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Transcendental syntax I: deterministic case

Published online by Cambridge University Press:  20 July 2015

JEAN-YVES GIRARD
JEAN-YVES GIRARD*
Affiliation:
Institut de Mathématiques de Marseille, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France Email: jeanygirard@gmail.com
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Abstract

We study logic in the light of the Kantian distinction between analytic (untyped, meaningless, locative) answers and synthetic (typed, meaningful, spiritual) questions. Which is specially relevant to proof-theory: in a proof-net, the upper part is locative, whereas the lower part is spiritual: a posteriori (explicit) as far as correctness is concerned, a priori (implicit) for questions dealing with consequence, typically cut-elimination. The divides locative/spiritual and explicit/implicit give rise to four blocks which are enough to explain the whole logical activity.

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