Este artigo é uma nota editorial de introdução ao dossiê temático ‘1892-2022: 130 anos Über Sinn und Bedeutung Frege’. Por meio do exame dos artigos publicados no dossiê, defendemos a tese que o projeto fundacional Frege 1892 mais amplo logicista em filosofia da matemática e se desenvolve longo quatro dimensões fundamentais: 1) desenvolvimento teoria semântica geral; 2) fundação filosófica ling...

For every prime m ≥ 2, we give a family of tautologies that require super-polynomial size constant-depth Frege proofs from Countm axioms, and whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Zm. This shows that constant-depth Frege systems with counting axioms modulo m do not polynomially simulate constant-depth Frege systems with counting ...

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.

We give a survey on truth theories for applicative theories. It comprises Frege structures, Universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.

In Arai (1996), we introduced a new inference rule called permutation to propositional calculus and showed that cut-free Gentzen system LK (GCNF) with permutation (1) satis es the feasible subformula property, and (2) proves pigeonhole principle and k-equipartition polynomially. In this paper, we survey more properties of our system. First, we prove that cut-free LK + permutation has polynomial...

that roles that Frege wanted to be filled by his notion of sense could be filled by a single thing. I will be taking as a starting point one aspect of the Fregean notion of sense to draw a distinction between sense based theories of reference and direct reference theories. I will not insist on the identification of what is true and what is the referent for Frege of a sentence in indirect discou...

Logicism is typically de ned as the thesis that mathematics reduces to, or is an extension of, logic. Exactly what “reduces” means here is not always made entirely clear. (More de nite articulations of logicism are explored in section 5 below.) While something like this thesis had been articulated by others (e.g., Dedekind 1888 and arguably Leibniz 1666), logicism only became a widespread subje...