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  1. LOGIC TEACHING IN THE 21ST CENTURY.John Corcoran - manuscript
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...)
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  2. Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-44.
    Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.
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  3. Inferential Quantification and the ω-rule.Constantin C. Brîncuș - forthcoming - In Antonio D’Aragona (ed.), Perspectives on Deduction.
    Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...)
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  4. Tarski’s Convention T: condition beta.John Corcoran - forthcoming - South American Journal of Logic 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  5. Wittgensteins Diagonal-Argument: Eine Variation auf Cantor und Turing.Juliet Floyd - forthcoming - In Joachim Bromand & Bastian Reichert (eds.), Wittgenstein und die Philosophie der Mathematik. Münster: Mentis Verlag. pp. 167-197.
    A German translation with 2017 postscript of Floyd, Juliet. 2012. "Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing." In Epistemology versus Ontology, Logic, Epistemology: Essays in Honor of Per Martin-Löf, edited by P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm, 25-44. Dordrecht: Springer Science+Business Media. An analysis of philosophical aspects of Turing's diagonal argument in his (136) "On computable numbers, with an application to the Entscheidungsproblem" in relation to Wittgenstein's writings on Turing and Cantor.
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  6. Gödel’s theorem and direct self-reference.Saul A. Kripke - forthcoming - Review of Symbolic Logic:1-5.
    In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that ‘direct’ self-reference can actually be used to prove his result.
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  7. Evidence in Logic.Ben Martin & Ole Thomassen Hjortland - forthcoming - In Maria Lasonen-Aarnio & Clayton M. Littlejohn (eds.), Routledge Handbook of the Philosophy of Evidence. Routledge.
    The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...)
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  8. Arthur N. Prior and the Lvov-Warsaw School.Zuzana Rybaříková - forthcoming - History and Philosophy of Logic:1-13.
    This paper presents the link between Arthur N. Prior and logicians that belonged to the Lvov-Warsaw School. Although certain members of the Lvov-Warsaw School influenced Prior’s views, the amount a...
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  9. Quentin Kammer, Jean-Philippe Narboux and Henri Wagner (eds). C. I. Lewis: The A Priori and the Given. [REVIEW]Robert Sinclair - forthcoming - Hopos: The Journal of the International Society for the History of Philosophy of Science.
  10. The limits and basis of logical tolerance: Carnap’s combination of Russell and Wittgenstein.Adam Tamas Tuboly - forthcoming - In Peter Stone (ed.), Bertrand Russell’s Life and Legacy. Vernon Press.
  11. Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930).Vasil Penchev - 2023 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 15 (1):1-61.
    The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...)
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  12. Completeness: From Husserl to Carnap.Víctor Aranda - 2022 - Logica Universalis 16 (1):57-83.
    In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...)
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  13. A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$ ε -operator.Nicola Bonatti - 2022 - Synthese 200 (5):1-26.
    Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...)
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  14. The Non-categoricity of Logic (I). The Problem of a Full Formalization.Constantin C. Brîncuș - 2022 - In Probleme de Logică/Problems of Logic. București, România: pp. 137-156.
    A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...)
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  15. The genealogy of ‘∨’.Landon D. C. Elkind & Richard Zach - 2022 - Review of Symbolic Logic:1-38.
    The use of the symbol ∨ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or”, vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead (...)
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  16. Bunge y la validez de la adición.Luis Estrada González & Christian Romero-Rodríguez - 2022 - In German Guerrero-Pino (ed.), Ciencia, Realismo y materialismo. Cali, Valle del Cauca, Colombia: pp. 191-202.
    En The paradox of Addition and its dissolution (1969), Mario Bunge presenta algunos argumentos para mostrar que la Regla de Adición puede ocasionar paradojas o problemas semánticos. Posteriormente, Margáin (1972) y Robles (1976) mostraron que las afirmaciones de Bunge son insostenibles, al menos desde el punto de vista de la lógica clásica. Aunque estamos de acuerdo con las críticas de Margáin y Robles, no estamos de acuerdo en el diagnóstico del origen del problema y tampoco con la manera en la (...)
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  17. Husserl on Kant and the critical view of logic.Mirja Hartimo - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):707-724.
    ABSTRACT This paper seeks to clarify Husserl’s critical remarks about Kant’s view of logic by comparing their respective views of logic. In his Formal and Transcendental Logic Husserl criticizes Kant for not asking transcendental questions about formal logic, but rather ascribing an ‘extraordinary apriority’ to it. He thinks the reason for Kant’s uncritical attitude to logic lies in Kant’s view of logic as directed toward the subjective, instead of being concerned with a ‘“world” of ideal Objects’. Whereas for Kant, general (...)
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  18. Susan Stebbing.Frederique Janssen-Lauret - 2022 - Cambridge, UK: Cambridge University Press.
    Susan Stebbing (1885–1943), the UK’s first female professor of philosophy, was a key figure in the development of analytic philosophy. Stebbing wrote the world’s first accessible book on the new polyadic logic and its philosophy. She made major contributions to the philosophy of science, metaphysics, philosophical logic, critical thinking, and applied philosophy. Nonetheless she has remained largely neglected by historians of analytic philosophy. This Element provides a thorough yet accessible overview of Stebbing’s positive, original contributions, including her solution to the (...)
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  19. The collapse of the Hilbert program: A variation on the gödelian theme.Saul A. Kripke - 2022 - Bulletin of Symbolic Logic 28 (3):413-426.
    The Hilbert program was actually a specific approach for proving consistency, a kind of constructive model theory. Quantifiers were supposed to be replaced by ε-terms. εxA(x) was supposed to denote a witness to ∃xA(x), or something arbitrary if there is none. The Hilbertians claimed that in any proof in a number-theoretic system S, each ε-term can be replaced by a numeral, making each line provable and true. This implies that S must not only be consistent, but also 1-consistent. Here we (...)
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  20. Łukasiewicz’s concept of logic and anti-psychologism.Zuzana Rybaříková - 2022 - Synthese 200 (2):1-14.
    In the nineteenth century, philosophy was at a crossroads. While the natural and technical sciences were developing in an unprecedented fashion, philosophy seemed to be stalled. Inspired by the progress of the natural sciences, many philosophers attempted to make such progress in philosophy and make philosophy a truly scientific discipline. This effort was also reflected in the philosophy of the Lvov-Warsaw school. While its founder, Kazimierz Twardowski, following his teacher Franz Brentano, promoted psychology as a method of scientific philosophy, one (...)
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  21. Peirce and Łukasiewicz on modal and multi-valued logics.Jon Alan Schmidt - 2022 - Synthese 200 (4):1-18.
    Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises from overlooking (...)
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  22. A.N. PRIOR's SYSTEM Q: A REVIEW. [REVIEW]Farshad Badie - 2021 - Логико-Философские Штудии 19 (3):161-174.
    Arthur Norman Prior was born on 4 December 1914 in Masterton, New Zealand. He studied philosophy in the 1930s and was a significant, and often provocative, voice in theological debates until well into the 1950s. He became a lecturer in philosophy at Canterbury University College in Christchurch in 1946 succeeding Karl Popper. He became a full professor in 1952. He left New Zealand permanently for England in 1959, first taking a chair in philosophy at Manchester University, and then becoming a (...)
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  23. An Argument for Completely General Facts.Landon D. C. Elkind - 2021 - Journal for the History of Analytical Philosophy 9 (7).
    In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I next (...)
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  24. In What Sense is J.N. Findlay the Founding Father of Tense-logic?David Jakobsen - 2021 - History and Philosophy of Logic 42 (2):180-188.
    In 1954, A. N. Prior discovered a way to formalize tense-logic—as such, there is no doubt that he is the father of modern tense-logic. Despite this, he considered his early teacher in p...
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  25. What he could have said (but did not say) about Gödel’s second theorem: A note on Floyd-Putnam’s Wittgenstein.Kaave Lajevardi - 2021 - Wittgenstein-Studien 12 (1):121-129.
    In several publications, Juliet Floyd and Hilary Putnam have argued that the so-called ‘notorious paragraph’ of the Remarks on the Foundations of Mathematics contains a valuable philosophical insight about Gödel’s informal proof of the first incompleteness theorem – in a nutshell, the idea they attribute to Wittgenstein is that if the Gödel sentence of a system is refutable, then, because of the resulting ω-inconsistency of the system, we should give up the translation of Gödel’s sentence by the English sentence “I (...)
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  26. Wittgenstein on Logic as The Method of Philosophy. Re-examining the Roots and Development of Analytic Philosophy.T. Lampert - 2021 - History and Philosophy of Logic 42 (2):194-197.
    In his Lecture on Ethics, Wittgenstein mentions the difficulty a recipient of his philosophy has in ‘seeing both the road he is led and the goal which it leads to’. Oskari Kuusela's b...
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  27. Gödel on Many-Valued Logic.Tim Lethen - 2021 - Review of Symbolic Logic:1-17.
    This paper collects and presents unpublished notes of Kurt Gödel concerning the field of many-valued logic. In order to get a picture as complete as possible, both formal and philosophical notes, transcribed from the Gabelsberger shorthand system, are included.
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  28. Reflections on Orlov.Graham Priest - 2021 - History and Philosophy of Logic 42 (2):118-128.
    In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant log...
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  29. Łukasiewicz, determinism, and the four-valued system of logic.Zuzana Rybaříková - 2021 - Semiotica 2021 (240):129-143.
    Jan Łukasiewicz is known primarily as the founder of the three-valued system of logic. It is also generally renowned that his reason for introducing many-valued systems of logic was an attempt to refute determinism. When he developed the three-valued and n-valued logic, he employed these systems in his arguments against determinism. On the contrary, Łukasiewicz preferred the four-valued system of logic that is not suitable for a refutation of determinism in his latest period. It seems, however, that determinism still interested (...)
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  30. Péter on Church's Thesis, Constructivity and Computers.Mate Szabo - 2021 - In Liesbeth De Mol, Andreas Weiermann, Florin Manea & David Fernández-Duque (eds.), Connecting with Computability. Proceedings of Computability in Europe. pp. 434-445.
    Abstract The aim of this paper is to take a look at Péter's talk "Rekursivität und Konstruktivität" delivered at the Constructivity in Mathematics Colloquium in 1957, where she challenged Church's Thesis from a constructive point of view. The discussion of her argument and motivations is then connected to her earlier work on recursion theory as well as her later work on theoretical computer science.
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  31. Logical categories, signs, and elucidation in Frege.Wim Vanrie - 2021 - Dissertation, University of Ghent
    Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different categories, (...)
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  32. On Infinitesimals and Indefinitely Cut Wooden Sticks: A Chinese Debate on ‘Mathematical Logic’ and Russell’s Introduction to Mathematical Philosophy from 1925.Jan Vrhovski - 2021 - History and Philosophy of Logic 42 (3):262-280.
    In the years following Bertrand Russell's visit in China, fragments from his work on mathematical logic and the foundations of mathematics started to enter the Chinese intellectual world. While up...
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  33. ‘Qinghua School of Logic’: Mathematical Logic at Qinghua University in Peking, 1926–1945.Jan Vrhovski - 2021 - History and Philosophy of Logic 42 (3):247-261.
    Mathematical logic was first introduced to China in early 1920s. Although, the process of introduction was facilitated by the lectures of Bertrand Russel at Peking University in 1921 and continued...
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  34. On Reading Leśniewski.Sen Wong - 2021 - History and Philosophy of Logic 42 (2):160-179.
    Leśniewski is known for his pedantry and idiosyncratic notation, which make it extremely difficult to read and follow. As reading comes before understanding, this paper therefore attempts only one...
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  35. Weyl Reexamined: “Das Kontinuum” 100 Years Later.Arnon Avron - 2020 - Bulletin of Symbolic Logic 26 (1):26-79.
    Hermann Weyl was one of the greatest mathematicians of the 20th century, with contributions to many branches of mathematics and physics. In 1918 he wrote a famous book, “Das Kontinuum”, on the foundations of mathematics. In that book he described mathematical analysis as a ‘house built on sand’, and tried to ‘replace this shifting foundation with pillars of enduring strength’. In this paper we reexamine and explain the philosophical and mathematical ideas that underly Weyl’s system in “Das Kontinuum”, and show (...)
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  36. Adaptive Fregean Set Theory.Diderik Batens - 2020 - Studia Logica 108 (5):903-939.
    This paper defines provably non-trivial theories that characterize Frege’s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.
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  37. The Bad Company Objection and the Extensionality of Frege’s Logic.Vincenzo Ciccarelli - 2020 - Perspectiva Filosófica 47 (2):231-247.
    According to the Bad Company objection, the fact that Frege’s infamous Basic Law V instantiates the general definitional pattern of higher-order abstraction principles is a good reason to doubt the soundness of this sort of definitions. In this paper I argue against this objection by showing that the definitional pattern of abstraction principles – as extrapolated from §64 of Frege’s Grundlagen– includes an additional requirement (which I call the specificity condition) that is not satisfied by the Basic Law V while (...)
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  38. Where is ‘There is’ in ‘∃’?Richard Davies - 2020 - History and Philosophy of Logic 42 (1):44-59.
    The paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift ; Peirce’s ‘Algebra of Logic’ ; Peano’s ‘St...
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  39. Towards a Feminist Logic: Val Plumwood’s Legacy and Beyond.Maureen Eckert & Charlie Donahue - 2020 - In Dominic Hyde (ed.), Noneist Explorations II: The Sylvan Jungle - Volume 3 (Synthese Library, 432). Dordrecht: pp. 424-448.
    Val Plumwood’s 1993 paper, “The politics of reason: towards a feminist logic” (hence- forth POR) attempted to set the stage for what she hoped would begin serious feminist exploration into formal logic – not merely its historical abuses, but, more importantly, its potential uses. This work offers us: (1) a case for there being feminist logic; and (2) a sketch of what it should resemble. The former goal of Plumwood’s paper encourages feminist theorists to reject anti-logic feminist views. The paper’s (...)
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  40. Frege: A Philosophical Biography: Dale Jacquette, Cambridge: Cambridge University Press, 2019. xiv + 667 pp. Hardcover $45.00. ISBN: 978-0-521-86327-8. Ebook $36.00, ISBN 978-1-108-36504-8. [REVIEW]Wolfgang Kienzler - 2020 - History and Philosophy of Logic 41 (2):199-202.
    Volume 41, Issue 2, May 2020, Page 199-202.
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  41. The horizontal in Frege’s Begriffsschrift.Junyeol Kim - 2020 - Synthese 198 (12):11625-11644.
    This paper addresses an issue with the sign ‘⊢’ in Frege’s mature version of Begriffsschrift, i.e., the version in ‘Function and Concept’ and Grundgesetze. The sign is a performative for asserting in that writing down ‘⊢p’ is equivalent to asserting that p. Frege further says that writing ‘ p’ is also equivalent to identifying the reference of ‘p’ with the truth-value True. It looks as if he holds that asserting that p consists in identifying the True with the reference of (...)
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  42. Russell on Negative Judgement.Anssi Korhonen - 2020 - Topoi 39 (3):727-742.
    This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell put forth at different times: a dual relation theory ; a multiple relation theory ; a psychological theory of judgement. Four issues are singled out for a more detailed discussion: quality dualism versus quality monism, that is, the question whether judgement comes in two kinds, acceptance and rejection, or whether there is only one judgement-quality ; the (...)
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  43. Kurt Gödel's Anticipation of the Turing Machine: A Vitalistic Approach.Tim Lethen - 2020 - History and Philosophy of Logic 41 (3):252-264.
    In 1935/1936 Kurt Gödel wrote three notebooks on the foundations of quantum mechanics, which have now been entirely transcribed for the first time. Whereas a lot of the material is rather technical in character, many of Gödel's remarks have a philosophical background and concentrate on Leibnizian monadology as well as on vitalism. Obviously influenced by the vitalistic writings of Hans Driesch and his ‘proofs’ for the existence of an entelechy in every living organism, Gödel briefly develops the idea of a (...)
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  44. Certain Modern Ideas and Methods: “Geometric Reality” in the Mathematics of Charlotte Angas Scott.Jemma Lorenat - 2020 - Review of Symbolic Logic 13 (4):681-719.
    Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references (...)
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  45. Frege, Gottlob (1848-1925).Nikolay Milkov - 2020 - Bloomsbury Encyclopedia of Philosophers.
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  46. Aristotelés, Łukasiewicz a prázdné termíny.Zuzana Rybaříková - 2020 - Filosoficky Casopis 68 (4):605-622.
    In recent times there has been a shift in the interpretation of Aristotle’s logic. Many researchers have pointed out that the concept of existential import appears in Aristotle’s logic and philosophy, and that Aristotle worked with the concept of empty terms although his concept differs from that which is used in modern logic. Additionally, his search for the “culprits” of old and incorrect interpretation has been tied to the development of modern interpretation. Apart from the traditional concept of the logical (...)
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  47. Peirce's Maxim of Pragmatism: 61 Formulations.Jon Alan Schmidt - 2020 - Transactions of the Charles S. Peirce Society 56 (4):580-599.
    Peirce is best known as the founder of pragmatism, but his dissatisfaction with how others understood and appropriated it prompted him to rename his own doctrine “pragmaticism” and to compose several variants of his original maxim defining it, as well as numerous restatements and elaborations. This paper presents an extensive selection of such formulations, followed by analysis and commentary demonstrating that for Peirce the ultimate meaning of an intellectual concept is properly expressed as a conditional proposition about the deliberate, self-controlled (...)
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  48. Tractatus, Application and Use.Martin Stokhof & Jaap van der Does - 2020 - Open Philosophy 3 (1):770-797.
    The article argues for a contextualised reading of Wittgenstein’s Tractatus. It analyses in detail the role that use and application play in the text and how that supports a conception of transcendentality of logic that allows for contextualisation. The article identifies a tension in the text, between the requirement that sense be determinate and the contextual nature of application, and suggests that it is this tension that is a major driver of Wittgenstein’s later ideas.
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  49. On Jan Łukasiewicz's ‘The Principle of Contradiction and Symbolic Logic’.Adam Trybus & Bernard Linsky - 2020 - History and Philosophy of Logic 41 (2):183-190.
    This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of (...)
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  50. Proof vs Provability: On Brouwer’s Time Problem.Palle Yourgrau - 2020 - History and Philosophy of Logic 41 (2):140-153.
    Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies (...)
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