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Published online by Cambridge University Press: 08 January 2010
In the preface to the Tractatus Wittgenstein acknowledged ‘Frege's great works’ as one of the two primary stimulations for his thoughts. Throughout his life he admired Frege both as a great thinker and as a great stylist. This much is indisputable. What is disputable is how he viewed his own philosophical work in relation to Frege's and, equally, how we should view his work in this respect. Some followers of Frege are inclined to think that Wittgenstein's work builds on or complements that of Frege. If that were true it would be plausible to suppose that the joint legacy of these two great philosophers can provide a coherent foundation for our own endeavours. But it is debatable whether their fundamental ideas can be synthesized thus. The philosophy of Wittgenstein, both early and late, is propounded to a very large extent in opposition to Frege's. They can no more be mixed than oil and water – or so I shall argue.
1 I haved discussed Wittgenstein's Tractatus criticisms of Frege in ‘Frege and the Early Wittgenstein’ (forthcoming). Here I merly summarize his conclusions.
2 For a more detailed discussion, see Baker, G.P., Wittgenstein, Frege and the Vienna Circle (Oxford: Blackwell, 1988). pp. 116–25.Google Scholar
3 In MS, 161, 55 he observed that he was inclined to invoke Frege's notion of sense in application to mathematical propositions. Both remarks implicitly confirm his earlier criticisms of the Fregean conception of sense for the central case of the empirical proposition.
4 To use Wittgenstein's own Blue Book metaphor, ‘Some of the greatest achievements in philosophy could only be compared with taking up some books which seemed to belong together, and putting them on different shelves; nothing more being final about their positions than that they no longer lie side by side’ (BB, 44f.).
5 It is noteworthy that Frege's brief foray into epistemology in ‘The Thought’(as well as in some remarks on ideas, colour perception and subjective experience in The Foundations of Arithmetic and in the preface to the Basic Laws) is implicitly and by intimation criticized in the private language arguments (cf. PI, §273, in which the phrase ‘uns Allen Gegenüberstehendes’ is quoted from Basic Laws, preface p. xviii (see Hacker, P. M. S., Wittgenstein: Meaning and Mind (Oxford: Blackwell, 1990)Google Scholar, Exegesis, ¬273)). Frege was committed to the two fundamental misconceptionsthat lie at the root of the galaxy of confusions that Wittgenstein assails, namely the epistemic privacy of experience and the privacy of ownership of experience. This will not be discussed here.
6 Other important points of convergence between the Tractatus and Frege are (i) the context principle, and (ii) the requirement of determinacy of sense. These will not be discussed in this paper.
7 Frege did not conceive of his logical investigations as being a ‘study of sign-language’, but rather a study of thoughts and their logical relations conducted by the use of a sign-language, preferably the ideal sign-language of his concept-script. By contrast, according to Wittgenstein, ‘It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone’ (TLP, 6.113), that ‘If we know the logical syntax of any sign-language, then we have already been given all the propositions of logic’ (TLP, 6.124).
8 One might distinguish here between ‘visual number’ and ‘inductive number’ (cf. PLP,105).
9 To be sure, there are many other reasons which Wittgenstein explored for faulting the Fregean and Tractatus demand for determinacy of sense. For detailed discussion, see Baker, G. P. and Hacker, P. M. S., Wittgenstein: Understanding and Meaning (Oxford: Blackwell, 1980), pp. 367–85.Google Scholar
10 Frege, in his polemic against formalists in arithmetic argued that mathematics is no mere game with signs, in which the rules for the use of signs may be arbitrarily stipulated. The mathematician is not concerned with numerals but with the numbers that are their meanings. Hence it is not the case that ‘the numerals are contentless marks, which are used according to arbitrary rules. Rather, the rules follow necessarily from the meaning of the signs.’ (BLA, ii, §158.) Wittgenstein characterized this as ‘the meaning-body conception’ and criticized it extensively (see Baker, G. P. and Hacker, P. M.S., Wittgenstein: Rules, Grammar and Necessity (Oxford: Blackwell, 1985), pp. 312–17.Google Scholar
11 Unlike Frege, he did not think that the value of a first-level concept for an object as argument is a truth-value. Nor did he think that the quantifiers are correctly construed as second-level functions taking first-level functions as arguments and mapping them on to truth-values - they are logical operations on elementary propositions (not functions whose arguments are first-level concepts) and the sense of a generalisation is a function of the senses of the elementary propositions in question. And he did not think that the sense of a sentence, what we understand when we understand an utterance, is the mode of presentation of its meaning as the value of a function for an argument.
12 Wittgenstein does not qualify his remark thus. But in other respects Frege's distinction is obviously not the same one. No one, prior to Frege, would have called ‘If £ is F, then if & is G, & is H’ ‘a predicate’0 or ‘the
13 To be sure, Wittgenstein recognised the intelligibility of alternative forms of thought - within limits. But the limits are indeterminate, as indeterminate as our concepts of thinking, inferring, and calculating. Nevertheless, they are not arbitrary but circumscribed ‘by natural limits corresponding to the body of what can be called the role of thinking and inferring in our life’ (RFM, 80).
14 For detailed discussion of the Augustinian picture as Wittgenstein conceived it, see Baker, G. P. and Hacker, P. M.S., Wittgenstein: Understanding and Meaning (Oxford: Blackwell, 1980), pp. 33–59Google Scholar and Wittgenstein: Rules, Grammar and Necessity (Oxford: Blackwell, 1985), pp. 3–24.Google Scholar
15 Geach, P. T., ed., Wittgenstein's Lectures on Philosophical Psychology 1946–7 (Hemel Hempstead: Harvester Wheatsheaf, 1988), preface p. xiv.Google Scholar
16 Geach, P. T., ‘Wittgenstein on Names’, in Terricabras, J.-M. ed., A Wittgenstein Symposium (Amsterdam: Rodopi, 1993), pp. 72f.Google Scholar
