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  1.  8
    Decoding Gentzen's Notation.Luca Bellotti - 2018 - History and Philosophy of Logic 39 (3):270-288.
    In this note we consider Gentzen's first ordinal notation, used in his first published proof of the consistency of Peano Arithmetic. It is a decimal notation, quite different from our current notations. We give a rule to translate this notation into our usual set-theoretic notation and we show some of its peculiarities. Then we indicate how to decode Gentzen's assignment of ordinal notations to derivations and give some examples. Finally, we go through his proof of their decrease after the application (...)
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  2.  13
    Avicenna on the Primary Propositions.Seyed N. Mousavian & Mohammad Ardeshir - 2018 - History and Philosophy of Logic 39 (3):201-231.
    Avicenna introduces the primary propositions as the most fundamental principles of knowledge. However, as far as we are aware, Avicenna’s primaries have not yet been independently studied. Nor do Avicenna scholars agree on how to characterize them in the language of contemporary philosophy. It is well-known that the primaries are indemonstrable; nonetheless, it is not clear what the genealogy of the primaries is, how, epistemologically speaking, they can be distinguished from other principles, what their phenomenology is, what the cause of (...)
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  3.  10
    The Early Formation of Modal Logic and its Significance: A Historical Note on Quine, Carnap, and a Bit of Church.Adam Tamas Tuboly - 2018 - History and Philosophy of Logic 39 (3):289-304.
    The aim of the paper is to show that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis’ systems and did not take Quine's arguments and remarks seriously—or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break (...)
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  4.  15
    Existential Import and an Unnecessary Restriction on Predicate Logics.George Boger - 2018 - History and Philosophy of Logic 39 (2):109-134.
    Contemporary logicians continue to address problems associated with the existential import of categorical propositions. One notable problem concerns invalid instances of subalternation in the case of a universal proposition with an empty subject term. To remedy problems, logicians restrict first-order predicate logics to exclude such terms. Examining the historical origins of contemporary discussions reveals that logicians continue to make various category mistakes. We now believe that no proposition per se has existential import as commonly understood and thus it is unnecessary (...)
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  5.  6
    A Note on Saying Nothing and Saying More in the Tractatus.Pasquale Frascolla - 2018 - History and Philosophy of Logic 39 (2):135-139.
    On the basis of an analysis of the relevant parts of Tractatus logico-philosophicus, a definition of the property of saying something, and of the obviously correlated property of saying nothing, is given. By applying that definition, both tautologies and contradictions are sanctioned as saying nothing, as lacking sense, in full agreement with Wittgenstein's explicit statements. On the other hand, a recent systematic attempt by A. Negro to extract from the Tractatus a criterion for sense containment and a criterion for saying (...)
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  6.  3
    Lewis Carroll’s Diaries: The Private Journals of Charles Lutwidge Dodgson /The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces.Amirouche Moktefi - 2018 - History and Philosophy of Logic 39 (2):187-200.
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  7.  6
    Bolzano’s Logical System.Jan Sebestik - 2018 - History and Philosophy of Logic 39 (2):164-186.
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  8.  12
    Kalmár's Argument Against the Plausibility of Church's Thesis.Máté Szabó - 2018 - History and Philosophy of Logic 39 (2):140-157.
    In his famous paper, An Unsolvable Problem of Elementary Number Theory, Alonzo Church identified the intuitive notion of effective calculability with the mathematically precise notion of recursiveness. This proposal, known as Church's Thesis, has been widely accepted. Only a few papers have been written against it. One of these is László Kalmár's An Argument Against the Plausibility of Church's Thesis from 1959. The aim of this paper is to present Kalmár's argument and to fill in missing details based on his (...)
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  9.  65
    The Sufi Path of Dialetheism: Gluon Theory and Wahdat Al-Wujud.Behnam Zolghadr - 2018 - History and Philosophy of Logic 39 (2):99-108.
    The theory of Wahdat al-Wujūd, or as it is called in English the Oneness of Being, is the core idea of Sufism. The founder of this theory is Ibn ‘Arabī. There are contradictions in Ibn ‘Arabī’s theory of the Oneness of Being. The most important one, which is my main concern in this essay, occurs in his explanation of the relation between Being, which is, according to him, the only real being, and other beings. According to Ibn ‘Arabī, Being is (...)
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  10.  10
    Prior's Grappling with Peirce's Existential Graphs.Peter Øhrstrøm - 2018 - History and Philosophy of Logic 39 (2):158-163.
    A. N. Prior very much admired the logic and philosophy of C.S. Peirce. In the spring of 1962 Prior went to Chicago to study Peirce's ideas. One of the topics that caught his attention was Peirce's existential graphs. This interest continued when he returned to England. In this paper Prior's grappling with the existential graphs will be discussed.
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  11.  19
    Simplex Sigillum Veri: Peano, Frege, and Peirce on the Primitives of Logic.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):80-95.
    We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...)
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  12.  17
    Introduction: History and Philosophy of Logical Notation.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):1-2.
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  13.  48
    ‘What the Tortoise Said to Achilles’: Lewis Carroll's Paradox of Inference. [REVIEW]Corine Besson - 2018 - History and Philosophy of Logic 39 (1):96-98.
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  14.  5
    Horrent with Mysterious Spiculæ’. Augustus De Morgan’s Logic Notation of 1850 as a ‘Calculus of Opposite Relations.Anna-Sophie Heinemann - 2018 - History and Philosophy of Logic 39 (1):29-52.
    The present paper expounds the logic notation proposed by Augustus De Morgan in 1850 from within the original context of De Morgan’s account of syllogistic logic and his approach to quantification. The notational system of 1850 is shown to be a flexible tool to state inferences, to prove their validity and to derive formulæ of the respective system by ‘blind’ application of transformation rules. These pertain to the swapping of operator signs, which are of inverse ‘character’ in a two-fold sense: (...)
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  15.  13
    Logic Diagrams in the Weigel and Weise Circles.Jens Lemanski - 2018 - History and Philosophy of Logic 39 (1):3-28.
    From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of using (...)
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  16.  22
    On Frege's Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs.Dirk Schlimm - 2018 - History and Philosophy of Logic 39 (1):53-79.
    Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...)
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