Pareceu-me que valeria a pena chamar a atenção para a seguinte linha de investigação:
A FORMALIZATION OF KANT’S TRANSCENDENTAL LOGIC T. ACHOURIOTI and M. VAN LAMBALGEN ILLC/Department of Philosophy, University of Amsterdam Abstract Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first-order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant’s ‘transcendental logic’ is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kant’s Table of Judgements in Section 9 of the Critique of Pure Reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant’s ‘general’ logic is after all a distinguished subsystem of first-order logic, namely what is known as geometric logic. Como podem ver abaixo, já há mais gente interessada nisto. JM ---------- Forwarded message ---------- From: Grigori Mints <gmi...@stanford.edu> Logic Seminar Tuesday October 11 Time: 4:15-5:30 Room: 380-380X A formalization of Kant's transcendental logic G. Mints (Stanford) Kant's theory of judgements is a subject of extensive and active studies. Kant's formal logic, on the contrary, is studied insufficiently and usually dismissed as 'terrifyingly narrow-minded and mathematically trivial'. Recent work by Theodora Achourioti and Michiel van Lambalgen A formalization of Kant's transcendental logic, The Review of Symbolic Logic, v.4 no 2, 2011, 254-289 ([AvL] below) seems to refute this verdict. They propose a translation of the philosophical language of Kant's theory of judgements into the language of elementary logic and provide a convincing justification of their view. In formal terms Kant's logic is identified with geometric logic, a subsystem of ordinary first order logic that has been isolated long ago in mainstream mathematics. The model has to elucidate a vast array of statements by Kant like the following: "Thus, if, e.g., I make the empirical intuition of a house into perception through the apprehension of its manifold, my ground is the necessary unity of space and of outer sensible intuition in general, and I as it were draw its shape in agreement with this synthetic unity of the manifold in space." [AvL] analyzes Kant's logic in terms of inverse limits of models, a construction widely used in mathematics that reminds one of Kripke models (of ``possible worlds'') or forcing, but inverts the direction in certain sense. We present basic definitions from [AvL] and translations of Kantian terms (as many as time permits) into logical language. The talk next week by Ulrik Buchholtz contains proofs of technical results. _______________________________________________ Logica-l mailing list Logica-l@dimap.ufrn.br http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
