Truth in Context - Introduction

Introduction

In the course of this century, a large segment of Anglo - American philosophy was persuaded to abandon the traditional conception of philosophy on which it is an a priori inquiry into the most general facts about reality . This conception was replaced with one or another of two naturalist conceptions of philosophy : philosophy as therapy designed to cure the linguistic illness of which philosophy itself is the cause, and philosophy as an a posteriori discipline within natural science. Expressing the former naturalist conception, Wittgenstein (1961 [ 1922], sec. 6.53) wrote in the Tractatus: The correct method in philosophy would really be the following : to say nothing except what can be said, i.e., propositions of natural science- i.e., something that has nothing to do with phi losophy - and then, whenever someone else wanted to say something metaphysical , to demonstrate to him that he had failed to give a meaning to certain signs in his propositions . This conception remained with him throughout his life . In the PhilosophicalInvestigations, Wittgenstein (1953, sec. 109) articulates his therapeutic conception of philosophy in the famous passage: [Philosophical problems ] are, of course, not empirical problems ; they are solved , rather, by looking into the workings of our language, and that in such a way as to make us recognize those workings : in despiteof an urge to misunderstand them. The problems are solved , not by giving new information , but by arranging what we have always known . Philosophy is a battle against the bewitchment of our intelligence by means of language. In an equally famous passage, Quine (1969a, 83) expresses the latter philosophy as natural science- - conception of philosophy : Our very epistemological enterprise, therefore, and the psychology wherein it is a component chapter, and the whole of natural science wherein psychology is a component book - all this is our

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own construction or projection from stimulations like those we were meting out to our epistemological subject. There is thus reciprocal containment , though containment in different senses: epistemology in natural science and natural science in epistemology. " " in Broadly, there are three doctrines called naturalism contemporary " . The first , which may be called onto logical naturalism philosophy " , claims that the universe consists exclusively of natural objects, that is, spatiotemporal objects belonging to the causal order in nature. This is the contemporary naturalism closest to the doctrines that have to as " naturalism ." The second doctrine , traditionally been referred " which may be called epistemological naturalism ," claims that knowledge is knowledge of natural objects. The third doctrine , which may be called " methodological naturalism ," claims that the only way we can obtain knowledge of the universe is through prescientific and scientific investigations of natural objects. Onto logical naturalists are epistemological and methodological naturalists , but epistemological and methodological naturalists mayor may not be onto logical natural ists. Since he thinks that our theories in natural science commit us to abstract objects because they involve ineliminable quantification over them , Quine, who is a methodological naturalist , is neither an onto 1 logical nor an epistemological naturalist . The naturalist hegemony is well established today in the form of programs to naturalize philosophy and philosophize naturalistically, in agendas to deflate one or another philosophical concept, in revivals of the late Wittgenstein ' s therapeutic positivism , in resuscitations of American pragmatism , and in construals of philosophy as an exclusively second-order discipline concerned with linguistic and / or conceptual analysis. These positions , which are at some points overlapping , at some points independent , and at some points even conflicting , are tied together by the privileged status they accord to natural objects and by their firm epistemological opposition to anything smacking of an autonomous metaphysics claiming to provide a priori knowledge about reality . This hegemony flourish es despite a number of prominent philosophers , such as Blanshard, Chisholm , Ewing, Langford , Thomas Nagel , P. F. Strawson, whose philosophizing is a continuation of just and Pap, ' 1. In the philosophy of mind , the term " naturalism " is often used just to mean antiCartesianism . Here it is better to use a term like " materialism ." In any case, my argument in this book is not directed against philosophers who take themselves to be " naturalists " in this sense, unless, of course, they are also naturalists in any of the sensesof " naturalism " in the text.

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such old -style metaphysics. The problem is not that such philosophers have failed to produce anything of recognized philosophical significance , but rather that their work lacks a substantive metaphilo sophical dimension , and that it either ignores important philosophical developments that have taken place within the prevailing naturalistic outlook or accommodates itself too much to that outlook . As a consequence , contemporary representatives of traditional philosophy have not articulated and defended a metaphilosophy with which to oppose the well -articulated and well - defended positions based on Wittgen stein' s and Quine ' s naturalism .2 One consequence of this was that the stereotype of traditional phi losophy as a series of interminable and inconclusive squabbles was allowed to go unchallenged . This stereotype has motivated critics of metaphysics from Kant to CaTnap, who see such squabbling to be characteristic of metaphysical philosophizing and to arise from the ' metaphysician s view that philosophy in and of itself is a legitimate source of a priori knowledge about reality . The critics are impatient with philosophical business as usual and , in the case of many of them , particularly the positivists and Quine, they are attracted by the ideal of a more amicable future in which an intellectual consensusof the sort that exists in sciencebecomes the way of philosophy .3The late Wittgen stein and his followers , of course, do not share this ideal. The critics agree in denying that philosophy can be a legitimate source of a priori knowledge about reality, but they disagree about why . There are two main diagnoses of what is wrong with thinking that philosophy can be a legitimate source of a priori knowledge about reality . According to the diagnosis popular among Wittgensteinians , logical empiricists , and ordinary language philosophers , the mistake is 2. Even the best of such philosophizing is disappointing from this perspective . Strawson's (1985) championingof the rationalisttradition doesnothing to articulatethe metaphilosophy inherent in that tradition, and, as I (1990b , 344, n. 1) have argued ' elsewhere , the book s discussionof intuition and evenof naturalismmuddiesthe waters. ' , which, I believe, makessignificantcontributions Nagels (1986) book, TheViewfrom Nowhere to severalmetaphysicaltopics, is contentsimply to endorsea rationalistperspective ' , 105- 9) overestimationof the againstQuineanempiricism. Further, Nagels (1986 force of Wittgensteinianphilosophy of language , particularly the rule-following argument , leadsto the absenceof a discussionof the essentialrole that mathematicalrealism plays in the formulation of rationalismand in the developmentof a metaphilosophy basedon realismand rationalism. 3. Of course, the positivist claim to eschewmetaphysicsdid not go unquestioned . The , rightly I believe, of doing metaphysics , as it were, under the positivistswere accused table. In particular, their criterion of cognitive significancewas criticized as either an a priori metaphysicalprincipleor a self- defeatingempiricalone. But their explicitdoctrine was that it was a convention. (Seechapter6, section3.)

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thinking of philosophy as a first -order discipline like the sciences, which , like them , has some aspect of reality as its subject matter. This is wrong becausethe sciencescover reality exhaustively. Once physics, chemistry, psychology, social science, history , and so on have staked their claims to their subject matters, there is no part of reality left for philosophy . With no domain of facts to settle issuesbetween conflicting metaphysical claims about reality, it is no wonder that metaphysicians, laboring under this misconception , should be involved in endless controversies : the controversies have no objective resolution because they are not about reality . Mary Warnock (1995) has aptly described this diagnosis in her recent reflections on the vicissitudes of ethics in this century. Speaking of philosophy at Oxford during and after World War II , she (1995, 22) writes : The new philosophy was contrasted with a supposed golden age, when philosophers were metaphysicians, and did not bother about the concepts, or words , actually embedded in language . . . . philosophers were allowed to pontificate about [causation , mind , and so forth ] . . . and use what concepts they chose to invent . In contrast, " the new philosophy ," she (1995, 21- 22) writes , . . . was a ' second-order ' subject. What we meant could be put in the following way : botanists, let us say, talk about plants and their genetic composition ; and historians write about events and people of the past. Philosophy, however, has no subject-matter of its own . There are no philosophical objects to be examined. Philosophy, unlike botany or history, does not apply concepts to things ; it is one step higher up the ladder of abstraction. . . . Philosophy considers the concepts that other subjects employ, and seeks clarification , or analysis, of them. It is out of this description of philosophy (which I still think is a good one), that there arose . . . the idea that philosophy is linguistic . The " new philosophers " took the phenomena about which traditional metaphysicians speculated to be natural phenomena belonging to the province of natural scienceslike physics and psychology. They concluded that genuine knowledge about causation, mind , and so forth is empirical knowledge in natural science. In order for there to be something beyond natural phenomena, there would have to be nonnatural objects and a priori knowledge . But the strong strain of naturalism and empiricism is the background of these " new philosophers " assured them that there are no non-natural phenomena and there is no

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a priori knowledge . Hence, having no first -order subject matter, either philosophy can deliver no genuine knowledge at all or it is asecond order subject which delivers second-order knowledge in the form of linguistic and / or conceptual analyses of first -order knowledge . There was, however, disagreement among these naturalists about how philosophy should be thought of in relation to the natural realm. The main issue is whether or not philosophy is kicked upstairs to become some sort of second-order discipline , with the task of clarifying the linguistic and conceptual matters in first -order disciplines . While many of the philosophers about whom Warnock is talking saw phi losophy as such a second-order discipline , the late Wittgenstein did not. He (1953, sec. 121) wrote : One might think : if philosophy speaks of the use of the word " " philosophy there must be a second-order philosophy . But it is not so: it is, rather, like the case of orthography, which deals with the word " orthography " among others without then being second-order. For him (1953, sec. 124), philosophy makes no contribution to human - - even second-order knowledge : " It leaves everything as it knowledge " is. Philosophy is a kind of linguistic therapy. Wittgenstein (1953, secs. 122 and 123) thinks it should just help us to " commanda clearview of the use of words " principally by helping us to " see connexions" in ". the uses of words through " finding and inventing intermediatecases ' s was the other Quine diagnosis of what is wrong with the traditional view that metaphysical philosophy can be a legitimate source of a priori about knowledge reality . He agrees with other naturalists that the sciences cover reality exhaustively. Once physics, chemistry, psychology , social science, history , and so forth have staked claims to their ' subject matters, there is nothing left . Hence, there can t be an autonomous ' metaphysical philosophy . But for Quine this doesn t mean that philosophy cannot legitimately address questions about reality. It only means that it must do so within natural science. The trouble with traditional metaphysics is that it took itself to be an autonomous discipline with the right to speculate about reality independently of the experiential and methodological constraints internal to natural science. Without such constraints, the traditional philosopher ' s conclusions were often unscientific speculations about scientific matters. On both diagnoses, the cure is to replace the traditional conception of the relation of philosophy to reality with a naturalistic one on which the sciencesare the only first -order disciplines . Beyond this , each form of twentieth - century naturalism has its own idea of how to understand the relation between philosophy and science. Except for the late

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Wittgenstein , naturalists see philosophy as at least a second- order discipline that is part of the scientific enterprise . But there is disagreement about the relation of philosophy to first -order scientific disciplines , and hence about the role philosophy plays in scientific . The disagreement turns on which aspect of what Quine investigation calls IIreciprocal containment " it is that a naturalistic metaphilosophy ither " epistemology in natural science" or " natural science stresse "~ ' in epistemology." Every scientistic naturalist accepts the view that philosophy is to some extent concerned with clarifying the linguistic and conceptual practices of first -order disciplines . But those who stress natural science in epistemology tend to think that it is entirely legitimate for philosophers - with suitable basic training in science- to get down there in the trenches with the scientists, not only to provide more scientific troops but also to further their own quest for philosophical enlightenment . On the other hand , those who stress epistemology in natural science tend to think of philosophers who do not stick to metascientific analysis as having gone native . Each form of twentieth - century naturalism thought that a proper dose of its medicine would cure philosophy of the diseaseof metaphysics . The interminable and inconclusive squabbling of the past would disappear and philosophy would enjoy a future in which honest philo sophical endeavor is rewarded with steady philosophical progress. But, as must by now be evident , we are not living in such a philosophical Canaan. Even a cursory look at the controversies in contemporary philosophy of language and logic , the philosophy of mathematics, the philosophy of mind , and so on shows that , although the cures have been tried , there is not the slightest sign of the disease going away. Indeed , it looks more as though the disease has spread to the hospital staff. Philosophical squabbles are going on as before with no serious prospect of abating, and , if anything, the range of controversy has only increased with the addition of the internal disagreements among Wittgensteinians and among Quineans and with the disagreements between Wittgensteinians and Quineans . Hence, some reassessmentof the " revolution in philosophy" is surely in order. The present book is one reassessment. It is a radical reassessment . Its broad aim is to provide the metaphilosophy and the arguments to show that abandoning the traditional conception of philosophy in favor of one or another form of naturalism was a fundamental mistake. Not that traditional versions of the metaphysical conception of philosophy did not deserve criticism , but the critics threw out the baby with the bathwater. Part of my case for this claim was presented in my (1990b) earlier book , TheMetaphysicsof Meaning. That

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book took the necessary first step of showing that Wittgensteinian and Quinean arguments do not justify abandoning the traditional metaphysical conception of philosophy . The present book takes the next step of formulating and justifying a new version of traditional realist and rationalist philosophy. This version is the position to which the title of this book refers. This enterprise of trying to revive the traditional conception of philosophy did not originate in nostalgia for the past. I spent my philosophically formative years during the flowering of logical empiricism , Quineanism , and ordinary language philosophy ; I was anaturalist and empiricist of the scientistic sort. Nevertheless, like nearly everyone who goes into philosophy, I was initially drawn in by the pull of philosophy' s uniquely puzzling questions: What is knowledge ? What is the relation between mind and body ? Is there free will ? Are ethical values universal ? and, particularly , its central question , What is philosophy ? My disillusionment with naturalism , as I will explain below, came as the result , on the one hand , of finding that naturalist and empiricist philosophies do not provide satisfying answers to the questions that first lure us into philosophy and, on the other, of coming to think that answering some of those questions requires a nonnaturalist position combining realism in ontology with rationalism in epistemology. Such a position differs from the naturalist positions intwentieth century philosophy in various ways . One way in which first -order and second-order disciplines can differ is in terms of the questions they ask. The distinction in this case is that a first -order discipline addresses questions about some domain of objects in the world and asecond order discipline addresses questions about the linguistic forms or concepts employed in first -order disciplines . Another way in which they can differ is in terms of their role in answering questions about the domain . The distinction in this caseis that the first - order discipline has a fact-finding and fact-systematizing role in the investigation of the scientific domain , and the second-order discipline does not. With respect to the former distinction between first -order and second - order disciplines , our non -naturalist position says that philosophy is both first - order and second-order. It thus rejects the naturalist positions that would restrict the questions it asks. Warnock' s " new philosophers " simply had too impoverished a conception of the range of questions a discipline can address. Mathematics addresses questions about a domain of numbers, sets, spaces, and so on, but , since metamathematics part of mathematics, mathematics also addresses questions about the technical language within which mathematical accounts of those domains are given . My suspicion is that , not having separated

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the two distinctions between first -order and second-order disciplines , those philosophers , already carried along by the linguistic turn , found it easy to assume that , since philosophy does not contribute to the empirical work of the natural sciences, its questions are, by default , restricted to the linguistic and / or conceptual structure of first -order disciplines . With respect to the second distinction , I think that the naturalist ' s diagnosis is a half -truth . The true part is that philosophy is not a first -order discipline in the hands- on sensein which the sciencesthemselves are. There is surely some room for doubt about this in connection with ethics and aesthetics, where there is more plausibility in thinking of philosophy as a first -order discipline than there is in the philosophy of science. But I believe that thinking of them in this way confuses the roles of moralist and moral philosopher and the roles of art critic and aesthetician. Ethics and aesthetics are better seen as second-order studies : respectively, studies of the work of moralists and art critics. Philosopher -moralists like Sartre and philosopher -art critics like Danto wear two hats. Furthermore , the universal scope of philosophy strongly suggests that it is a second-order discipline with general interests in the common epistemological and onto logical problems of first -order disciplines . Philosophy would hardly have this particular form of universal scope if it were literally a collection of first -order disciplines with circumscribed domains of objects as their subject matters. The correct part of the naturalist ' s diagnosis is that philosophy is a second-order discipline in the sense that it is not part of a scientific attempt to ascertain the facts about a domain and build a theory to explain them on the basis of deeper principles . On my non-naturalism , philosophy is a first -order discipline only in asking questions about the world . The traditional philosophers who took philosophy to be an inquiry into general facts about reality did not , I think , want to say that philosophy is part of the scientific enterprise in a hands-on way. Rather, I think their view was that philosophy is part of the scientific enterprise in another way. It has the status of a second-order discipline in having no fact-finding or fact-systematizing role in scientific investigation , but that does not restrict its epistemic contribution to serving as conceptual referee in someone else' s ball game. The false part of the diagnosis is the assumption that not being a first -order discipline in not having a fact-finding or fact-systematizing role in scientific investigation means that a discipline is not in a position to address substantive questions about reality . The possibility that the naturalist ' s diagnosis overlooks is that some questions that arise in the course of a scientific investigation of reality are not questions that can be answered by broadening the investigation to attain a wider scientific

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knowledge of the facts or better scientific knowledge of their underlying principles . This is becausethe questions are not scientific questions. They are philosophical questions. They concern the nature and validity of the very methodology on which such knowledge rests. For example, physics is in no position to dispel skeptical doubts about how we know that the future will be sufficiently like the past to justify our confidence in the scientific use of induction .4 Philosophical questions that arise in relation to mathematics are: Are numbers and sets objects? If so, what kind of objects are they ? What does the mathematician ' s knowledge of numbers and sets consist in ? Does mathematical knowledge depend on natural facts? and Why does the mathematician ' s knowledge of numbers and sets seem so much more certain than even the physicist ' s knowledge of matter ? Similar questions arise in connection with logic and linguistics . Such philosophical questions concern both the fundamental nature of the reality investigated in the first -order discipline and the methods that can provide knowledge of it . Those questions receive no answer in first -order mathematical , logical , and linguistic investigations , not simply because the focus of those investigations is on describing and explaining facts about the objects under study, but becausethose questions concern the status of the investigations and their methodological foundations .5 On our position , philosophy , conceived of as a second-order discipline with no role in the fact-finding and fact-systematizing of science, nonetheless answers certain questions about the objects in the domains of the sciences. How does it go about doing this? There is a long answer and a short answer to this question . The long answer, and it is only a partial answer at that , is this entire book , but particularly chapters 2, 4, 5, and 6. The short answer is that philosophy tries to answer such questions in the way that philosophers in the foundations of mathematics try to answer questions like what kind of things numbers are. Philosophical attempts to answer this question constitute the dialectic 4. Quine (1975,68) claimsthat skepticalquestionsare scientificquestions.I shall return to his claim below. I noteherethat his inability to sayanythingabouthow sciencemight resolvesuchdoubtsarguesin favor of the view in the text. SeeStroud (1984, 209-54). 5. Although mathematicians , logicians, and linguists normally confine themselvesto answeringquestionsabout the structureof objectssuch as numbers, sets, propositions, and sentences , some, like Frege, Hilbert, Brouwer, GOdel, and Chomsky, have not, for onereasonor another,beencontentto leavephilosophicalquestionsto the philosophers , but havesteppedout of their role as scientiststo addressepistemologicalor ontological issuesabout their discipline in a way that contributesimportantly to our philosophical understanding.Suchscientistsare rare, and we mark their specialstatusby ------- ; to them as both a scientistand a philosopher , as, for instance , in the title of the -Scientist : Philosopher volume AlbertEinstein .

~fprring Schilpp

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among realists, conceptualists, and nominalists that began in Greek philosophy and that continues, in a far more professionalized form , to the present. It is, moreover, hald to see how the foundations of mathematics , conceived of as a discipline the aim of which is to answer questions about the epistemology and ontology of mathematics, can be understood without taking it to be a second-order discipline (in the sense of the second first -order / second- order distinction ) that can provide knowledge of reality . Naturalism also was behind the positivist attack on traditional phi . s claim to provide a priori answers to substantive factual questions losophy' about reality . Note again the early Wittgenstein ' s (1961 [ 1922], sec. 6.53) remark quoted above: The correct method in philosophy would really be the following : to say nothing except what can be said, i.e., propositions of natural science- i.e., something that has nothing to do with phi losophy - and then, whenever someone else wanted to say something metaphysical , to demonstrate to him that he had failed to a give meaning to certain signs in his propositions . Schlick (1949, 285) thought that metaphysicians radically misjudge the nature of the philosophical questions they attempt to answer: . . . The error committed by the proponents of the factual a priori can be understood as arising from the fact that it was not clearly realized that such concepts as those of the colors have a formal structure just as do the numbers or spatial concepts, [which ] determines their meaning without remainder. . . . Thus, [the sentences that are the show -pieces of the phenomenological philoso] phy say nothing about existence, or about the nature of anything , but rather only exhibit the content of our concepts . . . they bring no knowledge , and cannot serve as the foundations of a special science. Such a science as the phenomenologists have promised us just does not exist. As I see it , the early positivists and more recent positivists such as Camap and the late Wittgenstein overestimate the scope of linguistic meaning . Linguistic meaning is not rich enough to show either that all metaphysical sentences are meaningless or that all alleged synthetic a priori propositions are just analytic a priori propositions . The idea that ' linguistic meaning can be used for such purposes was Frege s; in particular , it came from his expansion of the concept of analyticity , undertaken in order to provide a semantic basis for his logicist explanation of mathematical truth as analytic truth . To a philosopher like Schlick, Frege' s logical semantics together with Wittgenstein ' s philo -

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sophical foundations in the Tractatusseemed capable of accounting for aU of the phenomenologist ' s examples of synthetic a priori knowledge without resorting to faculties such as intuition . I believe that the program to explain away such examples of synthetic a priori knowledge as analytic a priori knowledge fails just as logicism does. The only way in which analyticity might be made powerful enough for such a positivist ' program is to adopt something like Carnap s (1956a, 222- 32; 1956b) approach, but Quine (1953c, 32- 57) shows that the approach doesn' t help . The approach provides no concept of analyticity, so there is no notion of the analytic a priori under which to bring the metaphy sician' s synthetic a priori propositions . Arbitrarily putting the disputed " " propositions on a list with the uninterpreted term analytic at the top is hardly a refutation of metaphysics.6 ' Although our conception of philosophy conflicts with Quine s (1974, 2) nonpositivistic , methodological naturalism , it shares Quine ' s (1969a, 69) characterization of epistemology as " concerned with the foundations of the sciences." What I reject are his claims that science is first philosophy and that philosophy is a scientific concern with scientific knowledge . Philosophy, as I see it , is not continuous with science; it is not of a piece with science.7 Philosophy, or at least one large part of it , is subsequent to science; it begins where science leaves off . ' Quine s case for naturalizing epistemology is based on what he (1969a, 75) refers to as the " [t ]wo cardinal tenets of empiricism " : first , " whatever evidence there is for science is sensory evidence," and, " second, inculcation of meanings of words must rest ultimately on " sensory evidence. He (1969a, 75) refers to them , and hence naturalized " " epistemology, as unassailable. This , however, is something of an exaggeration. They have been assailed, to my mind quite successfully, from various philosophical standpoints . Stroud (1984, 209- 54) has 6. This is not , as I seeit , a shortcoming of the notion of analyticity, but rather an inevitable consequenceof the Fregean notion of analyticity . As I will explain below, the original sin was to broaden the traditional Lockean and Kantian notion of analyticity in the way Frege did instead of revising it slightly to meet his criticisms . When it is revised, we retain a narrow analytic / synthetic distinction that vindicates the traditional metaphysical ' conception s focus on the explanation of synthetic a priori knowledge . 7. My position further departs from Quine ' s in rejecting his claim that formal science is continuous with natural science (and hence the extraordinary consequenceof his natu ralized Platonism that entities referred to in unapplied portions of mathematics do not exist). On a realist view of the formal sciences, they are about abstract objects, while on ' everyone s view of the natural sciences, they are about natural objects. Hence, the epistemologies of the formal and natural sciences will differ in the way that traditional rationalists always claimed they do. We shall see, however, that this difference can be given a much sharper statement than it has received at the hands of traditional rationalists .

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criticized Quine ' s naturalized epistemology from a Kantian standpoint for being unable, in principle , to explain the possibility of knowledge of the world . Kim (1993, 216- 36) has criticized it from a traditional ' epistemologist' s standpoint as irrelevant to the philosopher s attempt to understand knowledge . And I (1990b, 175- 202, ch. 5) have criticized it from the standpoint of the philosophy of language as resting on arguments against the theory of meaning that simply do not work . The difference between scienceand philosophy, particularly philoso phy of science, is a difference between their fundamental questions. The fundamental questions of philosophy - such as questions about our knowledge of universals and demonstrable truths , about the existence of the external world and other minds , about the relation of the future and the past to the present, and about the relation of the mind to the body - differ essentially from scientific questions. For one thing , some philosophical questions turn a Pyrrhonistic gaze toward science, calling into question the standards on which sciencesevaluate conflicting scientific claims and asking whether those standards can be justified in the face of philosophical doubt . Quine (1975, 68) would dispute the claim that philosophical skepticism is outside science, but the issue is not whether a philosopher has a theory that allows him to argue that " " sceptical doubts are scientific doubts , but whether it is plausible to make the claim that skeptical questions are scientific questions. Given science as we know it , it seems far -fetched to claim , for example, that the Cartesian question of whether there is an external world is a scientific question . For another thing , philosophical questions lead to a kind of metaphysical vertigo : the deeper we go into them , the more all the possible answers are buffeted by new and often more difficult objections, the more bewildered we become about whether anything works , and the more we come to suspect that perhaps there is something wrong with the questions themselves. We shall see below that even questions far removed from standard skepticism , such as those concerning the nature of mathematical truth , have engendered such a metaphysical vertigo in some of the best philosophers of mathematics. In an uncharacteristically essentialist moment , Wittgenstein (1953, sec. 133) once described " philosophical "questions as questions which bring [philosophy ] itself into question . The crisis of faith that some philosophers have when to philosophi they come to doubt whether there ultimately are answers ' cal questions reflects the deep truth of Wittgenstein s remark . Philo sophical questions are, at the very bottom , the question , What is a philosophical question ? That is hardly a scientific question . Thus, on the separation of philosophy from science, my view is more like the late Wittgenstein ' s, but it is unlike his in virtually every other

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respect. This is particularly so with respect to the nature of philosophy. Wittgenstein lost faith that philosophical thinking , particularly as embodied in the logico- semantic work of Frege and Russell, could accomplish the positivist task he had set himself in the Tractatus. He came to think that their work was part of the problem and had to be just as II " vigorously opposed as plain nonsense as the more classical metaphysics he had opposed in the Tractatus. The full task of showing that " " metaphysical sentencesare plain nonsense demanded a new conception of meaning and language. The shift to the new conception led to a comprehensive rejection of traditional philosophy. Everything goes: no theories, no explanation , no hidden essences, no analysis, no universals , no underlying meanings, and no discoveries in the traditional " " philosophical" sense. The real discovery, Wittgenstein (1953, sec. 133) now wrote , . . . is the one that gives philosophy peace, so that it is no " longer tormented by questions which bring itself into question . On my view , everything stays: theories, explanation , hidden essences , analysis, universals , meanings, and discoveries in the traditional philosophical sense. Furthermore , such discoveries are not limited to the sphere of language where philosophy and linguistics join forces to uncover hidden syntactic and semantic essencesand exhibit their epistemological and onto logical character. Philosophical discoveries include the extralinguistic sphere where philosophy joins forces with sciencesto uncover other hidden essences , substantiate the existence of abstract objects, and exhibit their epistemological and ontologi cal character. These reflections describe the ways in which the major naturalist and empiricist positions differ from the realistic rationalism I will set out here. How might someone holding one of the former positions come to think that it should be abandoned in favor of the latter position ? I will try to answer this question on the basis of a sketch of my own route from the scientistic naturalism I once held to the position I now hold . The significant issue for me concerning scientistic naturalism was one that divided the two principal forms of the position in the early sixties. The twin prophets of scientistic naturalism , Quine and Chomsky , both departed from Viennese and Oxford philosophy in taking the view that language is to be studied within the science of language. Philosophers should seek enlightenment about the nature of language in linguistics rather than in the elaboration of artificially constructed calculi or in the description of ordinary usage. Philosophers of language should be informed about the science of linguistics . But Quine and Chomsky disagreed over what kind of linguistics a scientifically informed philosopher ought to be informed about.

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Within linguistics , there were two quite different schools of thought about the nature of language. One was Bloomfieldian structuralism , which was the orthodoxy of the time . Quine, who favored this school, in his (1961b, 47- 64) paper " The Problem presented it to philosophers " of Meaning in Linguistics . The other was the new school of generative grammar that Chomsky himself was developing in opposition to Bloomfieldian structuralism . Philosophers got their first exposure to this approach in Chomsky' s (1957) SyntacticStructures. These two views presented very different pictures of the science of language, with very different implications for linguistic analysis in philosophy . On the Bloomfieldian picture , linguistics is a science of the distributional relations in speech. Linguistic orthodoxy conceived of sentences acoustically and meanings behavioristically . On the Chomsky an picture , ' linguistics is a science of the speaker s knowledge of the language rather than a science of speech. Instead of thinking of grammatical investigation taxonomically, on the model of botany or stamp collecting , Chomsky conceived of it generatively, on the model of systems of logic . Chomsky' s Syntactic Structures seemed to me to present the more plausible conception of the scientific study of natural language. But, despite its novel proposals about syntax and phonology, the book was silent on semantics. This was disappointing to a philosopher interested in applying linguistics to philosophy , since semantics is the area of linguistics with the greatest potential for shedding light on philosophi to me that the it seemed cal issues. Apart from this disappointment , failure of Syntactic Structures to say something about semantics in generative grammar was also a problem for the Chomsky an theory of generative grammar . For one thing , since linguistics was traditionally concerned with meaningfulness and samenessof meaning , Chomsky' s theory appeared incomplete . For another thing , even the theory' s own goals, as explicitly set forth in Syntactic Structures, could not be achieved without a semantic theory being part of the theory of generative . For example, the existence of nonambiguous expressions grammar " like " automated processing device that have different syntactic structures, i.e., [[automated ][processing device]] and [[automated processing][device]], shows that the phenomenon of ambiguity cannot be explicated (as Syntactic Structures claims) in terms of multiple nonequivalent syntactic derivations . A semantic theory is required to predict when two syntactically nonequivalent derivations are equivalent semantically. Thus, I was led (initially with Jerry Fodor and Paul Postal) to try to develop the semantic theory that was required for the theory of gen

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erative grammar . However , the development of such a theory, which at the time I saw as a means of showing that Chomsky' s conception of scientistic naturalism was preferable to Quine ' s, led eventually to my . Chomsky' s syntactic theory had taken linguistics abandoning naturalism from Bloomfield ' s nominalist view of the science, on which it is a branch of acoustic physics, to Chomsky' s own conceptualist view of linguistics , on which it is a branch of psychology. I came to think that the semantic theory originally developed to plug a gap in Chomsky' s theory of generative grammar is what leads to taking the next step: from linguistic conceptualism to linguistic realism. The problem that started the train of thought leading to this conclusion was the existence of two incompatible ways to interpret such a semantic theory. One came from the Chomsky an framework within which the semantic theory was developed and the other from the Fregean framework which provided the rationale for the theory' s posit of senses. Within the latter framework , senses are interpreted as abstract objects, but within the former framework , they are interpreted as concrete psychological objects. Hence, plugging the gap in the Chomsky an theory of generative grammar raises the question of whether the theory is to be interpreted realistically or psychologically . The overall theory of generative grammar cannot be a theory of concrete mental / neural reality and have a component semantic theory that is a theory of abstract objects. This situation has to be resolved in favor of a uniform realist interpretation or a uniform naturalist interpretation . Various considerations made a uniform realist interpretation seem an linguistics distinguished between competence, preferable. Chomsky the speaker' s knowledge of the language, and performance , the ' of that knowledge , but , in defining competence as speaker s exercise the speaker' s knowledge of the language, it also distinguished between the speaker' s knowledge and what the knowledge is knowledge of. Furthermore , although generative linguists frequently preached on the theme of linguistics as a natural science, as working linguists , they formulated principles about the structure of sentencetypes. Since what makes such principles true or false is the structure they are about , the structure of sentences rather than the structure of our knowledge of them , it seemed more in line with linguistic practice to take grammars to be theories of sentence types rather than theories of the speaker' s psychology. Another consideration in favor of adopting a realist interpretation of grammar was that a realist interpretation of senses makes it possible to explain how we can have a priori knowledge of the necessity of an " " analytic truth such as Squares are rectangles. Taking sentencesto be

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mental / neural entities cuts intensionalism off from such an explanation . The failure to explain analytic necessarytruth would be a serious defect in the position . Similar considerations in connection with syntax and phonology reinforce the case for a uniform realist interpretation . In the cases of both syntax and phonology , a realist interpretation provides a better account of the generality of linguistic structures. Sentences, the structure of which makes grammatical principles true or false, are types, not utterance tokens or mental / neural tokens, and hence sentences are abstract objects. The phonology of a sentenceis also an abstract object. If English phonological theory were just a theory of the human English ' speaker s voicing apparatus , as Chomsky and Halle (1968) contend , then a human English speaker' s voicing apparatus would be the only instrument that could pronounce English sentences. But it is as implausible to claim that no other apparatus can produce the sound patterns of English sentencesas it is to claim that no instrument other than the " " piano can produce the sound pattern of Twinkle Twinkle Little Star. If phonological theory is no more specifically about the human voicing apparatus than a tune is specifically for the piano , the structure represented in a phonological description , like the structure represented in a musical score, must be understood abstractly in order to be understood as pronounceable by any instrument that can produce tokens of the sound types the description represents. The initial break with naturalism resulting from these reflections was presented in my (1981) book Languageand Other Abstract Objects. It argued that linguistics is a science of languages, collections of sentences - not minds - and its theories are thus about abstract objects in the same sensein which mathematical realists claim that mathematical theories are about abstract objects. There was another aspect of my semantic theory that contributed to my change of attitude toward naturalism . This was the theory' s non Fregean definition of sense. The virtually universally accepted definition of sensethen, and no doubt still , is Frege' s (1952, 56- 60) definition of sense as the determiner of reference. Carnap (1956b, 234), who was ' Frege s" vicar in our time , defined it in much the same terms as Frege, as the general conditions which an object must fulfill in order to be denoted by [a] word ." In stark contrast to this definition of sense in terms of a relation between language and the world , my (1972, 1- 11) definition explained it in terms of factors purely internal to sentence structure . Senseis the determiner of senseproperties and relations , like meaningfulness and synonymy, rather than the determiner of referential properties and relations, like denotation and truth .

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The existence of such a non -Fregean definition of sense not only showed that a Fregean definition is not obligatory for intensionalists , but also raised the question of whether a Fregean definition is even desirable. In the late seventies, I began exploring the question of whether the difficulties from which the prevailing intensionalism was shown to suffer could mostly or entirely be laid at the door of Fregean intensionalism . I (1997) eventually came to think that the difficulties that Wittgenstein , Donnell an, Putnam , and Kripke had raised were difficulties for only an intensionalism based on Frege' s notion of sense. The difficulties raised by Wittgenstein ' s " Moses" example, Donnel lan' s " whale " example, Putnam ' s " cat" and " water " examples, and ' " " Kripke s gold example all derive from the Fregean requirement that intension determine extension. This requirement imposes too strong a constraint on the assignment of extensions to expressions. Wittgenstein (1953, sec. 84) had made the point in his criticism of Frege in his PhilosophicalInvestigations: the application of a word is not everywhere bounded by rules . . . rules [which ] never let a doubt creep in , but stop up all the cracks where it might . Putnam ' s and similar examples show that it is impossible to stop up all the cracks, but non -Fregean intensionalists are not Fregean masons who are committed to the principle that the sense of a word gives its application . With a non -Fregean definition of sense, the difficulties attributed to intensionalism are shown to belong only to Fregean intensionalism . Consider Putnam ' s (1975a) claim that " cat" does not have the senseof " feline animal " because" feline animal " does not determine the referent " " of cat in counterfactual situations where we are fooled into thinking robots are really cats. But on my definition of sense, according to which it does not determine reference, " cat" can mean " feline animal " and still refer to robots in Putnam ' s counterfactual situation . Furthermore , if , as I (1994a) think , problems about identity and opacity in connection with proper names cannot be handled by direct reference semantics, there is a big advantage in having a non -Fregean intensionalism that is free of the difficulties plaguing Fregean inten sionalism . Without our non -Fregean definition of sense, we are caught between two sets of very powerful but conflicting intuitions : on the one hand , the intuitions on which the counterfactual criticisms of descriptivism are based, and , on the other, the intuitions on the basis of which Frege introduced sensesfor names and other referring expressions . For, once we try to satisfy the former by eliminating senses, the

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problems about identity and opacity resurface. Our intensionalism provides a way of doing justice to both sets of intuitions . It handles the counterfactual problems that the critics raise for Frege' s intensionalism because, without the requirement that sense determine reference, the senses of proper names can be purely metalinguistic , containing no substantive predicates to cause counterfactual trouble . The Fregean problems that the critics themselves face are handled simply by the fact that proper names have senses. Thus, on the basis of SemanticTheory and subsequent work on linguistic semantics, together with my (1986, 1990b, and 1992) related work in the philosophy of language, I came to reject Frege' s intensionalism as undesirable as well as unnecessary. The new intensionalism complemented the rejection of naturalism based on linguistic realism. In The Metaphysicsof Meaning (l990b ), I ' s case for onto argued that Wittgenstein logical and epistemological ' naturalism and Quine s case for his uncompromising empiricism and methodological naturalism were based on weaknessesin the Fregean foundations for realism. Their criticisms were specifically tailored to Fregean intensionalism , exploiting problems that arise from its referential definition of sense, from its location of semantics within an attempt to construct a logically perfect language, and from its failure to extend realism about logic and mathematics to natural language. I argued that ' ' Wittgenstein s and Quine s criticisms , as a consequence, have no force against the radically different intensionalism that is available , given a non-Fregean definition of sense, the location of semantics within the study of natural languages in linguistics , and a realist philosophy of s linguistics . The last step needed to arrive at the new version of traditional realist and rationalist philosophy presented in this book was prompted by the realization that , however strong this response to Wittgenstein and Quine, the overall strength of the caseagainst empiricism and naturalism depends also on the success of realism in the philosophy of mathematics. Further, the arguments in both Languageand Other Abstract Objects (1981) and The Metaphysics of Meaning (1990b), while putting considerable weight on realism , make almost no attempt to address the issue of realism in the philosophy of mathematics. Finally, as realism was anything but a popular successthere, it was necessary to have a sequel to The Metaphysicsof Meaning which would vindicate realism in the philosophy of mathematics.

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Nozick (1981, 1) rightly says that questions about the meaning of life , free will , and the nature of the self are the ones that first move us to become philosophers , but he goes on to say, wrongly I believe, that the " exist can be fun for a time , [but ] question of whether sets or numbers " If the realist' s answer to the do not make us tremble. they question of whether sets and numbers exist actually is the means of restoring the rationalist conception of knowledge , thereby reversing the naturalist and empiricist thrust of twentieth -century philosophy , that answer ' ought to shake us up quite a bit , even if we don t tremble as we would on learning the meaning of life . The vindication of mathematical realism leads straightforwardly to the restoration of the traditional metaphysical conception of philosophy. The rationalist metaphilosophy required for this restoration will be there in the vindication . Thus, restoring the rationalist conception of philosophy depends on providing a convincing vindication of realism in the philosophy of mathematics. Realism has to succeed in the area of philosophy where the issue it addresses properly belongs and where philosophers have the expertise to decide it competently. Moreover , many, perhaps most, philosophers of mathematics today think realism has been refuted on the basis of certain well -known epistemological and" semantic objections. Remarks like the following are not infrequent : It may be true that realism has some advantages over other ways of understanding numbers and sets, but realism is a nonstarter, because, as everyone knows , there are overwhelming objections to " saying that mathematics is about abstract objects. In light of such sentiments in the philosophy of mathematics, and taking into consideration that philosophers outside of a highly technical field defer to the specialists on questions in it , it is clear that an attempt to restore the traditional metaphysical conception of philosophy will not beconvincing unless the objections to realism in the philosophy of mathematics are overcome. The bulk of this book is a systematic attempt to overcome them. There are basically three objections in the philosophy of mathematics to the realist claim that mathematics is about abstract objects. Each is based on a problem concerning an aspect of the claim . The most widely influential objection turns on the realist' s claim that numbers, sets, and other mathematical objects have no spatial or temporal location . If realism were right about the abstract nature of mathematical objects, we could not have causal accessto them , and without that , the critics claim , we could not have mathematical knowledge . The locus classicus of this objection is Benacerraf' s (1983 [ 1973]) influential paper " Mathematical Truth ." A second objection turns on the realist' s claim that numbers, sets, and other mathematical objects are determinate objects.

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The criticism here is that referenceto numbers (and other formal objects with a similar structure ) is indeterminate . The locus classicushere, too , is a paper of Benacerraf' s (1983 [ 1965]), his " What Numbers Could Not Be." The third objection turns on the traditional abstract/ concrete distinction that the realist presupposes. The objection is that the distinction cannot be coherently drawn . There is no locus classicusin this case, and, in fact, the alleged counterexamples to the distinction do not , as far as I know , figure among objections to realism in the literature . Nonetheless, in a certain respect, these examples pose as serious a problem to realism as the first two objections. The sentiment that the first objection refutes realism is sometimes part of a general malaise about the philosophy of mathematics that stems from doubts that any philosophical position can provide an acceptable epistemology and an acceptable ontology for mathematics. Both Benacerraf (1983 [ 1973]) and Putnam (1994) have expressed the " " feeling that nothing works in the philosophy of mathematics. It should be noted , however, that such pessimism, if justified , bodes ill for philosophy as a whole . No part of philosophy is an island . We can' t be satisfied with an epistemology that works for the natural sciences but not for mathematics and the other formal sciences. There are general philosophical questions about which we can say nothing without a position on the ontology and epistemology of the formal sciences, questions like : Is there knowledge which is so certain that it is irrational to doubt it ? Even for the skeptic to doubt it ? Is there knowledge which is absolutely a priori ? (I .e., can we know anything about the world without evidence from experience?) What kinds of things are there? and Can the normative force of value be fit into a world of fact? These questions cut across the different areas of philosophy . If it were really the case that nothing works in the philosophy of mathematics, there would be little hope for all the other areas of philosophy where those 9 general questions arise. More often , however, the sentiment that the first objection refutes realism is not part of a general pessimism about the philosophy of mathematics. Most antirealists aren' t the least bit pessimistic about the prospects for their own philosophy of mathematics. They see the objections as showing that realism is the least plausible of the alternative positions . Their belief is based on the thought that , in having 9. No part of naturalscienceis an island, either. Unlessa nominalistprogramlike Hartry Field' s (1980) canbe carriedthrough, knowledgeof mathematicalobjectsis a component in all scientificknowledge, so that no epistemologycan work for the natural sciences without having a componentthat works for knowledgeof numbers, sets, and so on. See malament(1982) for technicalobjectionsto Field' s program, and section2.2 of the next . chapterfor philosophicalobjections

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rejected a naturalistic view of the domain of mathematics, realists find themselves up against the intractable epistemological problem of how the fact of mathematical knowledge can be explained . The consensus among such antirealists is that true realism of the kind Godel advocated is to be dismissed out of hand. The force of these objections has been greatly exaggerated. The reason that antirealists believe that the epistemological objection is intractable is simply that that' s the way it looks when viewed through the lens of their own empiricism and naturalism . To be sure, all the objections are intractable within empiricism and naturalism . But whether they would be intractable outside them is another question . That question is begged when the argument for the intractability of any of the difficulties in question assumes, as I will try to show it does in the caseof the Benacerrafian objections, that they must be overcome within an empiricist or naturalist framework . After all , realists ought to claim that no account of our knowledge of mathematics can be given in empiricist or naturalistic terms. The fact that few of them do make this claim attests to the influence of empiricism and naturalism in Anglo American philosophy . The strength of empiricism derived in large part from its having an apparently unproblematical naturalist ontology which kept pace with the intellectual developments in this century to corroborate its epistemic vision . By contrast, rationalism had no such corroborating ontology . With an unproblematic realist ontology , rationalism could have provided a better explanation of the certainty of mathematical and logical truth than the empiricist ' s conventionalist explanations , ' psychological explanations , and even, as I shall argue, Quine s holistic explanation . For, as will be explained in chapter 3, section 5, realism can account for the certainty of mathematics and logic in terms of the necessity of mathematical and logical truths , and it can account for their necessity in terms of the unchangeable properties and relations of nonspatial and atemporal objects. Thus, with a corroborating realism , rationalists could have countered the influence of empiricism on the basis of the Leibniz -Kant criticism of empiricism that experience cannot teach us why mathematical and logical facts couldn ' t be other wise than they are. Since the absenceof a respectableontology was to a significant extent ' responsible for rationalism s troubles , a vindication of realism ought to go far towards resuscitating rationalism . But it works the other way around as well . Absence of a respectable theory of knowledge was to a significant extent responsible for the epistemic vulnerability of realism . In his epistemological objection to realism, Benacerraf (1983 [ 1973]), 412- 15) assumes that mathematical facts must figure casually

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in the mathematician ' s knowledge of them. He even says: " Some such view must be correct." He would hardly have felt in a position to make such a strong claim without argument had there been a respectable rationalist theory of knowledge around . Accordingly , it is not unreasonable to expect that a resuscitated rationalist theory of knowledge can go a long way in defending realism against the charge that it cannot explain mathematical knowledge . In any case, a rationalist epistemol ' ogy is realism s only hope of explaining how we can have knowledge of objects with which we cannot causally interact. One of the major themes of this book is the inseparability of realism and rationalism . Realism without rationalism is unbelievable and rationalism without realism is unstable. We have seen how implausible realism can be made to seem when its critics are allowed to assume that an account of mathematical truth has to meet an epistemic requirement set in terms of an empiricist theory of knowledge . We will see in the next chapter how, without rationalism , realism easily slides over into a form of antirealism . The integration of realism and rationalism in a single position provides realism with epistemological credibility and rationalism with onto logical stability . Here is the layout of the book . The core of its argument is contained in chapters 1, 2, 4, and 5. Their agenda is to show that the apparent force of the principal objections to realism rests on the implicit " divide and conquer " strategy which excludes rationalism from the defense of realism and realism from the defense of rationalism . I will argue that once they are integrated into a single position , there are strong replies to these objections. The replies to the epistemological and semantic objections are a matter of providing a comprehensive defense for Godel ' s formulation of realism. In the case of the epistemological objection, the defense must supply an appropriate rationalist theory of knowledge . This would block the much too fast dismissal of realism on the grounds that taking numbers to be abstract objects makes them unknowable . What is true is only that they are unknowable on the basis of an empiricist epistemology. In the case of the semantic objection, the defense must supply an appropriate intensionalist semantics. This would block arguments from the symmetry of intended and deviant interpretations within the mathematical sphere to the indeterminacy of reference to numbers. In the case of the onto logical objection to realism, the defense is a matter of developing a new onto logical theory within which the traditional abstract/ concrete distinction can be coherently drawn . This new onto logical theory turns out to have significant bearings on many of the sciencesas well as on a number of philosophical topics .

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. The first two chapters are a reply to the epistemological challenge to realism. Chapter 1 is concerned with preliminaries and chapter 2 contains the reply to Benacerraf (1983 [ 1973]) and the philosophers who have tried to turn his argument into a refutation of mathematical realism. It is a testament to the force of his statement of the epistemological criticism that it has also convinced a large number 'of uncommitted philosophers , many of whom recognize realism s evident philosophical strengths and considerable prima facie plausibility in actual mathematics. For example, there is a body of substantial arguments ' for mathematical realism , such as Frege s (1953, 1964) arguments ' in the Grundlagenand Grundgesetzeand Benacerraf s (1983 [ 1973]) own " Truth ," to the effect that , without mathematical argument in Mathematical ' realism , we can t have the same (Tarskian) semantics for mathematical sentencesthat we have for other sentencesand it is then unclear what we are to say about the semantics of mathematical sentences. Chapter 3 is a digression from the main line of argument , but it complements the reply to the epistemological challenge to realism in chapter 2 by posing an epistemological challenge to antirealists. It argues that antirealists face the epistemological challenge of explaining the special certainty of mathematical and logical knowledge , that ' Quine s response fails , and, as a consequence, that antirealists stand no chance of meeting this challenge. If both the reply to the epistemologi cal challenge to realism and this argument against antirealism work , we will have met the epistemological challenge to realism in a way that shows that it is the antirealist rather than the realist who faces an apparently insurmountable epistemic challenge. Hence, if the argument up to this point is correct, the proper attitude toward realism and antirealism ought to be the very opposite of what has been the received opinion in contemporary philosophy of mathematics. The doubts about the prospects for an adequate epistemology that have been widely directed toward realism are more appropriately directed toward antirealism . ' to the semantic challenge to realism in Benacerraf s Chapter 4 replies " " (1983 [ 1965]) What Numbers Could Not Be. I take a novel approach to Benacerraf' s argument . I first develop a strategy for blocking indeterminacy ' arguments generally and then show that Benacerraf s argument for the indeterminacy of reference to numbers is a special caseof such indeterminacy arguments . The strategy blocks not only Benacerraf ' s symmetry claim about intended and deviant interpretations of arithmetic but also related symmetry arguments such as those in ' ' of translation , Kripke s ruleQuine s argument for the indeterminacy ' following argument , and Putnam s argument for global referential indeterminacy .

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Chapter 5 replies to an onto logical challenge to realism. This is a challenge to the coherence of realism based on examples that a number of recent philosophers , including some realists, have thought to undermine the traditional abstract/ concrete distinction . Some are easily handled on the basis of considerations that have long been part of the realist position but the relevance of which has been overlooked in connection with the putative counterexamples. Others, particularly ' Frege s (1953, 35) famous equator example, are more difficult and far more interesting , requiring a significant addition to onto logical theory. I will argue not only that this addition shows that the distinction is not undermined , but also that it provides a new onto logical theory with applications to philosophical and scientific questions. As we noted above, it would be bad news for philosophy as a whole if nothing works in the philosophy of mathematics. H the line of argument in chapters 1- 5 is correct, the news that something works in the philosophy of mathematics ought to be good news for philosophy as a whole . Chapter 6 presents a rationalist metaphilosophy . It develops it out of the principles underlying the arguments of the previous chapters. The first section of the chapter explains how the rationalist epistemology in chapter 2 for knowledge in the formal sciences can be extended to provide a rationalist epistemology for certain types of philosophical knowledge as well . Our aim is to construct a unified conception of what it is to explain synthetic a priori knowledge in the formal sciencesand in their philosophical foundations . The second section of the chapter examines some of the philosophical implications of the metaphiloso phy. Here I try to set out some new thoughts about the rationalism / empiricism over the existence of synthetic a priori knowledge , ' controversy ' Carnap s positivist critique and Quine s naturalist critique of metaphysical philosophy, the philosophical distinction between internal and external questions, and the place of skepticism in a world of knowledge .