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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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.

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Citations of this work BETA

Connexive Restricted Quantification.Nissim Francez - 2020 - Notre Dame Journal of Formal Logic 61 (3):383-402.

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