Logic after Wittgenstein. (English) Zbl 1026.03006

Starting point is Wittgenstein’s later rejection of the “externalist Tractarian picture of logic according to which all rationally analysable discourse is properly understood as truth-functional” (p.43). The alternative of Wittgenstein’s Philosophical investigations is to relativise logic to language-games and, perhaps, to localise it to particular language-games [loc. cit.]. Logic after Wittgenstein could mean to investigate the question whether descriptions of the working of our language include descriptions of logical principles at work in this practise (pp. 44-45). The author proposes a formal analogue to natural language, intended to give the framework in which a simplification of the complexities of ordinary linguistic practice can be represented (p.51) forming, thus, a “logic after Wittgenstein”. Given the dialogical structure of the Philosophical investigations the author proposes a formal dialogue system, similar to that of P. Lorenzen and K. Lorenz [cf., e.g., Dialogische Logik. Darmstadt: Wissenschaftliche Buchgesellschaft (1978; Zbl 0435.03011)], but close to J. Mackenzie’s [cf., e.g., Stud. Log. 49, 567-583 (1990; Zbl 0733.03003)]. It is restricted to the speech acts of assertion, doubt, withdrawal, challenge, and exhibition of evidence.
The rules and acts of the formal dialogue system are given, and two cases are discussed, a formal dialogue in which the doubt cannot be grounded, and one in which it can be grounded.


03A05 Philosophical and critical aspects of logic and foundations
03B30 Foundations of classical theories (including reverse mathematics)
03-03 History of mathematical logic and foundations
01A60 History of mathematics in the 20th century
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