The Russell-Meinong Debate Janet Farrell Smith
Philosophy and Phenomenological Research, Vol. 45, No. 3 (Mar., 1985), 305-350. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28198503%2945%3A3%3C305%3ATRD%3E2.O.C0%3B2-X Philosophy and Phenomenological Research is currently published by International Phenomenological Society.
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Philosophy and Phenomenological Research Vol. XLV, NO. 3, March 1985
The Russell-Meinong Debate:' J A N E T FARRELL S M I T H
University of Massachusetts at Boston
I. INTRODUCTION The debates between Bertrand Russell and Alexius Meinong from 1904 to 1920 dealt with some fundamental issues in philosophy: reference, nonexistent objects, intentionality. Along with the enduring influence of Russell's philosophy, some misapprehensions about these exchanges have persisted. One is that Russell's objections to Meinong were definitive. The other stems from taking too seriously Russell's casual remark in 191 8 that Meinong's theories evidenced a deficient "sense of reality." Contrary to the impression left by this comment, Russell, during the most intensive years of the debate (1goq-1907), felt a real respect for Meinong's theories,' and his main concern lay elsewhere. The exchange did not center on "reality" or "realism," as is often believed, but on the classical laws of logic (noncontradiction, excluded middle) and the correct analysis of logical form, for instance, of existence statements. Russell also took a dim view of the modal concepts Meinong used to support the canons of object theory, but his main concern was that Meinong's overall analysis appeared to threaten the foundation of Russell's philosophical logic. Russell and Meinong's disagreement thus came down to competing logicai frameworks tied to different notions of what it is to be an object. In claiming that Russell's main objection to Meinong's theory was logical, I d o not mean to deny that ontology and metaphysics were in the forefront of Russell's concerns up to 1910 or that for him a correct foundational view of logic would tell us much about the way the world is. Russell's motivation for criticizing Meinong may well have been a concern with what is 'real', but his philosophical reasons for rejecting Meinong's *
0 1985 by Janet Farrell Smith See the newly published Theory of Knowledge, The 1913 Manuscript, Vol. 7 of Russell's Collected papers, edited by Elizabeth Eames and Kenneth Blackwell (Allen and Unwin, 1983). This manuscript, which contains many accurate references to Meinong's theories, was never published by Russell. He was apparently discouraged by Wittgenstein's criticism of his theory of judgment.
object theory in 1905-1907 had to do with logical principles and their reputed violations. Interestingly, during the years Russell was debating with Meinong most intensively (1904-1907) he was also struggling to find the solution to his paradox of classes. With his 1905 invention of the theory of descriptions, Russell believed he had simultaneously found a way to deal with apparent reference to nonexistents in ordinary grammar and a new analysis of classes. It seems that the two difficulties of paradoxical classes and nonexistent objects plagued Russell's sense of consistency in a parallel manner. In this paper I focus on giving an internal analysis of the objections and replies exchanged by Russell and Meinong to show that Russell's objections failed to be decisive and that the standoff between them came down to fundamentally different frameworks. Some scholarly evidence supports this interpretation as well. Russell's 1904 letter to Meinong emphasizes that what Meinong called "Theory of Objects" Russell had been accustomed to calling "Logic." [See Appendix]' In pressing his contradiction charge, Russell continued to evaluate Meinong's object theory by the standards of his own view of "logic." Lastly, evidence of a more circumstantial nature points to the parallelism of Russell's worries over nonexistent objects and classes. There are many issues of influence and disagreement between Russell and Meinong which I must leave out of this treatment. Russell's analysis of the nature of sensory awareness in his doctrine of acquaintance owes much to the Brentano-Meinong doctrine of intentionality and Vorstellen. To Meinong's theory of assumptions Russell reacted first with objections [ ~ q o qMTCA] , and then with sympathy [1913, TK]. The full complexities of intentionality of reference would require an essay of equal length, so I do not claim to deal with these here.' In addition, Meinong's views deserve attention in their own right, particularly his theories of mental apprehension and his object t h e ~ r yWhile . ~ some aspects of the latter will be mentioned, here I concentrate mainly on Russell's objections and Meinong's replies to them.
'
The Appendix contains translations of Russell's three letters to Meinong. See also the chronological Bibliography at the end of this paper. References to the key works are abbreviated in the text as noted in the Bibliography. See Roderick Chisholm, Brentano a n d Meinong Studies (Amsterdam: Rodopi, 1982), and The First Person, An Essay on Reference a n d Intentionality (Minneapolis: University of Minnesota Press, 1981). Some issues are treated in my "Meinong's Theory of Objects and Assumptions," in Phenomenology: Dialogues a n d Bridges, ed. R. Bruzina and B. Wilshire (Albany: State University of New York Press, 1982). In a longer study of book length I explore these and other issues in greater depth.
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There is one persistent confusion about Meinong's object theory which should be clarified at the outset. In "Theory of Objects" Meinong distinguished between (i) existing objects [signified by the verb 'Existieren'], e.g., concrete objects in space time, (ii) subsistent objects, e.g., abstract objects such as relations or objectives [which do not exist but have the kind of 'being' Meinong called 'Bestehen'], and (iii) nonexistent, nonsubsistent objects which possess no being of any kind, but are "beyond being and non-being."" Probably because of his doctrine that every object which is thinkable or can be mentioned has "being," Russell tended to assimilate Meinong's objects in category (iii) to category (ii). Thus when Russell ascribed "being" to Meinong's nonexistent, nonsubsistent objects (round squares, gold mountains), sometimes tacitly in the 1905-1907 period and later explicitly in 191 8, and 1943, he was missing a crucial distinction in Meinong. He was also missing a crucial principle of Meinong, the Independence of Sosein from Sein (Independence of being-so from being), which allows meaningful predications and true (or false) values assignable to these predications "whether the object has being or not.'' [TO, 861 The issues in this essay will be treated in the following order. Misleading impressions of Russell's rejection of Meinong are treated in the next section, 11. Section 111 summarizes each of Russell's objections and Meinong's replies. Section IV examines the pivotal paper "On Denoting" while Section V explores Russell's further objections to Meinong's replies. Sections VI and VII deal with Russell's "chief objection" to Meinong around contradiction. In Section VIII, Russell's classical logical framework is contrasted with what might have appeared to him as the "deviance" of Meinong's framework. Circumstantial evidence associating Russell's paradox of classes with his concern over nonexistents appears in Section IX. Section X suggests some overviews of the debate.
11. THE CONVENTIONAL ABANDONMENT THESIS According to the conventional thesis, Russell abandoned nonexistent objects and rejected Meinong's theories because he finally came to his senses. He overcame his youthful flirtation with such objects and rejected The "principle of the indifference of pure Objects to being" [Der Satz vom Aussersein des reinen Gegenstandes] allows nonexistent objects to be considered apart from any consideration of existence (or subsistence). See TO, 86. Although he spoke of the "infinitely graded abundance of Aussersein" in On Assumptions [OA, 1971, Meinong placed less emphasis on it after 1905.In discussing Russell's views I shall sometimes use the term 'nonexistent objects' to refer to those objects in category (iii), "beyond being and non-being" or Ausserseiend, although this should be understood strictly in the technical sense.
them for wreaking havoc with that "sense of reality" which he decided ought to be preserved everywhere in philosophy, even in logic. Russell went on to discover his sensible and brilliant theory of descriptions, and then to carve down the realism of his 1903 principle^.^ After vanquishing Meinong, Russell could settle into building the edifice of Principia. The "reformed Russell" proceeded anew on the questions of knowledge by description and with a new philosophy of language. This version of history interprets the course of development of Russell's philosophy primarily in terms of a concern with "reality" and "realism." The view is compelling and dramatic. Russell himself lends support to it when he says (not mentioning his own Principles ontology) in "My Mental Development" in 1943: "The desire to avoid Meinong's unduly populous realm of being led me to the theory of descriptions." [MMD, 131 This view, however, is partial at best and capricious at worst. The 1943 comment misrepresents the status of Meinong's objects as "Daseinfrei" [existence-free] and "Jenseits Von Sein und Nichtsein" [beyond being and non-being]. In his 1905 review of Meinong's "Theory of Objects," Russell did accurately characterize Meinong's position: [Theory of Objects] is not identical with metaphysics, but is wider in its scope; for metaphysics deals only with the real, whereas the theory of objects has no such limitations. [RTO, 781
In the same paper, Russell acknowledged Meinong's theory that mathematics "never deals with anything to which existence is essential" [RTO, 781, in contradistinction to his own 1903 theory in which classes, for example, exist. It was not, therefore Meinong's populous realm of being which disturbed Russell, but Meinong's populous realms of objects outside of both being and nonbeing. Perhaps, as some have suggested, it was also Russell's own populous realms of being which dimly merged in his
In addition to the oft-quoted passage in Principles of Mathematics on "Being" which is "that which belongs to every conceivable term, to every possible object of thought," [449] there are the further points that (i) "Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, 1 call a term. . . . A man, a moment, a number, a class, . . . a chimaera, or anything else that can be mentioned, is sure to be a term." [43] and (ii) "The proposition 'A is' . . . holds of every term without exception. The is . . . may be regarded as . . . really predicating Being of A," [49] In the Principles, Russell also recognizes nonexistent objects (which nevertheless have being): "Existence [in contrast to being], on the contrary, is the prerogative of some only amongst beings. To exist is to have a specific relation to existence . . . What does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being as that which belongs even t o the non-existent." [450] [Emphasis Added] Thus Russell recognizes objects which do not exist but have being (chimeras), whereas Meinong takes the further step of recognizing objects which do not exist, do not subsist, and have neither being nor non-being.
memory with Meinong's Daseinfrei objects. Having recognized Meinong's point that a theory of objects is independent of a theory of their apprehension, and that this independence has been obscured by what Meinong called the "prejudice in favor of the actual" [des Wirklichen, which Russell in 1905 translated as 'the existent'], Russell proceeded in later years to assimilate Meinong's theory to a set of views which Meinong did not hold. What led Russell to pass from respectful acknowledgment even of views he disagreed with from "so excellent a writer as Meinong" [POM, 4 I] to comments after 19 I 8 about Meinong's deficient feeling for reality? In his 1904 review of Meinong's O n Assumptions (1st ed.), Russell lavished praise on Meinong's methodology.' The Principles of 1903 is peppered with citations of Meinong's theories of magnitude and quantity. The 1910 and 1914 articles on knowledge by acquaintance credit Meinong with basic notions in Russell's theory. [See KAKD, NA] Russell's 1913 book on Theory of Knowledge details Meinong's views with attempts at technical accuracy. Two kinds of reasons emerge. One concerns the philosophical order of the debate, while the other has to do with a shift in Russell's philosophical enterprise. First, the Russell-Meinong debate can be seen as involving three aspects which did not necessarily coincide with the order in which the arguments were given. There is (i) the ancient question whether or not we refer to nonexistents, (ii) the 'ontological' or 'object-theoretic' [to use Meinong's nonprejudicial term] debate over such things as nonexistent entities, and (iii) the disagreement over sets of logical principles entailed by answers to the first two questions. The first aspect of the debate has so far received most attention in twentieth century philosophy of language. It involves questions such as the correct logical form of sentences allegedly referring to nonexistents, questions which Russell maintained Meinong answered wrongly due to his mistake of taking 'the round square', for example, as the logical as well as the grammatical subject of sentences beginning with that phrase. Russell countered his theory of descriptions to such an analysis. The second aspect of the debate involves issues on the nature of 'objects' or entities in general and whether or not they need always be actual. Russell argued against non-reducible modal properties which Meinong used to distinguish possibles and actuals. During 1904-1907, Russell's "chief objection" to Meinong's theory, however, lay in its
' "There is an empirical manner of investigating, which should be applied in every subjectmatter. This is possessed in a very perfect form by the works [Meinong's] we are considering." [MTCA, 27.1
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alleged violation of the law of noncontradiction. [RTO, 801 Thus the third aspect of the debate concerns the logical assumptions and framework which stand behind each theory. This stage of discussion can be found in writings less scrutinized, less available, but no less important in the assessment of the debate. To Russell's mind these issues may have been decisively closed by his objections on logical grounds and by his analysis in the theory of descriptions. So, he moved on to other concerns by 1918, emphasizing his "reality" comments and the questions on misleading grammatical form.' Around 1914 Russell's focus shifted from building the foundations of logic in Principia to applying its logical techniques to questions in theory of knowledge and metaphysics. Consequently he became more concerned with his method of logical construction. During the in'tensive debate with Meinong (1904-1907) he was still settling the major questions of analysis in Principia and (as will be discussed below in Section IX) searching for the proper solution to the paradox of classes. Indeed it is remarkable that, for all their notoriety, the "robust sense of reality" comments cannot be found until 1918, and then, interestingly, not only in connection with Meinong, but also with the proof of the of the axiom of infinity. [See IMP, 135, 14, 169. Also PLA, 216, 223-241 By 1918 what is "real" is informed not only by Russell's logical realism but also by his more clearly delineated empiricist theory, e.g., of sensedata. Russell in 1918 also tended to apply Occam's razor and adhered strongly to a principle of parsimony. ["Whenever possible, substitute constructions out of known entities for inferences to unknown entities."] Russell spoke of the 'inventory' of things there are in the world: In accordance with sort of realistic bias that 1 should like to put into all study of metaphysics, I should always wish to be engaged in the investigation of some actual fact o r set of facts, and it seems to me that that is so in logic just as much as it is in zoology. [Emphasis added] [PLA, 2161
By so delineating the scope of his metaphysics Russell ruled out in advance consideration of possible object^.^ There is another factor which may have offended Russell's sense of logical consistency, namely Meinong's deliberately paradoxical mode of expressing the odd status of nonreal objects:
There is some Archival material [drafts and notes] indicating that Russell became disenchanted with the Brentano doctrine of intentionality sometime in 1918, during his stay in Brixton prison where he wrote IMP. This move might indicate a change of sympathies with many of Meinong's views. See [AM, 14-19]. Not only Meinong's possible objects but also his own possible sense-data.
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Those who like paradoxical modes of expression could very well say: 'There are objects of which it is true that there are no such objects'. [TO, 831"
But such comments could be compared with Russell's own claim that the so-called "real" desk is "reduced to being a logical fiction." [PLA, 2731 He also said: I have so far talked about the unreality of the things we think real. I want to speak with equal emphasis about the reality of things we think unreal. [PLA, 2741
The issue of "real" objects will be pursued further in Section VII below. In the following sections I isolate and analyse the actual arguments which Russell lodged against Meinong and assess Meinong's replies. 111. SUMMARY OF THE ARGUMENTS The following are the major explicit objections Russell brought against Meinong's nonexistent objects. & NoncontraThe objects' "intolerable" violation of the ~ a of diction. [OD, RTO, RUSG] The mistaken views of existence and the embedded ontological argument involved in some nonexistent objects. [RTO, Letter 1904, RUSG] Rejection of modal notions required to define objects. [MTCA, Letter 19061 The objects' violation of the Law of Excluded Middle. [OD, Letter 19061 Mistakes in truth-value for some of the propositions following from Meinong's views. [OD, IMP, PM] Russell's contention that denoting phrases are not the proper logical subjects of propositions, that Meinong mistakenly assumed they have a subject-predicate logical form and, hence, mistakenly assumed that phrases such as 'the round square' denote nonexistents. [OD, IMP, PLA] Russell's claim that his theory of descriptions offers overall a superior and more efficient logical analysis than does Meinong's [or Frege's]. [OD]
lo
Chisholm remarks that the following translation would be closer to Meinong's intent: "It can be truly said, of certain objects, that these objects do not exist." Introduction to Realism and the Background of Phenomenology (Free Press, 1960), p. 8.
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(8)
Russell's claim that the postulation of nonexistent objects in literary, fictional and mythical contexts is deficient in the "feeling for reality" which logic ought to preserve, i.e., attention to the "actual" world. [PLA, IMP]
Meinong's philosophy provides an answer to each of the above. The Law of Noncontradiction was meant to apply to actuals and possibles, not to impossible objects. [USG] Existence is an "extranuclear predicate," i.e., not a determining predicate like ordinary predicate expressions ('red'). [USG, UMOG] Modal notions are critical for delineating the possible from the actual, and the possible from the impossible. [UA, USG, UMOG] Certain objects are "incomplete" and therefore not determined with respect to certain predicates. Negation must be distinguished in 'narrower' and 'wider' senses. [OA, USG, UMOG] The Principle of Independence of Sosein from Sein [of Being-so from Being] allows objects to take on properties regardless of their existential status and thus for true sentences to be made about nonexistent objects. [TO, USG, OA] Expressions such as, e.g., 'round square', 'gold mountain', have a Bedeutung [signification]. This signification is connected to language in use within a community. It is "as a part of life, . . . a signifying for someone." [Intentionality of Reference] P A , 251 Russell's analysis leaves aside some important questions. [USG] [See (37, (47, (871 The "prejudice in favor of the actual" in metaphysics restricts our attention to merely actual objects whereas there are many other types of objects which should be considered. This approach is fully compatible with "respect for facts." [OA, 292, TO, USG] [See also (3I)] Since Meinong did not provide a formal logical system for his theory of objects, a full defense against Russell's objections in (7) must be constructed using current formulations of alternative logics [e.g., Routley], free logic [Lambert], or a formal semantics of nonexistent objects [T. Par-
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sons]." Aspects of these philosophers' contributions are discussed below. Objections ( I ) and (6) are most familiar to many philosophers while some know only of (8). Meinong and Russell did not directly argue about (6'), which will be mentioned here only briefly. Russell did, however, claim that on his analysis of propositional attitudes, propositions containing definite descriptions in secondary occurrence turn out to be true. So his theory captures certain intentional idioms. Meinong's (6') presents a linguistic version of the Brentano doctrine of intentionality, that mental experiences are "directed towards" objects, or Gegenstande in Meinong's terminology. Gegenstande break down into Objekte (translated as 'objects') and Objektiue ('objectives'). The former are objects of ideas. The latter are objects of assumptions or judgments. To illustrate, my idea of a mountain concerns an Objekt which is embedded within an objective (that a mountain is gold) which may in turn be the object of my assumption or judgment. Objectives according to Meinong are like states of affairs except that they need not be factual. They subsist when their corresponding sentences are true, and fail to subsist when their corresponding sentences are false. Where (7') is concerned, existence is never a property of an Objekt but pertains only to objectives.
IV. RUSSELL'S ARGUMENTS I N " O N DENOTING" The year 1905 marked a watershed year in Russell's philosophy. With the theory of descriptions Russell rejected some of his previous key tenets in philosophy of language. First was the break with the equivocal doctrine of being in the 1903 Principles of Mathematics which distinguished between "Being" and "Existence." [POM, 43, 71, 4491 The 1903 view that "Being is that which belongs to every conceivable term, to every possible object of thought" assigned being to imaginary and fictional entities such as Apollo, the chimera, Hamlet. Such objects, which Russell might have expected to reside in Meinong's realm of subsistence [Bestand], were in Meinong's "Theory of Objects" relegated to the status of the "Aussersein of the Pure Object." Aussersein, which is really a way of declassifying objects as outside of being and nonbeing altogether, apparently troubled Russell in 1904. He remarked in a letter to Meinong:
" Richard Routley, Exploring Meinong's Jungle and Beyond (Monash: Australian National University, 1980). Karel Lambert, Meinong and the Principle of Independence (Cambridge University Press, 1983). Terence Parsons, Nonexistent Objects (Yale University Press, 1980).
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I have always believed until now that every object must be in some sense, and I find it difficult to recognize nonexistent objects. [See Appendix]"
Russell accordingly rejected his former doctrine that "every term is a logical subject." [POM, 441 He required what we can interpret as a strong presupposition of existence on the designatum of each logical subject (or referring expression). Russell devised a new logical analysis in which denoting phrases such as 'the round square' need not be taken as standing for anything whatsoever. Such phrases are not logical subjects in the propositions in which they occur. "On Denoting" presents this new viewpoint, announcing rather than explaining in detail the shifts which Russell had made. Russell did make explicit his 'fundamental principle', which, taken together with his assimilation of existence to the ekstential quantifier, allows the interpretation that he now requires that each genuinely referring expression must designate what exists. He had a solution for what to do with apparent 'constituents' of propositions denoted by phrases such as 'the present King of France': The propositions in which this thing is introduced by a denotingphrase do not really contain this thing as a constituent, but contain instead the constituents expressed by the several words of the denoting phrase. [OD, 561
The 'fundamental principle' that each proposition is reducible to its constituents was now stated in its version based knowledge by acquaintance: Thus in every proposition we can apprehend (i.e., not only in those whose truth o r falsehood we can judge of, but in all that we can think about), all the constituents are really entities with which we have immediate acquaintance. [OD, 561
Its ontological version would become important in the arguments with Meinong. Let us now turn to an analysis of the actual text of "On Denoting" and Russell's objections against Meinong. Russell featured objections ( I ) (violation of the Law of Noncontradiction) and ( 6 ) (objection from reference and logical form). He also mentioned ( 5 ) (mistaken truth-value), implied (4) (violation of the Law of Excluded Middle), and claimed (7), that his own theory provided a superior analysis to that of Meinong on alleged reference to nonexistent objects.
" Russell can be interpreted as follows: If an object is [an object] then it must have being of some kind. He has never thought that there could be an object which does not have being. [Cf. the "Being" passages of POM] Hence Meinong's Ausserseiend, "pure" object forces the issues more sharply for Russell although his way of putting the question is least sympathetic to Meinong's position. The very question, "How could there be an object which does not have being?" implies self-contradiction if "to be" is univocal.
Take (6) first, as Russell does. Russell's objection (6) consists in denying, contra Meinong, that denoting phrases function referentially:(6) is therefore a linguistic or semantic objection rather than an ontological objection to Meinong's theory. Russell claims that the evidence for his own theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meino w . [OD, 451
In this passage, Russell seems to be assuming that propositions are timeless objective unities reducible to components, i.e., 'constituents' which have being. [Cf. the 'fundamental principle'] Propositions are then expressed by linguistic constructions of which denoting phrases are a part of the grammatical form, but not, as Russell emphasizes, proper units of the underlying logical form. Russell does not then state precisely which "difficulties'' are involved in regarding denoting phrases as standing for "genuine constituents.'' But from the swift passage to the objection on contradiction, it appears that his objection is logical. Russell says the view that the present King of France is a genuine object, yet does not subsist (or have being in any other way) is "in itself a difficult view," (a point Meinong would confirm). He does not offer an explanation. His next point, however, may reveal one reason. Russell views these objects as "apt to infringe the law of contradiction." There cannot be anything which is contradictory. Therefore there are no such objects. If this is Russell's reasoning, the objection from reference (6) resolves to the objection on contradiction ( I ) . Let us take a look at that entire passage. [Meinong's] theory regards any grammatically correct denoting phrase as standing for an object. Thus 'the present King of France', 'the round square', etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round, etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred. [OD, 451
There is a tacit premise in Russell's reasoning here, that every proper constituent of a proposition has being. His assumption, taken over directly from his theory of denoting in the 1903 Principles of Mathematics, is consistent with the notion that, e.g., a unicorn has being in a weak sense, and so could function as the denotation of an expression in subject position. But if the denotation is self-contradictory, then the object cannot be, and therefore cannot be a constituent of a proposition. Another tacit
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premise is that there cannot be (in any sense of being) contradictory objects. The argument for this premise is complex enough to warrant treatment in a separate section on contradictions. (See Section VI below.) Russell's dilemma here consists in either dropping the assumption that each constituent of the proposition has being or exists, or giving some criterion for singular terms which do denote vs. those which do not denote. If he fails to deal with the anomaly of phrases which denote contradictory objects, he thinks he is faced with a contradictory theory of denoting. Russell's solution consisted in "abandoning the view that denotation is what is concerned in propositions which contain denoting phrases." [OD, 461 By sweeping away the possibility that a difficulty of this kind could occur, he cured Meinong's theory and his own former theory of anomaly. His theory need not give a criterion for referring vs. nonreferring singular expressions since the only kinds of singular terms which guarantee their own denotation are what he later called 'logically proper names'. Russell groups Meinong and Frege together on the strategy of providing a denotation "at first sight absent" for dealing with cases where a denoting phrase lacks reference within a proposition. Meinong provides the denotation by delivering up nonsubsistent objects, which Russell has already argued to be unacceptable because of the violation of the law of contradiction. Frege assigns the conventional denotation of the null class to nondenoting descriptions. Meinong's strategy is "to be avoided if possible." Frege's strategy is not quite so bad, according to Russell, but is artificial and lacks exactitude, although apparently it does not involve logical difficulties. Once again Russell does not express his reasons for dissatisfaction. What is unstated is the appeal to argument (7), namely the superiority of Russell's own method, exercised in the entire article. If we were to ask 'Why is it superior?', the answer might be "Because it avoids contradiction and the artificial null class assignment." Russell does not argue that here, but goes on to a demonstration of how his theory attacks three puzzles he thinks any good theory of denoting should solve. Each of the three puzzles in "On Denoting" concerns one of the major laws of classical logic. Russell evidently regards his solution in each case as superior to the alternatives because he preserves the integrity of each law more effectively. In the first puzzle he claims to provide a better solution than Frege while the second two relate to Meinong's theories. Puzzle I. Substitutivity of Identity. The first puzzle deals with the inference from 'George IV wished to know whether Scott was the author of Waverly', by substitutivity of identity (Scott = Waverly) to 'George IV wished to know whether Scott was Scott.' To forestall the inference Rus-
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sell paraphrases the first proposition so that 'the author of Waverly' is not a proper constituent to which the law can apply. Thus, the law remains intact without restricting its range of application. Russell thus avoids Frege's theory, which he had adopted in his 1904 letter to Meinong. For the above puzzle Frege's theory dictates that the reference of a description in indirect context takes its ordinary sense rather than its ordinary denotation. In evading Frege's solution, Russell avoids an entity which he might have regarded as uncomfortably close to certain of Meinong's suspect objects. The Fregean Sinn multiplies the number of types of objects to be reckoned in a theory of denoting, and in Russell's view, presents problems on how to relate the Sinn and Bedeutung. If, in Russell's view, we cannot get a,clear logical theory of how the two are related, how can one be substituted for the other by the law of substitutivity? This argument might have been Russell's thinking as he proposed his own solution. Puzzle 2 . The Law of Excluded Middle. The second puzzle concerns how either 'The present King of France is bald' or 'The present King of France is not bald' must be true if the present King of France occurs neither on the list of bald things nor on the list of things which are not bald. Here Russell takes a jab at the Hegelians, but his 1906 letter to Meinong [Appendix] confirms that he intended to dispense with the present King of France as well, an object whose disappearance Meinong apparently protested. Here objection (4)' that nonexistent objects disobey the law of excluded middle, seems to be implied. Meinong's solution to puzzle 2 would be to say that nonexistent objects are indeterminate with respect to some properties and do not conform to the law. E.g., the present King of France is not determinate with respect to baldness, and therefore the two propositions 'The present King of France is bald' and 'The present King of France is not bald' are neither true nor false. Russell's discussion does not mention Meinong's theory of incomplete objects, which was in any case not yet fully formulated at the time. [UMOG, 19151. But Russell was clearly aware of the threat to the law of excluded middle. His own solution depends on his analysis of ambiguity in ordinary language into 'primary' or 'secondary' occurrences of the denoting phrase in question. The affirmative proposition (i) 'The present King of lance is bald' is false because of the entailed existential presupposition 'there exists an object such that it is the present King of France'. When the occurrence of the denoting phrase is primary in the negation of (i),the result is false. When the occurrence of the denoting phrase is secondary, the proposition is true. [OD, p. 531 (i)
The present King of France is bald. (False) (Ex) (y) ((Fy . = .x = y) & Bx)
(iia)
The present King of France is not bald (False, Primary Occurrence) (Ex) (y) ((Fy . = . x = y) &-Bx)
(iib)
It is not the case that the present King of France is bald. (True, Secondary Occurrence) -(Ex) (y) ((Fy . = .x=y) & Bx)
In addition, bivalence is maintained and the truth value of the proposition depends precisely on the requirement or suspension of the existential presupposition. The latter is manipulated by means of analyzing the denoting phrase into primary or secondary occurrence. Russell has thus provided a solution which saves the law of excluded middle f r ~ mrestriction. [See Section VIII.] Puzzle 3. The Law of Noncontradiction. In the third puzzle we find once again the threat of violation of the law of noncontradiction [Objection (I)] in the form of the long-standing "paradox of reference." Citing the example, 'the difference between A and B does not subsist', uss sell questions how a nonentity can be the subject of a proposition. Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connexion with Meinong, that to admit being also sometimes leads to contradiction. [OD, 481
The contradiction follows from assuming that each singular term in subject position denotes an object which has being. Yet in certain propositions this being is denied in the predicate, resulting in a contradiction of the original assumption. Objection (6) on logical form also appears to be involved here. Russell's solution avoids the threat of contradiction by a paraphrase in which the troublesome singular term no longer appears as logical subject, allowing us to deal satisfactorily with "the whole realm of non-entities," including mythological and fictional objects (Apollo, Hamlet) as well as impossible objects such as the round square. "All these are denoting phrases which do not denote anything." (Russell's logical analysis yields false propositions, if, say, 'Apollo', has primary occurrence, and true propositions if it has secondary occurrence.) Russell then raises Objection (5) on mistaken truth value for propositions such as 'the round square is round'. On his theory this is a "false proposition, not, as Meinong maintains, a true one." [OD, 541 It is not clear whether (a) certain propositions with nondenoting descriptions are claimed to be false because of the correctness of Russell's theory, or (b)whether Russell's theory is correct because it accommodates the falsity of such propositions. On (a), the right truth value contributes
nothing to the adequacy of Russell's theory, but may be an important consequence. In this case it has n o force against Meinong's theories since Russell's strategy is to show how much better his theory explains the linguistic phenomena. If explaining better means giving the 'right' truth value, to assume (b) would be a petitio principii, since the proper truth value is in question.
V. RUSSELL'S FURTHER ARGUMENTS. MEINONG'S REPLIES Turning to Russell's objections in reviews and letters after "On Denoting" we find variations on objection ( I ) on contradiction, objection ( 2 )concerning the 'existent round square which does not exist', and rejection of the modal concept of necessity. [See 1906 letter, Appendix.] Russell continued to stress the superiority of his own method of analysis (7). In his review of Meinong's "Theory of Objects" [RTO, October, 19051 Russell'expanded his "chief objection" to Meinong's view, namely, that "it involves denying the law of contradiction when impossible objects are constituents." If 'A differs from B' and 'A does not differ from B' are to be both true, we cannot tell for example, whether a class composed of A and B has one member o r two. Thus in all counting, if our results are to be definite, we must first exclude impossible objects. [RTO, 801
T o reconstruct this condensed argument, suppose that the properties of some object, A, entail a difference from B and a nondifference from B. O n Meinong's view one can describe such a Sosein (although interpretation of its object-theoretic status is another matter). Then, Russell infers, we are unable to find a criterion to tell whether the class of A and B has one member or two. From this, Russell concludes that impossible objects must be excluded from counting. Russell now has given a reason why a contradiction in impossible objects is "intolerable." Taking the example of "the difference between A and B" which appeared in puzzle 3 of "On Denoting" one step further, Russell infers that admission of contradictory properties in such impossib l e ~prevents counting, which he viewed as a fundamental mathematical procedure. Also (though he does not mention this), it threatens to undermine uniqueness conditions for definite descriptions. If we cannot tell how many A's there are, how can we tell whether one and only one object satisfies such conditions? Without such "definite" results, and without countability, Russell seems to be asking, how could we do mathematics? Whether or not noncountability truly follows from the situation he describes is not obvious, however. One could argue that Russell jumped too quickly from the objects' impossible Sosein to the conclusion of noncountability. Meinong claims "We can count what does not exist." [TO,
791 One could reply that, depending on what object is supposed, there are two objects in question, each of which is both different and nondifferent from the other, where the second object has the additional property of being a second object. Possession of contradictory properties does not prevent an object from being countable. Hence Russell's conclusion does not follow. The above attempt to "save" Meinong, however, must confront a further objection proposed by Charles Parsons.I3 Russell argues that it is possible, on Meinong's theory, to suppose an object A which both has properties differing from B, and has properties not differing from B. Then, if we take A and B to compose a class, it is indeterminate (i.e., we do not know and can never know) whether the class {A,B) has one member or two members. To say, as above, that Meinong could reply that there are two objects, one different and one nondifferent from the other, does not evade Russell's objection. For Russell's point is precisely that, if A = B, then {A,B) has the cardinal number I , whereas if A #B, then {A,B) has the cardinal number 2 . {A,B) cannot have both cardinality I and 2; if it did classical mathematics would collapse. It is difficult to see how Meinong would reply to this argument, which undermines the position taken in the previous paragraph. One possibility for Meinong is to admit noncountability for {A,B) and relegate it to a status outside classical mathematics. On these lines, Meinong might concede that the 'class' {A,B) has contradictory properties, cardinality I and cardinality 2. Its contradictory Sosein necessarily precludes its existence or subsistence. It is not an object to be reckoned within the purview of classical mathematics, or perhaps, any mathematics. Since its supposed nature excludes it from mathematical reasoning in any ordinary sense, it does not threaten the foundations of logic or mathematics. Although I have not found a direct reply to Russell's specific argument here in Meinong's work, there are other considerations which could be brought to bear on this point. First, on Meinong's view, similarity and difference are "ideal" objects of "higher order." They "do not by any means exist (Existieren) and consequently cannot in any sense be real (Wirklich)." Meinong admits that under certain circumstances they might subsist, but "they are not a part of reality themselves." [TO, 791 Secondly, in considering an object, A, characterized only by its difference and nondifference from an object B, we are considering what Meinong might have called in 1915 a "defective object," and one which certainly would not have been admitted into the reasoning of classical mathematics. Such admission would be precluded "
The argument in this paragraph was suggested by Charles Parsons in conversation.
3 2 0 JANET
FARRELL SMITH
not only by its impossible nature, but also by a principle which Meinong articulated in his I 899 Objects of Higher Order, which Russell reviewed in 1904 [MTCA]. In 1915 Meinong stated this principle as follows. [It is] no more possible for a whole to contain itself as part or for a difference to be its own object of reference or its own foundation (Fundament). An object of higher order can never be its own subordinate. [EP, I I]
In the example given by Russell the compound difference-nondifference between A and B has no basis apart from being characterized as such.14 Hence it would violate the principle that an object of higher order cannot be taken as its own foundation, i.e., a difference cannot by itself be the basis of its own assertion. ["No relations can be based exclusively on relations as inferiora." EP, I I ] Therefore, the objects A and B which are both different and nondifferent from each other are "defective" and cannot be taken to compose a class. Some might detect here a resemblance to what Russell later called the "vicious circle principle." Indeed, in 191 5 Meinong discusses the example in the context of the "set which contains itself as an element." [EP, I 1-12] The root difference between Russell and Meinong might therefore come down to a disagreement over the range of "the laws of thought" which Frege in the Grundlagen claimed were intimately connected with the laws of number. There Frege asserted that the domain of what is numerable is the widest domain of all; for to it belongs not only the actual, not only the intuitable, but everything thinkable.Is
Russell appeared to side with this view insofar as he had an implicit criterion of what should count as an object at all. Meinong would have agreed that the laws of number govern what is actual, but that the "free creations of the human mind"16 yield objects which the human imagination can entertain, if not intuit in Frege's sense. These of course are not real, they are not actual. But they can be "given." Meinong was not as decisive in ascribing Aussersein, i.e. "givenness," to defective objects in 1915 as he was to the round square in 1904 or 1907. [TO, 84-86, USG, 14ffl. "
'I
I6
Even if the properties of A and B are specified so as to entail a difference and nondifference between A and B, the problem remains: The alleged difference is its own basis. Specification of the properties merely pushes the problem back one level. The objects clearly violate the laws of identity although Russell does not raise this issue in the text. Gottlob Frege, Die Grundlagen der Arithmetik, 1884. The Foundations of Arithmetic, trans. J. L. Austin (Evanston, Illinois: Northwestern University Press, 1968), par. 14, p. zIe. The phrase is Dedekind's in the preface to What Numbers Are and Should Be. N o resemblance between his theories and those of Meinong is implied.
THE RUSSELL-MEINONG DEBATE
3 21
If Aussersein cannot be denied to the round square how can it be denied to defective objects which in some respects pose fewer difficulties? [EP, zo]
He concluded that his doubts on the matter were not sufficient to revise his views, although future research might cause him to do so. [EP, 201 Russell, in contrast, concluded I should prefer to say that there is no such object as 'the round square' [RTO, 811
taking the following argument on existence as decisive. In putting forward objection (2), Russell employed a variation of an 'ontological argument' presumably following Meinong's claim that "the round square is surely round as it is square." [TO, 821 Inserting 'existent' into the subject term 'the round square', Russell deduces analytically that the existent round square exists. If his objection holds then Meinong's view entails not only contradiction but a paradoxical theory of existence. For if the round square is round and square, the existent round square is existent and round and square. Thus something round and square exists, although everything round and square is impossible. [RTO, 811
Russell claimed that Meinong could not avoid the objection by saying that existence is not a predicate. Russell took material from Meinong's student Ameseder (Meinong published his "Theory of Objects" with colleagues' and students' articles), who said that existing applies when and only when "being actual" (Wirklich) applies. The latter is a Sosein according to Ameseder, although it is highly doubtful that Meinong took this position. For Russell it was enough to conclude that Meinong could not evade his objection by the Kantian doctrine that existence is not a predicate. Meinong's famous reply to Russell's criticism distinguished between "exists" and "is existent." (In German: "Existiert," "Existierend sein.") The existent round square, said Meinong, is existent but does not exist. 'Is existent' can be taken as a Sosein (a property of an object in a sense similar to 'is golden') without existential import. From 'the existent round square is existent', however, we cannot conclude that there exists a round square. The difficulty, according to Meinong, lies with the grammatical forms of "existential predication" which do not ordinarily distinguish between a) "exists," indicating status in space-time, or "actuality" (Meinong's "Wirklichkeit"), and b) the merely verbal assertion "the existent A is existent." [USG, 171 Meinong's reply has puzzled many readers. Yet it is based on two key principles elaborated in "Theory of Objects." First is the view that the 'pure' object is indifferent to being or nonbeing. Questions of existence are properly raised in objectives concerning the pure object.
3 22
J A N E T FARRELL S M I T H
If the opposition of being and non-being is primarily a matter of the Objective and not of the Object, then it is, after all, clearly understandable that neither being nor non-being can belong essentially to the Object in question. [TO, 861
Meinong affirms that nothing about an object's existence can be implied by the (noncontradictory) Sosein of an object. This claim does indeed resemble Kant's claim that existence is not a predicate, contravening Russell's supposition that Meinong could not take refuge in that doctrine. The second principle supporting Meinong's reply to Russell's embedded ontological argument is his principle of the Independence of Sosein from Sein. [TO, 82, 861 By this principle properties can be ascribed to some supposed object resulting in true (or false) sentences regardless of the existential status of the object. When the expression 'existent' is cast into the set of described properties in 'the existent round square is existent' it is used merely as a grammatical predicate on a par with 'gold'. This is what Meinong means by calling 'existent' a Sosein in the above proposition. But it has no force in determining what is actual, a point he made by claiming that 'existent' in the above proposition is not a Soseinbestimmung, or what we could call a 'determining predicate'. [USG, 16-19] (The grammatical predicate 'is existent' is a "watered down" version of "exists". So it does not determine what is "factual.")" The ability to formulate the expression 'the existent round square' arises from the grammatical rules for well-formed sentences. These grammatical rules d o not reveal (rather sometimes they conceal) the underlying philosophical structure of existence assertions. It is curious that Russell did not see this point since he himself said later that existence was no ordinary property but the condition of a propositional function being satisfied. [PLA, 2331 Nevertheless in his 1907 review of ~ b e die r Stellung, Russell said briefly that he could see no difference between "exists" and "being existent,'' and for him the case was closed. [RUSG, 9 3 1 ' ~
"
18
See J. N. Findlay's explanation of Meinong's position on facts and factuality in Meinong's Theory of Objects and Values (Oxford University Press, 1963), pp. 74-75, 102-13. Charles Parsons notes in his "Objects and Logic" that Meinong "needs to make a distinction Russell could not see." Parsons considers a reading of Meinong's theory making outer quantifiers substitutional. These are "relative to objects in the range of the [inner] objectual quantifiers." His reading takes the outer quantifier as "the basic quantifier, the inner as expressing existence." "Objects and Logic," TheMonist, Vol. 65, No. 4 (1982), PP. 507-8.
VI. CONTRADICTIONS Contradictions within a theory can condemn it to incoherence. If Meinong's theory is profoundly riddled with them, we must seriously question it. If, on the other hand, Meinong's theory recognizes objects which are contradictory, but which do not affect the consistency and coherence of his theory, then Russell's dissatisfaction is misguided. T o take still another possibility, if Meinong's theory sanctions contradictory propositions, then Russell may have a devastating objection. Let us examine each of these pos~ibilities.'~ Taking first Russell's charge of contradictory objects, we find Meinong admitting, "I can in no way avoid this consequence." [USG, 161 But it is not so obvious what Meinong is admitting and what worries Russell. For when Meinong says in effect that of course certain impossibles violate the law of noncontradiction and declares that the law applies only to what is actual and possible, Russell counters with the claim that the law applies not to objects but to propositions about such objects. [RUSG, 92-93] Meinong's actual concession in ~ b e die r Stellung der Gegenstandstheorie in 1906 to Russell's charge of contradiction runs as follows: Russell lays greatest emphasis on the fact that recognition of such [impossible] objects would deprive the Law of Contradiction of its unrestricted validity. Of course I can in no way avoid this consequence . . . The Law of Contradiction is applied by everyone only to what is actual and what is possible. [USG, 161
Meinong is admitting in this passage that contradictory impossible objects violate the law of noncontradiction. But he certainly is not conceding that his theory is contradictory. Aristotle's distinction between the ontological and the logical formulations of the law of noncontradiction helps clarify this issue. The ontological formulation: The same attribute cannot at the same time belong and not belong to the same subject in the same respect. [Metaphysics 1oo5b 19-zo] [W. D. Ross translation]
The logical formulation: The most certain of all [principles] is that contradictory sentences are not true at the same time. [Metaphysics I O I ~b 13-14]
I9
Although Russell did not come right out and assert that Meinong's theory violates the law of contradiction, he implied that Meinong's theory is seriously defective on grounds of logical consistency. He claimed as an advantage of his own theory "that it is not contrary to the law of contradiction as might at first be supposed." [OD, 451
324
J A N E T FARRELL S M I T H
Russell in "On Denoting" lodged his objection in terms of the ontological formulation. After Meinong's response, Russell moved to the logical formulation. For Meinong, as apparently for Aristotle, the law of noncontradiction in its ontological formulation does have restricted validity.'" To Russell's charge on the logical formulation, Meinong's reply is another matter. Does the law of noncontradiction apply to what extends beyond the real and the possible? To be fair to Meinong's position we must distinguish two senses of 'apply'. He admits to one sense but not the other. In the first sense, impossible objects do indeed fall under the characterization, 'same property belonging and not belonging to the same thing at the same time'. Hence the law of noncontradiction applies in a descriptive sense. It is this sense which Meinong can "in no way, avoid." But in the second, prescriptive sense, the law is purportedly valid only for what is real (actual) or possible. Meinong stood firm on this point. Yet instead of engaging Meinong on the range of validity of the law, Russell moved to the logical formulation of the law of noncontradiction. This move, which strikes closer to the issue of an incoherent theory, shifted the level of the debate into discourse about contradictory objects. Meinong did not see his concession that the law of noncontradiction has restricted validity in its ontological formulation as a grave defect since for him the law was not meant to apply to impossibles in the first place. He later cited with approval Lukasiewicz' criticism of the unrestricted validity of the psychological formulation of the law of noncontradiction, saying that the "assumption," after all, "is in no wise bound by the principle of contradiction." [OA, 166, n. 12, 3021 Meinong certainly never went so far as to reject the law of noncontradiction. He would probably have agreed with Lukasiewicz' remark that although "it is within our power to ascribe any properties we like to existence-free objects [numbers, geometrical figures], nevertheless we cannot prove their freedom from contradiction." And Meinong did agree with the claim that "real objects . . . appear to be raised above all contradictions."" How then could Meinong respond to Russell's charge that his premises sanction contradictory propositions? A contemporary approach might frame the question in the following manner. Meinong could take two possible positions concerning:
10
21
On some interpretations Aristotle restricts the law to actual existents. This is implied, not stated outright. See Metaphysics IV 4, 1ooi.b 28-29. "For what is potentially and not actually is the indeterminate." Jan Lukasiewicz, "Aristotle on the Law of Contradiction" [ I ~ I O ]trans. , J. Barnes in Articles on Aristotle, Vol. 3 Metaphysics, ed. J. Barnes (St. Martin's Press, 1979), p. 61.
T H E RUSSELL-MEINONG DEBATE
325
(I)
The round square is round and non-round.
On position (A), ( I ) is not really a contradiction, because there is a "way out." On position B, ( I )is a straightforward contradiction and there is no way around it. However, on position (A) or (B),Meinong's theory could be reconstructed in such a way as to avoid formal inconsistency or incoherence. So even if certain propositions are contradictory, or certain objects have contradictory properties, these could be construed as not devastating to the central theoretical premises of object theory. Meinong apparently took strategy (B), that ( I ) is a contradiction," although this position must be qualified as I shall do presently. As we shall see, some contemporary philosophers offer grounds for taking (A) as closer to the spirit of Meinong's position. Their approaches may help explain why Meinong did not regard the alleged co~tradictionas in any way rendering his theory incoherent or inconsistent. Russell of course argued position (B) to the end. He saw contradiction in such objects as "the round square" or in propositions about such objects as damaging anomalies which demand theoretical revision. When Russell recognized these anomalies in his own 1903 theory of denoting and ontology, his sense of consistency demanded that he either abandon the theory or revise it in such a way that the anomaly di~appeared.'~ Although it would be misleading to say that Meinong did not see impossible objects and propositions about such objects as anomalous, one can say that each philosopher had a different way of handling these. What Russell saw as "intolerable" Meinong saw as not devastating. Meinong reasoned consistently with his earlier Principle of Independence of Sosein from Sein. Merely analytic judgments expressed by ( I ) pertain only to Sosein. Even if it appears that we are able to infer contradictory properties about such objects as the round square this would be devastating since the 'nature' of such objects never intrudes into the realms of
" There is another problem of consistency here. If the ontological (or object-theoretic, to
''
use Meinong's non-prejudicial term) and logical formulations of the law of noncontradiction are taken to be equivalent, then for Meinong to admit to violation on the objecttheoretic level but explain away contradiction on the logical level (the sentential form of the law) would seem a bit odd. This position would be consistent, however, if he considered the contradictory 'objects' in question to be "defective" and only questionable objects in the full sense. He appears to open the door for such a strategy in 1915. [EP, 10-221 Compare puzzle 3 [OD] with [POM, 481: "Thus the contradiction which was to have been avoided, of an entity which cannot be made a logical subject, appears to have here become inevitable. This difficulty, which seems to be inherent in the nature of truth and falsehood, is one with which I do not know how to deal satisfactorily."
being. So, on strategy B, which concedes that propositions such as ( I ) are contradictions, nothing is implied about the structure of the actual world. These propositions are merely the result of thinking certain properties in certain combinations. Did Meinong take position (B) that 'the round square is round and non-round' is a straightforward contradiction? Interpreting him as adopting position (A) does not seem accurate to his text. But simply assimilating (B) to Meinong's views is an oversimplification because "straightforward contradiction" covers several possibilities: (i) that affirming the contradictory Sosein of certain objects results in truths on the object-theoretic level; (ii) that logical falsehoods are implied by (i); and (iii) that logical falsehoods must occur within any formal representation of object-theory by (i) and (ii). As interpreted here, Meinong admitted ( I ) to be a contradiction in sense (i) but not in sense (ii) and emphatically not in sense (iii). Although in his text, Meinong did not address the issue precisely as posed here, he did appear to recognize contradiction on the object-theoretic level in sense (i). [USG, 16 ff.Iz4 The gist of his replies to Russell supports our interpretation that he denied contradiction in senses (ii) and (iii) as affecting his system in any harmful way. Meinong's underlying reasoning here is that a contradiction resulting from an analytic judgment like ( I )will not possess existential import; that is, there will be no existent (or subsistent) object possessing these characteristics. Further, there is no possibility of any existent object possessing these characteristics. Meinong appears to rely on the view introduced in "Theory of Objects" that a contradictory Sosein (collection of properties) in an object entails its nonexistence. So he does not extend the validity of the rules of traditional logic to nonexistent objects. These objects have a different logic from the traditional logic Meinong knew, and from the foundations of logic set down by Frege and Russell. Put another way, l4
As was pointed out by Ernst Mally, Meinong's student and interpreter, we must distinguish between an impossible and a contradictory Sosein. A round square is a contradictory, not an impossible Sosein. Hence, from its Sosein alone (i.e., from the assumed properties alone), it must follow that the round square is round. Mally's point may be illustrated by his example. Consider, simply, squareness. Given squareness, it is impossible that squareness be circular. Consider in contrast a round square. Given a round square, it is not impossible, but rather "necessary," as Mally says, that a round square be both round and square, even though it is impossible that there be an object which is both round and square. So the contradictory Sosein, the roundness of the round square, differs from the impossible Sosein, the circularity of (the given) squareness. These considerations may show why Meinong wanted to affirm ( I ) .See E. Mally, "Untersuchungen zur Gegenstandstheorie des Messens," in Untersuchungen zur Gegenstandstheorie, ed. A. Meinong (Leipzig: Barth, 1904), pp. 128-29.
these impossible nonexistents require an elaboration of classical logic which Russell would not accept. There is one extremely important reason Meinong is forced to restrict traditional laws of logic concerning propositions about nonexistent impossibles: If he held that ( I ) is indeed a contradiction in sense (ii), namely a logical falsehood, then within a formal deductive system, any proposition can be deduced from it. Therefore, for Meinong's position to be consistent, there must be provisions in his theory for a different application of inferential rules for sentences concerning nonexistent impossibles. Otherwise, a Meinongian assertion that ( I ) is contradictory threatens an incoherent theory. Unless that possibility is curbed, Meinong's theory of objects c~llapses.'~ Even though Meinong did not exactly consider the question of contradiction as a choice between positions (A) and (B), it is possible to reconstruct a position for him along lines of (A).Such a reconstruction attempts to find a way out of the conclusion that recognizing ( I ) results in a logical falsehood. Let us accept Russell's formulation of the law of contradiction. [No proposition can be both true and false.] If we assume, with Russell, that the negation of a false sentence is true and the negation of a true sentence is false, it still does not necessarily follow that ( I ) is both true and false, because, in the following, ( ~ bis) not the simple negation of ( ~ a ) . Consider (I)
The round square is round and non-round.
( ~ a ) The round square is round. ( ~ b ) The round square is non-round. ( ~ b ' ) It is not the case that the round square is round. There are various ways to analyze the above by delineating different forms of negation. O n one strategy, ( r b ) and ( ~ b 'exhibit ) property negation and sentence negation respectively, so they are not equivalent. So ( r b ) is not the negation of (ra),which has the result that ( I ) is not a straightforward c~ntradiction.'~ In theories which utilize a notion of complement, "non-P" is not a complement of "P." There too ( ~ bis)not the negation of (~a)." 'j
16
"
See K. Lambert's discussion of alternatives in Meinong and the Principle of Independence (Cambridge University Press, 1983), esp. pp. 134 ff. See Routley, Exploring Meinong's Jungle, pp. 88-91. Terence Parsons in "The Methodology of Nonexistence" defines "one property [as] a complement of another just in case any object that has the one lacks the other, and vice versa." Journal of Philosophy, Vol. 76, No. I I (1970)~p. 658. See also H. N. CastaAeda,
A further strategy adapts Meinong's distinction between nuclear negation and a "wider sense of negation" pertaining to what he called "extra-nuclear predicates."28 Terence Parsons has devised a formal semantics of nuclear vs. extranuclear properties. On his theory, if 'non-square' is used for the nuclear negation of 'square' then 'non-square' in the proposition (2)
the non-square square is both square and non-square.
is nuclear, though it is not the "proper" negation of 'square', and so ( 2 ) is not ~ontradictory.'~ For ( I )Terence Parsons proposes philosophical and mathematical considerations to block the inference of 'The round square is both round and non-r~und.'~" There is still another Meinongian approach to analyzing propositions about contradictory impossibles. This relies on Meinong's reflections in 1915 that certain impossibles are "defective" objects. [EP, 10-221 Moreover, cases such as the round square and the spheroid which is not a spheroid could be taken as "objects of a higher ~ r d e r . " ~Objects ' of higher order are ''built upon" other objects ("inferioran). ["For example, the relation of difference is a superiorus relative to what is different." [SELB, 2251 ] (See Section V above) Meinong allows that superiora can be inferiora for "even higher superiora." [SELB, 2261 What if we were to take cases such as the round square and the non-spheroid spheroid as defective objects of higher order? Strictly speaking these would be superiora which in turn would be based, or "founded" as Meinong says, on other superiora. In other words, the object of (higher) higher order, the non-spheroid spheroid, is founded upon the inferiorus the spheroid, which in turn logically contradicts its superiorus. The result would be that the description "the spheroid which is not a spheroid" stands for a double object residing on two different levels. It would not, on this interpretation, be a "Philosophical Method and the Theory of Predication and Identity," Notis, Vol. I 2, No. 2 (1978), and W. Rapaport, "Meinongian Theories and a Russellian Paradox," Notis, Vol. 12, NO. z (1978). See [UMOG, 1741 and J. N. Findlay, Meinong's Theory of Objects and Values, p. 161. '9 Terence Parsons, "The Methodology of Nonexistence," p. 658. '"Terence Parsons, Nonexistent Objects, pp. 38-42. On T. Parsons' view there are no contradictory objects, i.e., objects which infringe the law of contradiction. " Russell was advised by Stout, editor of Mind, to read Meinong's Gegenstande hoherer Ordnung. [Letter dated 6 August goo] Evidence that Russell tried out Meinong's theory of objects of higher order occurs on p. 172 of an unpublished logic manuscript. ["Unclassified Notes" April - M a y 1906, perhaps a continuation of "On Substitution" of the same date] Russell considers a division between "individuals" and "Gegenstande hoherer Ordnung." The latter include propositions, classes, and relations. Russell calls these "logical objects" and says that they are incapable of existence. This is basically Meinong's theory. Materials are in the Russell Archives.
"type-theoretically proper definite de~cription."~'Each respective object designated belongs to a distinct "higher order." So each expression designating the respective objects of distinct "higher orders" occurs on different (implicit) logical levels within the definite description. (Meinong, it must be noted, did not make the linguistic extension of his theory of objects of higher order presented here. But it seems a reasonable elaboration of his views.) The upshot is that the predicate 'non-spheroid' ascribed to the superiorus (Non-Spheroid) cannot rightly be viewed as the negation of the predicate 'spheroid' ascribed to the inferiorus (Spheroid).Another way to put this would be, following Meinong, to call the predicate 'non-spheroid' a "wider form of negation," or perhaps an "extra-nuclear predicate." Then, if 'spheroid' and 'non-spheroid' are not the proper negations of one another, the proposition (3)
The Spheroid which is not a Spheroid is both spheroid and non-spheroid.
is not a straightforward contradiction in the sense of a logical falsehood. A similar analysis could be applied to the round square or the non-square square. If the Non-Spheroid Spheroid in question is not precisely a "defective" object in Meinong's sense, it is at least an "odd object" like the round square because [at least on some geometries] the predicates in the definite description derive from a superiorus which excludes the inferiorus on which it is founded.33 The above considerations show that Meinong's recognition of contradictory objects does not necessarily lead to the truth of contradictory propositions. Since Meinong in no sense recognized the being of impossible objects, he can claim that they pose no threat to his theory about reality. As far as mathematics is concerned, his provisions for negation, objects of higher order, and "defective" objects can be interpreted to rule out disasters in formal systems. Russell was therefore wrong if he concluded that the supposed contradictory objects entailed an incoherent theory.
3' 33
See Lambert, Meinong and the Principle of Independence, p. 63. The round square differs from the non-spheroid spheroid because it is obtained by predicating 'round' (a property of a circle, which in turn is a higher superiorus) of the object, square. The geometrical relation between circle and square differs from the relation between spheroid and non-spheroid.
VII. EVALUATIONS One factor which may have led Russell to view ( I ) ('The round square is round and non-round') as so threatening was his confusion about the locus of contradiction. In 1904-1905Russell regarded propositions ontologically, that is, as unities somewhat like states of affairs which contained entities in the world as their constituents. [OD, NT] Russell frequently conflated his own propositions with Meinongian objectives. For example, in the following passage Russell replies to Meinong's claim that the law of noncontradiction was not meant to apply to impossible objects. This response seems to overlook the fact that it is of propositions (i.e., of 'Objectives' in Meinong's terminology) not of subjects that the law of contradiction is asserted. T o suppose that two contradictory propositions can both be true seems equally inadmissible whatever their subjects may be. [RUSG, grIJ4
If Meinong could put forth the theory in which an apparently contradictory proposition was true, then, on Russell's tacit reasoning, Meinong was also putting forth a theory in which a contradictory entity was real. The "reality" of contradictory objects was "intolerable" for Russell. So Meinong's theory had to be wrong. If the above was Russell's view. then he misunderstood Meinong. O n Meinong's view, objectives of false sentences (-that today is Wednesday) d o not subsist (when today is T u e ~ d a y )Objectives .~~ of true sentences d o subsist (-that the round square is round). Yet contradictory objects such as the round square are "beyond being and non-being," or as Meinong sometimes put it, Ausserseiend. Meinong's theory in O n Assumptions made a clear separation between sentences (Satze) and objectives (Objektive). Sentences (Satze) signify their references (Bedeutugen), which Meinong says, are objectives, or roughly, states of affairs. [OA, chap. z] Objekte [usually translated 'objects'] are the "parts" which make up Objektive. For example grass and green are the bbjekte of which the objective -that
the grass is green
is composed. When the sentence 'the grass is green' is true, the objective (-the being green of the grass) or (-that the grass is green), subsists. But the Objekte are "parts" of the whole only in a special sense. Meinong specifically denied that the objective reduces to the Objekte which it is 34
'I
Compare [KAKD, 2171: "The law of contradiction ought not to be stated in the traditional form 'A is not both B and not-B' but in the form 'no proposition can be true and false."' Russell did make this mistake explicitly in [PLA, 2231: "To suppose that in the actual world there is a whole set of false propositions going around is to my mind monstrous."
T H E RUSSELL-MEINONG DEBATE
33 I
about, in the way that a whole can be broken down to its component parts. [TO, 851 Russell, in contrast, affirms a fundamental principle in which propositions reduce to their constituents. In its ontological version, this principle required that each constituent have being. Meinong and Russell were thus operating on two different concepts of sentence or proposition and two different notions of part-whole relations for Meinongian objectives and Russellian propositions, respectively. It is no wonder, then, that their disagreements often seem to have stemmed from misunderstanding of the other's position. Meinong's attempts to clarify himself frequently met with Russell's restatement of his own viewpoint, e.g., on the part-whole relation involved in objectives or propositions: I should have thought that the subject of a proposition was a constituent of a complex in the fundamental sense from which all others are derivative. [RTO, 801
In this comment Russell reveals his mistaken premise from which some of his arguments against Meinong's theories are deduced. On Meinong's theory, a sentence is not as complex as it is on Russell's 1905 view of propositions. [MTCA, 73-76]36It is a linguistic expression which has an objective as its reference. Moreover, an objective is not reducible to its "parts." The objective -that
the round square is round and non-round
does not presuppose on Meinong's theory the "being" of the Objekt, round square. Nor does the objective the nonbeing of the round square presuppose the "being" of the round square. So in the latter objective we do not get the "contradiction" involved in the paradox of reference. [Puzzle 3, OD] Neither do we get the "being" of the round square in the former objective. This is so despite the fact that each objective in Meinong's terminology, subsists. The objective (-the nonbeing of the round square), says Meinong, is not the simple addition of nonbeing to the round square. The 'second stage' of the Russell-Meinong debate on contradictory propositions thus rested on a series of misunderstandings. It is in no way clear that Russell's objections engage Meinong's actual theory, although
J6
Objectives are not complexes in Russell's sense of the term in [PM, 441, i.e., they are not reducible t o constituents. Neither are they strictly complexes for Meinong. See discussion in J. N. Findlay, pp. 95-98. The manner of expressing objectives as '-that p' emphasizes that objectives are not propositions o r sentences but objects of assumptions o r judgments, as in 'A judges that p'.
332
JANET FARRELL SMITH
they may be definitive against the doctrine of the "being of every term" and the view that each term is a proper constituent of a proposition, i.e., a logical subject. [Cf. POM] Russell might have gotten a stronger objection to Meinong's theory by challenging whether it was coherent to call the round square round at all. If he had argued along these lines he would have placed himself in the classical tradition in which there is no true predication save of existent^.^' The lines of disagreement would then have been drawn more sharply, since Meinong's contention in "Theory of Objects" is that true assertions can be made about nonexistent, nonsubsistent objects. Indeed, this underlying issue is what the dispute over truth value of propositions concerning alleged nonexistents seems to be about. Russell's objection (5) on mistaken truth value for, e.g., 'the round square is round', appears to derive from his logical analysis.3sHence it is contingent on his objection (7) that his own method of analysis is superior to that of Meinong. Yet some versions of contemporary free logic have shown there are coherent logical analyses of ( I )which preserve certain intuitions and do not court contradiction. So Russell's objection (5) is far from d e v a ~ t a t i n g . ~ ~ Russell's (7), on the superiority of his own paraphrase, can also be called into question. Meinong's analysis, as noted, makes 'the golden mountain is golden' true. Russell's paraphrase makes it false. Roderick Chisholm asks "How can a false statement be an adequate paraphrase of a true one?" And, "how are we to decide who is right without begging the basic question that is i n ~ o l v e d ? " ~In" addition, Russell's paraphrase makes "The mountain I am thinking of is golden" false. But on Meinong's theory the statement is true. As Chisholm interprets Meinong the above "sentence speaks of me, . . . and my thoughts, and presumably my thoughts can be taken to be states of me. But the problem is that these states of me are intentional; they have objects. And it is of the essence of an intentional attitude, according to Meinong, that it 'have' an object 'even though the object does not exi~t."'~'This interpretation implies that the Meinongian Bedeutung is unlike the Fregean Bedeutung which Russell more easily assimilated to this theory of denoting. Meinong emphasized the thesis of intentionality within the Bedeutung, o r signification, in his theory of language: "
j9
40
4'
Aristotle, Categories, 13b 12-29. "Neither 'Socrates is ill' nor 'Socrates is well' is true if Socrates does not exist at all." See PM '' 14.22, where Russell claims "the man who squared the circle squared the circle" is a false proposition. See Lambert, Meinong a n d the Principle of Independence. "Homeless Objects," p. 61. "Beyond Being and Nonbeing," p. 38.
T H E RUSSELL-MEINONG DEBATE
333
We may ask what signifying really consists in . . . in the case of words. In answering this question one cannot let one's considerations terminate in the word; one must stick with the person who utters it meaningfully. As a part of life, signifying is surely always a signifying for someone. [OA, 2 5 , Emphasis Added]
The above also makes clear that Meinong would have had trouble with Russell's paraphrase since it leaves aside questions of intentional signification. Russell's analysis of propositional attitudes and scope indicators for what he called secondary occurrences do make some sentences true (e.g., "Sara believes that the unicorn is white.") But these d o not draw intentionality into the signification of the words themselves, and consequently the objects which these words signify. Meinong's theory could be said to involve another theory of signification which Russell's method of paraphrase does not address. Consequently, Russell's objection (6) cannot be taken as definitive since it does not engage Meinong's theory on the above view of language. Here one could of course challenge Meinong to reveal his own method of paraphrase or underlying structure of language based on his view of the Bedeutungen of words. Concerning objection (3), Russell's paraphrase also leaves aside a distinction between the modal status of the golden mountain and that of the round square. Given that a purely golden mountain is merely geologically nonexistent, and should properly be called a possible nonexistent object (or, perhaps, given the earth's geological history, a physically impossible object). The round square, however, is on Euclidean geometry contradictory, and hence should properly be classified as geometrically impossible. Meinong might have protested along these lines, for in his 1906 letter Russell wrote that he recognizes no concept of necessity such as Meinong's. The above distinctions are not captured by Russell's analysis of 'necessary' as 'always true' and 'possible' as 'sometimes true'. Hence Russell's paraphrase is, on Meinong's view, inadequate. As for Russell's objection (8) regarding imaginary and fictional objects, Meinong emphasized, from the "Theory of Objects" onward, that only a "prejudice in favor of the actual'' restricts metaphysics to actuality. Discarding this bias is in no way incompatible with a feeling for reality. Indeed in the second edition of O n Assumptions Meinong remarked that doing so is compatible with what he called a "respect for facts." [OA, 2921 Contemporary treatments of fictional objects such as Terence Parsons' Nonexistent Objects, show a high degree of formal sophistication and ingenuity while at the same time exhibiting logical consistency as well as an ability to distinguish the actual from the possible. Russell's objection (8) is therefore misguided.
334
JANET FARRELL SMITH
Thus the objections (3) on modalities, (5) on truth value, ( 6 )on logical form, and (7) on superiority of Russell's method of paraphrase are therefore not definitive. They are not definitive in the sense that Russell makes certain presumptions that Meinong does not accept. Neither d o many contemporary philosophers accept these presumptions, e.g., on modalities o r on the scope of the law of excluded middle. This does not show that Russell was wrong but that the framework out of which he was operating cannot automatically be presumed to be the correct one. Moreover each of these objections can be met by devising a formal theory which casts some of Meinong's basic insights into more rigorous form. T o the extent that these theories have been and are being devised, the issues debated by Russell and Meinong must be left as open questions. While the above are left as open questions (or in the case of (5) perhaps as a petitio principii), objections ( I ) and ( 2 ) on contradiction and existence are more complex. In order to evaluate them we can break down Russell's objection on contradiction into no less than five variations. (i) T o summarize the first, Russell called a theory of contradictory objects "in itself a difficult view;" he has always recognized that an object must be in some sense. Meinong's responded that "what it is to be" an object is equivocal, not univocal. "To be an object" in cases such as contradictory objects is indeed a rather tenuous sense of what it is "to be an object," but it in no way affects the realm of the actual, or "real." Rather it illuminates the admittedly strange nature of some objects which may be "given" to consideration by postulating a certain Sosein. The law of noncontradiction was not meant to apply to such objects. (ii) Even so, Russell countered, Meinong's theory licenses contradictory propositions. Here Russell conflated his own propositions with Meinong's objectives which d o not rest on a part-whole relation in which the objective reduces to its component parts. So if the objective of 'the round square is round' subsists (as on Meinong's theory it does), then the subsistence of the object, the round square, is not implied. The view is also generally supported by Meinong's Principle of Independence of Sosein from Sein. (iii) False propositions subsist, says Russell, and this is intolerable in the case of "the difference between A and B does not subsist." [The 'paradox of reference' in puzzle 3 of OD] O n Russell's 1904 view of propositions, false propositions subsist. [MTCA] But on Meinong's view, sentences are merely linguistic expressions. Their objectives subsist when the propositions are true. But their objectives d o not subsist when the propositions are false.
T H E RUSSELL-MEINONG DEBATE
335
(iv) Contradictory objects are not countable. A reconstructed version of Meinong's theory of defective 'objects of higher order' allows the interpretation that they are not countable, but that they can be relegated to a status outside of mathematics, as well as outside of "being and nonbeing." So they d o not threaten the foundations of mathematics. (v) According to Russell, objection ( 2 ) on 'the existent round square' yields the contradiction that the existent round square is existent but does not exist. O n Meinong's theory 'is existent' is only a grammatical predicate and not a 'determining predicate'. It does not imply space-time status in the actual world (i.e., existence). So it does not imply a contradiction. Neither does it imply subsistence. In (i) there is a fundamental difference between Russell and Meinong on what it is to be an object. This, as I shall elaborate below, is a difference concerning philosophical frameworks, not solely a difference concerning contradictions. Variations (ii)-(v)of Russell's argument on contradiction can be taken as definitive only if Meinong's replies are misunderstood or ignored. Of course this is not to deny that there are difficulties in Meinong's overall theory of objects. For example, there is the question of how he maintains both that theory of objects is to be divorced from 'psychologism' and that the signification of words has an intentional aspect. But this was not among the issues Russell raised. VIII. MODALITY, LOGICAL LAWS AND "DEVIANCE" Russell's objections to Meinong's object theory issued from a framework in which what it is to be an object is closely tied in with the brand of classical logic associated with Russell's logicism. A 'classical' logic is one which, in Russell's view, preserves classical mathematics. 'Orthodox' or 'classical' logics may be taken to include those which adhere to a strict form of excluded middle and to bivalence, do not define different forms of negation, and define modalities, if at all, in terms of truth-functions or q~antification.~' Russell's objection (3) on modalities, objection (4) on violation of excluded middle, objection ( I )on contradiction, especially in the countability argument, and the implied issues of identity, all figure into this general framework. Russell recognized that object theory depends heavily on modal notions. For instance: "Some of [Meinong's] most important arguments fail if necessity is not admitted." [MCTA, 261 Meinong devoted much energy to providing a philosophical basis for modalities. [UMOG] Rus-
4'
See W. V. Quine, Philosophy of Logic (Prentice-Hall, 1970), chapter 6; Susan Haack, Deviant Logic (Cambridge University Press, 1974); John Woods, Critical Notice of S. Haack, Deviant Logic, Canadian lournal of Philosophy, Vol. VII, No. 3 (1977).
sell, on the other hand, was adamant against modalities which could not be reduced to quantification over variables or to propositional functions. Even when he was willing to accept intensional notions as part of an explanation of meaning, of classes [POM, 671 or of propositional functions, he tolerated no modalities. To Russell in the 1903 Principles, Kant's notion of necessity "appears radically vicious . . . The only logical meaning of necessity appears to be derived from implication." [POM, 4541 Russell, however, was not about to do away with the terminology of necessity, contingency, and possibility. In 1904 he explained the "feeling" of necessity and contingency as due to tensed verbs. [MCTA, 26-27] In 1918 he called a propositional function possible when it is 'sometimes true', necessary when it is 'always true', and impossible when it is 'never true'. [PLA, 23 I, 25 5, IMP, 1651 Meinong protested "the attempt to analyze all necessity out of the world," saying that it collapsed crucial distinctions in object theory. Not the least of these is the delineation of what is factual from what is not. [UA, 292, USG, 51ff.I Russell's objection (4) on nonexistent objects' violation of excluded middle was implied in puzzle 2 of "On Denoting." It is not unlikely that Russell knew then of Meinong's 1899 theory that objects of higher order are 'unfinished' or 'incomplete' [Unfertig] with respect to certain properties.4z [HO, 1441 (Russell reviewed Objects of Higher Order in 1904 [MTCA].) Russell's solution to puzzle 2 in "On Denoting" and his avowal that he meant to demolish the present king of France which is on a level with the golden mountain [RUSG, 931, indicate that for Russell, any object worthy of the term must conform to the law of excluded middle. Frege's reaction to Russell's paradox also affirmed the close connection of the notion of what it is to be an object with logical laws. The importance of Frege's system to Russell hardly requires emphasis, since Frege's axiomatizations of the theories of classes and numbers spurred Russell's own foundational work. In his Appendix I1 to the Grundgesetz Frege pondered the appropriate response to the paradox: What should be our attitude to this? Are we to suppose that the law of excluded middle does not hold for classes? O r are we to suppose that there are cases in which to an unexceptional concept n o class corresponds as its extension? In the first case we should find ourselves obliged to deny that classes are objects in the full sense; for if classes were proper objects the law of excluded middle would have to hold for them.44
4'
44
Meinong's later theory in 1915 maintained that certain mathematical objects are incomplete with regard to certain properties and therefore do not obey the law of excluded middle. [UMOG, 17off.I Grundgesetze der Arithmetik, Vol. 11, Appendix [ ~ g o r ] trans. , M. Furth, The Basic Laws of Arithmetic (University of California Press, 1964), p. 128 ff.
T H E RUSSELL-MEINONG DEBATE
3 37
Frege went on to consider functions which take as arguments both proper and improper objects. ["Certainly the relation of identity would be of this kind."] But he rejected this approach since he thought it "inconceivable" that various kinds of identity should occur. Russell, who must have been aware of these musings, was also suspicious of admitting "improper objects" which involve suspending or modifying excluded middle and identity. Throughout his career he consistently rejected deviations from excluded middle. His reaction to the intuitionist philosophy of mathematics is a case in point. He was opposed to Brouwer's rejection of the law of excluded middle as he apparently was opposed to Meinong's suspension of it in limited cases. He firmly rejected finitist methods in 1 9 3 6 . ~He ~ criticized restrictions on the law of . excluded middle where no decision method exists on the ground that "large parts of analysis, which.for centuries have been thought well established, are rendered doubtful." [Introduction to 2nd edition, POM, vi] For example, without the law of excluded middle, the proof that there are more reals than rationals fails. Finally, in 1940 Russell wrote "Logic collapses and much hitherto accepted reasoning, including large parts of mathematics, must be rejected as invalid, if we loosen the law.'' From 1903 forward Russell took identity as an explicit criterion of what is involved in being an object.46 The threatened violations of excluded middle and noncontradiction in nonexistent objects also called into question identity requirements, as in the countability arguments analysed above in Section V. In a 1904 critique of idealism, Russell remarked that the view that all objects are psychical (specifically refuted by Meinong) leads to insoluble difficulties as regards identity . . . In short, no logic is possible which does not admit identity to be independent of any judgment as to identity; and this decides that outside judgment there are objects and there is identity. [MCTA, 641
Confronted with the objects A and B which are both different and nondifferent from each other, Russell must have realized that not only countability, but the axioms of identity were jeopardized. Even though consideration of the laws of identity did not rise to the surface of the debate, they may well have been one cause of Russell's dissatisfaction.
4r
46
B. Russell, "The Limits of Empiricism," Proceedings of the Aristotelian Society (1936), P. 145. See [POM, 43-44]. "Whatever may be an object of thought or may be counted as one I call a term . Another mark which belongs to terms is numerical identity with themselves and numerical diversity from all other terms."
..
What is now meant by the contemporary term "deviance" could be used to express one of the dangers Russell may have thought followed from the Meinongian theory of nonexistent object^.^' T o depart from the classical laws of logic (identity, excluded middle, and noncontradiction) in formulating the boundaries of objects may have been to Russell's mind to invite deviations of a sort he deemed "intolerable." Russell's adherence to his own logical viewpoint appeared to blind him to certain of Meinong's distinctions and concepts (e.g., the distinctions between merely grammatical and actual assertions of existence). Russell also seems to have been less cognizant than Meinong of the regulative status of these logical laws, especially nonc~ntradiction.~'These laws play a role in some prior implicit framework which determines how we lay down the criteria for the very notion of an object. Yet the fact that we can consistently construe, say, negation of properties, o r completeness and incompleteness of objects, in ways which differ from the Frege-Russell foundational system seemed not to have occurred (meaningfully) to Russell. "Deviance," however, is a relative term. The progenitor of 'classical' logic, Aristotle, adopted a mildly 'deviant' strategy when he suspended excluded middle for propositions with vacuous subject or predicate terms. Meinong's strategies are much less radical than, for example, the intuitionists'. As has often been noted, what is now 'classical' was once innovative. In the latter part of the twentieth century, formal systems which capture Meinongian insights increasingly address the questions Russell raised and provide responses to his doubts, sometimes within the frame of the classical laws of logic. For example, in Terence Parsons' Nonexistent Objects, identity "is meaningfully applicable to all objects existent and nonexistent alike." T. Parsons' theory provides answers to Quine's questions on identity criteria for possible objects, e.g., How many possible men are there in that doorway?49Therefore, despite the differ47
Russell of course never used the term "deviance" in discussing Meinong. He was, however, inclined to say "Pure logic and pure mathematics (which is the same thing), aims at being true, in Leibnizian phraseology, in all possible worlds, not only in this . . . job-lot of a world in which chance has imprisoned us. There is a certain lordliness which the logician should preserve: he must not condescend to derive arguments from the things he sees about him." [IMP, 1921 Perhaps Meinong paid too much attention to this job-lot of a world. Russell takes the law of noncontradiction to be "about things, and not merely about thoughts." It is a ". . . fact concerning things in the world." Problems of Philosophy (Oxford, 1912), p. 89. See Manley Thompson's discussion in "On A Priori Truth," Journalof Philosophy, Vol. 78, No. 8 (1981), pp. 468-69. See also Hilary Putnam, "There Is at Least One A Priori Truth," in Realism and Reason, Philosophical Papers Vol. j (Cambridge University Press, 1g8j), for a discussion of the a priori status of the law of noncontradiction.
THE RUSSELL-MEINONG DEBATE
3 39
ences between Russell's philosophical logic and Meinong's object theory, some aspects of object theory can be reconstructed within classical logic.
IX. CIRCUMSTANTIAL EVIDENCE Thus far I have presented internal evidence for the view that Russell rejected Meinong's objects primarily for reasons concerning logical principles, reasons which issued from his overall framework of classical logic. There are other important but more circumstantial grounds for this view. We find a strong case for the primacy of logical concerns in Russell's early intellectual work. His youthful abiding purpose, to discover the logical status of mathematical truths, took form in the logicist program of reducing mathematics to logic. The overwhelming snare in this project was Russell's discovery in June of 1901 of the contradiction of the class which both is and is not a member of itself. With this discovery, Russell's intellectual progress stopped and he concentrated on resolving the contradiction. In the vivid accounts of this period given in his Autobiography, Russell's efforts to solve the contradiction appear more intense than any subsequent intellectual endeavor. The Principles of Mathematics went to press in 1903 with the first published statement of the paradox. Then apparently came a period which Russell later described as "something very near to despair." H e could not sustain his initial hope that the contradiction was "due to some trivial error in the reasoning" and could be resolved swiftly. [AUT, 2211 "Throughout 1903 and 1904," Russell says, "I pursued will-o-the-wisps and made no progress." A "glimmer of hope" appeared however in the spring of 1905 when Russell fell upon a different problem, one which he tied very closely to his encounter with Meinong's philosophy. The "glimmer of hope" was the theory of descriptions, which gave Russell the opportunity to eliminate by contextual definition not only denoting ~ h r a s e sbut also ~lasses.~" Those years spent pursuing "will-o-the-wisps" were thus also occupied with the writing of the "Meinong's Theory of Complexes and Assumptions" in I 904. 49
I"
Terence Parsons, Nonexistent Objects, p. 28. W. V. Quine, "On What There Is," in From a Logical Point of View (New York: Harper and Row, 19 53). For a recent discussion by Quine on the question of bivalence, see "What Price Bivalence?" Journal of Philosophy, Vol. 78, No. r (1981). Quine sees Russell as freeing himself of Meinong's impossibles by the doctrine of incomplete symbols in 190j. "Classes were next." [In the 1908 paper "Mathematical Logic as Based on the Theory of Types. "1 See W. V. Quine, "Russell's Ontological Development," in B. Russell, A Collection of Critical Essays, ed. D. F. Pears (New York: Doubleday Anchor, 197r), p. 294.
340
J A N E T FARRELL S M I T H
Given these events it is hard not to see parallelism in Russell's concern over the contradiction of classes and over the alleged contradiction implied by the impossible (or "homeless") objects such as the round square. If we look for an answer to the question 'why was Russell so concerned with Meinong's impossible objects?' we might find it in the superficial resemblance between paradoxical classes, objects which produced deep mathematical chaos, and Meinongian objects, which produced contradiction. Another clue to the connection between logical foundations and objects which disobey classical logical laws may be found in Frege's speculation that because of the paradox, classes would not obey the law of excluded middle. [See Section VIII above] Frege, however, was more inclined to locate the source of the contradiction in Axiom 5 of the Begriffs~hrifft.~'In his 1902 letter to Russell, as is well known, Frege lamented the undermining of the "sole possible foundations of arithme ti^."^' His thought, which Russell shared, emphasized that progress toward a solution to the contradiction of classes was prerequisite to further progress in building the foundations of mathematics and logic. No wonder that contradiction loomed large in Russell's thought around 1902-1910.
Yet despite the apparent similarities of symptoms, Russell proceeded to apply very different treatments to classes and to Meinong's nonexistent objects. Russell's no-class theory allowed him to be agnostic on the nature and existence of classes. Meinong's nonexistent objects, in contrast, were according to Russell successfully "demolished" by the analysis in the theory of descriptions. However, what is important for our purpose is that in Russell's own conception of his intellectual progress, the theory of descriptions led to a solution of the contradiction in the form of a no-class theory. Russell experimented with various solutions to the paradox beginning with the early theory of types proposed in 1903. [POM, AppB] After he discovered his theory of descriptions, he developed three solutions in his 1905 paper "On Some Difficulties in the Theory of Transfinite Numbers." These were the zigzag theory, the theory of limitation of size, and the "no-classes" theory in which "classes and relations are banished altogether." [TTN, 1541 Having noted in the body of the paper that the no-class theory is one, though not the way of avoiding contradictions, Russell added in a note at the end of the paper in 1906 his conviction that
I'
I'
Grundgesetze, Appendix on Russell's Paradox, p. 128ff. Gottlob Frege, Letter to Russell (rgoz), in From Frege to Godel, ed. Jean van Heijenoort (Harvard University Press, 1 9 6 7 ) ~p. 126.
THE RUSSELL-MEINONG DEBATE
341
he "now feel[s] hardly any doubt that the no-classes theory affords the complete solution of all the difficulties" of the paradoxes. [TTN, 1641 Thus, in Russell's view during the most intensive period of controversy over Meinong's objects, the no-class theory figured centrally in solving the paradox. According to this theory, which appears in modified form in Principia, classes, as Godel puts it, "never exist as real objects, and sentences containing these terms are meaningful only to such an extent as they can be interpreted as a f a ~ o nde parler, a manner of speaking about other things. "53 Russell finally proposed several solutions to the paradoxes: the vicious circle principle and type theory in addition to the no-class theory. Charles Chihara has proposed an overview of these solutions which fits well with the view sketched here. He suggests that Russell provided a two-part solution to the paradoxes, consisting of a "negative" theory, i.e., the vicious circle principle, and a "positive" theory, i.e., type theory with restrictions on illegitimate totalities. These latter restrictions, Russell said, must not be a d hoc but result "naturally and inevitably from our positive doctrines," [ML, 631 through the analysis of key concepts, such as "class." The no-class theory served this purpose, and, as Chihara emphasizes, it was preceded by the theory of descriptions which "paved the way for [Russell's] no-class theory by serving as the Russell's no-class theory was therefore important in his view for dispensing with talk of the troublesome classes,55as his theory of descriptions was important for dispensing with talk of troublesome nonexistent objects. Russell was motivated in his work on the foundations of kathematics to avoid committing himself to objects which engendered contradiction. Similarly, he was motivated in his dealings with Meinong's
') Kurt Godel,
14
"Russell's Mathematical Logic," in The Philosophy of Bertrand Russell, ed. P. Schilpp (Evanston: Open Court, 1 9 4 4 ) ~p. 133. Godel also remarks that "classes can be dispensed with [in PM] but only if one assumes the existence of a concept whenever one wants to construct a class." (p. 141) W. V. Quine claims that Russell's confusion of uselmention led to his (mistaken) belief that he had "disposed of classes in some more sweeping sense than reduction to attributes." "Russell's Ontological Development," p. 296. See also "Whitehead and the Rise of Modern Logic," in The Philosophy o f A. N. Whitehead, ed. P. Schilpp (Open Court, 1941). Charles Chihara, Ontology and the Vicious Circle Principle (Cornell, 1972), chap. I, part of which is reprinted in B. Russell: A Collection of Critical Essays, ed. D. F. Pears (New York: Doubleday Anchor, 1972), pp. 259-63. Charles Parsons, on another interpretation, notes: "It is hard to see what is left of Russell's no-class theory once the axiom of reducibility is admitted." Russell himself says that the axiom of reducibility accomplishes "what common sense effects by the admission of classes." [ML, 811 See C. Parsons, "What is the Iterative Conception of Set?" in Mathematics in Philosophy (Cornell University Press, 1983), p. 293, f. 37.
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objects to avoid an analysis which would commit him to contradictory objects. If we view these two phenomena in tandem, then Russell's reaction to Meinong becomes an important -and positive -part of his intellectual development.
X. CONCLUSION Historically speaking Russell emerged from the debate with the upper hand in terms of influence lasting through the mid-twentieth century. Indeed his arguments have been taken as so persuasive that in some quarters to be compared with Meinong is to be condemned by association. As my interpretation shows, this is unfair. But this phenomenon must also be seen as continuous with Russell's role in the shifts which marked the beginnings of analytic philosophy in the early twentieth century. Russell initiated a new disciplinary approach and set of problems, which were highlighted by his vivid comments and refutations of Meinong's nonexistent objects. This approach became part of "normal method" in the sense that those who followed in his tradition accepted a certain way of doing philosophy.s6 Meinong played a curious role in this shift during 1904-1920. In 1904 Russell imported Meinong's theories from the continent to support his and Moore's realism in the attack on idealism. Russell and Meinong were fairly close in advocating a realist account of perception, in how they analysed the intentional aspects of sensory acquaintance, and even in some respects, the notion of object in the principle^.^' Their shared starting point preceded a debate which culminated in 1905-1907 in a sharp divergence based on the differing frameworks of Russell's "logic" and Meinong's "object theory." Philosophically speaking it is by no means clear that Russell emerged with the upper hand. Each of his objections can be met by theories elaborated in Meinong's writings, as summarized in Section VII. Not only are Russell's objections not definitive, they sometimes rest on misunderstandings of Meinong's major principles. The debate comes down to a standoff on the critical notion of what it is to be an object, not in terms of concrete objects of space-time, but in the hazier area of possible and impossible nonexistent (nonsubsistent) objects. These challenge the classical laws of logic, as shown particularly in objection ( I )on contradiction. These trou-
56
"
See Terence Parsons, Nonexistent Objects, pp. 5-9. See footnote 6 above. In [POM] a 'term' is defined as "whatever may be an object of thought." In [POM, 551 Russell notes that the indefinite descriptions "a man" and "some man . . . denote objects." He then refers the reader to Meinong's discussion of the indefinite article [in "a man"] in "Abstrahiren und Vergleichen." See also Nicholas Griffin, "Russell on the Nature of Logic (1903-1913)," Synthese 45 (1980), p. 1r7ff.
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blesome objects forced the issues for both philosophers. As I hope to have shown, Russell and Meinong were operating out of different but still comparable sets of premises on these questions. Indeed the points at which their theories clash are critical ones for any object-theoretic or ontological investigation. Although Russell's reasons for objecting to Meinong's nonexistent objects centered on classical logical laws, these were closely bound up with his criteria for the notion of object. Meinong's views raised challenging issues for such criteria, then as now. As Charles Parsons has remarked after considering ways in which Meinong's views can be formally represented in contemporary logic, "the lesson of our discussion of Meinong should be that we need to put more flesh onto the bare form given by formal logic in order to understand the notions of object and existence, even in mat he ma tic^."^^ A distinction must be drawn between classical logic and the philosophical views on logic associated with logicism. T o be a classicist is not necessarily to be a logicist. Russell's version of strict adherence to classical laws was informed by his views on the universality of laws of logic. For him, every thing reasonable and communicable falls within these laws, and there can be no intelligible viewpoint which stands above and outside of Meinong, on the other hand, although he was not a logicist, was more 'classical' than popular accounts would suggest. He limited the laws of noncontradiction and excluded middle not in the cases of concrete objects but in the cases of some objects of higher order and of some nonactual (possible or impossible) objects. So the suspension of classical laws is strictly limited in Meinong's theory. It does not affect what is actual or "real." Meinong's theory of possibles and impossibles arose out of his motivation to consider at the level of 'objects' the widest scope of what can be entertained (even if not conceived) by human imagination and language. Russell's motivation, in keeping with a principle of parsimony and his attempt to construct only with "known entities," was to take such 'objects' as fictions and analyze them away. Differing motivations and frameworks help explain how Meinong and Russell each regarded the apparent contradictions which arise out of description in natural language (e.g., the round square which is both round and non-round). On the level of objects, Russell may have seen these contradictions as paradoxes, whereas Meinong saw them as "belonging" in the realms of "homeless objects," and therefore not as
58
r9
"Objects and Logic," p. 509. See Warren Goldfarb, "Logic in the Twenties," Journal of Symbolic Logic, Vol. 44, No. 3 (1979), for a discussion of the logicist framework. Also, J. van Heijenoort, "Logic as Calculus and Logic as Language," Synthese, Vol. 32 (1967).
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veridical paradoxes. T o put it less metaphorically, the sense of what it is "to be" an object was equivocal for Meinong in a way that Russell could not accept. Meinong took these sentences as surface perturbations which could be analyzed according to his theories of existence, negation, extranuclear properties, incomplete objects and objects of higher order. Meinong thus presents the claim of a consistent and coherent theory. His views yield many fertile ideas which should provide the basis for further exploration.60
SELECTED BIBLIOGRAPHY O F WRITINGS BY RUSSELL AND MEINONG* ::. ::. :&
I8
I 899
* ::.1902
%;
k,
.. ..
1903
.. ..
1904
..
1904 1904
.. ..
1905
..
1905
..
" " 1906 . .
60
Objects of Higher Order [Gegenstande hoherer Ordnung], trans. M. Kalsi. Nijhoff, 1978. [HO] . Review of A. Meinong's ~ b e die r Bedeutung des Webershen Gesetzes. Mind, n.s. 8. . ~ b e Annahmen. r First Edition. Leipzig: Barth. [UA] . Principles of Mathematics. London: Cambridge University Press. (Second Edition with new Introduction, London: Allen and Unwin, 1937). [POM] . "Meinong's Theory of Complexes and Assumptions," Mind, n.s. 13. [MTCA] In Essays in Analysis, ed. D. Lackey. [MTCA] . Letter to Meinong (12 December). [See Appendix] . "Theory of Objects" [ " ~ b e rGegenstandstheorie"] in Realism and the Background of Phenomenology, ed. Roderick Chisholm. Free Press, 1960. Originally published in Untersuchungen zur Gegenstandstheorie, along with articles by others [Mally, Ameseder]. Leipzig: Barth. [TO] . "On Denoting," Mind, n.s. 14. In Logic and Knowledge, ed. R. C. Marsh. Allen and Unwin, 1956. [OD] . Review of "Theory of Objects," Untersuchungen, Mind, n.s. 14. In Essays in Analysis, ed. D. Lackey. [RTO] . ijber die Erfahrungsgrundlagen unseres Wissens. Berlin: Springer. "Toward an Epistemological Assessment of Memory," in Empirical Knowledge, ed. R. Chisholm and R. Swartz. Prentice-Hall, 1973. [MEM]
I must thank the following persons for helpful suggestions o n earlier drafts: R. Chisholm, A. Danto, W. Demopolous, N. Griffin, C. Parsons, M. Sainsbury, R. Shope, and P. Simons. Any mistakes, of course, are mine.
"" Meinong's works are starred. Russell's left unstarred. Abbreviations follow in brackets.
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1906
...
Review of " ~ b e die r Erfahrungsgundlagen," Mind, n.s. [RMEM] . . . ~ b e rdie Stellung der Gegenstandstheorie im System der Wissenschaften. Leipzig: Voightlander. [USG] . . . "On Some Difficulties in the Theory of Transfinite Numbers and Order Types," in Essays in Analysis, ed. D. Lackey. [TTN] . . . Letter to Meinong (5 November). [See Appendix] . . . Letter to Meinong (5 February). [See Appendix] . . . Review of Meinong's ~ b e rdie Stellung der Gegenstandstheorie, Mind, n.s. 16. (Reply to Meinong's point that Law of Contradiction does not apply to impossibles, and rejection of "being existent" vs. "exists" distinction.) In Essays in Analysis, ed. D. Lackey. [RUSG] . . . "Mathematical Logic as Based on Theory of Types," in Logic and Knowledge. [ML] . . On Assumptions. Second Edition, trans. J. Heanue. University of California, 1983. [OA] . . . "Knowledge by Acquaintance and Knowledge by Description," in Mysticism and Logic. Barnes and Noble, 19 17. [KAKD] . . . "On the Nature of Truth and Falsehood," in Philosophical Essays. Longmans. [NT] . . . Principia Mathematica, Vol. I, with A. N. Whitehead. Cambridge University Press. (Second Edition with new introduction by Russell, 1925). [PM] . . . Theory of Knowledge, The 1913 Manuscript, ed. E. Eames and K. Blackwell, Vol. 7 of Collected Papers. Allen and Unwin, 1983. [TK] . . . "On the Nature of Acquaintance," in Logic and Knowledge. (These articles are the first three chapters of TK above). [NA] . . . ~ b e Mtiglichkeit r und Wahrscheinlichkeit (On Possibility and Probability). Leipzig: Barth. Vol. VI of Gesamtausgabe, ed. R. Chisholm. Graz, 1972. [UMOG] . . . O n Emotional Presentation [chap. z, "Defective Objects"], trans. M. Kalsi. Northwestern University Press, 1972. [EPI . . . The Philosophy of Logical Atomism, in Logic and Knowledge. [PLA] I 5.
""1906 1906
1906 1907 1907
1908 :D'"1910
1910
1910 1910
1913
1914
" "1915 :."1917
1918
k, .C*
1919
. . . Introduction
1920
..
1921 1944
.. ..
1951
..
1959
..
to Mathematical Philosophy. Allen and Unwin. [IMP] . "Selbtsdarstellung," in Die Philosophie der Gegenwart in Selbstdarstellung, ed. Raymond Schmidt. Leipzig: Felix Meiner Verlag, 1921. (Portions translated in Appendix I, 11, to R. Grossman, Meinong. Routledge and Kegan Paul, 1974.) [ S E W . Analysis of Mind. Allen and Unwin. [AM] . "My Mental Development," in The Philosophy of Bertrand Russell, ed. P. A. Schilpp. Northwestern University Press. [MMD] . Autobiography, Volume I (1872-1914). Little Brown. [AUTI . My Philosophical Development. Simon and Schuster. [MPDI
APPENDIX RUSSELL'S THREE LETTERS T O MEINONG"
+
Russell's First Letter to Meinong, 1904 Ivy Lodge Tillford Farnham I~.XII.1904 My Dear Sir, Many thanks for your kind letter and for the work "Theory of Objects" (" ~ b e Gegenstandstheorie"). r I have read this work as well as Nos. I1 and VIII of Dr. Ameseder with great interest. I find myself in almost complete agreement with the general viewpoint and the problems dealt with seem to me very important. I myself have been accustomed to use the name "Logic" for that which you call "Theory of Objects," and the reasons you cite against this use on p. zoff appear to me hardly decisive. Still, this is a matter of secondary importance, and 1 admit that a new viewpoint should be signified by a new name.
"
My translation follows Russell's German as closely as possible. The original lctters are in the University Library in Graz. The letters are published in German in A. Meinong, Philosophenbriefe, ed. R. Kindinger (Graz, Austria: Akademische Druck - u. Verlagsanstalt, 1965),pp. 150-54.My thanks to Akademische Druck - u. Verlagstanstalt for permission to publish these translations. I am grateful to Peter Simons for suggestions on improving the translations.
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I have always believed until now that every object must be in some sense, and I find it difficult to recognize nonexistent objects. In a case such as the golden mountain or the round square one must distinguish between sense and reference (in accordance with Frege's distinction). The sense is an object and has being, whereas the reference on the other hand is not an object. One sees the difference between sense and reference best in mathematical examples: "The positive square root of 4" is a complex sense, whose reference is the number 2. I am in complete agreement with the view that mathematics is theory of objects. This is in fact one of the main theses of my Principles of Mathematics. If you do not possess this book, I shall gladly send it to you. Its entire first part is explicitly concerned with questions concerning object theory. Of course there are many discussions whose purpose is purely formal, that is, serving only to lead into technical mathematical procedures. Yet the general (non-technical) questions are the essential matters treated there. I find a certain difficulty with what you say about metaphysics on p. 40, although I agree with the main thesis. Empiricism, it seems to me, cannot instruct us on all that exists. Consequently, if there is a metaphysics, it must be of an a priori nature. I hope that your philosophical methods will soon be widely known and it will be a pleasure to me to contribute to this as much as possible. Respectfully yours,
Bertrand Russell
Russell's Second Letter to Meinong, 1906 Bagley Wood, Oxford 5.XI.1906 My Dear Professor, Many thanks for your kind letter and for the interesting article " ~ b e r die Stellung der Gegenstandstheorie in System der Wissenschaften." (The Place of Object-Theory in the System of Knowledge). I am also of the opinion that the differences between us are entirely unimportant. In general I find myself to have almost exactly the same viewpoint as you. In
particular I agree with you when you assert that mathematics is 'daseinfreies Wissen'-knowledge indifferent to being-and properly belongs to object theory. Concerning impossible objects, I am not offended by the consequence that the golden mountain must be rejected along with the round square. That was why in my article "On Denoting" I used the King of France as an example. As you know, I recognize no fundamental concept of necessity. That is why I cannot distinguish between impossible and non-existing objects. Moreover, I cannot understand how one can distinguish between 'existieren' and 'existierend sein' [between 'existsy and 'is existent']. I of course do not deny that one can compose true as well as false propositions in which impossible objects occur as the subjects. However, I believe that such propositions must be interpreted in the manner which I explained in my article "On Denoting." What you say on p. 5 I about Frege pleases me greatly. He has been read very little because of his extraordinary difficulty. Yet he is in my opinion worthy of the highest degree of recognition. Most respectfully yours,
Bertrand Russell
Russell's Third Letter to Meinong, 1907 Nr. 6282 0. UB. Bagley Wood, Oxford 5.11.1907 My Dear Colleague: Many thanks for your sending me the second article of " ~ b e die r Stellung der Gegenstandstheorie in System der Wisserischaften," which interests me very much. I have carefully read what you have written on the concept of necessity and I believe the difference of opinion between us is not so great as it appears at first sight. In theory of knowledge I fully recognize the difference between a priori and empirical knowledge. It appears to me, however, that the distinction connected with it in the corresponding Objectives consists wholly in the fact that those which are known a priori are daseinfrei (indifferent to being) whereas those which are known empirically are always existential. The word 'necessary' is
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however very ambiguous in ordinary usage, and only a rather long discussion would investigate all possible senses of the word. Unfortunately I do not agree with what you write on Non-Euclidean Geometry. I have defended my own views more than once against Poincare in the "Revue de Metaphysique et de Morale," and also in Principles of Mathematics, Part VI, and very briefly in Mind, July 1905, pp. 414-5. Non-Euclidean geometry does not assert that two parallel lines can intersect; on Non-Euclidean geometry it is doubtful whether there are parallels. I am also of the opinion that geometry is daseinfrei knowledge (indifferent to being) insofar as geometry is pure mathematics. As pure mathematics all geometries are equally true. Insofar as they prove merely what follows from certain premises, they are all eqyally hypothetical. There is however, one space which exists, or in some way belongs to existence, so that we can refer to it as the space of the real physical world. Now whether this space furnishes an example of Euclidean or Non-Euclidean geometry, can only, it seems to me, be decided empirically. That two parallels cannot intersect remains indubitable. Yet one can question whether the space of the real world allows parallels at all. In order for the possibility of empirical knowledge of spatial relations to be meaningful, one must of course grant that real relations can be given empirically. Then one asks: Are the spatial relations which are perceived (or at least recognized in perception) of an Euclidean or Non-Euclidean nature? Mathematics proves that any one class which an Euclidean space through relations, simultaneously generates through other subsistent relations all non-Euclidean spaces. Of all these systems of relations, however, there is only one system of which one can say in a sense that the relations of which it consists (besteht), exist (existieren). In your discussion I find nothing, so far as I see, which contradicts this view. On the whole I agree with your work; it can therefore be useful to discuss details. With friendly regards I remain, Yours truly,
Bertrand Russell
