the exclusion of the rational ones on which the field is consciously focused. The latter deserve a central place in representations of the discipline, for they play important causal roles. We are simply pointing out that they cannot tell the whole story; if we want to understand the practice of philosophy in a broader sense, we need to look beyond ideas and arguments alone. Naturalized metaphilosophy is more than a study of error. It is not an attempt to debunk philosophy or scandalously reveal socially induced failures of reason. Instead, we prefer to think of it as a study of success. If we can identify circumstances in which social forces cause philosophers to stumble in their pursuit of truth, we can also identify circumstances in which social forces nurture good philosophy—circumstances in which philosophical inquiry is most successful or most productive or most transformative. And then, equipped with that knowledge, we can improve the social structure of the discipline to ensure that the circumstances in which we actually do philosophy are as close to those ideal circumstances as possible.

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Synthese (2011) 182:315–333 DOI 10.1007/s11229-009-9663-0

Noesis and the encyclopedic internet vision Anthony F. Beavers

Received: 15 April 2009 / Accepted: 1 June 2009 / Published online: 5 November 2009 © Springer Science+Business Media B.V. 2009

Abstract Noesis is an Internet search engine dedicated to mapping the profession of philosophy online. In this paper, I recount the history of the project’s development since 1998 and discuss the role it may play in representing philosophy optimally, adequately, fairly, and accessibly. Unlike many other representations of philosophy, Noesis is dynamic in the sense that it constantly changes and inclusive in the sense that it lets the profession speak for itself about what philosophy is, how it is practiced, and why it is important. In this paper, I explain how Noesis is dynamic and inclusive. I close by suggesting why such a communitarian representation of the profession is both timely and necessary. Keywords

Philosophy · Noesis · Search engine · Open access

The question that frames this discussion of Noesis is no small one: that of how best to “represent” philosophy. First off, the questions of what it means to represent something and indeed what a representation is are fiercely debated. Second, we would be hard pressed to reach a consensus, even among professional philosophers, about what philosophy is, much less about its role in any collective body of knowledge and wisdom, why it is important to study, and so on. Assuming anything about either representation or philosophy could land one in philosophical quagmire. Yet, we do “represent philosophy” in various ways, mostly through the publishing mechanisms of the journal and book business, through the structure of our professional associations and conferences, through several initiatives to build compilations of philosophy in the

A. F. Beavers (B) Department of Philosophy and Religion, The University of Evansville, Evanville, IN 47722, USA e-mail: [email protected]

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form of textbooks, encyclopedias, bibliographies etc., and through the partitioning of the discipline that gives structure to curricula and determines what gets taught and learned. The fact that we already represent philosophy, but often do so uncritically by adopting these mechanisms inherited in history, is sufficient reason to address this question. More significantly, since the way that philosophy is represented determines in part what philosophy is, both in theory and in practice, and what it will become, the question is not only important, but also pressing, and more so given that emerging technologies are providing us with many choices that directly impact its direction, for better or worse. Nonetheless, if we take it that the goal of representing philosophy, however we might wish to define those terms, is to render the discipline of philosophy transparent as it is, that is, to represent the profession optimally, adequately, fairly, and accessibly, then emerging information technology may well provide what we need to respond to that goal without having to settle the questions raised above and without having to resort to artificial canons cut off from the whole by people who must, of necessity, always make decisions about what constitutes philosophy and what does not. Philosophy is what philosophers do when they practice it. While this definition initially looks empty as such, it nonetheless provides a useful parameter for determining the outer most limits for what a representation of philosophy must include. To fill it out, we must only then determine who the philosophers are and when it is that they are doing philosophy. While answering these questions requires stipulating criteria as well, perhaps it is fair to define philosophers as those who have been certified as such by the institutions of philosophy who have it as their task precisely to make this determination. As for when philosophers are practicing philosophy, this too is defined by the institutional context in which we work. I will refer to this general notion of letting the profession as a whole come together to represent philosophy as “the openness of Noesis,” and I offer it here as a technological antidote to the human dangers of “closing in on philosophy.” The risks of the latter are apparent whenever some philosophers take it as their task to tell other philosophers that what they are doing is not philosophy, and that, for reasons of protecting the integrity of our discipline, they should be excluded from the project of helping to guide humanity toward “wisdom” and “truth,” however they might be defined. In what follows, I will attempt to describe how Noesis embodies and facilitates this communitarian notion of representing philosophy. I will not promise that Noesis can put an end to debates about what should and should not count as the content of our discipline, though it will, no doubt, help to provide us with real, concrete evidence of our actual practices, as opposed to mere impressions and anecdotes, and add some truth to the defining debates that continue to haunt it. I will begin here with a little history of the Noesis project and then describe its current and future goals. I will end this paper with how the representation of philosophy achievable by Noesis can help to ground these and other fundamental debates about our discipline.

1 Representing philosophy: considerations, constraints and techniques Noesis can foster a communitarian approach to representing philosophy with what, in principle, is a rather basic notion made possible because of the affordances offered by

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the Internet and because so much philosophy is currently available online. It consists of specifying which parts of the Internet will be searched when a search request is executed. This is accomplished technically by defining the search space for a particular search in philosophy. This strategy has two complementary components: it simultaneously determines the relevance of resources, and it provides a way to filter resources qualitatively. How this strategy works will become apparent below where I will offer a brief history of the project and the work leading up to it. Before doing so, however, it will prove useful to offer a few thoughts about search engines more generally, since it is quite easy to miss the full import of what they are doing and, hence, what they can be made to do. A list of print resources on a particular topic is a bibliography, and it remains so when it is put online. However, when each item in that list is hyperlinked to an actual resource, something important has changed. From the perspective of the user, that list has now become more like a library than a bibliography (Beavers 1998b; Suber 2002). When such a list is compiled by hand, it reflects the agenda and the judgment of the person who compiled it. But such a list can also be compiled by software agents in answer to a variety of criteria, some of which can be determined by software designers and some by users. A search engine is precisely this kind of tool. Taking a search return set as an automated kind of the list just described, a search engine dynamically creates a momentary “library” to suit the immediate needs of a user. It does so through the interaction of three separate and distinct components. A search return set is (1) a subset of a larger dataset, here, the search space, (2) organized and processed by a program or set of programs, (3) in response to a search request submitted by a user. Each of these components can be controlled independently to produce these dynamic library-like lists. The first can be controlled by the determination of the search space as indicated above. If the larger dataset from which a search return set is culled is limited in its topical domain, so too will the return set be limited. In the case of Google, the search space is (almost) the entire World Wide Web. In the case of Noesis, the search space is, in principle, just the sections of it dedicated to professional philosophy. The second component can be controlled, of course, by what the programs are made to do. Elements controllable by such programs include things like sort order, processing diacriticals, preparation of any accompanying information that goes with the items returned in a set, such as excerpts from the documents, file size etc., management of Boolean operators, and so on. Most of the challenging work of search engine design falls in this second category. Google’s famous PageRank algorithm is a good example. (The current release of Noesis is built on the backbone of Google, thankfully sparing us from much of the hard work, at least for the time being.) Finally, the third component is controllable by the way that users formulate search requests. Though seasoned search engine users might think that forming search requests is intuitive, log file analysis shows that many users are not quite on target with the task and need to be helped with interactive, navigational tools like topic trees and dynamic visualizations (see Hölscher and Strube 2000; Spink et al. 2000; Jansen et al. 2000). The primary focus of Noesis is on the first component, that of determining the search space for professional philosophy; the task of helping users with their searching is now sufficiently addressed by the Indiana Philosophy Ontology Project (InPhO)

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(Buckner et al. 2010). Even though it is a separate project, a tight affiliation between Noesis and InPhO will add to the utility of both projects. I will say more about this affiliation later in this paper. In the meantime, the following brief history will shed additional light on these preliminary comments and provide the context for our goals with the next release of Noesis.

1.1 A little pre-history In 1994, before the arrival of the search engine, Internet users could go to the WWW Virtual Library at CERN in Switzerland, where they would be greeted with a note announcing that the Internet “had no top,” making it clear that they were truly in the midst of a network. Navigating the Internet was not as easy as today, but it could be done, because people who maintained pages on Plato, for instance, would hand link them to other relevant pages, allowing users to pass from page to page in something of an organized way. Between 1994 and 1996, the exponential increase in the number of pages online started to make it too much of a chore for an individual to keep comprehensive lists of resources, and that task was increasingly left to people or communities of people who were dedicated to particular topic areas. Ross Scaife’s “Diotima: Materials for the Study of Women and Gender in the Ancient World” and Pedar Foss’s “Romarch: Roman Art and Archaeology” were two examples well-known to scholars of the ancient world. This explosion of resources necessitated the search engine, and by 1996 they had already carved out a place online. With their arrival came a variety of questions and concerns, often centered around the fact that almost anyone anywhere could put anything online, leaving Internet readers in the precarious position of having to determine for themselves what was worthwhile and reliable. This problem was exacerbated by the fact that with the search engine users now would most often find a webpage directly rather than passing through any identifying homepage that might have a statement of a document’s source and authorship. The first search engines were no help in the matter either. (Google still is not, but Google Scholar is a rather remarkable step in the right direction.) In 1996, a search for the term “Plato” on one of the well-known, early leaders among search engines, AltaVista, returned 44,000 “hits”, including references early in the return set to a few software packages, an ale in Ireland, a consulting firm, a small town in Illinois, the Spanish word for “plate,” and a story about the “Lizard of Oz” (Beavers 1998a). Even when the resources did concern the Plato that we philosophers know and love, they were of mixed quality and included articles written by high school students, bizarre accounts of Plato that would probably never survive any peer-review process in the academy, and a few scholarly accounts. Clearly, the situation was such that any teacher who sent her students to AltaVista to find resources for a paper was deserving of what she was going to get, and those of us working on professional scholarship saw little in these early search engines to warrant their academic use. At the same time, to make a step toward advancing the scholarly use of the Internet, Hiten Sonpal and I developed what would be our first “Limited Area Search Engine” (LASE) based on the principle that if we could control the shape of a search space,

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we could create a search engine with a kind of built-in filter to regulate relevance and quality. “Argos: Limited Area Search of the Ancient and Medieval Internet” was developed as our first implementation of this strategy. It worked by crawling a set of associate sites and everything to which they linked. These associate sites were web indices, like Diotima and Romarch mentioned above, carefully selected on the basis of their academic nature and the quality of their links. Eight other sites were selected as well, including Chuck Jones’s ABZU index dedicated to ancient near Eastern art and archaeology at the Oriental Institute in Chicago and Gregory Crane’s “Perseus Project” at Tufts University. The collective effect of searching these sites and the pages selected by their editors was that control over what could show up in one of Argos’ search return sets was passed to the editors of the associate sites. Their actions directly determined content, and so Argos could claim a kind of peer review; indeed, it was the first search engine online that could make this claim. The improvements in the quality and relevance of items in a search return set were instantly noticeable. On our first run of Argos, a search for “Plato” turned up around 300 “hits,” but all of them referred to pages that talked about the Plato from ancient Greece, and all of them were academic resources with the proper authorial credentials (Beavers 1998a). The search return sets from Argos were so clean, in fact, that we could use them as an encyclopedic index to support further research for those using another website, “Exploring Ancient World Cultures” (EAWC), that I designed to supplement the World Cultures Program at the University of Evansville. Strategically placed links from EAWC were hyperlinked directly into Argos. On our page for the Roman Empire, for instance, we linked directly from terms like “Rome,” “Vergil” etc. to Argos, and when a user clicked these links, Argos would respond with a library of relevant and quality academic resources. This was certainly a step in the right direction, and so the Argos model was duplicated for the discipline of philosophy in a LASE we named Hippias and put online under the direction of Peter Suber of Earlham College. A similar version was also produced to power searches in law as part of Bernard Hibbitt’s Jurist website at the University of Pittsburgh. Argos did nothing to help with browsing and could not thereby respond to the third factor mentioned above, namely, helping users to find resources by formulating the right kind of search requests. But a close affiliation with the associate sites meant that users could browse resources topically by visiting each of the associates independently and capitalizing on the structure of the individual associate sites. By 1998, the work of maintaining the associate sites was starting to become a clear burden. Pages were moved frequently or removed from the Internet altogether, meaning that the associates were frequently needing to be updated to cope with broken links, and the work to do this was escalating, even though the Argos-style search engines would report broken links back to their associates. This problem, compounded by the escalating growth of the Internet between 1996 and 1998 (The ISC Domain Survey 2009), made it clear that the Argos model could at best be a temporary solution. The additional need to standardize the search return item format and other metadata components was also becoming clear in the absence of any widespread agreement on tagging standards. Attempts like the Dublin Core Metadata Initiative promised such standards, even as early as 1995, but it was clear by 1998 that it would be some time before anyone could claim to have established anything standard. (It is still apparent

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today that no consensus has been reached on how to use the title tag that is a regular feature of html.) Thus, in 1998, we turned away from the Argos model to the first Noesis prototypes, continuing our research in the newly formed Internet Applications Laboratory (IALab) at the University of Evansville.

1.2 The early Noesis models The first version of Noesis included its own database, effectively removing the associate editors from the equation. Each page that Noesis would search was individually selected and manually catalogued in a data structure that would allow for easy updating (Uzgalis 2000). It may seem silly today to think that this ever could have worked. But it worked then, and the reasoning seemed sound in that context. It took about 1 min to hand catalog a link, much shorter than the time it took to process a library book. Furthermore, unlike in library cataloging for manuscripts in print, a process that would have to be repeated in each library that would hold the item, once an item was catalogued in Noesis, it was catalogued for the whole world. So, the trade offs made the process seem worthwhile. By 2001, Noesis consisted of around 100,000 hand-catalogued links on philosophy, and the project was already showing signs that the apparent success of online scholarship meant that even this solution could not continue indefinitely. There were other issues as well. Eliminating the associate editors from the equation raised once again the problem of how to limit scope and determine quality. The absence of the associates also made it clear that somehow Noesis was going to have to assist users with their search and browse practices. We attempted solutions to both of these, with greater success on the former than the latter, but with nothing definitive. The ‘failure’ (if it is fair to use that term in this experimental context) of both is instructive, and hence worth recounting here. The relevance/quality problem was handled by imposing a criterion on what we would include in the index. In order to qualify, a document had to be written by someone holding an advanced degree in philosophy or a related field, or the document had to be published in a peer-reviewed initiative. The rationale was simple, and we still rely on a version of it in today’s Noesis. Agreeing up front that some graduate programs are better than others in preparing philosophy scholars and teachers (though without also conceding that the most established scholars are necessarily the best at such preparation), institutions offering advanced degrees already represent a credentialing system for the discipline, and, consequently, the attainment of such a degree says something concrete and definitive about the competence of an individual to work in the field. Though this kind of credentialing in no way employs the same kind of standards of peer-review used by journals, which suit purposes of their own, it does do something that the journals cannot do, namely, it allows for some form of meaningful dissemination that is freed from the judgments of just a few people. For all that can be said in its favor, standard peer-review remains controversial. (See Shatz 2004, for arguments for and against.) It usually consists of the judgment of just three people, two reviewers and an editor. While it is true that attempts to publish something in another journal, failing acceptance in a first, widens this pool to six, and

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so on, if a document is accepted on the first go round, it is because just two or three people thought it worthwhile. While it is true that the strategy of including documents in Noesis based on their authorial provenance rather than individual document review also falls back on the judgments of people, the cross-section of evaluators is much more diverse and wide-spread in the credentialing of people than in the credentialing of documents. Thus, while documents appearing in Noesis were not necessarily peer-reviewed, they nonetheless did bear a mark of quality that was determined by the practice of the profession itself. (I say “not necessarily peer-reviewed” here because many of the items that did turn up in search returns were reprints of things that were peer-reviewed or part of a peer-reviewed electronic initiative.) I do not want to say that “in theory” the procedures used by the first Noesis should have worked. They did work, but so much depends on getting the language just right and communicating precisely what we were trying to do. There were, in other words, complaints, most often by those not holding the advanced degrees we required for representation in Noesis. We were sometimes accused of academic elitism for excluding those not professionally trained from the dataset and who might nonetheless have contributions to make. Unlike in traditional peer-review, we did not verify documents individually without considering authorship. This fact made it all too easy to miss something truly important. Non-professionals need access to publishing venues to protect us from becoming too inbred as a profession, or so the criticism went. (In principle, blind review is not subject to this criticism, but one may fairly wonder just how often amateur philosophers are actually published in professional journals, and given that Noesis was not intended to be the sole mechanism of dissemination for the profession, the objection is a bit of a non-starter in the first place.) More pressing and legitimate complaints challenged a lack of a clear and stated criterion for deciding what was a field “related to philosophy.” Linguists, computer scientists, psychologists, literary critics and political scientists at one time or another suggested that their individual work was sufficiently philosophical to warrant inclusion in the dataset, and we did our best to evaluate each on a case by case basis. Some were gratified by our decisions, others frustrated. But the criticism in general was a fair one, even though how best to answer to the need for a stated criterion remains problematic. Determining what relates to philosophy depends on having a pretty clear notion of what philosophy is. Then as now, we try to steer clear of making precisely this determination so as to allow Noesis to be open, but at some point, lines must be drawn. If we were to let everything in, then Noesis would no longer be dedicated to philosophy and its utility would be limited for learning more about the discipline. The question is a matter of determining precisely where to draw these lines, and to draw them flexibly. I will say more about these matters later. As for the issue of helping users with their search and browse practices, the first Noesis engine allowed a team of associate topic editors to log in, develop a taxonomy on a particular area of philosophy to which they had been assigned, and move individual resources from our broader dataset into the proper part of their taxonomy. Users could then search various subsections of the Noesis search space or browse resources topically. These search and browse mechanisms worked well, but the associate editors did not. Scholars are busy people, and in the absence of clear incentives, it was simply too much to ask them to log in regularly to manage their portion of the tree. But this

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hard lesson was instructive, and it has been a lesson learned by several people trying to develop interactive Web 2.0 applications. It is simply not the case that if designers build it, people will use it. In fact, it turns out to be quite difficult to get them to use it. A sure sign that many in the Internet community have been stung by this lesson is that it has now become an interesting question of why Facebook is so successful. (At the time of this writing, Facebook reports more than 175 million active users. See http:// www.facebook.com/press/info.php?statistics for the latest statistics. For evidence of concern over such success, readers can peruse the search return set for “Facebook Success” on Google.) One solution to the problem of user engagement is to develop mechanisms that translate the actions that users normally perform in managing their own online affairs into meaningful information. Both Google and Amazon follow this approach. So, too, will the new version of Noesis. Between the version of Noesis just described and the version that went online in 2006, a few other possible models were discussed, and one even made it to a prototype. The 3.0 version was based on parallel distributed processing using a client/server model (popular at the time with networks like Napster and Gnutella) in which both clients and servers participated in the needed computer processing. In simple terms, the 3.0 version worked by tracking an individual’s link library, a special bookmark file reserved for communication with a central server. In turn, the server would crosscorrelate all of the individual link libraries, spot authorities and partition philosophy based on the collective actions of individual users. This approach was begun partly in response to the inactivity of the associate editors mentioned above. Our thinking was that if we could get enough people to interact with the server, we could use emergent methods for determining expertise and would not need to fall back on the professional credentialing discussed above. Amazon uses similar methods in the way that it recommends books and rates reviewers (Linden et al. 1998). Initial results were promising but the practical problems of maintaining software that would be installed on any number of computers across the Internet were well beyond the resources of the small undergraduate laboratory responsible for the prototype. Late in 2006, Google announced procedures allowing individuals to build Custom Search Engines (CSEs) as part of their Co-op platform. These CSEs work very much according to the principles that governed the LASEs described above. By restricting the scope of a search space to whatever criterion a designer might want to use, individual or “custom” search engines could easily be created that would search a subset of the Internet mapped by Google. This possibility invited us to rethink how best to approach the problem of search space construction for academic disciplines, and immediately we set to work addressing the problem geographically, according to where resources are stored, rather than by considering them topically. Partnership with Google also simplified much of the hard work involved in running crawlers, compiling searchable data structures, keeping these structures up to date, and so on. At the same time, the Indiana Philosophy Ontology Project (InPhO) was being developed to provide a workable solution to the problem of helping users browse and search for philosophy resources online. Together, these initiatives go a long way in making the Noesis concept easy to implement while increasing the range of affordances that we can offer. The remainder of this section of this paper will be dedicated to their contributions to Noesis and our goals that result from interaction with them.

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1.3 Partitioning the profession: fixed, custom and dynamic search space construction The Google CSE works, as just noted, by allowing search engine designers to specify a search space that is a subset of the overall space covered by Google. Designers may do so by logging into a web-based interface or by uploading files in a few different formats, including XML. Designers may also specify individual files they wish to have searched, or they may use wildcard characters to specify whole directories. Of course, Google cannot search everything in the named directory, since it does not have complete access to its contents. It can only search resources it can find, namely, those hyperlinked into the web and picked up by Google’s web crawlers. Additionally, designers can store their search space definitions in Google’s databases, or, more important for our purposes, they may pass an address for a search space definition file to Google at the same time that an individual search request is passed. This last option means that designers can build a search engine on the fly to reflect a variety of user-determined decisions. There are other factors that can be manipulated as well, but wildcard specification of directories and the ability to pass search space definitions to Google at run-time are most important for present purposes. I will discuss each in turn in the context of explaining what they afford Noesis and how we plan to use them. Wildcard specification of a directory (and with it any subdirectories) invites a geographical solution to the question of how best to isolate the regions of the Internet to search for limited area access to academic philosophy. In a few words, the matter is now one of determining where one is likely to find philosophy and search there. Though this might at first sound like a tall order, it really is not, since professional philosophy shows up (for the most part) in a limited variety of places; one must simply isolate the places where philosophers are likely to turn up in their professional capacities. Professional associations, conferences, departments at universities and colleges, and the journals and reference works where they publish are great candidates, along with pre-print archives, individual faculty websites, and online forums like mailing list archives and blogs, though one may fairly wonder about the utility of indexing the last two. (But, then again, what justification is there to leave them out, given that they can be included or excluded in a search according to the wishes of the user?) Assuming that we have a complete list of all associations, conferences, departments, journals, faculty web pages and so on—our goal over time—users of Noesis can search the entire reach of professional philosophy in a single pass, or they may search any one of these regions independently. Even in the minimal version now online, for instance, users may easily select reference works and search both the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy simultaneously, or search all and only the online philosophy journals indexed by Noesis. Limited area searching still provides the mechanism for control over relevance and quality, as with our first versions, but wildcard searching minimizes the problem of keeping records up to date, since it hands editorial control over the contents of Noesis to the profession of philosophers itself. Once we index a journal, for instance, we no longer need to track individual items, since they will automatically be picked up by Google as they turn up online (provided that they are appropriately linked to other pages picked up by Google) and will already fall under the wildcards in our search space dataset. Since the entire search space covered by Noesis is managed by pro-

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fessional philosophers or their delegates (as may be the case with some professional associations), all of the individual resources in Noesis are collectively determined by the body of professional philosophers who, in the process of maintaining their own websites, implicitly add to, edit and delete from the contents available through Noesis. Without any additional work beyond maintaining their own websites, they are therefore the real editors of Noesis. At these outer horizons, we have then a representation of the discipline that is inclusive of everyone and everything in philosophy insofar as philosophy itself is collectively defined by the practices of the profession already in place. Of course, at this point, this representation is in the form of a search space definition only, hardly useful for much beyond fixing the quality and relevance of search return sets. We can get more out of this representation by affiliation with the InPhO project to be discussed momentarily. To help the following discussion, I will use the term “fixed” as opposed to “custom” and “dynamic” search space construction to designate the most basic partitioning of the profession that Noesis provides. This fixed space is partitioned according to the geography of online philosophical resources; it is determined by where resources are located and not by considering their particular contents. However, in the next release of Noesis, users will have the ability to log in and create their own partitions by selecting from among the individual items mapped by Noesis. In other words, they will be able to customize their own philosophy search engines built from the professional resources included in our main dataset. This service will allow users to mix and match resources according to their own criteria, selecting any combination of individual journals, departments, reference works etc. Since they can also create an engine for just their own site by selecting only it, Noesis can offer users the ability to increase or decrease the scope of their search. For the purposes of clarity, I will refer to these mechanisms as custom, variable scope, search engines. To understand the power of variable scope searching, it might be helpful to imagine a search space as consisting of four concentric circles for a moment, with the inner circle representing the search space of a particular website and the outer circle representing all of the area covered by Google. From the center outward, the second circle here could be a custom search space established by the editor of the site represented in the inner circle, and the third circle out could be all of the space mapped by Noesis (see Fig. 1). To use an example, if the site in question were the Stanford Encyclopedia of Philosophy, the second region would include the SEP plus all of the individually selected journals and archives chosen by its editor. Users starting with a search box on the SEP site would then have the option of deciding the scope of their search at runtime and could easily search the SEP, or a subsection of the Internet defined by the editorial choices of SEP administrators, or all of Noesis, or all of Google. Thus, custom search space construction affords further refinement of the quality and relevance of a particular search space. At the same time, it provides Noesis with evidence to help determine more precisely the quality and relevance of the individual resources it maps. Dynamic search space construction refers to search spaces determined automatically by semantically sensitive search mechanisms. The general idea here was hinted at above, where I discussed the role that Argos played with Exploring Ancient World

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Fig. 1 Custom, variable-scope search space definition

Cultures (EAWC), the online undergraduate textbook supplement mentioned earlier. Previously, I noted that the finely tuned search return sets from Argos were sufficient to provide encyclopedic access to quality online resources for the users of EAWC. A hyperlink on the word “Rome,” for instance, would pass a search request directly to Argos, which would respond, in turn, with a list of academic resources answering precisely to that request. The idea behind dynamic search space construction with Noesis is similar, though more refined than in our earlier attempts. So that the reader is fairly apprised of the state of things, our plans here are theoretical (i.e., untried) at this point, and so, even though I am confident that we can make them work, I might rightfully be charged with talking about ‘vaporware’ in describing them. Theoretically, then, using the referring URL information that is passed with a particular hyperlink, Noesis will be able to retrieve the document from which a linked search request originated, analyze it, if it has not already done so, and then use that information to generate a search space definition dynamically suited to the context in which the search request is embedded. Thus, for instance, users reading a paper on Fodor’s representational theory of mind could encounter a hyperlinked search request on the term “representation.” When clicked, Noesis would respond with a search for the term “representation” across a space dynamically suited to resources in the philos-

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ophy of mind and, perhaps more narrowly, responding to the representational theory of mind, in particular. These dynamic search spaces could be combined with the idea of variable scope searching described above to allow users to configure a setting to determine the “range of context” for a given search, i.e., in rough terms, a percentage of the degree of overlap needed for the dynamic mechanisms to include an item in a search return set. To make things easier, rather than having individuals mark these hyperlinks by hand, we would prefer to provide a mechanism that creates an overlay for a particular document that automatically links the proper terminology to Noesis. These ideas on dynamic search space construction are speculative, as I said, and to quote Herbert Simon, “In the computer field, the moment of truth is a running program; all else is prophecy” (1965, p. xv). So, we will have to see. But the matter is on the experimental agenda for Noesis.

1.4 Inphorming Noesis and expanding the scope of its inphormation Earlier I mentioned the need to include in a search engine some mechanism to help users with their search and browse habits. I also noted that the existing version of Noesis represents philosophy in the form of a search space definition, which has an admittedly limited utility. The Indiana Philosophy Ontology Project (InPhO) discussed elsewhere in this volume provides a partial solution to the need for a taxonomic index that does justice to the organic nature of the profession while adding additional utility and power to Noesis. InPhO is an organic and emergent taxonomy of the discipline of philosophy that uses artificial intelligence algorithms to “read” the Stanford Encyclopedia of Philosophy (SEP) in collaboration with feedback from human users (Niepert et al. 2007). It is designed to identify philosophically rich vocabulary insofar as it is distributed in the SEP, isolate patterns of generality and specificity, and present this to the user in the form of a topic tree. (Other visualizations are being considered as well, but they exceed the scope of the current discussion.) InPhO’s tree allows users to explore the topical terrain of philosophy by expanding and collapsing parts of it as needed. An additional affordance is the ability to pass computer-configured search requests to various search services, including the SEP, Google Scholar and Noesis. A single click then supplies the user with a list of resources answering to that request. In addition to helping with the search and browse problem discussed earlier, the affiliation between InPhO and Noesis overcomes (in part) what is sometimes called the discovery problem, the problem of making users aware of resources that they do not know exist, but that they may need to consider. If users do not know they exist, they cannot search for them in particular; hence the need for computer-aided search and browse strategies to bring them to light. Such strategies can make connections that are initially rather distant explicit and therefore available for philosophical reflection. A favored example from the affiliation is that a search for “mental representation” turns up connections with “divine illumination” in medieval philosophy that, in turn, shed light on the heritage of the concept of representation and its reception into the philosophy of mind via modern philosophy. Further research on how to use computers to find and explore these connections will, no doubt, add additional utility, and we

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will perhaps one day learn novel information about the profession from a variety of automated procedures. The affiliation between Noesis and InPhO also promises to help each project overcome limitations of scope. I noted earlier in conjunction with the first Noesis, for example, a set of objections concerning what qualified as a discipline related to philosophy. If Noesis is going to be dedicated to academic philosophy online, somehow it must be sensitive to resources of a philosophical nature that do not come from within the discipline itself. Scholars from outside the formal institutional context of philosophy are often by no means philosophical amateurs and have earned a proper place in the canons of our discipline. Physicists, for instance, can and do engage in philosophy of physics, as economists sometimes engage in philosophy of economics, medical practitioners in matters of ethics, literary critics and art historians in aesthetics, and cognitive scientists in epistemology and the philosophy of mind. It would be a mistake to define the scope of philosophy in such a way that, by definition (even by search space definition!), these others are excluded. Yet, without going back to inspecting each resource by hand for inclusion in Noesis, which in turn requires a perspective on the discipline that no human being (or small set of human beings) has, the problem is how to identify them, especially given that we do not want all of medicine, art history and cognitive science in the dataset, just those parts of them that overlap in important ways with philosophical research. InPhO is not just a mechanism for generating a browsable topic tree, it is also a partitioned map of the semantic space of philosophy, and, as it continues to develop, it will be more so. As such, it holds part of the key to identifying philosophical documents automatically. The geographical strategy outlined above for building Noesis’ fixed search spaces picks up resources that are located where professional philosophers tend to appear. If some among them work in philosophy of physics, to cite an example, then resources written by professional philosophers of physics will be picked up. However, resources in the philosophy of physics that are written by physicists may well be missed, unless they are published in an online philosophy journal or are put online by an official representative of philosophy like a professional association or academic department. Over time, InPhO will help us identify a “semantic signature” for philosophical resources that will prove useful for comparison with documents not in our search space to determine which should be added. Experiments will be necessary to determine the best way to proceed, but we do have on hand some things to try, and, in any case, if such mechanisms cannot do the trick themselves, they will no doubt go along way in pre-filtering resources for human inspection. But pursuing this course will be a last result only if our artificial intelligence strategies cannot be made to work. Less speculatively, Noesis can be used to help overcome the limitations of scope in the InPhO project. InPhO is seeded by the SEP, and its topic tree and semantic maps are only as good as the SEP. Thankfully, the SEP is excellent and currently provides the best representation (in terms of scope and quality) of philosophy online and, possibly, in print as well. At the time of this writing, it includes 1,105 articles in over 40 subject areas carefully managed and reviewed under the auspices of 115 area editors. Though it grew primarily out of the analytic tradition, it has quickly expanded beyond to include a fair representation of other areas, including ethics, feminism, and

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continental philosophy. Its holdings in the history of philosophy are also extensive, and the credentials of its authors are hard to beat. Still, it is limited and probably falls short of providing the complete range of vocabulary used by the profession to the InPhO project. I say probably because the only way to know for sure is to compare it against the broader corpus of professional philosophy online to see. Given that Noesis plans to map the entire space of professional philosophy online, it will prove useful as a tool to help test the adequacy of the SEP as a semantic representation of philosophy. If it is inadequate, we will be able to know this and, more importantly, know precisely where it is lacking. In conjunction with the InPhO project, Noesis then will be able to help the editors of the SEP know where additional coverage is needed.

2 Making philosophy transparent: toward real evidence about the state of the profession In addition to helping users find quality and relevant philosophical resources and supplying the InPhO project with a broader pool for its semantic analysis, there are other affordances for the profession (and beyond) that make the Noesis project important. Some of these affordances are common to other initiatives and are already well documented in the literature of the open access movement. They concern matters like helping to free the direction of scholarship from the exigencies of the marketplace and bringing quality resources to developing countries that cannot afford to build print libraries of their own. The need to free scholarship from the marketplace is critical for the future of philosophy, especially for the areas that are not part of the “mainstream” movements within it. A cursory review of market trends might easily lead one to believe that philosophy today concerns the philosophy of mind and ethics, and slightly less so the philosophy that relates to science (as with the many resources concerning evolution) and public policy. But this is an illusion created by the fact that resources on topics that will sell are more likely to get published by an industry that must be concerned with income to stay in business. Consequently, topics that are likely to attract a wider readership come to represent philosophy precisely because they are popular among readers. This might be a fair way to measure the spread of interest in a topic across the profession more broadly, but it does not do justice to what is really going on in the actual practice of the discipline, and allowing the institutions of commerce to determine what of the world’s wisdom we should protect might be objectionable on other grounds as well. For instance, there is the perennial threat of a “feedback loop” that perpetuates the popularity of resources in a given area. Books on topics that sell generate interest which in turn encourages more books on the same topics and create topical “ruts” that impact the scope and utility of philosophy in potentially harmful ways. Projects like Noesis that provide focused access to open-access resources contribute to providing a more adequate representation of philosophy because they serve also to open access to a broader range of philosophy. Concerning the matter of spreading resources globally, even though Noesis indexes resources primarily in English at this time, the prototype version now online regularly serves pages to over fifty different countries weekly, including Argentina, Australia,

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Ecuador, India, Iran, Japan, Kuwait, Mexico, Rwanda, Thailand, the Russian Federation, and Venezuela, to pick a representative dozen, and it is linked to pages in several different language domains, including Arabic, Danish, Dutch, French, Italian, Norwegian, Slovak, Spanish, Swiss, and, of course, English. As Noesis continues to develop, we expect a truly global presence, if we do not have that already. As a world full of people find their way to Noesis, they are simultaneously finding their way to other open access initiatives in philosophy. So, Noesis will provide a broader representation of philosophy across a broader populace than many (any?) other avenues of professional dissemination. However, though service to the open access movement and crossing political and cultural boundaries to serve the growing academic needs of developing countries are important matters that should not be minimized, I will use the space remaining in this paper to address an issue that is not commonly a part of the literature—the literature concerning electronic resources in philosophy, at least—and that ties more centrally to the exigencies of representing philosophy itself.

2.1 Profession, know thyself! The first release of Noesis was dedicated to scholarly articles and primary historical texts, much like the impressive PhilPapers project recently put online by David Bourget and David Chalmers. (See http://philpapers.org/.) In the latest release, Noesis expands beyond the scholarly output of philosophers to include information tied to the social and administrative aspects of the profession and the way that the profession taxonomizes itself in the form of professional associations, conference programs, tables of contents, bibliographies etc. In short, we are now interested in mapping the profession of philosophy as it is practiced and not solely in terms of its scholarly output. In this way, Noesis represents parts of the profession that are not typically included in conventional representations of the discipline, but that are nonetheless a part of the way that philosophy gets practiced and determinative of its direction in history. (See Morrow and Sula 2010 elsewhere in this volume, for hints about how social elements of the profession might be relevant here.) The profession of philosophy is so varied that it is possible for someone to be at the center of one of its parts and virtually unknown to people working elsewhere within it, as demonstrated by a recent exchange on the Philos-L mailing list concerning the status of the intellectual accomplishments of Slavoj Zizek. (Some people were arguing that he was a non-contender and a “no name” in philosophy, while others were arguing that he was something of a shining star with maximal impact on certain sectors within the profession. It turns out, by the way, that he is an important figure, but that his research is not disseminated in what, according to some, are the “more mainstream” sectors of philosophy.) Professional blind spots are easily created by the fact that we often take our exposure to the profession to be representative of the whole, even while we realize that we only frequent the venues or read the texts that suit our research and teaching interests. Anecdotes abound about what is going on elsewhere in the profession, and they often substitute as evidence of the true state of affairs, leading to value claims about what is important and what is not. (I am not making indictments

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here. Human reason is limited by perspective and this limitation, of course, affects our judgments, even when we are careful to employ reason “objectively”.) Furthermore, the fact that other people share my judgment often looks like corroborative evidence in favor of its objectivity, when it may mean only that my view is popular (and among my interlocutors, at that!), especially if those sharing my views were indoctrinated into the profession by the same teachers, institutions, or schools of thought. Even though most of us in the profession are trained in informal fallacies and other strategies of poor reasoning, we often seem to succumb to them all the same, especially when it comes to “water cooler” talk about the profession that nonetheless has an impact on people’s careers and the direction of the discipline. In the past, appeal to anecdote was perhaps excusable, given that other kinds of evidence were not readily available. In the absence of access to facts on the profession, impressions were allowed to suffice, but this situation is changing quickly. Recent changes in communications technology over the past decade and a half make it easy for us to study neighboring and distant institutions, look up the scholarly credentials of our colleagues, see who has published what and when, and also how such publications are being received etc. Since 1994, a new data pool on the profession has emerged, and while it is already present in piecemeal form to anyone wishing to have a look, it has yet to be collected, collated and cataloged. Here is one place, then, where a tool like Noesis can be instrumental in making us self-reflective about the profession we practice and our place within it. Without going into the details of data mining (and admitting that we still have a way to go with what is really still an emerging technology), it is possible to identify a variety of empirical data on the profession that are already available in the Internet terrain that will be marked out by Noesis’ geographical search space strategy. Here is a partial list, leaving out for the moment items that refer to philosophical content and acknowledging that a significant amount of information on content is available as well: • which departments have the widest diversity of faculty in terms of coverage, • which departments are focused on particular topics and the relative strength of their faculty, where strength is defined according to a variety of user-configurable criteria, • which departments are the most unstable in terms of faculty departures and arrivals, • which types of courses are most frequently taught where, • which universities are most successful at placing their graduates in teaching positions, • which undergraduate institutions fare best at placing their graduates into top graduate programs and, ultimately, into the profession, • which scholars are most widely published and with whom they are most often published. The answers to such questions (and others like them) that we will be able to cull from Noesis in time will not be like the impressions and anecdotes that have powered our discipline in the past. They will be data-driven answers that reflect in real-time genuine quantitative metrics about a constantly changing profession. In this connection, I cannot resist the need to mention here The Philosophical Gourmet, compiled by Brian Leiter and, hence, also known as the Leiter Report, a

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website that purports to provide metrics on “faculty quality and reputation” for Ph.D. granting philosophy departments in the English speaking world. (See http://www. philosophicalgourmet.com/.) The fact that the report has become the standard metric of overall departmental ranking, despite its claims to the contrary, in just a short time attests to the fact that metrics are needed. At the same time, it demonstrates how quickly the Internet can act in getting information out that can restructure our profession, since it is no longer uncommon to hear professionals speak of “Leiter rankings” in the hiring of faculty or to find graduate students acknowledge that the Leiter Report weighed heavily in their selection of a graduate program. Reports such as these may present themselves as descriptive, but their use makes them prescriptive. If philosophy has anything to offer the success of our species and the well-being of its individuals, it is imperative that we represent it adequately, optimally, fairly, and accessibly. Given that how philosophy is represented determines in no small measure what philosophy is, both in theory and in practice, and what it will become, attempting an accurate and adequate representation might be something of a moral imperative as well, and this applies no less to metrics about faculty quality and reputation than it does to other aspects of the profession. Such reports therefore should invite caution and careful scrutiny. In the case of The Philosophical Gourmet, for instance, 95% of the advisory board for the 2009 Leiter Report work at Leiter ranked schools, and 57% of them work at schools that are ranked in the top ten for their respective countries. More importantly, however, is that 80% of the respondents surveyed to determine the rankings have connections to schools that ranked in the top ten for their respective countries, while a full 97% of them have connections to schools somewhere in the rankings. 81% of the respondents work at Leiter ranked schools, and 93% of them went to ranked schools. Furthermore, the institutions to which respondents are connected are distributed across the top of the rankings. I just noted that 80% have connections to top ten schools. But 15% of them have connections to secondranked (overall) Oxford, 10% to fourth-ranked Princeton, 8% to third-ranked Rutgers and another 8% to seventh-ranked Harvard. Even though respondents are not allowed to rank their home institutions or those from which they received their degree, it is still quite clear that people from a handful of institutions are handing out high marks to other institutions in that same handful to the neglect of several institutions that are not presented for assessment in the first place. Leiter explains: The survey presented 99 faculty lists [from institutions up for assessment], from the United States, Canada, United Kingdom, and Australia and New Zealand. Note that there are some 110 Ph.D.-granting programs in the U.S. alone, but it would be unduly burdensome for evaluators to ask them to evaluate all these programs each year. The top programs in each region were selected for evaluation, plus a few additional programs are included each year to “test the waters” (http://www.philosophicalgourmet.com/reportdesc.asp). Top programs are pre-selected to determine which of the existing programs are in the top. Certainly, something smells a little fishy, and even an undergraduate in a critical thinking class would be tempted to see several fallacies operating here. Notwithstanding the possibility that Leiter may have hit on a heuristic of some sort that does in fact track faculty quality and reputation across the profession, the fact remains

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that his anecdotal survey approach can only leave us guessing about this possibility. We need some way either to verify or debunk the report, and here is one place where Noesis may be able to help. Furthermore, given the wealth of information about the profession that is available online and what is at stake, soon there will be simply no need to fall back on such simple anecdotal measures in any case. I suspect that we will find they are not worth much, or perhaps more so, that genuine evidence may provide us with better intuitions about the profession and reshape our anecdotes to fit better with the actual state of affairs. Noesis’ contribution to this issue of acquiring knowledge about the profession here is akin to the one mentioned above about testing the adequacy of the Stanford Encyclopedia of Philosophy as a representation of the semantic content of the profession. Though various data mining techniques will, no doubt, prove useful over time, the planned custom and dynamic search space strategies described above go part of the way toward responding to the need for adequate information. Using the procedures outlined above, we will be able to partition the profession in any way we see fit, run a set of searches across the various partitions and compare the results. Thus, comparative analysis is one of the affordances that will emerge naturally from Noesis. Though human users will be able to build their own partitions for comparative purposes, more interesting exploration will, no doubt, follow from automated procedures that create, compare and then adjust partitions until evidence-based sectoring gives us a computermediated picture of what the profession looks like. There is no reason to think that such a picture be static or that there be a single picture either. Dynamic representations and representations adjusted to serve a variety of user-defined purposes are definite possibilities. 3 Conclusion The really interesting work for the Noesis project is in the next phase of development. For now, we are interested in circumscribing the profession of philosophy online, building an evidence pool as it were, a search space, for further analysis down the line. Even without the vision of the profession sketched immediately above, Noesis promises to offer an unprecedented access to philosophy as it is practiced in real-time. Combined with other tools, such as the InPhO, we will provide a research tool never before possible in history. Acknowledgments This paper and the development of Noesis announced herein are possible because of a 2008–2009 Digital Humanities Fellowship awarded to me by the National Endowment for the Humanities. I would like to thank Peter Suber for our many conversations about Noesis over the past decade and Colin Allen for his help in developing the project further and commenting on this paper. Though several people have worked on Noesis over the years, five programmers are particularly invested in the project: Josh Burger, Brian Moffat, Siddartha Naidu, and, most critically, Hiten Sonpal and Trent Kriete. I would also like to acknowledge Eric Steinhart and two anonymous reviewers for their helpful comments on this paper. Any views, findings, conclusions, or recommendations expressed in this publication do not necessarily reflect those of the National Endowment for the Humanities.

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References The papers below that discuss earlier versions of Noesis present some ideas that will never be developed. Over the past decade unanticipated changes in technology have somewhat resituated the project’s direction. The current paper represents our most recent vision along with a summary of highlights from the earlier versions. Beavers, A. (1998a). Evaluating search engine models for scholarly purposes: A report from the internet applications laboratory. D-Lib Magazine: The Magazine of Digital Library Research, The Corporation for National Research Initiatives, December. Beavers, A. (1998b). Noesis: Philosophical research on-line—An experiment in progress. Newsletter on Philosophy and Computers, American Philosophical Association, Vol. 98.2. Buckner, C., Allen, C., & Niepert, M. (2010). From encyclopedia to ontology: Toward dynamic representation of the discipline of philosophy. Synthese (current volume). Hölscher, C., & Strube, G. (2000). Web search behavior of Internet experts and newbies. Computer Networks, 33, 337–346. Jansen, B., Spink, A., & Saracevic, T. (2000). Real life, real users, and real needs: A study and analysis of user queries on the web. Information Processing & Management, 36.2, 207–227. Leiter, B. (2009). The 2009 philosophical Gourmet report: Brian Leiter’s ranking of graduate programs in philosophy in the English-speaking world. Retrieved on March 31, 2009, from http://www. philosophicalgourmet.com/. Linden, G., Jacobi, J., & Benson, E. (1998). Collaborative recommendations using item-to-item similarity mappings. Patent number 626649. Google Patent Search. Retrieved on March 31, 2009. Morrow, D., & Sula, C. (2010). Naturalized metaphilosophy. Synthese (current volume). Niepert, M., Buckner, C., & Allen, C. (2007). A dynamic ontology for a dynamic reference work. In E. M. Rasmussen, R. R. Larson, E. Toms, & S. Sugimoto (Eds.), Proceedings of the 7th ACM/IEEE-CS Joint Conference on Digital Libraries, June 18–23 (pp. 288–297). BC, Canada: Vancouver. Shatz, D. (2004). Peer review: A critical inquiry. Lanham, MD: Rowman & Littefield. Simon, H. (1965). The shape of automation: For men and management. New York: Harper & Row. Spink, A., Wolfram, D., Jansen, B., & Saracevic, T. (2000). Searching the web: The public and their queries. Journal of the American Society for Information Science and Technology, 52.3, 226–234. Suber, P. (2002). Noesis: Is it a library with built-in searching or a search engine with a built-in library? Campus Technology. The ISC Domain Survey. Internet Systems Consortium. Retrieved on March 31, 2009, from https:// www.isc.org/solutions/survey. Uzgalis, B. (2000). Searching phenomenology and cyberspace: An interview with Anthony Beavers. Newsletter on Philosophy and Computers. American Philosophical Association, Vol. 00.1.

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