Paul Hertz’s Systems of Propositions As a Proof-theoretical Conception of Logic

Abstract

Paul Hertz was an outstanding German physicist, who also devoted himself to mathematical logic and wrote a series of papers that remained rather unnoticed, even if they influenced the development of proof theory and particularly Gentzen's work. This paper aims to examine Hertz's logical theory placing it in its historical context and remarking its influence in Gentzen´s sequent calculus. The analysis of the formal structure of proofs was one of Hertz´s most important achievements and it can be regarded as an anticipation of a “theory of proofs” in the current sense. But also, it can be asserted that Hertz´s systems played the role of a bridge between traditional formal logic and Gentzen´s logical work. Hertz´s philosophical ideas concerning the nature of logic and its place in scientific knowledge will be also analysed in this paper. Paul Hertz was an outstanding German physicist, who also devoted himself to mathematical logic and wrote a series of papers that remained rather unnoticed, even if they influenced the development of proof theory and particularly Gentzen´s work. This paper aims to examine Hertz´s logical theory placing it in its historical context and remarking its influence in Gentzen´s sequent calculus. The analysis of the formal structure of proofs was one of Hertz´s most important achievements and it can be regarded as an anticipation of a theory of proofs in the current sense. But also, it can be asserted that Hertz´s systems played the role of a bridge between traditional formal logic and Gentzen´s logical work. Hertz´s philosophical ideas concerning the nature of logic and its place in scientific knowledge will be also analysed in this paper.