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Wittgenstein and the Philosophical Investigations. (English) Zbl 0878.03002

Routledge Philosophy Guide Books. London: Routledge. x, 216 p. (1997).
The book gives a comprehensive interpretation of Ludwig Wittgenstein’s “Philosophical investigations”, which were first published in 1953. The philosophy of mathematics is no topic in this classic of analytical philosophy. Among other things Wittgenstein develops his language-in-use theory, his language-game conception, and his denial of any private language. Very often, however, Wittgenstein uses examples from elementary mathematics, such as the addition of numbers or the development of a series. This is especially the case in his considerations on rule-following, treated in chapter 3 of the volume under review which covers the paragraphs 138-242 of Wittgenstein’s book. First of all the author criticizes the reconstruction of a skeptical argument in Wittgenstein which Saul A. Kripke presents in his “Wittgenstein on rules and private language” (Oxford, Blackwell, 1982). By analyzing sentences like “I mean addition by ‘+”’ or “Jones means addition by ‘+”’, Kripke arrives at the result that there is no fact about me (or Jones) that distinguishes between my meaning a definite function by “plus” or anything else or even nothing. The author rejects this reconstruction. She emphasizes Wittgenstein’s idea of grammatical investigations which can be seen as a reflection on how the use of language is going on, i.e. on our ordinary language games. Wittgenstein’s questions are, “what does it mean to know how a given series can be extended?”, or, “what does it mean to follow a rule, or to think that one follows a rule?”.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
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