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Methods of Logic

Harvard University Press (1950)

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  1. Conditionals: A Theory of Meaning, Pragmatics, and Inference.Philip Johnson-Laird & Ruth M. J. Byrne - 2002 - Psychological Review 109 (4):646-678.
    The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...)
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  • Satisfying Predicates: Kleene's Proof of the Hilbert–Bernays Theorem.Gary Ebbs - 2015 - History and Philosophy of Logic 36 (4):346-366.
    The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for (...)
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  • Identity, Indiscernibility, and Ante Rem Structuralism: The Tale of I and –I.Stewart Shapiro - 2008 - Philosophia Mathematica 16 (3):285-309.
    Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...)
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  • The Defective Conditional in Mathematics.Mathieu Vidal - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):169-179.
    This article focuses on defective conditionals ? namely indicative conditionals whose antecedents are false and whose truth-values therefore cannot be determined. The problem is to decide which formal connective can adequately represent this usage. Classical logic renders defective conditionals true whereas traditional mathematics dismisses them as irrelevant. This difference in treatment entails that, at the propositional level, classical logic validates some sentences that are intuitively false in plane geometry. With two proofs, I show that the same flaw is shared by (...)
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  • Can First-Order Logical Truth Be Defined in Purely Extensional Terms?Gary Ebbs - 2014 - British Journal for the History of Philosophy 22 (2):343-367.
    W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism (...)
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  • Problems for Logical Pluralism.Owen Griffiths - 2013 - History and Philosophy of Logic 34 (2):170 - 182.
    I argue that Beall and Restall's logical pluralism fails. Beall?Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ?settled core? of consequence: they believe that truth-preservation, necessity, formality and normativity are ?settled? features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their (...)
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  • Eligibility and Inscrutability.J. Robert G. Williams - 2007 - Philosophical Review 116 (3):361-399.
    Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...)
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  • A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...)
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  • Presupposition.David I. Beaver - 1997 - In Johan van Bentham & Alice ter Meulen (eds.), Handbook of Logic and Language. MIT Press.
    We discuss presupposition, the phenomenon whereby speakers mark linguistically the information that is presupposed or taken for granted, rather than being part of the main propositional content of a speech act. Expressions and constructions carrying presuppositions are called “presupposition triggers”, forming a large class including definites and factive verbs. The article first introduces the range of triggers, the basic properties of presuppositions such as projection and cancellability, and the diagnostic tests used to identify them. The reader is then introducedto major (...)
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  • Completion, Reduction and Analysis: Three Proof-Theoretic Processes in Aristotle’s Prior Analytics.George Boger - 1998 - History and Philosophy of Logic 19 (4):187-226.
    Three distinctly different interpretations of Aristotle?s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle?s remarkable degree of metalogical (...)
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  • "If-Then" as a Version of "Implies".Matheus Silva - manuscript
    Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey of basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if-then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the premise and (...)
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  • Context, Cognition and Conditionals.Chi-Hé Elder - 2019 - Basingstoke: Palgrave Macmillan.
    This book proposes a semantic theory of conditionals that can account for (i) the variability in usages that conditional sentences can be put; and (ii) both conditional sentences of the form ‘if p, q’ and those conditional thoughts that are expressed without using ‘if’. It presents theoretical arguments as well as empirical evidence from English and other languages in support of the thesis that an adequate study of conditionals has to go beyond an analysis of specific sentence forms or lexical (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • One True Logic?Gillian Russell - 2008 - Journal of Philosophical Logic 37 (6):593 - 611.
    This is a paper about the constituents of arguments. It argues that several different kinds of truth-bearer may be taken to compose arguments, but that none of the obvious candidates—sentences, propositions, sentence/truth-value pairs etc.—make sense of logic as it is actually practiced. The paper goes on to argue that by answering the question in different ways, we can generate different logics, thus ensuring a kind of logical pluralism that is different from that of J. Beall and Greg Restall.
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  • Zitierte Zeichenreihen.Olaf Müller - 1996 - Erkenntnis 44 (3):279 - 304.
    We use quotation marks when we wish to refer to an expression. We can and do so refer even when this expression is composed of characters that do not occur in our alphabet. That's why Tarski, Quine, and Geach's theories of quotation don't work. The proposals of Davidson, Frege, and C. Washington, however, do not provide a plausible account of quotation either. (Section I). The problem is to construct a Tarskian theory of truth for an object language that contains quotation (...)
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  • Natural Deduction and Arbitrary Objects.Kit Fine - 1985 - Journal of Philosophical Logic 14 (1):57 - 107.
  • Russell and the Universalist Conception of Logic.Ian Proops - 2007 - Noûs 41 (1):1–32.
    The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.
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  • Aristotle's Theory of the Assertoric Syllogism.Stephen Read - manuscript
    Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...)
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  • Prototype Effect and the Persuasiveness of Generalizations.Christian Dahlman, Farhan Sarwar, Rasmus Bååth, Lena Wahlberg & Sverker Sikström - 2016 - Review of Philosophy and Psychology 7 (1):163-180.
    An argument that makes use of a generalization activates the prototype for the category used in the generalization. We conducted two experiments that investigated how the activation of the prototype affects the persuasiveness of the argument. The results of the experiments suggest that the features of the prototype overshadow and partly overwrite the actual facts of the case. The case is, to some extent, judged as if it had the features of the prototype instead of the features it actually has. (...)
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  • Indian Logic Revisited: Nyāyapra Veśa Reviewed. [REVIEW]Brendan S. Gillon & Martha Lile Love - 1980 - Journal of Indian Philosophy 8 (4):349-384.
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  • De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity.Paul Égré, Lorenzo Rossi & Jan Sprenger - 2021 - Journal of Philosophical Logic 50 (2):187-213.
    This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: (...)
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  • The Prospects for a Monist Theory of Non-Causal Explanation in Science and Mathematics.Alexander Reutlinger, Mark Colyvan & Karolina Krzyżanowska - forthcoming - Erkenntnis:1-21.
    We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...)
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  • Decision Theory, Intelligent Planning and Counterfactuals.Michael John Shaffer - 2008 - Minds and Machines 19 (1):61-92.
    The ontology of decision theory has been subject to considerable debate in the past, and discussion of just how we ought to view decision problems has revealed more than one interesting problem, as well as suggested some novel modifications of classical decision theory. In this paper it will be argued that Bayesian, or evidential, decision-theoretic characterizations of decision situations fail to adequately account for knowledge concerning the causal connections between acts, states, and outcomes in decision situations, and so they are (...)
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  • Relational Modality.Kathrin Glüer & Peter Pagin - 2008 - Journal of Logic, Language and Information 17 (3):307-322.
    Saul Kripke’s thesis that ordinary proper names are rigid designators is supported by widely shared intuitions about the occurrence of names in ordinary modal contexts. By those intuitions names are scopeless with respect to the modal expressions. That is, sentences in a pair like (a) Aristotle might have been fond of dogs (b) Concerning Aristotle, it is true that he might have been fond of dogs will have the same truth value. The same does not in general hold for definite (...)
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  • On Universals: An Extensionalist Alternative to Quine’s Resemblance Theory. [REVIEW]Nathan Stemmer - 2005 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (1):75 - 90.
    The notion of similarity plays a central role in Quine’s theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine’s theory has been ignored by several philosophers (see, e.g., Armstrong, D. M. (1978a). Nominalism and (...)
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  • Suppose Yalcin is Wrong About Epistemic Modals.Joshua D. Crabill - 2013 - Philosophical Studies 162 (3):625-635.
    In “Epistemic Modals,” Seth Yalcin argues that what explains the deficiency of sentences containing epistemic modals of the form ‘p and it might be that not-p’ is that sentences of this sort are strictly contradictory, and thus are not instances of a Moore-paradox as has been previous suggested. Benjamin Schnieder, however, argues in his Yalcin’s explanation of these sentences’ deficiency turns out to be insufficiently general, as it cannot account for less complex but still defective sentences, such as ‘Suppose it (...)
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  • Philosophical Accounts of First-Order Logical Truths.Constantin C. Brîncuş - 2019 - Acta Analytica 34 (3):369-383.
    Starting from certain metalogical results, I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these (...)
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  • Zif Would Have Been If: A Suppositional View of Counterfactuals.David Barnett - 2010 - Noûs 44 (2):269-304.
    Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.
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  • The Price of Inscrutability.J. R. G. Williams - 2008 - Noûs 42 (4):600 - 641.
  • 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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  • The Revenge of the Semantics‐Pragmatics Distinction.Josh Dever - 2013 - Philosophical Perspectives 27 (1):104-144.
  • The Primary Process of Groups, its Systematics and Representation.Guy E. Swanson - 1974 - Journal for the Theory of Social Behaviour 4 (1):53–69.
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  • Geach, Aristotle and Predicate Logics.Alex Orenstein - 2015 - Philosophical Investigations 38 (1-2):96-114.
    Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special restricted quantifiers in a (...)
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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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  • Some Notes on Boolos’ Semantics: Genesis, Ontological Quests and Model-Theoretic Equivalence to Standard Semantics.Francesco Ferrari - 2018 - Axiomathes 28 (2):125-154.
    The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ (...)
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  • Proceedings of Sinn Und Bedeutung 9.Emar Maier, Corien Bary & Janneke Huitink (eds.) - 2005 - Nijmegen Centre for Semantics.
  • 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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  • An Incompatible Pair of Subjunctive Conditional Modal Axioms.David Butcher - 1983 - Philosophical Studies 44 (1):71 - 110.
  • Probabilities and Temporal Parts.Michael F. Patton - 2002 - Acta Analytica 17 (1):39-52.
    Adopting temporal parts theory is the most popular way of addressing a host of puzzles about diachronic identity. For example, it is not obvious how I am the same person as the baby who shared my name. With the theory, sameness of person, e.g., consists in being comprised by the same temporally extended, four-dimensional object. However, temporal parts theory has unacceptable consequences for notions of freedom and probability. I show that the only acceptable reading of four-dimensionalism entails that the four (...)
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  • The Myth of the Categorical Counterfactual.David Barnett - 2009 - Philosophical Studies 144 (2):281 - 296.
    I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be (...)
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  • On a Derivation of the Necessity of Identity.John P. Burgess - 2014 - Synthese 191 (7):1-19.
    The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.
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  • Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...)
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  • Shallow Analysis and the Slingshot Argument.Michael Baumgartner - 2010 - Journal of Philosophical Logic 39 (5):531-556.
    According to the standard opinions in the literature, blocking the unacceptable consequences of the notorious slingshot argument requires imposing constraints on the metaphysics of facts or on theories of definite descriptions (or class abstracts). This paper argues that both of these well-known strategies to rebut the slingshot overshoot the mark. The slingshot, first and foremost, raises the question as to the adequate logical formalization of statements about facts, i.e. of factual contexts. It will be shown that a rigorous application of (...)
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  • Frege and the Determination of Reference.Gilead Bar-Elli - 1981 - Erkenntnis 16 (1):137 - 160.
  • Formalization and the Objects of Logic.Georg Brun - 2008 - Erkenntnis 69 (1):1 - 30.
    There is a long-standing debate whether propositions, sentences, statements or utterances provide an answer to the question of what objects logical formulas stand for. Based on the traditional understanding of logic as a science of valid arguments, this question is firstly framed more exactly, making explicit that it calls not only for identifying some class of objects, but also for explaining their relationship to ordinary language utterances. It is then argued that there are strong arguments against the proposals commonly put (...)
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  • Implication and Entailment in Navya-Nyāya Logic.V. K. Bharadwaja - 1987 - Journal of Indian Philosophy 15 (2):149-154.
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  • Proper Names as Variables.Takashi Yagisawa - 1984 - Erkenntnis 21 (2):195 - 208.
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  • Bivalence and Subjunctive Conditionals.Timothy Williamson - 1988 - Synthese 75 (3):405 - 421.
    Writers such as Stalnaker and Dummett have argued that specific features of subjunctive conditional statements undermine the principle of bivalence. This, paper is concerned with rebutting such claims. 1. It is shown how subjective conditionals pose a prima facie threat to bivalence, and how this threat can be dissolved by a distinction between the results of negating a subjective conditional and of negating its consequent. To make this distinction is to side with Lewis against Stalnaker in a dispute about possible (...)
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  • Are Species Sets?Bradley E. Wilson - 1991 - Biology and Philosophy 6 (4):413-431.
    I construe the question Are species sets? as a question about whether species can be conceived of as sets, as the term set is understood by contemporary logicians. The question is distinct from the question Are species classes?: The conception of classes invoked by Hull and others differs from the logician's conception of a set. I argue that species can be conceived of as sets, insofar as one could identify a set with any given species and that identification would satisfy (...)
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  • On the Semantics of the Ought-to-Do.Hector-Neri Castañeda - 1970 - Synthese 21 (3-4):449 - 468.
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