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  1.  10
    Function and Argument in Begriffsschrift.Badesa Calixto & Millán Joan Bertran-San - 2017 - History and Philosophy of Logic 38 (4):316-341.
    It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...)
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  2.  11
    Function and Argument in Begriffsschrift.Calixto Badesa Cortes & Joan Bertran-San Millán - 2017 - History and Philosophy of Logic 38 (4):316-341.
    It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...)
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  3. Paul of Venice and Realist Developments of Roger Swyneshed's Treatment of Semantic Paradoxes.Miroslav Hanke - 2017 - History and Philosophy of Logic 38 (4):299-315.
    In the 1330s Roger Swyneshed formulated a solution to semantic paradoxes based on the distinction between correspondence with reality and self-falsification as truth-making factors. Since Swyneshed states that some valid inferences are not truth-preserving, his view implies the question of the general definition of validity which he does not address explicitly. Logical works attributed to Paul of Venice contain developments of Swyneshed's contextualist semantics substantially modified by the assumption that sentential meanings are objective propositional entities. The main goals of this (...)
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  4.  55
    Talking About Numbers: Easy Arguments for Mathematical Realism. [REVIEW]Richard Lawrence - 2017 - History and Philosophy of Logic 38 (4):390-394.
  5.  35
    Frege's Begriffsschrift is Indeed First-Order Complete.Yang Liu - 2017 - History and Philosophy of Logic 38 (4):342-344.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is concerned. (...)
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  6.  4
    The Status of Value-Ranges in the Argument of Basic Laws of Arithmetic I §10.Thomas Lockhart - 2017 - History and Philosophy of Logic 38 (4):345-363.
    Frege's concern in GGI §10 is neither with the epistemological issue of how we come to know about value-ranges, nor with the semantic-metaphysical issue of whether we have said enough about such objects in order to ensure that any kind of reference to them is possible. The problem which occupies Frege in GGI §10 is the general problem according to which we ‘cannot yet decide’, for any arbitrary function, what value ‘’ has if ‘ℵ’ is a canonical value-range name. This (...)
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  7.  8
    Making Sense of Sense Containment.Antonio Negro - 2017 - History and Philosophy of Logic 38 (4):364-385.
    Proposition 5.122 of Wittgenstein’s Tractatus has been the source of much puzzlement among interpreters, so much so that no fully satisfactory account is yet available. This is unfortunate, if only because the containment account of logical consequence has a venerable tradition behind it. Pasquale Frascolla’s interpretation of proposition 5.122 is based on a valid argument and one true premise. However, the argument explains sense containment only in an indirect way, leaving some crucial questions unanswered. Besides, Frascolla does not address the (...)
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  8.  4
    Notule Libri Priorum. [REVIEW]José Filipe Silva - 2017 - History and Philosophy of Logic 38 (4):388-390.
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  9.  6
    Abstractiones. [REVIEW]Joke Spruyt - 2017 - History and Philosophy of Logic 38 (4):386-387.
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  10.  5
    The Modal Equivalence Rules of the Port-Royal Logic.John Grey - 2017 - History and Philosophy of Logic 38 (3):210-221.
    The Port-Royal Logic includes a brief discussion of modal propositions, containing several mnemonic devices for rules of equivalence governing the possibility, necessity, impossibility, and contingency of propositions. When the mnemonics are decoded, it can be seen that these rules treat possibility and contingency as formally equivalent modes. The aim of this paper is twofold: to show that this identification of possibility and contingency follows from the Logic’s formal treatment of those modes; and to show that such a treatment of these (...)
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  11.  8
    John Buridan on the Possibility of Defining Definition.Rodrigo Guerizoli - 2017 - History and Philosophy of Logic 38 (3):201-209.
    The study of the medieval reception of Aristotle’s Topics has largely been oriented toward debates on dialectical argumentation. And this is surely right. Nonetheless, I wish to approach John Buridan’s commentary on the Topics from another perspective, which highlights some semantic features of the set of predicates around which the work is organized. Thus, in my paper I will first reconstruct Buridan’s account of the identification of the predicates discussed in the Topics. I will argue that, for him, they are (...)
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  12.  19
    Graham Priest's Mathematical Analysis of the Concept of Emptiness.Eberhard Guhe - 2017 - History and Philosophy of Logic 38 (3):282-290.
    In his article ‘The Structure of Emptiness’, 467–80. doi: 10.1353/pew.0.0069[Crossref], [Web of Science ®] [Google Scholar]) Graham Priest examines the concept of emptiness in the Mādhyamaka school of Nāgārjuna and his commentators Candrakīırti and Tsongkhapa from a mathematical point of view. The approach attempted in this article does not involve any commitment to Priest's more controversial dialethic Mādhyamaka interpretation. The purpose of the present paper is to explain Priest's sketchy but very insightful interpretation of objects as non-well-founded sets in greater (...)
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  13.  4
    Essay Review.Anna-Sophie Heinemann - 2017 - History and Philosophy of Logic 38 (3):291-296.
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  14.  5
    Wittgenstein's Ab-Notation: An Iconic Proof Procedure.Timm Lampert - 2017 - History and Philosophy of Logic 38 (3):239-262.
    This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his (...)
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  15.  12
    Routes for Roots: A Mapping Shorthand Symbolism with Reference to Nelson Goodman’s Hidden Ars Combinatoria.Gerald Moshammer - 2017 - History and Philosophy of Logic 38 (3):263-281.
    A shorthand symbolism for the relational mapping of categories is introduced and developed on the basis of Nelson Goodman's structural methodology. Through a reconstruction of extensional isomorphism that Goodman introduces as a criterion for definitional accuracy, and a brief reminder of the argument structure behind his ‘new riddle of induction’, Goodman's radical ontological relativism is turned into a protological principle of what I call ‘domain constituting philosophy’. MSS is demonstrated with reference to Goodman's symbol theory, particularly his notion of exemplification, (...)
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  16.  7
    Book Review of “Gentzen's Centenary”. [REVIEW]Francesca Poggiolesi - 2017 - History and Philosophy of Logic 38 (3):297-298.
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  17.  6
    On the Justification Problems: Towards a Peircean Diagnosis and Solution.Liuhua Zhang - 2017 - History and Philosophy of Logic 38 (3):222-238.
    Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...)
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  18.  10
    Popper's Notion of Duality and His Theory of Negations.David Binder & Thomas Piecha - 2017 - History and Philosophy of Logic 38 (2):154-189.
    Karl Popper developed a theory of deductive logic in the late 1940s. In his approach, logic is a metalinguistic theory of deducibility relations that are based on certain purely structural rules. Logical constants are then characterized in terms of deducibility relations. Characterizations of this kind are also called inferential definitions by Popper. In this paper, we expound his theory and elaborate some of his ideas and results that in some cases were only sketched by him. Our focus is on Popper's (...)
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  19.  17
    Frege's Cardinals Do Not Always Obey Hume's Principle.Gregory Landini - 2017 - History and Philosophy of Logic 38 (2):127-153.
    Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as objects set out in Frege's Grundgesetze. (...)
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  20.  6
    Term Kinds and the Formality of Aristotelian Modal Logic.Mendelsohn Joshua - 2017 - History and Philosophy of Logic 38 (2):99-126.
    Recent formalizations of Aristotle's modal syllogistic have made use of an interpretative assumption with precedent in traditional commentary: That Aristotle implicitly relies on a distinction between two classes of terms. I argue that the way Rini employs this distinction undermines her attempt to show that Aristotle gives valid proofs of his modal syllogisms. Rini does not establish that Aristotle gives valid proofs of the arguments which she takes to best represent Aristotle's modal syllogisms, nor that Aristotle's modal syllogisms are instances (...)
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  21.  7
    Essay Review.Enrico Moriconi - 2017 - History and Philosophy of Logic 38 (2):190-200.
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  22.  23
    Frege on Thinking and Its Epistemic Significance. [REVIEW]Carlo Cellucci - 2017 - History and Philosophy of Logic 38 (1):92-95.
  23.  3
    Thinking About Persons: Loci Personarum in Humanist Dialectic Between Agricola and Keckermann.Stefan Heßbrüggen-Walter - 2017 - History and Philosophy of Logic 38 (1):1-23.
    Loci personarum, ‘topics for persons’ were used in Latin rhetoric for the description of persons, their external circumstances, physical attributes, or qualities of character. They stood in the way of fusing rhetoric and dialectic, the goal of sixteenth-century ‘humanistic’ logic: the project of a unified theory of invention depends on the exclusion of loci personarum from the domain of dialectic proper. But still they cannot easily be replaced in the class room. Bartholomaeus Keckermann resolved these difficulties: he proposed to abandon (...)
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  24.  6
    Rescuing Poincaré From Richard’s Paradox.Laureano Luna - 2017 - History and Philosophy of Logic 38 (1):57-71.
    Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, indefinite (...)
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  25.  7
    Mathematical Knowledge and the Interplay of Practices. [REVIEW]Madeline Muntersbjorn - 2017 - History and Philosophy of Logic 38 (1):89-92.
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  26.  5
    R. M. Martin’s Logic of Belief.David Parsons - 2017 - History and Philosophy of Logic 38 (1):72-86.
    In this paper I revisit R. M. Martin’s logic of belief. As with much of Martin’s work, his formal studies into belief and belief reports have gone largely unnoticed. However, in my article I suggest reasons for thinking that these studies warrant revisiting. One reason is that Martin adopted an account of the notion of belief which was more comprehensive than that employed by most rival theorists. Another reason is that Martin couched his theory in a formal pragmatics which utilised (...)
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  27.  6
    Le Nécessaire Et L’Universel—Analyse Et Critique de Leur Corrélation. [REVIEW]F. Pataut - 2017 - History and Philosophy of Logic 38 (1):87-89.
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  28.  8
    The History and Philosophy of Polish Logic. Essays in Honour of Jan Woleński. [REVIEW]Rafal Urbaniak - 2017 - History and Philosophy of Logic 38 (1):95-97.
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  29.  18
    L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an Introduction.Mark Van Atten & Göran Sundholm - 2017 - History and Philosophy of Logic 38 (1):24-47.
    We present a new English translation of L.E.J. Brouwer's paper ‘De onbetrouwbaarheid der logische principes’ of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. (...)
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  30.  2
    König's Infinity Lemma and Beth's Tree Theorem.George Weaver - 2017 - History and Philosophy of Logic 38 (1):48-56.
    König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with a root has (...)
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