“Transcendental syntax” (Girard 13) is the name of a proposal (or maybe a pamphlete) by Jean-Yves Girard which means to rethink fundamental aspects of formal logic, of syntax/semantics. According to Girard, linear logic and Geometry of Interaction are but exercises in transcendental syntax (Girard 13b).
While Girard’s prose is notoriously demanding, exegesis may be found in (Abrusci-Pistone 12, Rouleau 13).
Girard describes four levels of semantics: alethic, functional, interactive, and deontic. They descend into the depths of meaning, and thus are numbered from -1 to -4. The negatively first, alethic, is the layer of truth or models. The negatively second, functional, is the layer of functions or categories. The negatively third, interaction, is the layer of games or game semantics. The negatively fourth, deontic, is the layer of normativity or formatting. (Equivalent eXchange)
Jean-Yves Girard, Transcendental syntax 2.0, 2013 (pdf)
Jean-Yves Girard, Geometry of Interaction VI: a Blueprint for Transcendental Syntax, 2013 (CiteSeer)
Vito Michele Abrusci, Paolo Pistone, On Transcendental syntax: a Kantian program for logic?, 2012 (pdf)
Vincent Laurence Rouleau, Towards an understanding of Girard’s transcendental syntax: Syntax by testing, PhD thesis 2013 (pdf)
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