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  1.  10
    Aristotelian Logic Axioms in Propositional Logic: The Pouch Method.Enrique Alvarez-Fontecilla & Tomas Lungenstrass - 2018 - History and Philosophy of Logic 40 (1):12-21.
    A new theoretical approach to Aristotelian Logic based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof method for PL (...)
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  2.  4
    The Great Formal Machinery Works. Theories of Deduction and Computation at the Origins of the Digital Age.L. Bellotti - 2018 - History and Philosophy of Logic 40 (1):98-99.
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  3.  13
    Abstractionism. Essays in the Philosophy of Mathematics.F. Boccuni - 2018 - History and Philosophy of Logic 40 (1):100-103.
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  4.  5
    Fārābī and Avicenna on Contraposition.Asadollah Fallahi - 2018 - History and Philosophy of Logic 40 (1):22-41.
    The rule of contraposition has been investigated thoroughly by Arabic logicians. In this paper, we study the work done by Fārābā and Avicenna, the fathers of Arabic logic. Fārābā studied contraposition of universal affirmatives, discussed its four forms, and discovered a relation between one form and the conversion of negative universals. Although Fārābā and logicians before him have used contraposition only for conditionals, as well as for indefinite and universal affirmative categorical propositions, Avicenna generalized the rule to all the four (...)
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  5.  16
    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’, Mind, 69, 499–533; 1979. Naturalism and Ontology, Reseda, CA: Ridgeview Publishing Company] argues that the truth of a second-order sentence, e.g., 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 (...)
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  6.  5
    Varieties of Demonstration in Alfarabi.Riccardo Strobino - 2018 - History and Philosophy of Logic 40 (1):42-62.
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  7.  12
    From Wittgenstein’s N-Operator to a New Notation for Some Decidable Modal Logics.Fangfang Tang - 2018 - History and Philosophy of Logic 40 (1):63-80.
    Wittgenstein’s N-operator is a ‘primitive sign’ which shows every complex proposition is the result of the truth-functional combination of a finite number of component propositions, and thus provides a mechanical method to determine logical truth. The N-operator can be interpreted as a generalized Sheffer stroke. In this paper, I introduce a new ‘primitive sign’ that is a hybrid of generalized Sheffer stroke and modality, and give a uniform expression for modal formulas. The general form of modal formula in the new (...)
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  8.  10
    Mereology in Aristotle's Assertoric Syllogistic.Justin Vlasits - 2018 - History and Philosophy of Logic 40 (1):1-11.
    How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness and completeness (...)
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  9.  6
    ‘My Future Son is Possibly Alive’. Existential Presupposition and Empty Terms in Abelard's Modal Logic.Irene Binini - 2018 - History and Philosophy of Logic 39 (4):341-356.
    The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions maintains its validity when some of the terms included in these propositions are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for the truth of propositions (...)
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  10.  7
    Hegel and the Consequentia Mirabilis.Elena Ficara - 2018 - History and Philosophy of Logic 39 (4):357-364.
    In this paper I argue that Hegel’s treatment of dialectical inferences, in particular of Plato’s dialectics in the Lectures on the History of Philosophy, belongs to the history of the logical rule that, from Gerolamo Cardano to Bertrand Russell, is known as consequentia mirabilis. In 1906 Russell formalises it as follows: and its correspondent positive form as My paper has two parts. First, I show that dialectical inferences, for Hegel, involve sentences of the form and. Hegel, following Plato, stresses that (...)
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  11.  22
    The Context of Inference.Curtis Franks - 2018 - History and Philosophy of Logic 39 (4):365-395.
    There is an ambiguity in the concept of deductive validity that went unnoticed until the middle of the twentieth century. Sometimes an inference rule is called valid because its conclusion is a theorem whenever its premises are. But often something different is meant: The rule's conclusion follows from its premises even in the presence of other assumptions. In many logical environments, these two definitions pick out the same rules. But other environments are context-sensitive, and in these environments the second notion (...)
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  12.  7
    Aristotle, Logic, and QUARC.Jonas Raab - 2018 - History and Philosophy of Logic 39 (4):305-340.
    The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by Ben-Yami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for a more adequate reconstruction (...)
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  13.  95
    Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge. [REVIEW]Panu Raatikainen - 2018 - History and Philosophy of Logic 39 (4):401-403.
  14.  11
    Logic Lectures. Gödel's Basic Logic Course at Notre Dame.Jan von Plato - 2018 - History and Philosophy of Logic 39 (4):396-401.
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  15.  9
    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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  16.  17
    Husserl's Logical Grammar.Ansten Klev - 2018 - History and Philosophy of Logic 39 (3):232-269.
    Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...)
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  17.  15
    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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  18.  15
    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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  19.  17
    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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  20.  8
    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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  21.  4
    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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  22.  11
    Bolzano’s Logical System.Jan Sebestik - 2018 - History and Philosophy of Logic 39 (2):164-186.
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  23.  16
    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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  24. 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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  25.  11
    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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  26.  21
    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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  27.  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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  28.  65
    ‘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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  29.  14
    [Review]Amirouch Moktefi and Francine F. Abeles What the Tortoise Said to Achilles: Lewis Carroll's Paradox of Inference.Corine Besson - 2018 - History and Philosophy of Logic 39 (1):96-98.
  30.  8
    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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  31.  15
    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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  32.  26
    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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