We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church’s Logic of Sense and Denotation. Church understands such senses themselves to be “sense-functions,” functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain u...

It is argued that the semantic difference between sentences of the form ”a = a” and ”a = b” reflects a difference in their truthmakers. My account of these truth-makers combines a referential semantics – singular terms are deemed to contribute nothing but their reference to the meaning of sentences in which these occur – with an ontology of logically complex individuals. Against analyses in whi...

∗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...

O conceito de Bedeutung é central na filosofia Frege, entretanto existe uma grande divergência literatura sobre sua adequada interpretação. Dummet, Sluga, Carl, Burge, Tugendhat e outros comentadores Frege irão apresentar discordantes interpretações acerca Bedeutung, as quais se comprometem com aspectos gerais das perspectivas lógico/filosóficas fregeanas. Com base nisso, o objetivo principal d...

Motivated by the fundamental lower bounds questions in proof complexity, we initiate the study of matrix identities as hard instances for strong proof systems. A matrix identity of d × d matrices over a field F, is a non-commutative polynomial f(x1, . . . , xn) over F such that f vanishes on every d × d matrix assignment to its variables. We focus on arithmetic proofs, which are proofs of polyn...

The cutting plane refutation system CP for propositional logic is an extension of resolution and is based on showing the non-existence of solutions for families of integer linear inequalities. We deene the system CP + , a modiication of the cutting plane system, and show that CP + can polynomially simulate Frege systems F. In 8], it is shown that F polynomially simulates CP + , so both systems ...

Though Peirce and Frege played crucial roles in the development of modern logic, there has been so far little scholarly work comparing their positions on the nature of logic. I offer here a comparative study of their views on logic and I show that, although they developed their views independently from each other and with very different projects in mind, their positions are extremely similar (e...