Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-j5sqr Total loading time: 0.476 Render date: 2022-10-05T08:54:45.335Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

EARLY STRUCTURAL REASONING. GENTZEN 1932

Published online by Cambridge University Press:  18 August 2015

ENRICO MORICONI*
Affiliation:
Dipartimento di Filosofia
*
*DIPARTIMENTO DI FILOSOFIA UNIVERSITY OF PISA VIA P. PAOLI, 15 56127 PISA ITALIA E-mail: enrico.moriconi@unipi.it

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
Copyright
Copyright © Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Arndt, M., & Tesconi, L. (2014). Principles of explicit composition. In Moriconi, E. and Tesconi, L., editors. Second Pisa Colloquium in Logic, Language and Epistemology. Pisa: Edizioni ETS, pp. 1967.Google Scholar
Bernays, P. (1965). Betrachtungen zum Sequenzen-Kalkul. In Tymieniecka, A.-T., editor. Contributions to Logic and Methodology in Honor of J.M. Bocheński. Amsterdam: North-Holland Publishing Company, pp. 144.Google Scholar
Franks, C. (2010). Cut as consequence. History and Philosophy of Logic, 31, 349379.CrossRefGoogle Scholar
Franks, C. (2013). Logical completeness, form, and content: An archaeology. In Kennedy, J., editor. Interpreting Gödel: Critical Essays. Cambridge: Cambridge University Press, pp. 78106.Google Scholar
Gentzen, G. (1932). Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsysteme. Mathematische Annalen, 107, 329–50. English translation in Szabo (1969).CrossRefGoogle Scholar
Gentzen, G. (1934–1935). Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39, 176210, 405–431. English translation in Szabo (1969).CrossRefGoogle Scholar
Gentzen, G. (1936). Die Widerspruchsfreiheit der reine Zahlentheorie. Mathematische Annalen, 112, 493565. English translation in Szabo (1969).CrossRefGoogle Scholar
Moriconi, E. (2014). On the source of the notion of semantic completeness. In Moriconi, E. and Tesconi, L., editors. II Pisa Colloquium on Logic, Language and Epistemology. Pisa: Edizioni ETS, pp. 213244.Google Scholar
Schroeder-Heister, P. (2002). Resolution and the origin of structural reasoning: Early proof-theoretic ideas of Hertz and Gentzen. The Bulletin of Symbolic Logic, 8, 246265.CrossRefGoogle Scholar
Szabo, M., editor (1969). The Collected Papers of Gerhardt Gentzen. Amsterdam: North-Holland Publ. Co.Google Scholar
Tennant, N. (2015). On Gentzen’s structural completeness proof. In Wansing, H., editor. Dag Prawitz on Proofs and Meaning, Studia Logica series Outstanding Contributions to Logic, pp. 385414.Google Scholar
von Plato, J. (2009). Gentzen’s logic. In Gabbay, D. M. and Woods, J., editors. Handbook of the History of Logic, Vol. 5. Amsterdam: North-Holland, pp. 667721.Google Scholar
von Plato, J. (2012). Gentzen’s proof systems: Byproducts in a work of genius. The Bullettin of Symbolic Logic, 18(3), 313367.CrossRefGoogle Scholar
4
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

EARLY STRUCTURAL REASONING. GENTZEN 1932
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

EARLY STRUCTURAL REASONING. GENTZEN 1932
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

EARLY STRUCTURAL REASONING. GENTZEN 1932
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *