Substitutional Quantification

Edited by Geoff Georgi (West Virginia University, University of Southern California)
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  1. Special Quantifiers: Higher-Order Quantification and Nominalization.Friederike Moltmann - manuscript
    Special quantifiers are quantifiers like 'something', 'everything', and 'several things'. They are special both semantically and syntactically and play quite an important role in philosophy, in discussions of ontological commitment to abstract objects, of higher-order metaphysics, and of the apparent need for propositions. This paper will review and discuss in detail the syntactic and semantic peculiarities of special quantifiers and show that they are incompatible with substitutional and higher-order analyses that have recently been proposed. It instead defends and develops in (...)
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  2. Special Quantification: Substitutional, Higher-Order, and Nominalization Approaches.Friederike Moltmann - forthcoming - In Alex Grzankowski & Anthony Savile (eds.), Thought: its Origin and Reach. Essays in Honour of Mark Sainsbury. Routledge.
    Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...)
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  3. The Quantified Argument Calculus with Two- and Three-valued Truth-valuational Semantics.Hongkai Yin & Hanoch Ben-Yami - 2022 - Studia Logica 111 (2):281-320.
    We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of (...)
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  4. The Quantified Argument Calculus and Natural Logic.Hanoch Ben-Yami - 2020 - Dialectica 74 (2):179-214.
    The formalisation of Natural Language arguments in a formal language close to it in syntax has been a central aim of Moss’s Natural Logic. I examine how the Quantified Argument Calculus (Quarc) can handle the inferences Moss has considered. I show that they can be incorporated in existing versions of Quarc or in straightforward extensions of it, all within sound and complete systems. Moreover, Quarc is closer in some respects to Natural Language than are Moss’s systems – for instance, is (...)
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  5. First-order swap structures semantics for some Logics of Formal Inconsistency.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Journal of Logic and Computation 30 (6):1257-1290.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  6. On being called something.Geoff Georgi - 2017 - Linguistics and Philosophy 40 (6):595-619.
    Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...)
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  7. A propositional semantics for substitutional quantification.Geoff Georgi - 2015 - Philosophical Studies 172 (5):1183-1200.
    The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional quantification, namely, theories (...)
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  8. Peter van Inwagen, Substitutional Quantification, and Ontological Commitment.William Craig - 2014 - Notre Dame Journal of Formal Logic 55 (4):553-561.
    Peter van Inwagen has long claimed that he doesn’t understand substitutional quantification and that the notion is, in fact, meaningless. Van Inwagen identifies the source of his bewilderment as an inability to understand the proposition expressed by a simple sentence like “,” where “$\Sigma$” is the existential quantifier understood substitutionally. I should think that the proposition expressed by this sentence is the same as that expressed by “.” So what’s the problem? The problem, I suggest, is that van Inwagen takes (...)
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  9. Chapter 3: The Semantics of Special Quantifiers in Predicate Position.Friederike Moltmann - 2012 - In Abstract Objects and the Semantics of Natural Language. Oxford, United Kingdom: Oxford University Press.
    This chapter argues that special quantifiers such as 'something' when occurring in argument position are not ordinary or substitutional quantifiers; rather they have a reifying force introducing a domain of tropes or kinds of tropes to quantify over.
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  10. A substitutional theory of truth? [REVIEW]Marian David - 2006 - Philosophy and Phenomenological Research 72 (1):182–189.
    Contribution to book symposium on C. Hill's: Thought and World. Focus is primarily on the intelligibility of Hill's substitutional quantification into propositions.
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  11. On the sameness of thoughts. Substitutional quantifiers, tense, and belief.Marco Santambrogio - 2006 - Grazer Philosophische Studien 72 (1):111-140.
    In order to know what a belief is, we need to know when it is appropriate to say that two subjects (or the same subject at two different times) believe(s) the same or entertain the same thought. This is not entirely straightforward. Consider for instance1. Tom thinks that he himself is the smartest and Tim believes the same2. In 2001, Bill believed that some action had to be taken to save the rain forest and today he believes the same.What does (...)
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  12. Nominalizing quantifiers.Friederike Moltmann - 2003 - Journal of Philosophical Logic 32 (5):445-481.
    Quantified expressions in natural language generally are taken to act like quantifiers in logic, which either range over entities that need to satisfy or not satisfy the predicate in order for the sentence to be true or otherwise are substitutional quantifiers. I will argue that there is a philosophically rather important class of quantified expressions in English that act quite differently, a class that includes something, nothing, and several things. In addition to expressing quantification, such expressions act like nominalizations, introducing (...)
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  13. About Games and Substitution.Manuel Rebuschi - 2003 - In Jaroslav Peregrin (ed.), Meaning: the dynamic turn. Oxford, UK: Elsevier Science. pp. 241--257.
    Kripke’s substitutional interpretation of quantifiers is usually said to be unsatisfactory for independence-friendly (IF) languages. The purpose of this paper is to question this claim. Two accounts of substitutional semantics for IF sentences will be written down, and the objection of the so-called ‘dummy variables’ will be ruled out. Moreover, it will be argued, against the traditional view, that Game-Theoretical Semantics (GTS) should be conceived of as substitutional. The paper ends with some remarks concerning the reasons why substitution is especially (...)
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  14. There Is A Problem with Substitutional Quantification.Philip Hugly & Charles Sayward - 2002 - Theoria 68 (1):4-12.
    Whereas arithmetical quantification is substitutional in the sense that a some-quantification is true only if some instance of it is true, it does not follow (and, in fact, is not true) that an account of the truth-conditions of the sentences of the language of arithmetic can be given by a substitutional semantics. A substitutional semantics fails in a most fundamental fashion: it fails to articulate the truth-conditions of the quantifications with which it is concerned. This is what is defended in (...)
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  15. Review. Russell's hidden substitutional theory. G Landini.M. Byrd - 2000 - British Journal for the Philosophy of Science 51 (2):357-362.
  16. A Substitutional Framework for Arithmetical Validity.Fernando Ferreira - 1998 - Grazer Philosophische Studien 56 (1):133-149.
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  17. Quantification: Objectual or substitutional?James E. Tomberlin - 1997 - Philosophical Issues 8:155-167.
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  18. Quantifying over the reals.Philip Hugly & Charles Sayward - 1994 - Synthese 101 (1):53 - 64.
    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 (...)
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  19. Meaning, truth-conditions, and substitutional quantification.Michael Hand - 1992 - Philosophical Studies 68 (2):195 - 216.
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  20. Why Substitutional Quantification Does Not Express Existence.Philip Hugly & Charles Sayward - 1987 - Theory and Decision 50:67-75.
    Fundamental to Quine’s philosophy of logic is the thesis that substitutional quantification does not express existence. This paper considers the content of this claim and the reasons for thinking it is true.
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  21. In Defense of Substitutional Quantification.M. Dako - 1986 - International Logic Review 33:50.
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  22. Substitutional Quantification and Existence.B. J. Copeland - 1985 - Analysis 45 (1):1 - 4.
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  23. Substitutional quantification and nonstandard quantifiers.H. A. Lewis - 1985 - Noûs 19 (3):447-451.
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  24. Systems of substitutional semantics.Daniel Bonevac - 1984 - Philosophy of Science 51 (4):631-656.
    I investigate substitutional interpretations of quantifiers that count existential sentences true just in case they have true instances in a parametric extension of the language. I devise a semantics meeting four criteria: (1) it accounts adequately for natural language quantification; (2) it provides an account of justification in abstract sciences; (3) it constitutes a continuous semantics for natural and formal languages; and (4) it is purely substitutional, containing no appeal to referential interpretations. The prospects for a purely substitutional theory of (...)
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  25. (1 other version)Dale Gottlieb, Ontological Economy: Substitutional Quantification and Mathematics. [REVIEW]Hartry Field - 1984 - Noûs 18 (1):160-165.
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  26. Referential and nonreferential substitutional quantifiers.Alex Orenstein - 1984 - Synthese 60 (2):145 - 157.
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  27. Ontological Economy: Substitutional Quantification and Mathematics.Stanley Martens - 1983 - Philosophical Review 92 (4):636.
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  28. A note on the Barcan formula and substitutional quantification.B. J. Copeland - 1982 - Logique Et Analyse 25 (97):83.
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  29. Indenumerability and substitutional quantification.Philip Hugly & Charles Sayward - 1982 - Notre Dame Journal of Formal Logic 23 (4):358-366.
    We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains such that substitutional quantification deviates (...)
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  30. Ontological Economy: Substitutional Quantification and Mathematics by Dale Gottlieb. [REVIEW]Michael Jubien - 1982 - Journal of Philosophy 79 (12):781-786.
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  31. Substitutional quantification and mathematics. [REVIEW]Charles Parsons - 1982 - British Journal for the Philosophy of Science 33 (4):409-421.
  32. Ontological Economy: Substitutional Quantification and Mathematics.Mary Tiles - 1982 - Philosophical Books 23 (2):90-94.
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  33. (2 other versions)Review: Dale Gottlieb, Ontological Economy: Substitutional Quantification and Mathematics. [REVIEW]T. S. Weston - 1982 - Journal of Symbolic Logic 47 (2):473-475.
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  34. Why I don't understand substitutional quantification.Peter van Inwagen - 1981 - Philosophical Studies 39 (3):281 - 285.
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  35. A note on substitutional quantification.Martin Davies - 1980 - Noûs 14 (4):619-622.
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  36. Ontological economy: substitutional quantification and mathematics.Dale Gottlieb - 1980 - New York: Oxford University Press.
    Shows that when Qyuine's criterion of ontological commitment is modified to allow for the legitimacy of substitutional quantification, two consequences follow: (i) fundamental questions of ontology cease to be settled by mere appeal to logical form and truth, and (ii) a powerful method for reducing ontological commitments becomes available.
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  37. Russell's substitutional theory.Peter Hylton - 1980 - Synthese 45 (1):1 - 31.
  38. Substitutional quantification and set theory.Dale Gottlieb & Timothy McCarthy - 1979 - Journal of Philosophical Logic 8 (1):315 - 331.
  39. Kripke, Pseudo-Kripke, and Wallace.Thomas Baldwin - 1978 - Analysis 38 (4):173 - 181.
    It is argued that kripke has not shown that an explanatory truth theory for quantifiers which employs a substitutional approach does not require the hypothesis and that everything in the domain has a name, As wallace had claimed. It is further argued that kripke's substitutional quantifiers are best regarded as an extension of a device for abbreviating conjunctions and disjunctions.
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  40. Nominalism and the Substitutional Quantifier.Ruth Barcan Marcus - 1978 - The Monist 61 (3):351-362.
    It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. I should like in this paper to explore that claim.
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  41. The Substitutional Quantifier.James B. Scoggin - 1978 - The Monist 61 (3):408-425.
    If the substitutional interpretation of quantification is tenable, it provides a basis for reinterpreting any formal language-system as nominalist: each substituend for the variables of quantification either designates a concrete object or it is empty.
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  42. Quantification and Brentano's Logic.Burnham Terrell - 1978 - Grazer Philosophische Studien 5 (1):45-65.
    Brentano's innovations in logical theory are considered in the context of his descriptive psychology, with its distinction between differences in quality and in object of mental phenomena. Objections are raised to interpretations that depend on a parallel between Urteil and assertion of a proposition. A more appropriate parallel is drawn between the assertion as subject to description in a metalanguage and the Urteil as secondary object in inner perception. This parallel is then applied so as to suggest a reinterpretation of (...)
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  43. Truth and meaning: essays in semantics.Gareth Evans & John McDowell (eds.) - 1976 - Oxford [Eng.]: Clarendon Press.
    Truth and Meaning is a classic collection of original essays on fundamental questions in the philosophy of language.
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  44. Is There a Problem About Substitutional Quantification?Saul A. Kripke - 1976 - In Gareth Evans & John McDowell (eds.), Truth and meaning: essays in semantics. Oxford [Eng.]: Clarendon Press. pp. 324-419.
  45. Much ado about substitutional quantification.Charles Parsons - 1976 - Journal of Philosophy 73 (18):651-653.
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  46. Truth and substitution quantifiers.Joseph L. Camp - 1975 - Noûs 9 (2):165-185.
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  47. Substitutionalism and Substitutional Quantification.R. D. Gallie - 1975 - Analysis 35 (3):97 - 101.
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  48. Translational Indeterminacy and Substitutional Quantifiers.James D. Carney & Zak Van Straaten - 1974 - Foundations of Language 11 (4):533-541.
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  49. Roger Gallie and Substitutional Quantification.L. Jonathan Cohen - 1974 - Analysis 34 (3):69 - 73.
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  50. A. N. Prior and Substitutional Quantification.R. D. Gallie - 1974 - Analysis 34 (3):65 - 69.
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