Logic after Wittgenstein. (English) Zbl 1026.03006

Tomassi, Paul

Nord. J. Philos. Log. 6, No. 1, 43-70 (2001).

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.

Reviewer: Volker Peckhaus (Paderborn)

MSC:

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

Keywords:

language-games; dialogue logic; game theoretical logic

Citations:

Zbl 0435.03011; Zbl 0733.03003