Ways of branching quantifers

Linguistics and Philosophy 13 (4):393 - 422 (1990)
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Abstract

Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, non-linearly structured quantiiier-prefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partially-ordered) quantifier-prefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, the resources of standard lst-order languages and we will consider the new form in the context of 1st-order logic with 1- and 2-place ‘Mostowskian` generalized quantifiers.2..

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Gila Sher
University of California, San Diego

Citations of this work

Positive Polarity - Negative Polarity.Anna Szabolcsi - 2004 - Natural Language and Linguistic Theory 22 (2):409-452..
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Number-Neutral Bare Plurals and the Multiplicity Implicature.Eytan Zweig - 2009 - Linguistics and Philosophy 32 (4):353-407.
Polyadic Quantifiers.Johan Van Benthem - 1989 - Linguistics and Philosophy 12 (4):437-464.

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References found in this work

Philosophy of Logic.W. V. Quine - 1970 - Harvard University Press.
Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
The Foundations of Arithmetic.Gottlob Frege - 1884/1950 - Evanston: Ill., Northwestern University Press.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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