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From constants to consequence, and back
Stockholm University, Faculty of Humanities, Department of Philosophy.
2011 (English)In: Synthese, ISSN 0039-7857, E-ISSN 1573-0964, Vol. 187, no 3, 957-971 p.Article in journal (Refereed) Published
Abstract [en]

Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation =>_X. We present this in a precise and abstract form, in particular studying minimal sets of symbols generating =>_X. Then we present a method for going in the other direction: extracting from an arbitrary consequence relation => its associated set C_=> of constants. We show that this returns the expected logical constants from familiar consequence relations, and that, restricting attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion).

Place, publisher, year, edition, pages
2011. Vol. 187, no 3, 957-971 p.
Keyword [en]
logical constants, consequence relations
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
URN: urn:nbn:se:su:diva-66325DOI: 10.1007/s11229-011-9902-zOAI: oai:DiVA.org:su-66325DiVA: diva2:467462
Available from: 2011-12-19 Created: 2011-12-19 Last updated: 2017-12-08Bibliographically approved

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