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What is logic? (English) Zbl 0878.03005

Puhl, Klaus (ed.), Wittgenstein’s philosophy of mathematics. Proceedings of the 15th international Wittgenstein-Symposium, August 16-23, 1992, Kirchberg am Wechsel, Austria. Part II. Wien: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 20/II, 11-23 (1993).
The author does not really answer the question asked in the title. He rather relates Wittgenstein’s conception of logic, which is based on the thesis that the essence of logic is the order of possibilities which must be common to both world and thought (Philosophical Investigations), to that of the “Frege-Gödel conception”, as the author calls it (characterized by the primacy of concepts), and to intuitionistic predicate logic based on Brouwer’s philosophy of mathematics. The author emphasizes the intensional side of the theory of concepts, starting from the correct observation (as Gödel did as well in discussions with the author) that one has to distinguish two versions of Russell’s paradox, the extensional variant about sets and classes and the intensional variant (paradox of non-predicability) about predicates and concepts. The author sees similarities between Wittgenstein’s logic as presented in “On Certainty” and Hegel’s logic, based on the (rather weak) criterion that for both logic has to be contentful and related to grammar.
For the entire collection see [Zbl 0836.00023].

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03-03 History of mathematical logic and foundations
01A55 History of mathematics in the 19th century
00A30 Philosophy of mathematics
01A60 History of mathematics in the 20th century

Biographic References:

Wittgenstein, Ludwig
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