Rule-Following and the Limits of Formalization: Wittgenstein’s Considerations Through the Lens of Logic

Paolo Pistone (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 ROMA TRE - Università degli Studi Roma Tre = Roma Tre University

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.

Mots clés: epistemology; mathematical logic and foundations; philosophy of science

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Paolo Pistone. Rule-Following and the Limits of Formalization: Wittgenstein’s Considerations Through the Lens of Logic. From Logic to Practice, 308 (Part II), Springer International Publishing, pp.91-110, 2014, Boston Studies in the Philosophy and History of Science, 978-3-319-10433-1. ⟨10.1007/978-3-319-10434-8_6⟩. ⟨hal-01309218⟩