Journal of Philosophical Logic 43 (6):1153-1172 (2014)

Nissim Francez
Technion, Israel Institute of Technology
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.
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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The Taming of the True.Neil Tennant - 1997 - Oxford University Press.
Absolute Generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - Oxford University Press.

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