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EARLY STRUCTURAL REASONING. GENTZEN 1932

Published online by Cambridge University Press:  18 August 2015

ENRICO MORICONI
ENRICO MORICONI*
Affiliation:
Dipartimento di Filosofia
*
*DIPARTIMENTO DI FILOSOFIA UNIVERSITY OF PISA VIA P. PAOLI, 15 56127 PISA ITALIA E-mail: [email protected]
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Abstract

This paper is a study of the opening section of Gentzen’s first publication of 1932, Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen, a text which shows the relevance of Hertz’s work of the 1920’s for the young Gentzen. In fact, Gentzen borrowed from Hertz the analysis of the notion of consequence, which was given in terms of the rules of thinning (Verdünnung) and cut (Schnitt) on sequents (there called “sentences”(Sätze)). Moreover, following Hertz again, he also judged it necessary to justify the forms of inference of the system by providing a semantics for them, so that it became possible to make precise the informal notion of consequence, and to show that the inference rules adopted are correct and sufficient.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 662 - 679
Copyright
Copyright © Association for Symbolic Logic 2015 

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References

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