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  • Crispin Wright, On Quantifying Into Predicate Position: Steps Towards a New(Tralist) Perspective.
    In the Begriffschrift Frege drew no distinction—or anyway signalled no importance to the distinction—between quantifying into positions occupied by what he called eigennamen—singular terms—in a sentence and quantification into predicate position or, more generally, quantification into open sentences—into what remains of a sentence when one or more occurrences of singular terms are removed. He seems to have conceived of both alike as perfectly legitimate forms of generalisation, each properly belonging to logic. More accurately: he seems to have conceived of quantification as such as an operation of pure logic, and in effect to have drawn no distinction between first-order, second-order and higherorder quantification in general.
    Higher-Order Logic, Misc in Logic and Philosophy of Logic
    Second-Order Logic in Logic and Philosophy of Logic
    Logic and Philosophy of Logic, General Works in Logic and Philosophy of Logic
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Similar books and articles
  • 73.2Bert Mosselmans (forthcoming). Aristotle's Logic and the Quest for the Quantification of the Predicate. Foundations of Science.
    This paper examines the quest for the quantification of the predicate, as discussed by W.S. Jevons, and relates it to the discussion about universals and particulars between Plato and Aristotle. We conclude that the quest for the quantification of the predicate can only be achieved by stripping the syllogism from its metaphysical heritage.
    Science, Logic, and Mathematics
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  • 71.6Tobias Rosefeldt (2008). 'That'-Clauses and Non-Nominal Quantification. Philosophical Studies 137 (3).
    This paper argues that ‘that’-clauses are not singular terms (without denying that their semantical values are propositions). In its first part, three arguments are presented to support the thesis, two of which are defended against recent criticism. The two good arguments are based on the observation that substitution of ‘the proposition that p’ for ‘that p’ may result in ungrammaticality. The second part of the paper is devoted to a refutation of the main argument for the claim that ‘that’-clauses are (...) singular terms, namely that this claim is needed in order to account for the possibility of quantification into ‘that’-clause position. It is shown that not all quantification in natural languages is quantification into the position of singular terms, but that there is also so-called ‘non-nominal quantification’. A formal analysis of non-nominal quantification is given, and it is argued that quantification into ‘that’-clause position can be treated as another kind non-nominal quantification. (shrink)
    Propositions in Philosophy of Language
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  • 61.6Philip Hugly & Charles Sayward (1994). Quantifying Over the Reals. Synthese 101 (1).
    Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)
    Quantifiers in Philosophy of Language
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  • 60.5Nicholas Denyer (1999). Names, Verbs and Quantification Again. Philosophy 74 (3):439-440.
    There are enormous differences between quantifying name-variables only, quantifying verb-variables only, and quantifying both. These differences are found only in the logic of polyadic predication; and this presumably is why Richard Gaskin thinks that they distinguish names from transitive verbs only, and not from verbs generally. But that thought is mistaken: these differences also distinguish names from intransitive verbs. They thus vindicate the common idea that on the difference between names and verbs we may base grandiose metaphysical distinctions, and undermine (...) Gaskin's idea that both names and verbs may be said to designate objects. (shrink)
    Names in Philosophy of Language
    Verbs in Philosophy of Language
    Quantifiers in Philosophy of Language
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  • 60.0Juha Kontinen & Jakub Szymanik (2008). A Remark on Collective Quantification. Journal of Logic, Language and Information 17 (2).
    We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective (...) quantification in natural language. (shrink)
    Formal Semantics in Philosophy of Language
    Generalized Quantifiers in Philosophy of Language
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