Frege, Thomae, and Formalism

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.

Frege, Contextuality and Compositionality

The name ‘Frege’s principle’ is well known: it is discussed, obeyed or rejected in philosophy, linguistics, logic and computer science (see e.g. [33] and[45]). Surprisingly, two completely different principles which are denoted by that name. In most fields it refers to ‘the principle of compositionality of meaning’: The meaning of a compound expression is a function of the meaning of its parts ...

Frege Systems

Frege, Boolos, and Logical Objects

∗This paper was published in the Journal of Philosophical Logic, 33/1 (2004): 1–26. The authors would like to thank C.A. Anderson, Thomas Hofweber, Jeffrey Kegler, and Kai Wehmeier for their comments on this paper. The paper was presented in its current form at the Seminar für Philosophie, Logik, und Wissenschaftstheorie, Universität München. We gratefully acknowledge the audience feedback. †An...

Frege, Russell and Wittgenstein

Frege, Russell and Wittgenstein were founders (although not by any means the sole founders) of the analytic tradition in philosophy; but they did not found the philosophy of language, which has roots stretching back much further. Their principal contribution, indeed, could be regarded as being in the opposite direction: it is not so much that they applied philosophical methods to the study of l...