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  The semantics of frege's grundgesetze
 
 
Titel: The semantics of frege's grundgesetze
Auteur: Martin, John N.
Verschenen in: History and philosophy of logic
Paginering: Jaargang 5 (1984) nr. 2 pagina's 143-176
Jaar: 1984
Inhoud: Quantifiers in Frege's Grundgesetze like [image omitted]  are not well-defined because the part Fx & Gx stands for a concept but the yoking conjunction is horizontalised and must stand for a truth-value. This standard interpretation is rejected in favor of a substitutional reading that, it is argued, both conforms better to the text and is well-defined. The theory of the horizontal is investigated in detail and the composite reading of Frege's connectives as made up of horizontals is rejected. The sense in which the Grundgesetze has a many-valued but classical logic is explained by proving that its propositional fragment (under the standard interpretation) and Bochvar's 3-valued logic are instances of the same metatheoretic methods. Historically, the paper argues for a more naive but well-defined reading of the text. Theoretically, it provides a formally adequate statement of that semantics, as well as developing the abstract metatheory which embraces Bochvar's language and the Fregean fragment.
Uitgever: Taylor & Francis
Bronbestand: Elektronische Wetenschappelijke Tijdschriften
 
 

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