%0 Book Section %T Rule-Following and the Limits of Formalization: Wittgenstein’s Considerations Through the Lens of Logic %+ Institut de Mathématiques de Marseille (I2M) %+ Università degli Studi Roma Tre = Roma Tre University (ROMA TRE) %A Pistone, Paolo %@ 978-3-319-10433-1 %B From Logic to Practice %I Springer International Publishing %S Boston Studies in the Philosophy and History of Science %V 308 %N Part II %P 91-110 %8 2014-11-06 %D 2014 %R 10.1007/978-3-319-10434-8_6 %K epistemology %K mathematical logic and foundations %K philosophy of science %Z 03A10 %Z Mathematics [math]/History and Overview [math.HO]Book sections %X 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. %G English %L hal-01309218 %U https://hal.science/hal-01309218 %~ CNRS %~ UNIV-AMU %~ EC-MARSEILLE %~ INSMI %~ I2M %~ I2M-2014-