Boris Eng. A gentle introduction to Girard’s Transcendental Syntax for the linear logician. 2022.

https://hal.science/hal-02977750v7/document

Girard’s philosophical motivation for the transcendental syntax is to establish a whole new architecture for logic which would be free of any logical preconception but also explain the whole logical activity. In this idea, logic is a formatting of computation: everything starts from a chosen very general, simple and natural model of computation. This is what Girard calls the analytics, in reference to Kant. We require that the model includes reducible objects which can be evaluated (what Girard calls performance) to an irreducible object (Girard’s constat). Both are separated by indecidability: the fact that an reducible object cannot always be reduced to its potential results (infinite loop may appear).