From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

Introduction

Michael 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’ (1993, 128) has been criticized on the grounds that it excludes seminal figures in the analytical tradition such as GE Moore and Bertrand Russell (for example in Monk and Palmer, 1996). In this paper I begin by suggesting that Dummett’s characterization has some validity if restricted to what Alberto Coffa (1991) has called ‘the semantic tradition’ (that part of the analytical tradition represented by figures such as Frege, the Russell of ‘On Denoting’, the early Wittgenstein, Carnap, Tarski and Quine), in which the role played by logical analysis based on mathematical techniques is central. The restricted applicability of Dummett’s characterization, even when suitably qualified in this way, is instructive because it allows for a clearer view of the extent to which it is possible and/or meaningful to characterize the analytical tradition as a whole and its relation to what Dummett calls ‘other schools’ (1993, 4).

1. The Linguistic Turn

Stated without further qualification, Dummett’s characterization of analytical philosophy raises obvious objections. It is simply not the case that the seminal thinkers of the analytical tradition form a united front around the notion that a philosophical account of thought can only be achieved through a philosophical account of language. Apart from the examples of Moore and Russell already mentioned, Frege is equally problematic, on account not only of his lifelong ambivalent attitude towards imprecise natural language but also his ‘realist’ view that thoughts unthought by a thinker are still true or false (53, 1900).

Dummett’s characterization has the virtue, from his own perspective, of bringing together those components of the thought of Frege and late Wittgenstein to which he is particularly sympathetic. It is hard not to think, however, that he has been led astray by his almost exclusive concern upon the historical relations between Frege and Husserl in Origins of Analytical Philosophy, which, given Husserl’s commitment to a phenomenology of pure consciousness, could lead to the conclusion that the linguistic turn is distinctive of the analytical school as against other philosophical approaches.¹

While no one would deny the centrality of linguistic considerations to the analytical tradition, Dummett’s formulation is too rough-grained to offer any meaningful characterization of a particular tradition. A better approach would be to focus on the origins of what Alberto Coffa has called ‘the semantic tradition’, a tradition which includes many of the major thinkers of analytical philosophy. What unifies these figures, however, is not so much an emphasis upon linguistic meaning and rejection of intuition (Russell and Quine are counter-examples to this thesis), as a belief in the capacity of logical analysis to illuminate traditional philosophical problems.

2. Frege’s new logic

When we read Dummett’s characterization of analytical philosophy in the context of his views on Frege’s place in the history of ideas it in fact accords with the privileged place of logical analysis. According to Dummett, ‘only with Frege was the proper object of philosophy finally established’ (1975, 458). 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 thinking, and, finally, that the only proper method for analysing thought consists in the analysis of language’ (1975a, 458).

For Dummett, therefore, Frege began a revolution in philosophy as overwhelming as that of Descartes (1973, 665-666 and 1975, 437-458). 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 (1973, 666). Dummett here means logic in the broad sense of a theory of meaning or the search for a model for what the understanding of an expression consists in (1973, 669). The thought is that 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’ (1973, 669).

In appealing to the linguistic turn as decisive for analytical philosophy, Dummett therefore points towards the introduction of semantic considerations that he takes to be embodied in Frege’s employment of the context principle in Die Grundlagen der Arithmetik (1884). Faced with the Kantian question concerning how it is possible to be given numbers, when we do not have representations or intuitions of them (1993, 5), Frege, Dummett alleges, converted ‘an epistemological problem, with ontological overtones’ into one about ‘the meaning of sentences’ (1991, 111).

It is Frege’s new predicate logic introduced in Begriffsschrift, based on the extension of function-argument analysis from mathematics to logic, which provides the technical means to carry out this strategy. In The Logical Basis of Metaphysics, Dummett argues that while the philosophy of thought has always in a sense been regarded as the starting point of the subject ‘where modern analytical philosophy differs is that it is founded on a far more penetrating analysis of the general structure of our thoughts than was ever available in past ages, that which lies at the base of modern mathematical logic and was initiated by Frege in 1879’ (1991, 2).

Dummett’s defence of analytical philosophy against ‘the objections of laymen’, who lament the abandonment of ‘fundamental’ questions for technical investigations, sets out from the fact that the analysis of inference carried out in modern logic presupposes an analysis of the structure of propositions. From this point of view, one could see why an adequate syntactic analysis of our language has priority in philosophical explanation. If we grant the further thesis that Frege’s new language of quantifiers and variables represents the most perspicuous means of representing natural language, we can apparently in good conscience justify the privileged role of logical analysis in analytic philosophy.

To privilege the role of Frege’s predicate logic is not to understate the importance for the semantic tradition of either the attack on psychologism, which Dummett calls ‘the extrusion of thoughts from the mind’, or the context principle. This is because these two 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 concept as a function of an argument, we can understand the process of concept formation without appeal to extraneous psychological considerations. 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 expressions such as df(x) or dx rather than seeking to explain them in isolation.

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, however, 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’ (1973) 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 historically 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 (1879, XI), 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 (1879, XII). On account of its seemingly limitless generality, the new predicate calculus, with its expressive power to represent functions and 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.

3. Transformative Analysis and Semantic Logicism

Recent work by Michael Beaney (2007) and Robert Brandom (2006) further clarifies the distinctive philosophical perspective of the semantic tradition. Brandom’s characterization of the notion of ‘semantic logicism’ is particularly revealing, in that it provides a way of bringing together philosophers for whom logical analysis of language and meaning is the core concern and naturalistic and empiricist approaches which are less easily accommodated by Dummett’s fundamental axiom.

Beaney explicates three conceptions of analysis in the Western philosophical tradition, claiming that the third of these - transformative analysis - is characteristic of analytical philosophy in its classical phase as embodied by Frege, Russell, the early Wittgenstein and Carnap. The first form of analysis is the decompositional - the breaking of a concept down into its more simple parts. The decompositional approach is prevalent in early modern philosophy and encapsulated in Descartes’ 13th rule for the direction of the mind 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. Classic 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.

Robert Brandom introduces the notion of ‘semantic logicism’ to characterize ‘classical’ analytical philosophy. According to Brandom, analytical philosophy in its classical phase is concerned with the relations between vocabularies – ‘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’ (2006, 1). So, what is distinctive of analytical philosophy is that ‘logical vocabulary is accorded a privileged role’ (2006, 2) in specifying semantic relations that are thought to make the true epistemological and ontological commitments of the former explicit.

In explicating the classical project of analysis as ‘semantic logicism’, Brandom notes that it involves, to employ Dummettian phraseology, the translation of epistemological and ontological questions into a semantic key. Brandom describes how two core programs of classical analytical philosophy, empiricism and naturalism, were transformed in the twentieth century ‘by the application of the newly available logical vocabulary to the self-consciously semantic programs they then became’ (2006, 2). 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 is elaborated by the use of logical vocabulary’ (2006, 3).

Brandom’s characterization of semantic logicism is more inclusive than Dummett’s fundamental axiom, but nonetheless does not completely cover the range of philosophers who would commonly be considered analytic. Apart from thinkers like Moore and Ryle, to whom it does not seem strictly applicable, more recent analytical thinkers have in fact placed the basic thesis of semantic logicism in question.

Brandom suggests that the main challenge to analytical philosophy in its classical phase came from Wittgenstein’s rejection of the assumption that, following a codification of the meanings expressed by one vocabulary, through the use of logical vocabulary, into that of another vocabulary, we can derive properties of use. Emphasising the dynamic character of linguistic practice, Wittgenstein rejects the assumption of classical semantic analysis that vocabularies are stable entities with fixed meanings, replacing this model with a piecemeal account of the uses to which language is put in various language games.

From this perspective, if we accept that semantic logicism is in some way characteristic of analytical philosophy in it classical phase, the pragmatist challenge of Wittgenstein and subsequent thinkers such as Rorty, is best viewed as a response to the original assumptions of the semantic tradition based on a realization of the limits of the application of mathematical techniques to natural language and everyday experience. As has often been noted, these responses in fact share much in common with the thought of major twentieth century continental thinkers, such as Heidegger and Gadamer. The fact that many dominant programs in contemporary analytical philosophy, such as contextualism, no longer have unmitigated faith in the program of logical analysis is also a recognition of the limits of the original aspirations of logical analysis.

As Michael Friedmann has suggested, the Carnap-Heidegger debate is highly instructive here, in that it highlights two radically different philosophical attitudes not only to logic and mathematics but also to the modern natural science built upon their edifice. This explains why the work of thinkers like Davidson, McDowell and Brandom, who have sought to explicate the logical space of reasons and reintroduced hermeneutic considerations, is accurately thought to represent a rapprochement between divergent traditions.

4. Conclusion

In this paper I have argued that Dummett’s fundamental axiom of analytical philosophy is inadequate not only because of what it excludes, but also insofar as it risks understating the role of logical analysis for that part of the tradition which he himself privileges. While representative of his own commitment to a position which reconciles semantic logicism with the dictum that meaning is use, Dummett’s axiom is at risk of covering over both the true origins of analytical philosophy in its classical phase and the extent to which its original project has been placed in question.

To provide a more complete characterization of analytical philosophy and its relation to ‘other schools’ one would need to spell out the relation between ‘instrumental’ and ‘reflective’ rationality. Arguably, the failure of ‘other schools’ in the twentieth century, with some notable exceptions, was precisely their inability to present an adequate account of an alternative account of rationality to the instrumental i.e. their critique of instrumental rationality was indiscriminate in the sense that it was often prosecuted against rationality per se. This is why the recent ‘hermeneutic’ turn in analytical philosophy represents a more significant development than the earlier ‘pragmatist challenge’.