Metodo

International Studies in Phenomenology and Philosophy

Book | Chapter

176846

Rule-following and the limits of formalization

Wittgenstein's considerations through the lens of logic

Paolo Pistone

pp. 91-110

Abstract

In the Tractatus, it is stated that questions about logical formatting ("why just these rules?") cannot be meaningfully formulated, since it is precisely the application of logical rules which enables the formulation of a question whatsoever; analogously, Wittgenstein's celebrated infinite regress argument on rule-following seems to undermine any explanation of deduction, as relying on a logical argument. On the other hand, some recent mathematical developments of the Curry-Howard bridge between proof theory and type theory address the issue of describing the "subjective" side of logic, that is, the concrete manipulation of rules and proofs in space and time. It is advocated that such developments can shed some light on the question of logical formatting and its apparently unintelligible paradoxes, thus reconsidering Wittgenstein's verdict.

Publication details

Published in:

Lolli Gabriele, Panza Marco, Venturi Giorgio (2015) From logic to practice: Italian studies in the philosophy of mathematics. Dordrecht, Springer.

Pages: 91-110

DOI: 10.1007/978-3-319-10434-8_6

Full citation:

Pistone Paolo (2015) „Rule-following and the limits of formalization: Wittgenstein's considerations through the lens of logic“, In: G. Lolli, M. Panza & G. Venturi (eds.), From logic to practice, Dordrecht, Springer, 91–110.