DUMMETT AND THE ORIGINS OF ANALYTICAL PHILOSOPHY GEORGE DUKE MICHAEL DUMMETT is perhaps the most prominent analytical philosopher to venture a book length account of the origins of his own tradition. In Origins of Analytical Philosophy (1993), Dummett compares and contrasts the work of Frege and Husserl, as representatives of the analytical and phenomenological schools respectively, in the course of arguing that the linguistic turn is the decisive moment in the birth of the analytical tradition and what distinguishes that tradition from other movements.1 This characterization of analytical philosophy can be contested on a number of grounds, including that it does not take into account the centrality of British thinkers like Russell and Moore for early analytical philosophy, excludes much contemporary naturalism and philosophy of mind, and underestimates the role played by linguistic considerations in so called continental thought. In this paper, my initial concern is not with the limitations of Dummett’s characterization of analytical philosophy as a school but with his account of Frege’s role as its progenitor.2 Certain considerations will Correspondence to: Dr George Duke, School of Philosophy, Anthropology and Social Inquiry, Faculty of Arts, University of Melbourne, 3010, Australia. 1 Michael Dummett, Origins of Analytical Philosophy (Cambridge, Massachusetts: Harvard University Press, 1994), 128; hereafter OAP. OAP is the book version of a series of lectures presented at the University of Bologna in 1987. 2 There is good reason to doubt the cogency of attempts to provide a one sentence characterization of analytical philosophy of the kind that is suggested by Dummett’s claim that “the fundamental axiom of analytical philosophy [is] that the only route to the analysis of thought goes through the analysis of language.” Dummett, OAP, 128. This is not because the term “analytical philosophy” denotes a sociological construct, but rather, as Glock suggests, because it designates a diverse tradition held together by certain family resemblances rather than a specific doctrine. The ease of producing counter examples to Dummett’s axiom and other similar attempts attests to this. See Hans-Johann Glock, What is Analytic Philosophy? (Cambridge: Cambridge University Press, 2008). The Review of Metaphysics 250 (December 2009): 329–347. Copyright © 2009 by The Review of Metaphysics. 330 GEORGE DUKE arise in the course of examining Dummett’s account of Frege’s influence, however, which point the way towards a more complete characterisation of the origins of the analytical tradition. Dummett’s views on the historical significance of Frege are outlined in the final chapter of Frege: Philosophy of Language (1973).3 From Dummett’s perspective, Frege began a revolution in philosophy as overwhelming as that of Descartes.4 Whereas the Cartesian revolution consisted in giving the theory of knowledge priority over all other areas of philosophy, Frege’s primary significance consists in the fact that he made logic the starting point for the whole subject.5 Dummett here means logic in the unusually broad sense of a theory of meaning or the search for a model of what the understanding of an expression consists in.6 For Frege, in contrast to his contemporaries, who were still working within the epistemological framework of Descartes, “the first task, in any philosophical enquiry, is the analysis of meanings.”7 According to Dummett, therefore, Frege inaugurated an epoch in which “the theory of meaning is the only part of philosophy whose results do not depend upon those of any part, but which underlies all the rest.”8 This implies that the philosophy of language assumes the central place for philosophical investigation subsequent to Frege. In his 1975 paper “Can Analytical Philosophy be Systematic, and Ought it to Be?” Dummett extends this account of Frege’s historical significance. According to Dummett, it was “only with Frege” that “the proper object of philosophy” was “finally established.”9 This involves the thesis, first, that the goal of philosophy is the analysis of the structure of thought; secondly, that the study of thought is to be sharply distinguished from the study of the psychological process of 3 Michael Dummett, Frege: Philosophy of Language (London: Duckworth, second edition, 1981); hereafter FPL. 4 Dummett, FPL, 665–6. 5 Dummett, FPL, 666. 6 Dummett, FPL, 669. 7 Dummett, FPL, 667. 8 Dummett, FPL, 669. 9 Michael Dummett, “Can Analytical Philosophy be Systematic, and Ought it to Be?” (1976) in Truth and Other Enigmas (London: Duckworth, 1978), 458. DUMMETT AND ANALYTICAL PHILOSOPHY 331 thinking, and, finally, that the only proper method for analysing thought consists in the analysis of language.10 It is this view of Frege as having discovered the proper method of philosophical enquiry which informs Dummett’s much quoted statement in the Origins of Analytical Philosophy that what distinguishes analytical philosophy, in its diverse manifestations, from other schools is the belief, first, that a philosophical account of thought can be attained through a philosophical account of language, and, secondly, that a comprehensive account can only be so attained.11 Frege’s turn towards thoughts, or the senses of linguistic expressions, is exemplified by his rejection of the psychologistic assumptions of much late nineteenth-century philosophy of mathematics and logic. Dummett argues persuasively that Frege’s great advance over conceptual analysis based on the description of psychic experience is found in the decision to begin with content rather than attempting to explain content in terms of our grasp of it.12 By starting with the objective component of knowledge, Frege avoids the conflation of presented contents and the presentation of contents that is distinctive of both early modern epistemology and nineteenth century psychologism.13 The absurdity and incoherence of Husserl’s position on number in his Philosophie der Arithmetik (1893), for example, is contained in the attempt to give an account of how a concept is formed before attaining clarity about what the concept is.14 In a move just as common in early modern rationalism and German 10 Michael Dummett, “Can Analytical Philosophy be Systematic, and Ought it to Be?”, 458. 11 Dummett, OAP, 4. 12 Michael Dummett, Frege: Philosophy of Mathematics (London: Duckworth, 1991), 14; hereafter FPM. 13 Dummett states: “We can arrive at a plausible account of sense only if we first have a workable conception of content – of that which is grasped; and that is why Frege arrived, for the first time in the history of philosophical enquiry, at what was at least the beginnings of a plausible account of sense and thus of understanding. Those who started with the conception of the inner grasp of meaning floundered in confused descriptions of irrelevant mental processes, achieving nothing towards explaining either the general notion of meaning or the meanings of specific expressions.” See Dummett, FPM, 15. 14 Dummett, FPM, 20. 332 GEORGE DUKE critical philosophy as in British empiricism, Husserl substitutes an examination of the process of concept formation for an analysis of the concept. A clear distinction between objective content and the subjective process of thought, however, is not in itself sufficient to explain Frege’s significance as the founder of analytical philosophy. Subsequent to Philosophie der Arithmetik, in his Logische Untersuchungen (1900), Husserl acknowledges the importance of maintaining a distinction between ideal objects of knowledge and the psychic acts in which they are instantiated.15 Indeed, the Prolegomena to the Logische Untersuchungen exerted more influence over the downfall of psychologism in the early part of the twentieth century than Frege’s similar polemics in Die Grundlagen der Arithmetik (1884). While Husserl is unequivocal in Logische Untersuchungen that the primary concern of the philosophy of mathematics and logic is with meaning or content rather than psychological processes, he bases his account on a theory of intentional acts and their objects. When we consider what distinguishes the Husserl of Logische Untersuchungen from Frege, therefore, it would indeed appear instructive to say, with Dummett, that where the latter differs is in anticipating the linguistic turn through a rejection of the modern presumption that an account of philosophical intuition can provide an adequate account of the objectivity of thought. For Dummett, this turn towards linguistic 15 Husserl writes: “Die Zahl Fünf ist nicht meine oder irgend jemandes anderen Zählung der Fünf, sie ist auch nicht meine oder eines anderen Vorstellung der Fünf. In letzterer Hinsicht ist sie möglicher Gegenstand von Vorstellungsakten, in ersterer ist sie die ideale Spezies einer Form, die in gewissen Zählungsakten auf Seiten des in ihnen Objektiven, des konstituierten Kollektivum, ihre konkreten Einzelfälle hat. In jedem Falle ist sie ohne Widersinn nicht als Teil oder Seite des psychischen Erlebnisses, somit nicht als ein Reales zu fassen.” (The number five is not mine or anyone else’s counting of five, it is also not mine or anyone else’s representation of five. It is in the latter respect a possible object of acts of representation, whereas in the former it is the ideal species of a form, whose concrete instances are contained in what becomes objective in acts of counting. In each case without exception it is not to be grasped as a part or aspect of psychic experience, therefore not as something real). See Edmund Husserl, Logische Untersuchungen (Hamburg: Felix Meiner Verlag) 1900, 109–10. The translation is mine. Husserl goes on to say that the same applies to logic: acts of logical reasoning need to be sharply demarcated from the ideal content of those acts. DUMMETT AND ANALYTICAL PHILOSOPHY 333 meaning and analysis is embodied in Frege’s use of the context principle in Grundlagen. Frege’s employment of the context principle in Grundlagen is, according to Dummett, the first “clear example” of the linguistic turn.16 Faced with the question how is it possible to be given numbers, when we do not have representations or intuitions of them, Frege, Dummett alleges, converts “an epistemological problem, with ontological overtones” into one about “the meaning of sentences.”17 The principle that we should only ask after the meaning of a word in the context of a sentence teaches us that we do not need to look outside of language in order to determine the meaning, and hence truth conditions, of statements. It is truly revolutionary, therefore, Dummett argues, because it enables us to dispense with epistemological atomism or the myth of the unmediated presentation of concrete objects to the mind. According to the epistemological atomist, we can have an awareness of distinguishable objects through prediscursive perception.18 The context principle teaches that such knowledge would be impossible if we did not bring to experience a linguistic criterion of identity which enables us to recognise an object “as the same again.” Our experience of objects, whether abstract or concrete, is according to this account always mediated by sortal concepts that enable us to pick out something as falling under determinate identity conditions. It is the sense of a linguistic expression, Dummett contends, which embodies these identity conditions and hence informs our capacity to refer to objects of different kinds. It is worth exploring this point in more detail. According to Dummett, empiricist thinkers such as Mill thought that the sense of a name consisted in a bare association with a referent, as if the world already came to us sliced up into objects and all we had to learn is which label to tie to which object. It is rather the case, he claims, that the names, and corresponding sortal terms which we use, “determine principles whereby the slicing up is to be effected, principles which are acquired with the acquisition of the uses of these words.”19 What is 16 Dummett, OAP, 5. Dummett, FPM, 111. 18 Michael Dummett, The Interpretation of Frege’s Philosophy, (London: Duckworth, 1981) 367. 19 Dummett, FPL, 179. 17 334 GEORGE DUKE in question here is our tendency to relapse into the view that “learning the sense of a proper name consists in learning to attach a label to an object already picked out as such.”20 We are well positioned to reject this illusion, Dummett contends, once we realise that the presupposition of such labeling is an ability to employ other names of the same kind. Asking after the meaning of a name in isolation is to ignore that objects are always given to us as objects of a certain type, which is to say given to us as mediated by the employment of linguistic categories. Against the epistemological atomist, therefore, Dummett argues that “our ability to discriminate, within reality, objects of any particular kind results from our having learned to use expressions, names or general terms, with which are associated a criterion of identity which yields segments of reality of just that shape.”21 The revolutionary content of the context principle is consequently found not so much in its explanation of linguistic understanding but in its account of the relation between such understanding and extralinguistic reality. When joined with the syntactic priority principle, or priority of syntactic over ontological categories defended by Dummett in Frege: Philosophy of Language, the context principle putatively allows us to determine questions regarding the ontological status of entities through linguistic and logical analysis. In the process, the question of existence becomes concomitant with the notion of the reference of a term that is mediated by a particular sense. It is no longer the case that we work back from objects that are given in experience, whether directly or through the activity of the understanding, in determining our ontology. Rather, our ontology is regarded as the realm of possible referents of the expressions of our language to which we gain access through an account of the meaning of sentences. Against this background Dummett has argued, in The Logical Basis of Metaphysics (1991) and elsewhere, that the way in which to resolve the metaphysical and ontological disputes which have troubled philosophy throughout its Fregean prehistory is by constructing a systematic theory of meaning based on a semantic theory for logic. 20 Michael Dummett, “Nominalism” (1955) in Truth and Other Enigmas (London: Duckworth, 1978), 55. 21 Dummett, FPL, 503. DUMMETT AND ANALYTICAL PHILOSOPHY 335 Dummett’s account of Frege’s place in the history of philosophy is somewhat revisionist. Frege’s reflections on language took place in the context of his logicist project in the philosophy of mathematics and can only, with significant retrospective license, be read as intended to constitute the articulation of a systematic theory of meaning which underlies the rest of philosophical inquiry. This is not to suggest that Frege’s introduction of predicate logic with quantifiers, formulation of the context principle, and account of the distinction between sense and reference are not fundamental insights presupposed by the kind of theory of meaning Dummett envisages as forming the foundation of philosophy. Frege, himself, however, did not have a theory of meaning in the relevant sense, considered as a systematic meaning theoretical framework based on a semantic theory and allowing for the resolution of previously insoluble metaphysical disputes.22 Moreover, as Dummett has acknowledged, Frege’s attitude towards natural language was too ambivalent for him to be attributed with initiating the linguistic turn except in a highly qualified sense.23 Indeed, it is arguable, given the implications of Frege’s attempt to provide an account of our knowledge of external objects in the 1919 essay “Der Gedanke,” that he was still caught up to a large degree in the epistemological antinomies of early modernity. The interpretative assumptions behind Dummett’s reading of Frege’s significance for the subsequent analytical tradition are not, however, indicative of a lack of hermeneutic self-consciousness. Dummett explicitly notes in the preface to Origins of Analytical Philosophy that he will deliberately disregard important figures from the early analytical tradition like Russell and Moore, who did not hold to the fundamental axiom regarding the impossibility of giving an account of thought other than through an account of language, and that he will also be scarcely “concerned to respect historical causation 22 Even to attribute a semantic theory in the contemporary sense to Frege is problematic. While the formal system presented in Grundgesetze (1893) contains an inchoate differentiation between object language and metalanguage, the notion of a logical interpretation for a formalized language was an insight attained by Tarski long after Frege’s ambitious logicist project had gone to ground as a result of the Russell paradox. Frege’s status as the founder of modern mathematical logic is, however, less contentious. 23 Dummett, OAP, 6–7. 336 GEORGE DUKE at all.”24 Dummett justifies this strategy on the grounds that “the history of ideas is full of developments that cannot be explained by historical enquiries of the usual sort.”25 This is because, in the history of thought, ideas are “in the air,”26 in the sense that it is a common occurrence that two thinkers arrive at the same idea or thought without having read each other’s work. If we are interested “in the history of thought rather than of thinkers,” it is therefore “these kind of developments that will concern us, rather than those discoverable by the processes of genuine historical enquiry.”27 Dummett accordingly states that he will “talk about the directions in which various philosophical ideas led and what were legitimate developments from them, without much troubling … about who read whose work or whether X derived a certain idea from Y or arrived at it independently.”28 Moreover, an adequate historical account would need to take into account Frege’s own precursors, whereas for Dummett “the interesting links are between Frege and what comes after, and not Frege and what comes before.”29 Dummett’s justification for neglecting genuine history of philosophy is ambiguous. In a way reminiscent of the Fregean critique of psychologism, it seems to recommend an approach oriented by the important thoughts of a philosophical tradition, which could be taken to possess transhistorical cogency if not eternal validity, rather than by the historical facts surrounding the thinkers who happened to have formulated those thoughts. In itself, this is an unobjectionable assumption. When combined with the thesis that ideas are “in the air” at a certain time in history, however, it has troubling hermeneutic consequences. It is one thing to acknowledge the independence of philosophical content from the historical agents responsible for its formulation, but something else altogether to disregard the historical context of philosophical theories. This is because the importance of history of philosophy for contemporary philosophical work is not found in the pedantic desire to trace the concrete contingencies in 24 Dummett, OAP, 2. Dummett, OAP, 2. 26 Dummett, OAP, 3. 27 Dummett, OAP, 3. 28 Dummett, OAP, 3. 29 Dummett, OAP, 171. 25 DUMMETT AND ANALYTICAL PHILOSOPHY 337 which certain thoughts arise but rather to lay bare the conceptual presuppositions of a particular philosophical theory. An adequate analysis of the conceptual presuppositions of philosophical theories is what seems to be precluded by Dummett’s interpretative approach. Even if we acknowledge that Dummett’s interpretative approach leads him towards an anachronistic view of the historical significance of Fregean philosophy, however, this does not completely diminish the capacity of such a reading to provide an illuminating account of Frege’s influence upon the subsequent analytical tradition.30 Dummett’s orientation by the originality of Frege and his influence upon twentieth century thought, while based on questionable interpretative assumptions from an historical perspective, certainly illuminates his philosophical significance in the contemporary context. Indeed, it could be argued that it constitutes a compelling account of the origins of one important branch of the analytical tradition precisely insofar as it lays bare the aspects of Fregean thought, first formulated in an inchoate manner by Frege himself, which made many of the most distinctive doctrines of that tradition possible. The problem with Dummett’s account, however, is that it does not adequately recognize the extent to which Frege’s methods and problems, the methods and problems handed down to his successors, have roots in the early modern response to the scientific revolution. As stated above, as one of the heirs to the Fregean tradition, Dummett has argued that the way in which we can resolve previously insoluble metaphysical and ontological disputes is by constructing a systematic theory of meaning based on a semantic theory. Against this background it is easy to see why Dummett should ascribe to Frege the insight that the theory of meaning is the part of philosophy which underlies all the rest. In itself, the context principle is not as revolutionary as Dummett suggests. It is anticipated by Kant’s theory of judgment, according to which our experience of objects is always 30 This would seem to be Dummett’s own stance. In a 1987 interview with Joachim Schulte Dummett expresses regret that he wrote FPL so “unhistorically” and did not put a full list of references in the first 1973 edition. He then reiterates that “the interesting links are between Frege and what comes after, and not between Frege and what came before.” See Dummett, OAP, 171. Of course, it is difficult to judge the legitimacy of this verdict without undertaking precisely the kind of conceptual “history” that Dummett neglects to carry out. 338 GEORGE DUKE mediated by concepts derivative from the categories of the understanding. Even more significantly, many of Kant’s contemporaries and successors, both romantic critics and sympathetic interpreters, held the view well in advance of analytic philosophy that it is only at the level of sentences or the whole language that we can regard words as having genuine significance.31 It is when the context principle is combined with the turn towards semantic analysis that we have one of the distinctive doctrines of the analytical school, at least in what Robert Brandom has called its classical phase. According to Brandom, analytical philosophy in its classical phase is concerned with the relations between vocabularies in that “its characteristic form of question is whether and in what way one can make sense of the meanings expressed by one kind of locution in terms of the meanings expressed by another kind of locution.”32 This culminates in a project which Brandom calls semantic logicism, insofar as the privileged language or locution in the analysis of meanings is the predicate logic with quantifiers introduced by Frege in Begriffsschrift (1879). What is distinctive of analytical philosophy in its classical phase, therefore, is that “logical vocabulary is accorded a privileged role”33 in specifying semantic relations that are thought to make our true epistemological and ontological commitments fully explicit. Brandom’s account of semantic logicism squares well with Michael Beaney’s account of the centrality of the notion of transformative analysis for the classical phase of the analytic tradition 31 An interesting example is J. G. von Herder’s 1774 essay “Vom Empfinden und Erkennen der menschlichen Seele” in J. G. von Herder, Werke in zehn Bänden, eds. Martin Bollacher, Jürgen Brummack, Ulrich Gaier, Gunter E. Grimm, Hans Dietrich Irmscher, Rudolf Smend, Rainer Wisbert, Thomas Zippert (Frankfurt: Deutscher Klassiker Verlag, 1985). Herder argues that the understanding of a particular word presupposes the whole sentence and can only be understood and interpreted through it. More generally, the long history of reflection on the mutual dependency of language and thought in the German tradition since the time of Kant, which includes thinkers as diverse as Herder, von Humboldt, Cassirer, and more recent philosophers such as Gadamer, is an obvious problem with Dummett’s fundamental axiom. 32 Robert Brandom, John Locke Lectures (Oxford: Oxford University, 2006), 1. The emphasis is the author’s here and elsewhere unless otherwise noted. 33 Brandom, John Locke Lectures, 1. DUMMETT AND ANALYTICAL PHILOSOPHY 339 embodied by Frege, Russell, the early Wittgenstein, and Carnap.34 Beaney explicates three conceptions of analysis in the Western philosophical tradition. The first form of analysis is the decompositional and involves the breaking of a concept down into its more simple parts. Decompositional analysis is prevalent in early modern philosophy and encapsulated in Descartes’ 13th rule for the direction of the mind; namely, that if we are to understand a problem we must abstract from it every superfluous conception and by means of enumeration, divide it up into its smallest possible parts. The second kind of analysis is regressive analysis, according to which one works back towards first principles by means of which something can be demonstrated. This conception is predominant in classical Greek thought, for example in Euclidean geometry. Transformative analysis works on the assumption that statements need to be translated into their correct logical form before decomposition and regression can take place. Paradigmatic examples are Frege’s attempt to reduce mathematics to logic and Russell’s theory of definite descriptions. The epistemological and ontological explanatory power of Frege’s predicate logic would thus appear to be the major assumption of analytical philosophy in its classical phase.35 Brandom recognises, in his interpretation of the classical project of analysis as a form of semantic logicism, that it involves, to employ Dummettian phraseology, the translation of epistemological and ontological questions into a semantic key. In this context, Brandom describes how two core programs of analytical philosophy, empiricism and naturalism, were transformed in the twentieth century “by the application of the newly available logical vocabulary to the selfconsciously semantic programs they then became.”36 The generic challenge posed by such projects is to demonstrate how target vocabularies, for example, statements about the external world, can be reconstructed from “what is expressed by the base vocabulary when it 34 It also conforms to the account given in J. Alberto Coffa’s The Semantic Tradition from Kant to Carnap (Cambridge: Cambridge University Press, 1991). 35 See Michael Beaney, “The Analytic Turn in Early Twentieth Century Philosophy,” in The Analytic Turn: Analysis in Early Analytic Philosophy and Phenomenology, ed. Michael Beaney (London, Routledge, 2007), 1–30. 36 Brandom, John Locke Lectures, 2. 340 GEORGE DUKE is elaborated by the use of logical vocabulary.”37 An example of such a project is Carnap’s Der Logische Aufbau der Welt, in which phenomenal experiences are reduced to their pure logical form. All this accords well with the Dummettian account of the relation between meaning theories and metaphysical questions outlined in his most ambitious work, The Logical Basis of Metaphysics. It is indeed in The Logical Basis of Metaphysics, rather than in Origins of Analytical Philosophy, that Dummett gives his most comprehensive account of the importance of Frege’s new logical vocabulary to the analytical project. Here Dummett defends analytical philosophy against the objections of philosophically engaged “laymen,” who lament the abandonment of larger questions for narrow technical investigations. According to Dummett, contemporary philosophy is necessarily technical because Frege’s mathematical logic represents the best possible analysis of thought, which is the subject matter of philosophy.38 “[I]t is misplaced to ask how much mathematical logic has contributed to philosophy,” insofar as analytic philosophy is “written by people to whom the basic principles of the representation of propositions in the quantificational form that is the language of mathematical logic are as familiar as the alphabet.”39 Here Dummett privileges the role of Frege’s new predicate logic, introduced in Begriffsschrift, in the genesis of analytical philosophy insofar as it provides the technical apparatus necessary for a correct analysis of the thoughts or meanings expressed in everyday language. To privilege Frege’s predicate logic as the key discovery for the dominant branch of early analytical philosophy is not to understate the importance for the semantic tradition of the attack on psychologism (the extrusion of thoughts from the mind) or the context principle. This is because these tenets of analytical philosophy in its classical phase are coeval with the introduction of Frege’s new logical symbolism. Frege’s notions of concept and object are correlative to the symbolic notions of function and argument; by taking a concept as a function of an argument, we can understand the process of concept formation without appeal to extraneous psychological considerations. 37 Brandom, John Locke Lectures, 3. Michael Dummett, The Logical Basis of Metaphysics (Harvard: Harvard University Press, 1991), 2; hereafter LBM. 39 Dummett, LBM, 2–3. 38 DUMMETT AND ANALYTICAL PHILOSOPHY 341 And, the context principle is, as Frege states explicitly, inspired by the rigorisation of the calculus, whereby infinitesimals are banished through an explanation of the meaning of contexts containing functional expressions (such as df[x] or dx) rather than seeking to explain them in isolation. By placing emphasis upon the centrality of Frege’s new logic for the analytical tradition, one also provides an intuitive, if not sufficient, means of contrasting it with other philosophical schools of the twentieth century. It is generally acknowledged that the introduction of quantifier notation and bound variables was the single most important advance in logic since Aristotle. Frege’s way of parsing sentences involving quantifiers offers a tremendous increase in expressive power insofar as it can adequately represent the statements of multiple generality that had troubled traditional syllogistic. Although the significance of Frege’s revolution in logic is well known, the original intention informing his development of his new conceptual notation is easily understated in the contemporary context. Dummett’s statement that “the original task which Frege set himself to accomplish, at the outset of his career, was to bring to mathematics the means to achieve absolute rigor in the process of proof”40 is obviously accurate but, informed by an awareness of the incompleteness of second-order proof procedures, also understates the extent of Frege’s ambition. An unprejudiced reading of the preface to Begriffsschrift cannot avoid the conclusion that Frege conceived of his new formula language as a vital contribution to the realization of the Enlightenment project of a mathesis universalis, a universal methodical procedure capable of providing answers to all possible problems. While conceding the slow advance in the development of formalized languages, he notes recent successes in the particular sciences of arithmetic, geometry, and chemistry, and also suggests that his own symbolism represents a particularly significant step forward insofar as logic has a central place with respect to all other symbolic languages and can be used to fill in the gaps in their existing proof procedures.41 On account of its seemingly limitless generality, the new predicate calculus, with its expressive power to represent functions and 40 41 Dummett, FPL, 1. Gottlob Frege, Begriffsschrift, (Halle, 1879), xi―xii. 342 GEORGE DUKE relations of higher level, is conceived by Frege as the most significant advance yet made on the way towards Leibniz’s grandiose goal of a universal characteristic. What is truly revolutionary about the Fregean predicate calculus in this context is the extension of mathematical function argument analysis to the logical analysis of statements. In order to see that this is the case it is instructive to consider the general consensus on the status of formal logic and mathematics from the time of Descartes until Frege. For Descartes, as well as for Vieta and Stevin, the founders of modern mathematics, what is distinctive about the new algebraic methods coterminous with the idea of a universal science is that they enable the mathematician to practice an art of invention (ars inveniendi).42 This aspect of the great art (ars magna) of algebra is explicitly contrasted with the sterile truths (steriles veritates) of premodern mathematics and scholastic logic. It is precisely this aspect of post Cartesian mathematics, its blurring of the boundaries between pure science on the one hand and the art of invention or technics on the other, mediated by the employment of algebraic symbolism, which is the decisive step on the path towards the mathematical physics which dominates the modern worldview.43 As Jacob Klein has argued in Greek Mathematical Thought and the Origin of Algebra (1936), two of the distinctive conceptual features of algebra are the identification of an object with its means of representation and replacement of the real determinateness of an object with the possibility of making it determinate.44 It is on the basis 42 See Jacob Klein, “Modern Rationalism,” in Lectures and Essays, eds. Robert B. Williamson and Elliott Zuckerman (Annapolis, Maryland: St John’s College Press, 1985), 59. The very idea of such a mathematical physics is revolutionary within an Aristotelian framework, according to which mathematics deals with unchanging beings that possess no independent existence and physics deals with changing beings that do possess independent existence. 43 In a series of works, including The Emergence of a Scientific Culture: Science and the Shaping of Modernity, 1210–1685, (Oxford: Clarendon Press, 2006), Stephen Gaukroger has illuminated, in both philosophical and political terms, the blurring of the boundaries between natural science and technics distinctive of the modern scientific worldview. This modern view is contrasted with the contemplative and private ideal of philosophy and the philosopher distinctive of the premodern conception. 44 Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, trans. Eva Brann (New York: Dover, 1968), 123. DUMMETT AND ANALYTICAL PHILOSOPHY 343 of the unprecedented universality of the notion of an object as an “indeterminate empty anything whatsoever” that the formal symbolic reasoning distinctive of the new mathematical physics takes hold. Despite the obvious explanatory power and practical applicability of the new science of nature, however, the process of increasing formalisation and abstraction threatens a division between a selfenclosed system of signs and the world of everyday experience, insofar as a formal system can be justified primarily with regard to its internal coherence. From this perspective, the problem of empirical applicability becomes that of matching the external world with a prearticulated formal symbolic system manipulated according to certain techniques or rules. It is at this point, as Klein suggests, that from the scientific perspective “the things of the world are no longer understood as countable beings . . . rather the structure of the world . . . is understood as a lawfully ordered course of events.”45 Although algebraic methods allow for the mathematisation of nature, however, they appear less well equipped to deal with the articulation of our everyday experience found in natural languages. Frege’s predicate calculus was regarded by its founder as offering a better representation of thought than that available in natural language, which on account of its ambiguity and reliance on context is an inappropriate medium for the representation of mathematical proof. Indeed, Frege suggests that it is one of the fundamental tasks of philosophy to break the power of words over the human mind and free thought from the ordinary linguistic means of expression.46 While Frege himself was predominately interested in statements of scientific discourse and placed in question the amenability of everyday natural language to the predicate calculus, some of his more ambitious heirs, including the early Wittgenstein and Carnap, attempted to extend the powerful new method to an account of the structure of reality as represented through linguistic means. Dummett’s philosophical project is in large part based on this more ambitious reading of the 185. 45 Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, 46 Frege, Begriffsschrift, xii. 344 GEORGE DUKE explanatory power of Frege’s conceptual notation in relation to the realm of natural language.47 In order to understand the extent of Dummett’s ambition for Frege’s logic, it is instructive to consider his adherence to the priority of syntactic over ontological categories mentioned earlier in this paper. According to the “syntactic priority thesis,” the application of ontological categories, such as concept and object, are dependent upon the application of linguistic category terms, such as predicate and proper name, and not the converse.48 On this model, a Fregean syntax not only represents the best possible representation of thought, it is also constitutive of our ontology. Dummett accordingly insists that it is contrary to Frege’s intention to claim, as did Peter Geach, that we are to count numerical terms as proper names because they refer to Fregean objects; rather, we must regard numbers as objects because we are compelled to recognize numerical terms as proper names.49 For Dummett, the distinction between proper names and expressions of other types must be one that can be drawn in wholly linguistic terms, without the necessity for any scrutiny of the things for which the respective expressions stand.50 On the basis of his adherence to the syntactic priority principle, it would not appear inaccurate to attribute to Dummett a form of linguistic idealism. It is, moreover, a form of linguistic idealism that has significant affinity with the idealism of Kant, according to which the categories of the understanding are at the same time the conditions of the possibility of the experience of an object and the conditions of the possibility of something being an object of experience. Kant’s great project was that of reconciling the laws of Newtonian physics with our intuitive experience of the world.51 By his emphasis upon the 47 Subsequent events have suggested the highly ambitious character of this project and its need for supplementation by a theory of praxis, interpretation or intentionality. The privileged role of Frege’s predicate logic in the genesis of the semantic tradition is therefore instructive not only for understanding that tradition in its more ambitious early manifestations but also in terms of the challenges of pragmatism and naturalism which followed its inevitable decline. 48 Dummett, FPL, 69. 49 Dummett, FPL, 56. 50 Dummett, FPL, 57. 51 Kant’s central position in relation to modern philosophy is largely explained by his attempt to mediate between conflicting poles of modernity DUMMETT AND ANALYTICAL PHILOSOPHY 345 capacity of Fregean syntactic categories to give the most accurate representation of thought, and the assertion that these syntactic categories are constitutive of the objects and concepts of experience, Dummett follows a distinctly Kantian path. What is significant in this context, however, is the extent to which Kantian idealism is a response to epistemological problems created by modern mathematical physics. Kant’s categories and synthetic a priori, which explain how the fundamental concepts of Newtonian physics are possible, is concomitant with a rejection of the idea that an object can be given prior to judgment, a rejection in turn best understood in terms of the peculiarly modern skepticism arising out of a division between subjective apprehension of phenomena and things as they are in themselves. The recognition of the conceptually determined character of all perception is here based on the premise that the most reliable criterion of identity is something that we ourselves introduce, rather than something prediscursive embodied in determinate identity conditions. The split between the realm of law explicated by natural science, in particular by mathematical physics, and the intuitive world of everyday experience, is perhaps the fundamental problem of modernity. As McDowell has suggested in Mind and World (1994), this split has tended to result in an oscillation in epistemology between opened up by the scientific revolution. This is why one productive way of tracing the analytical/continental split is in terms of the different school of neo-Kantianism dominant in the late eighteenth and early nineteenth century. For the Marburg neo-Kantians the advances of the Naturwissenschaften are understood as the fact from which philosophical inquiry should begin, even if it is the forms and measures of the human intellect that are the presupposition of scientific intelligibility. For the Southwest school of neoKantianism, by contrast, we need to begin from our everyday intuitive experience and acknowledge the independent claim to legitimacy of the Geisteswissenschaften. The abstract theoretical frameworks of natural science, mathematics and logic accordingly need to be understood as derivative from a more primordial source. These different interpretations of Kant culminate in the dispute between Carnap and Heidegger over the philosophical priority of logic and the exact sciences. See Rudolf Carnap, “Die Überwindung der Metaphysik durch logische Analyse der Sprache” in Erkenntnis vol. 2 (1931–32), 219–41 and Martin Heidegger, “Was ist Metaphysik?” (1929) in Gesamtausgabe Band 9 (Frankfurt am Main: Vittorio Klosterman, 1965). Michael Friedman gives an account of the significance of the dispute between Carnap and Heidegger in his The Parting of the Ways: Carnap, Cassirer and Heidegger (Illinois: Open Court, 2000). 346 GEORGE DUKE the frictionless spinning in the void of coherentism and the myth of the given embodied in bare naturalism. Whereas the semantic tradition has tended to focus upon the laws contained in formal systems and the project of transformative analysis, more naturalistic approaches have concentrated upon the law like regularities postulated to exist in the causal realm. In other words, the semantic tradition, with its emphasis upon formal systems and meaning, has tended to veer towards a form of coherentism, whereas more empirically minded analytical philosophers have tended to move towards the kind of naturalized epistemology and deference to natural science suggested by the work of Quine.52 In Frege: Philosophy of Mathematics, Dummett argues that Frege’s life work can be understood as a continuation of Bolzano’s project of removing intuition from number theory and analysis.53 The rejection of intuition embodied in the rigorisation of the calculus and similar advances were motivated as much by the desire for clarity as certainty. It is nonetheless superficial to see either the linguistic turn or increased use of technical formal symbolic techniques, contemporary with or subsequent to Frege, as constituting a radical break with the modern philosophical project. Despite his rejection of the synthetic a priori, Dummett’s insistence that “there is no such thing as an immediate apprehension of an object,”54 is aligned with a model of philosophy that has its roots in early moderns such as Descartes and which finds its exemplary expression in Kant. Dummett’s claim that it “is only by coming to grasp the use of proper names, or other terms, referring to them that we form any conception of objects as persisting constituents of a heterogeneous, changing reality and as identifiable as the same again, unless some criterion of identity with which we are already familiar is presumed”55 should be read in this light. The modern epistemological premises of Dummett’s thought are also evident in the global statement of this view, namely that “all 52 It is worth noting in this regard that the so called “return of metaphysics” has been accompanied by a continued acceptance of the transformative method on the one hand and the priority of natural scientific causal explanations on the other. Such a stance is paradigmatically embodied in the Quinean dictum that “to be is to be the value of a bound variable.” 53 Dummett, FPM, 223. 54 Dummett, FPM, 203. 55 Dummett, FPM, 204. DUMMETT AND ANALYTICAL PHILOSOPHY 347 conceptual thought involves the imposition of form upon an amorphous reality.”56 Here, Dummett appears to fall prey to the coherentism identified by John McDowell as one side of the modern oscillation. The attempt to reconcile the space of reasons with the causal realm of nature culminates in the view that thinking is making, as a result of the denial of a pretheoretical intelligibility to nature that could mediate between the two realms. An adequate characterisation of the origins of the analytic tradition presupposes an account of the fundamental conceptual shift that occurred during the time of the scientific revolution and the epistemological problems that arose in conjunction with this shift. This is why it is misleading to assert, with Dummett, that the really interesting developments in terms of understanding the analytical tradition are subsequent to Frege. The most productive contrast in terms of understanding the origins of the analytical tradition is not between pre and post Fregean thought, but between modern and premodern conceptions of philosophy and its relation to the world of everyday experience. Moreover, the split between analytical and continental schools is best understood in terms of the fundamental change in the way philosophy was conceived which originated in early modernity, namely in terms of different stances towards the kind of instrumental rationality that is embodied in the methodical stance favored by the exact sciences of nature. The University of Melbourne 56 Dummett, FPM, 42.