Listy Gottloba Fregego. Uwagi o polskim wydaniu [rec. Gottlob Frege: Korespondencja naukowa]

Gottlob Frege final

Gottlob Frege Patricia A. Blanchette Abstract Gottlob Frege (1848-1925) made significant contributions to both pure mathematics and philosophy. His most important technical contribution, of both mathematical and philosophical significance, is the introduction of a formal system of quantified logic. His work of a more purelyphilosophical kind includes the articulation and persuasive defense of a...

Frege Systems

Propositional Proofs in Frege and Extended Frege Systems (Abstract)

We discuss recent results on the propositional proof complexity of Frege proof systems, including some recently discovered quasipolynomial size proofs for the pigeonhole principle and the Kneser-Lovász theorem. These are closely related to formalizability in bounded arithmetic.

The Curse of Frege

I mention two methodological problems with AI's study of inference that have to do with excessive faith in classical logic. The first is the familiar bias toward formalisms that incorporate deductive patterns of argument: a bias against inductive patterns of reasoning. The second is the pretension that inference can be studied with no regard for one's habits of representation. By implicating Fr...

Universes over Frege structures

We investigate universes axiomatized as sets with natural closure conditions over Frege structures. In the presence of a natural form of induction, we obtain a theory of proof-theoretic strength 0 .