History and Philosophy of Logic 5 (2):143-176 (1984)

Quantifiers in Frege's Grundgesetze like 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
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DOI 10.1080/01445348408837068
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References found in this work BETA

Methods of Logic.W. V. O. Quine - 1950 - Harvard University Press.
The Development of Logic.W. C. Kneale - 1962 - Oxford University Press.
Logics and Languages.Maxwell John Cresswell - 1973 - London: Methuen [Distributed in the U.S.A. By Harper & Row.

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Decomposition and Analysis in Frege’s Grundgesetze.Gregory Landini - 1996 - History and Philosophy of Logic 17 (1-2):121-139.

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