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Philosophy of Logic (2nd Edition)

Cambridge, MA: Harvard University Press (1986)

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  1. Contingentism and fragile worlds.Christopher James Masterman - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Propositional contingentism is the thesis that there might have been propositions which might have not have been something. Serious actualism is the thesis that it is impossible for a property to be exemplified without there being something which exemplifies it. Both are popular. Likewise, the dominant view in the metaphysics of modality is that metaphysical possibility and necessity can be understood – in some sense – in terms of possible worlds, i.e. total ways the world could have been. Here, I (...)
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  • (What) Is Feminist Logic? (What) Do We Want It to Be?Catharine Saint-Croix & Roy T. Cook - 2024 - History and Philosophy of Logic 45 (1):20-45.
    ‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...)
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  • Existence Is Not Relativistically Invariant—Part 1: Meta-ontology.Florian Marion - 2024 - Acta Analytica 39 (3):479-503.
    Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...)
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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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  • How to Conquer the Liar and Enthrone the Logical Concept of Truth.Boris Culina - 2023 - Croatian Journal of Philosophy 23 (67):1-31.
    This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...)
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  • Quine’s conflicts with truth deflationism.Teemu Tauriainen - 2022 - Asian Journal of Philosophy 1 (46):1-25.
    Compared to the extensive amount of literature on various themes of W.V.O. Quine’s philosophy, his immanent concept of truth remains a relatively unexplored topic. This relative lack of research contributes to a persistent confusion on the deflationary and inflationary details of Quine’s truth. According to a popular reading, Quine’s disquotational definition of the truth predicate exhausts the content of truth, thus amounting to a deflationary view. Others promote opposing interpretations. I argue that by relying on Tarski’s semantic conception of truth, (...)
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  • Constructivism: Social Discourse & Knowledge.Jesús Aparicio de Soto - 2022 - Scientific Research, an Academic Publisher (OJPP) 12 (3):376-396.
    Constructivism is frequently met with objections, criticism and often equated with nihilism or relativism. Sometimes even blamed for what some would randomly picture as unwanted side effects of radicalism or of a progressivist era: such misconceptions are not only due to an imprecise grasp of the premises shared by the constructivist family of systems. The structure of media, political systems, and economic models, still up today impel societal understandings of knowledge on neo-positivistic grounds. The first part of this essay outlines (...)
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  • There is no tenable notion of global metainferential validity.Rea Golan - 2021 - Analysis 81 (3):411-420.
    The use of models to assign truth values to sentences and to counterexemplify invalid inferences is a basic feature of model theory. Yet sentences and inferences are not the only phenomena that model theory has to take care of. In particular, the development of sequent calculi raises the question of how metainferences are to be accounted for from a model-theoretic perspective. Unfortunately there is no agreement on this matter. Rather, one can find in the literature two competing model-theoretic notions of (...)
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  • Brandom and Quine on Perspectivally Hybrid De Re Attitude Ascription: A Solution to a Problem in the Explanation of Action.Sean Crawford - 2022 - Journal of Transcendental Philosophy 3 (1):103-121.
    In Making it Explicit Robert Brandom claims that perspectivally hybrid de re attitude ascriptions explain what an agent actually did, from the point of view of the ascriber, whether or not that was what the agent intended to do. There is a well-known problem, however, first brought to attention by Quine, but curiously ignored by Brandom, that threatens to undermine the role of de re ascriptions in the explanation of action, a problem that stems directly from the fact that, unlike (...)
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  • Moral hinges and steadfastness.Chris Ranalli - 2021 - Metaphilosophy 52 (3-4):379-401.
    Epistemic rationality seems to permit a more steadfast response to disagreements over our fundamental convictions than it does for our ordinary beliefs. Why is this? This essay explores three answers to this question: web-of-belief conservatism, moral encroachment, and hinge theories, and argues that hinge theories do a better job than the alternatives at vindicating the intuition that there is a rationally permissible asymmetry in our responses to disagreements over ordinary beliefs and fundamental convictions. The essay also shows how hinge theorists (...)
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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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  • Plurals and Mereology.Salvatore Florio & David Nicolas - 2020 - Journal of Philosophical Logic 50 (3):415-445.
    In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...)
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  • Rivalry, normativity, and the collapse of logical pluralism.Erik Stei - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (3-4):411-432.
    Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all variants (...)
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  • The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2017 - Philosophy and Phenomenological Research 99 (1):81-114.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...)
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  • From Mathematical Fictionalism to Truth‐Theoretic Fictionalism.Bradley Armour-Garb & James A. Woodbridge - 2014 - Philosophy and Phenomenological Research 88 (1):93-118.
    We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.
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  • (1 other version)Anti-exceptionalism about logic.Ole Thomassen Hjortland - 2017 - Philosophical Studies 174 (3):631-658.
    Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy, Priest, Russell, and Williamson. Although these authors agree on many methodological issues about logic, (...)
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  • The Justification of the Basic Laws of Logic.Gillian Russell - 2015 - Journal of Philosophical Logic 44 (6):793-803.
    Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form \.Γ can be empty. If you don’t like my examples, feel free to choose your own, everything I have to say should apply to those as well. Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to (...)
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  • An “I” for an I: Singular terms, uniqueness, and reference.Stewart Shapiro - 2012 - Review of Symbolic Logic 5 (3):380-415.
    There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...)
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  • Propositional or Non-Propositional Attitudes?Sean Crawford - 2014 - Philosophical Studies 168 (1):179-210.
    Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such as the (...)
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  • De Re and De Dicto Explanation of Action.Sean Crawford - 2012 - Philosophia 40 (4):783-798.
    This paper argues for an account of the relation between thought ascription and the explanation of action according to which de re ascriptions and de dicto ascriptions of thought each form the basis for two different kinds of action explanations, nonrationalizing and rationalizing ones. The claim that de dicto ascriptions explain action is familiar and virtually beyond dispute; the claim that that de re ascriptions are explanatory of action, however, is not at all familiar and indeed has mostly been denied (...)
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  • The Development of Logic as Reflected in the Fate of the Syllogism 1600–1900.James Van Evra - 2000 - History and Philosophy of Logic 21 (2):115-134.
    One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...)
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  • (1 other version)The Founding of Logic: Modern Interpretations of Aristotle’s Logic.John Corcoran - 1994 - Ancient Philosophy 14 (S1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  • New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.
    We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...)
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  • Quine’s Tarskian Angle on Truth: Immanence, Semantic Ascent and the Importance of Generality.Gary Kemp - 2024 - Philosophers' Imprint 24 (1).
    There are two main parts to this article: (1) Quine's view of truth is substantive in a way that is not generally recognized. There are elements in the view of deflationism, minimalism, and of course disquotationalism to be sure, but from Quine's perspective the capacity for generalization - ascribing truth not to explicitly given sentences but to kinds of sentences - requires a full-bore Tarskian apparatus. This is necessary in order for truth to play what for Quine are its vital (...)
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  • Motivating a Pragmatic Approach to Naturalized Social Ontology.Richard Lauer - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):403–419.
    Recent contributions to the philosophy of the social sciences have motivated ontological commitments using appeals to the social sciences (_naturalized_ social ontologies). These arguments rely on social scientific realism about the social sciences, the view that our social scientific theories are approximately true. I apply a distinction formulated in metaontology between ontologically loaded and unloaded meanings of existential quantification to argue that there is a pragmatic approach to naturalized social ontology that is minimally realist (it treats existence claims as true (...)
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  • Logic, Philosophy and Physics: A Critical Commentary on the Dilemma of Categories.Abhishek Majhi - 2022 - Axiomathes 32 (6):1415-1431.
    I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be beneficial for science as a whole. However, such a change can come at the cost of looking beyond the categories of the disciplines of logic, philosophy and physics. It is through self-inquiry that such a change is possible, along with the realization of the (...)
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  • A Pragmatic-Semiotic Defence of Bivalence.Marc Champagne - 2021 - History and Philosophy of Logic 43 (2):143-157.
    Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...)
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  • The Functional Composition of Sense.Bryan Pickel - 2021 - Synthese 199 (3-4):6917-6942.
    A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...)
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  • Beyond Logical Pluralism and Logical Monism.Pavel Arazim - 2020 - Logica Universalis 14 (2):151-174.
    Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical (...)
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  • Theorizing about truth outside of one’s own language.Graham Seth Moore - 2020 - Philosophical Studies 177 (4):883-903.
    A theory of truth is language-transcendent if it ascribes truth conditions to truth-bearers that are not expressible in our natural language; a theory is language-immanent if it is not language-transcendent. In this paper, I argue for the following theses. Whether the correct theory of truth is language-transcendent or language-immanent will have significant consequences for general philosophy. Prima facie, a language-transcendent theory is preferable. However, language-transcendent theories tend to require substantive metaphysical commitments concerning truth. Deflationist theories are particularly interesting in this (...)
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  • First‐order logical validity and the hilbert‐bernays theorem.Gary Ebbs & Warren Goldfarb - 2018 - Philosophical Issues 28 (1):159-175.
    What we call the Hilbert‐Bernays (HB) Theorem establishes that for any satisfiable first‐order quantificational schema S, there are expressions of elementary arithmetic that yield a true sentence of arithmetic when they are substituted for the predicate letters in S. Our goals here are, first, to explain and defend W. V. Quine's claim that the HB theorem licenses us to define the first‐order logical validity of a schema in terms of predicate substitution; second, to clarify the theorem by sketching an accessible (...)
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  • Anaphoric Deflationism, Primitivism, and the Truth Property.Pietro Salis - 2019 - Acta Analytica 34 (1):117-134.
    Anaphoric deflationism is a prosententialist account of the use of “true.” Prosentences are, for sentences, the equivalent of what pronouns are for nouns: as pronouns refer to previously introduced nouns, so prosentences like “that’s true” inherit their content from previously introduced sentences. This kind of deflationism concerning the use of “true” (especially in Brandom’s version) is an explanation in terms of anaphora; the prosentence depends anaphorically on the sentence providing its content. A relevant implication of this theory is that “true” (...)
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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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  • (1 other version)On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture.Juliette Kennedy - 2013 - Bulletin of Symbolic Logic 19 (3):351-393.
    In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the (...)
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  • Identity and indiscernibility.Jeffrey Ketland - 2011 - Review of Symbolic Logic 4 (2):171-185.
    The notion of strict identity is sometimes given an explicit second-order definition: objects with all the same properties are identical. Here, a somewhat different problem is raised: Under what conditions is the identity relation on the domain of a structure first-order definable? A structure may have objects that are distinct, but indiscernible by the strongest means of discerning them given the language (the indiscernibility formula). Here a number of results concerning the indiscernibility formula, and the definability of identity, are collected (...)
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  • Existential-Import Mathematics.John Corcoran & Hassan Masoud - 2015 - Bulletin of Symbolic Logic 21 (1):1-14.
    First-order logic haslimitedexistential import: the universalized conditional ∀x[S(x) → P(x)] implies its corresponding existentialized conjunction ∃x[S(x) & P(x)] insome but not allcases. We prove theExistential-Import Equivalence:∀x[S(x) → P(x)] implies ∃x[S(x) & P(x)] iff ∃xS(x) is logically true.The antecedent S(x) of the universalized conditional alone determines whether the universalized conditionalhas existential import: implies its corresponding existentialized conjunction.Apredicateis a formula having onlyxfree. Anexistential-importpredicate Q(x) is one whose existentialization, ∃xQ(x), is logically true; otherwise, Q(x) isexistential-import-freeor simplyimport-free. Existential-import predicates are also said to beimport-carrying.How (...)
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  • Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW]I. Grattan-Guinness - 2011 - Logica Universalis 5 (1):21-73.
    A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories, and ‘ubiquitous’ notions that form dependent parts, or moments, of (...)
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  • Remarks on the Theory of Quasi-sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1-2):101 - 124.
    Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are also (...)
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  • Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
    What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.
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  • Truth via Sentential Quantification.Mark Textor - 2005 - Dialogue 44 (3):539-550.
    This paper is a critical evaluation of Kuenne's attempt to define truth via quantification into the position of a sentence.
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  • Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of (...)
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  • Abstraction Principles and the Classification of Second-Order Equivalence Relations.Sean C. Ebels-Duggan - 2019 - Notre Dame Journal of Formal Logic 60 (1):77-117.
    This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation E is defined without nonlogical vocabulary, then the bicardinal slice of any equivalence class—those equinumerous elements of the equivalence class with equinumerous complements—can have one of only three profiles. The improvements to Fine’s theorem allow for an analysis of (...)
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  • Sellars, Second-order Quantification, and Ontological Commitment.Andrew Parisi - 2018 - History and Philosophy of Logic 40 (1):81-97.
    Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come to understand (...)
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  • Deviance and Vice: Strength as a Theoretical Virtue in the Epistemology of Logic.Gillian Russell - 2018 - Philosophy and Phenomenological Research 99 (3):548-563.
    This paper is about the putative theoretical virtue of strength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well-defined property of logical strength is neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic of (...)
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  • Deflationism and Referential Indeterminacy.David E. Taylor - 2016 - Philosophical Review 126 (1):43-79.
    This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...)
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  • Why Non-individuality? A Discussion on Individuality, Identity, and Cardinality in the Quantum Context.Jonas Rafael Becker Arenhart & Décio Krause - 2012 - Erkenntnis (1):1-18.
    Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situation comprising multiple particles there is a well-defined (...)
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  • Set-theoretical Invariance Criteria for Logicality.Solomon Feferman - 2010 - Notre Dame Journal of Formal Logic 51 (1):3-20.
    This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has quite divergent characterization results depending (...)
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  • Reconsidering ordered pairs.Dana Scott & Dominic McCarty - 2008 - Bulletin of Symbolic Logic 14 (3):379-397.
    The well known Wiener-Kuratowski explicit definition of the ordered pair, which sets ⟨x, y⟩ = {{x}, {x, y}}, works well in many set theories but fails for those with classes which cannot be members of singletons. With the aid of the Axiom of Foundation, we propose a recursive definition of ordered pair which addresses this shortcoming and also naturally generalizes to ordered tuples of greater lenght. There are many advantages to the new definition, for it allows for uniform definitions working (...)
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  • The new correspondence theory of truth without the concept of fact.Bo Chen - 2023 - Philosophical Forum 54 (4):261-286.
    Traditional correspondence theory of truth with the concept of fact encounters many serious difficulties, main one of which is that it is too difficult to explain clearly the concept of ‘fact’ and how propositions ‘correspond’ to facts. This does not mean that we should abandon the traditional correspondence theory of truth and turn to some other type theories of truth. In order to guarantee the objectivity of truth, any reasonable theory of truth must adhere to the core insight of the (...)
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