The Definition of Logical Validity - Hardcover

Halbach, Volker

Hardcover

ISBN 10: 019894554X ISBN 13: 9780198945543

Verlag: Oxford University Press, 2025

Inhaltsangabe

According to the semantic definition of logical consequence or validity, an argument is logically valid if, and only if, the conclusion is true under all interpretations under which also all premisses are true. The semantic definition is only a general pattern, and Volker Halbach presents a specific way of spelling out this definition. In contrast to the predominant approaches, truth is taken to be a primitive notion, which is not reduced away by a mathematical definition. An interpretation of a sentence is obtained by replacing non-logical terms uniformly with arbitrary other terms of the same grammatical kind. This conception of interpretations is in line with naïve and straightforward understandings of interpretations that hark back at least to the middle ages.

The resulting definition of logical validity combines two advantages: first, it is universal in the sense that it applies not only to a restricted language, but to the entire in which the definition is stated. This is in contrast to definitions of logical validity in higher-order languages. Secondly, it admits the intended interpretation, that is, the interpretation of sentences at their face value without any re-interpretation. Thus, logical consequence is trivial preserving truth. The usual model-theoretic definition lacks this property, although it has always taken to be fundamental to logical consequence and warrants its usefulness in philosophy.

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Über die Autorin bzw. den Autor

Volker Halbach, Professor of Philosophy and Fellow of New College, University of Oxford

Volker Halbach is Professor of Philosophy at the University of Oxford and a Fellow of New College. Before coming to Oxford in 2004, he held a position at the University of Constance. He has published numerous books and articles mainly in logic and the philosophy of logic, including The Logic Manual, which has been adopted as introductory textbook at many universities across the world.

Details zur Ausgabe

• Verlag: Oxford University Press
• Erscheinungsdatum: 2025
• Sprache: Englisch
• ISBN 10: 019894554X
• ISBN 13: 9780198945543
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 256
• Kontakt zum Hersteller: ORIGINAL KAISER; https://corp.oup.com/; ; Via Liguria 4; San Giuliano Milanese ; MI; 20098; Italien