Journal of Philosophical Logic 43 (6):1153-1172 (2014)
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Abstract |
Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors . A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard first-order logic, and shows that the proof-theoretic meanings of both logics coincide. The paper criticizes Frege’s original regimentation of quantified sentences of natural language, and argues for advantages of the proposed variant.
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Keywords | Subnectors Quantifiers First-order logic Proof-theoretic semantics Harmony and stability Frege’s translation |
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DOI | 10.1007/s10992-014-9312-z |
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References found in this work BETA
Articulating Reasons: An Introduction to Inferentialism.Robert Brandom - 2000 - Harvard University Press.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Begriffsschrift: Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.Gottlob Frege - 1879 - Halle a.d.S.: Louis Nebert.
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Citations of this work BETA
A Three-Valued Quantified Argument Calculus: Domain-Free Model-Theory, Completeness, and Embedding of Fol.Ran Lanzet - 2017 - Review of Symbolic Logic 10 (3):549-582.
Connexive Restricted Quantification.Nissim Francez - 2020 - Notre Dame Journal of Formal Logic 61 (3):383-402.
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