Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both approaches are compatible with the traditional ...

We define propositional quantum Frege proof systems and compare it with classical Frege proof systems.

The question I am interested in in this paper is "How do words obtain their meanings?" The author I shall ask for help in answering this question is Gottlob Frege. This may appear surprising, since Frege is known as not being interested in the question posed. Frege wanted to provide mathematics with solid foundations. To achieve this, he aimed at constructing from scratch logical systems that m...

The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this pap...

The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this pap...

In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege’s debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege’s critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it ...

Frege is the real culprit, rather than Russell. Hintikka views his dispute with Frege as pertaining to "the logic of being" (a phrase apparently coined by him; cf 1979, end of section 10: "Game-theoretical semantics is thus much closer to Aristotle's views on the logic of being than is the received view [Frege's]", emphasis mine, but the theoretical and historiographical opposition to Frege con...

We give exponential size lower bounds for bounded-depth Frege proofs of variants of the bijective (‘onto’) version of the pigeonhole principle, even given additional axiom schemas for modular counting principles. As a consequence we show that for bounded-depth Frege systems the general injective version of the pigeonhole principle is exponentially more powerful than its bijective version. Furth...

The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this pap...