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3 THE CALCULUS VIEW OF LANGUAGE MEANING AND RULES Arecurrent theme in Wittgenstein’s writings and lectures from 1930–34 is the critique of the idea that there is a single calculus of propositions that underlies every possible symbolism. He remarks that “Frege and Russell made up a calculus which looked to be the calculus underlying the correct use of language” (Lectures 1932–35, p. 68). He also points out that in the Tractatus he shared this “mistaken idea” with Frege and Russell: I had the mistaken idea that propositions belong to just one calculus . There seemed to be one fundamental calculus, viz., logic, on which any other calculus could be based. This is the idea which Frege and Russell had [. . .]. If one has the idea of a single logic then one must be able to give one general formula of logic, the general formula of a proposition. I thought I had found this formula in the T-F table, an equivalent of the word “proposition” and the word “logic.” (Lectures 1932–35, p. 138) Wittgenstein now argues that the logical calculus is just “one calculus among others” (Lectures 1932–35, p. 13), and its rules do not have any special privilege. Each propositional system determines the form of its propositions autonomously, that is, according to its own rules of grammar. So Wittgenstein proposes to adopt “as a leading principle” in philosophy that there is no such thing as “the calculus of all calculi” (PG §72). However, as some commentators have pointed out,78 the view of language as a calculus remains at the core of Wittgenstein’s philosophy in the early 1930s. In Philosophical Remarks Wittgenstein refers to a system of proposition as “a calculus” or “system of rules” (PR §152). In a conversation with Schlick and Waismann from September 1931 he remarks: “I am 55 56 The Calculus View of Language saying that our way of using signs constitutes a calculus, and I am saying this deliberately. For this is not a mere analogy between our way of using words in a language and a calculus” (WWK p. 168). And in Philosophical Grammar he argues that “philosophy is concerned with calculi,” although not with “the calculus of all calculi” (PG §72). What Wittgenstein finds objectionable is the idea that there is a privileged, overarching calculus that can fix the logical form of every proposition. But he retains the idea that “a general propositional form determines a proposition as part of a calculus” (PG §80). There is nothing wrong with the idea of a calculus as long as it is diversified so as to account for the specificity of a genuine plurality of propositional forms. As late as 1933–34 Wittgenstein still holds that “language is a calculus ” (PG §140). But although the calculus view of language of this period has its roots in the Tractatus, it contrasts with the Tractarian account of language in important respects. In the early 1930s the Tractarian view of language as a calculus is transformed in three ways. In the first place, the notion of calculus is pluralized: language cannot be reduced to a single propositional calculus; it is composed of a set of autonomous calculi. In the second place, propositional calculi are thought to be conventional systems: their rules are arbitrary stipulations (PG §§81–82); they do not spring of necessity from the essence of the proposition (“what we call a proposition is more or less arbitrary”; Lectures 1932–35, p. 12). In the third place, the propositional calculi in which language consists are no longer hidden beneath the statements of ordinary language: these calculi operate on the very surface of language use; they are composed of ordinary-language statements (cf. PG pp. 210–211). This chapter will cover the development of the calculus view of language from 1930 to 1934. The main point of evolution in this period is the repudiation of the thesis of the logical independence of propositional systems . This repudiation marks the transition from the local holism of the Satzsystem view to the radical holism79 of Philosophical Grammar and the 1932-35 lectures. In section 1, I will examine the leitmotif that gives unity to Wittgenstein’s thought during this period: the attempt to develop a deflationary account of meaning as use. In section 2, I will analyze the problems facing the account of meaning sketched in Philosophical Remarks and the 1930–32 lectures, which finally led to the rejection of the thesis of logical independence. Finally, in...

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