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Nominalist platonism

In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press. pp. 73-87 (1998)

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  1. On the Infinite in Mereology with Plural Quantification.Massimiliano Carrara & Enrico Martino - 2011 - Review of Symbolic Logic 4 (1):54-62.
    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...)
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  • Necessitism, Contingentism, and Plural Quantification.Timothy Williamson - 2010 - Mind 119 (475):657-748.
    Necessitism is the view that necessarily everything is necessarily something; contingentism is the negation of necessitism. The dispute between them is reminiscent of, but clearer than, the more familiar one between possibilism and actualism. A mapping often used to ‘translate’ actualist discourse into possibilist discourse is adapted to map every sentence of a first-order modal language to a sentence the contingentist (but not the necessitist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables (...)
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  • Skolem Redux.W. D. Hart - 2000 - Notre Dame Journal of Formal Logic 41 (4):399--414.
    Hume's Principle requires the existence of the finite cardinals and their cardinal, but these are the only cardinals the Principle requires. Were the Principle an analysis of the concept of cardinal number, it would already be peculiar that it requires the existence of any cardinals; an analysis of bachelor is not expected to yield unmarried men. But that it requires the existence of some cardinals, the countable ones, but not others, the uncountable, makes it seem invidious; it is as if (...)
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  • A Defense of Second-Order Logic.Otávio Bueno - 2010 - Axiomathes 20 (2-3):365-383.
    Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980 ). Therefore, (...)
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  • Review of H. Laycock, Words Without Objects: Semantics, Ontology, and Logic for Non-Singularity[REVIEW]Thomas J. McKay - 2008 - Canadian Journal of Philosophy 38 (2):pp. 301-323.
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  • Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.
    There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.
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  • Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.
    On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carry-on baggage? Probably not. In ordinary language, ‘everything’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’, ...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs’ is true as uttered in a (...)
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  • Plural quantification exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
    This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.
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  • Plurals and complexes.Keith Hossack - 2000 - British Journal for the Philosophy of Science 51 (3):411-443.
    Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...)
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  • On plural reference and elementary set theory.Helen Morris Cartwright - 1993 - Synthese 96 (2):201 - 254.
    The view that plural reference is reference to a set is examined in light of George Boolos's treatment of second-order quantification as plural quantification in English. I argue that monadic second-order logic does not, in Boolos's treatment, reflect the behavior of plural quantifiers under negation and claim that any sentence that properly translates a second-order formula, in accordance with his treatment, has a first-order formulation. Support for this turns on the use of certain partitive constructions to assign values to variables (...)
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  • The logic and meaning of plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
    In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...)
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  • New foundations for imperative logic I: Logical connectives, consistency, and quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
    Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...)
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  • Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
    Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...)
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  • The Logic of Potential Infinity.Roy T. Cook - forthcoming - Philosophia Mathematica.
    Michael Dummett argues that acceptance of potentially infinite collections requires that we abandon classical logic and restrict ourselves to intuitionistic logic. In this paper we examine whether Dummett is correct. After developing two detailed accounts of what, exactly, it means for a concept to be potentially infinite (based on ideas due to Charles McCarty and Øystein Linnebo, respectively), we construct a Kripke structure that contains a natural number structure that satisfies both accounts. This model supports a logic much stronger than (...)
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  • Metaphysical explanation and the cosmological argument.Thomas Oberle - 2024 - Philosophical Studies 181 (6):1413-1432.
    A premise of the Leibnizian cosmological argument from contingency says that no contingent fact can explain why there are any contingent facts at all. David Hume and Paul Edwards famously denied this premise, arguing that if every fact has an explanation in terms of further facts ad infinitum, then they all do. This is known as the Hume–Edwards Principle (HEP). In this paper, I examine the cosmological argument from contingency within a framework of metaphysical explanation or ground and defend a (...)
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  • The negative theology of absolute infinity: Cantor, mathematics, and humility.Rico Gutschmidt & Merlin Carl - 2024 - International Journal for Philosophy of Religion 95 (3):233-256.
    Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...)
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  • Possible Worlds as Propositions.Daniel Deasy - forthcoming - Philosophical Quarterly.
    Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...)
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  • Substitutional Validity for Modal Logic.Marco Grossi - 2023 - Notre Dame Journal of Formal Logic 64 (3):291-316.
    In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.
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  • On Type Distinctions and Expressivity.Salvatore Florio - 2023 - Proceedings of the Aristotelian Society 123 (2):150-172.
    Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.
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  • Pure Logic and Higher-order Metaphysics.Christopher Menzel - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...)
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  • Hume’s Principle, Bad Company, and the Axiom of Choice.Sam Roberts & Stewart Shapiro - 2023 - Review of Symbolic Logic 16 (4):1158-1176.
    One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all sufficiently (...)
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  • Penelope Rush.* Ontology and the Foundations of Mathematics: Talking Past Each Other.Geoffrey Hellman - 2022 - Philosophia Mathematica 30 (3):387-392.
    This compact volume, belonging to the Cambridge Elements series, is a useful introduction to some of the most fundamental questions of philosophy and foundations of mathematics. What really distinguishes realist and platonist views of mathematics from anti-platonist views, including fictionalist and nominalist and modal-structuralist views?1 They seem to confront similar problems of justification, presenting tradeoffs between which it is difficult to adjudicate. For example, how do we gain access to the abstract posits of platonist accounts of arithmetic, analysis, geometry, etc., (...)
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  • Logicality and model classes.Juliette Kennedy & Jouko Väänänen - 2021 - Bulletin of Symbolic Logic 27 (4):385-414.
    We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi [46]. We investigate which characteristics of logics, such as variants of the Löwenheim–Skolem theorem, Completeness theorem, and absoluteness, are relevant from the logicality (...)
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  • Composition and plethological innocence.Jonathan D. Payton - 2022 - Analysis 82 (1):67-74.
    According to Composition as Identity, a whole is distinct from each of its parts individually, but identical to all of them taken together. It is sometimes claimed that, if you accept CAI, then your belief in a whole is ‘ontologically innocent’ with respect to your belief in its parts. This claim is false. But the defender of CAI can claim a different advantage for her view. Following Agustín Rayo, I distinguish ontology from plethology. I then show that CAI allows us (...)
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  • Higher‐order metaphysics.Lukas Skiba - 2021 - Philosophy Compass 16 (10):1-11.
    Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...)
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  • Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
    Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...)
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  • Presentism and Times as Propositions.Luca Banfi & Daniel Deasy - 2021 - Philosophical Studies 179 (3):725-743.
    Some Presentists—according to whom everything is present—identify instants of time with propositions of a certain kind. However, the view that times are propositions seems to be at odds with Presentism: if there are times then there are past times, and therefore things that are past; but how could there be things that are past if everything is present? In this paper, we describe the Presentist view that times are propositions ; we set out the argument that Presentism is incompatible with (...)
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • Composition, identity and plural ontology.Roberto Loss - 2020 - Synthese 198 (10):9193-9210.
    According to ‘Strong Composition as Identity’, if an entity is composed of a plurality of entities, it is identical to them. As it has been argued in the literature, SCAI appears to give rise to some serious problems which seem to suggest that SCAI-theorists should take their plural quantifier to be governed by some ‘weak’ plural comprehension principle and, thus, ‘exclude’ some kinds of pluralities from their plural ontology. The aim of this paper is to argue that, contrary to what (...)
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  • Idealism and the Identity Theory of Truth.Robert Trueman - 2020 - Mind 130 (519):783-807.
    In a recent article, Hofweber presents a new, and surprising, argument for idealism. His argument is surprising because it starts with an apparently innocent premiss from the philosophy of language: that ‘that’-clauses do not refer. I do not think that Hofweber's argument works, and my first aim in this paper is to explain why. However, I agree with Hofweber that what we say about ‘that’-clauses has important metaphysical consequences. My second aim is to argue that, far from leading us into (...)
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  • Logic, Metalogic and Neutrality.Timothy Williamson - 2013 - Erkenntnis 79 (2):211-231.
    The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...)
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  • In defence of Higher-Level Plural Logic: drawing conclusions from natural language.Berta Grimau - 2019 - Synthese 198 (6):5253-5280.
    Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing more than the austere ontology (...)
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  • Propositions and Cognitive Relations.Nicholas K. Jones - 2019 - Proceedings of the Aristotelian Society 119 (2):157-178.
    There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception of (...)
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  • Metalogic and the Overgeneration Argument.Salvatore Florio & Luca Incurvati - 2019 - Mind 128 (511):761-793.
    A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...)
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  • Massimiliano Carrara, Alexandra Arapinis, and Friederike Moltmann , Unity & Plurality: Logic, Philosophy, and Linguistics, Oxford: Oxford University Press, 2016, xv + 259 pp., £45 , ISBN 9780198716327. [REVIEW]Lorenzo Azzano - 2018 - Dialectica 72 (2):309-315.
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  • Mereological Composition and Plural Quantifier Semantics.Manuel Lechthaler & Ceth Lightfield - 2018 - Philosophia 46 (4):943-958.
    Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity (...)
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  • Everything, and then some.Stephan Krämer - 2017 - Mind 126 (502):499-528.
    On its intended interpretation, logical, mathematical and metaphysical discourse sometimes seems to involve absolutely unrestricted quantification. Yet our standard semantic theories do not allow for interpretations of a language as expressing absolute generality. A prominent strategy for defending absolute generality, influentially proposed by Timothy Williamson in his paper ‘Everything’, avails itself of a hierarchy of quantifiers of ever increasing orders to develop non-standard semantic theories that do provide for such interpretations. However, as emphasized by Øystein Linnebo and Agustín Rayo, there (...)
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  • A Notion of Logical Concept Based on Plural Reference.Carrara Massimiliano & Martino Enrico - 2018 - Acta Analytica 33 (1):19-33.
    In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical concepts. (...)
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  • Isomorphism invariance and overgeneration.Owen Griffiths & A. C. Paseau - 2016 - Bulletin of Symbolic Logic 22 (4):482-503.
    The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five (...)
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  • Nominalist Realism.Nicholas K. Jones - 2017 - Noûs 52 (4):808-835.
    This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...)
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  • Quantifier Variance and Indefinite Extensibility.Jared Warren - 2017 - Philosophical Review 126 (1):81-122.
    This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...)
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  • Stuff and coincidence.Thomas J. McKay - 2015 - Philosophical Studies 172 (11):3081-3100.
    Anyone who admits the existence of composite objects allows a certain kind of coincidence, coincidence of a thing with its parts. I argue here that a similar sort of coincidence, coincidence of a thing with the stuff that constitutes it, should be equally acceptable. Acknowledgement of this is enough to solve the traditional problem of the coincidence of a statue and the clay or bronze it is made of. In support of this, I offer some principles for the persistence of (...)
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  • Grounding Megethology on Plural Reference.Massimiliano Carrara & Enrico Martino - 2015 - Studia Logica 103 (4):697-711.
    In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...)
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  • On What Actually Is.Fredrik Haraldsen - 2015 - Erkenntnis 80 (3):643-656.
    The actually-operator, understood as a rigidifier, has been employed for a range of purposes in natural language semantics. In this article I argue that the properties of the operator do not correspond to any feature of natural language or feature natural language users have access to. Nor is it needed to provide a formal representation of natural language sentences—the examples usually provided to illustrate the indispensability of the operator are much more plausibly interpreted using plural quantifiers. This lack of connection (...)
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  • Simple Generics.David Liebesman - 2010 - Noûs 45 (3):409-442.
    Consensus has it that generic sentences such as “Dogs bark” and “Birds fly” contain, at the level of logical form, an unpronounced generic operator: Gen. On this view, generics have a tripartite structure similar to overtly quantified sentences such as “Most dogs bark” and “Typically, birds fly”. I argue that Gen doesn’t exist and that generics have a simple bipartite structure on par with ordinary atomic sentences such as “Homer is drinking”. On my view, the subject terms of generics are (...)
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  • Russell, Presupposition, and the Vicious-Circle Principle.Darryl Jung - 1999 - Notre Dame Journal of Formal Logic 40 (1):55-80.
    Prompted by Poincaré, Russell put forward his celebrated vicious-circle principle (vcp) as the solution to the modern paradoxes. Ramsey, Gödel, and Quine, among others, have raised two salient objections against Russell's vcp. First, Gödel has claimed that Russell's various renderings of the vcp really express distinct principles and thus, distinct solutions to the paradoxes, a claim that gainsays one of Russell's positions on the nature of the solution to the paradoxes, namely, that such a solution be uniform. Secondly, Ramsey, Gödel, (...)
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  • Strong logics of first and second order.Peter Koellner - 2010 - Bulletin of Symbolic Logic 16 (1):1-36.
    In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant (...)
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  • Pluralism in logic.Hartry Field - 2009 - Review of Symbolic Logic 2 (2):342-359.
    There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...)
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  • Parthood.Theodore Sider - 2007 - Philosophical Review 116 (1):51-91.
    There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..
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  • Did Tarski commit "Tarski's fallacy"?Gila Sher - 1996 - Journal of Symbolic Logic 61 (2):653-686.
    In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...)
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