Frege on Consistency and Conceptual Analysis

Propositional Consistency Proofs

Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomialsize proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow’s theorem th...

Conceptual Analysis and Analytical Definitions in Frege

A Study of Frege’s Influence on A. J. Ayer’s Theory of Emotivism

No doubt, Gottlob Frege and A. J. Ayer are considered to be among the most prominent contemporary philosophers. Insofar as one of them has revolutionized the linguistic domain while the other has influenced the domain of ethics in a diametrical fashion. Ayer’s theory of emotivism is regarded as one of the most controversial moral theories in the past century. We believe that Frege, as a linguis...

Francesca Boccuni On the Consistency of a Plural Theory of Frege ’ s

PG (Plural Grundgesetze) is a predicative monadic second-order system which is aimed to derive second-order Peano arithmetic. It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.

Frege and Hilbert on Consistency1

Frege's work in logic and the foundations of mathematics centers on claims of logical entailment; most important amongst these is the claim that arithmetical truths are entailed by purely logical principles. Occupying a less central but nonetheless important role in Frege's work are claims about failures of entailment. Here the clearest examples are his theses that the truths of geometry are no...