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The KK Principle and the Strong Notion of Knowledge: Hintikka’s Arguments for KK Revisited History and Philosophy of Logic (IF 0.5) Pub Date : 2024-02-14 Chen Bo
In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, Kp→KKp) principle (KK for short). However, his system of epis...
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Meditating and Inquiring with Imagination: Leibniz, Lambert, and Kant on the Cognitive Value of Diagrams History and Philosophy of Logic (IF 0.5) Pub Date : 2024-02-07 Lucia Oliveri
Reasoning with diagrams is considered to be a peculiar form of reasoning. Diagrams are often associated with imagistic representations conveyed by spatial arrangements of lines, points, figures, or...
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Sign-inferences in Greek and Buddhist Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2024-01-16 Andrew Schumann
The Yogācāra school of logic developed a theory of sign-inferences that has many features of the Stoic and Epicurean logical teachings with small inclusions of Aristotelian ideas. In the Nyāyabindu...
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Leksykon logików polskich. 1900–1939 History and Philosophy of Logic (IF 0.5) Pub Date : 2024-01-07 Gabriela Besler, Sebastian Stokłosa
Published in History and Philosophy of Logic (Ahead of Print, 2024)
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The Place of Reduction in Aristotle's Prior Analytics History and Philosophy of Logic (IF 0.5) Pub Date : 2024-01-04 George Boger
Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects...
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The Centrality of Simplicity in Frege's Philosophy History and Philosophy of Logic (IF 0.5) Pub Date : 2023-12-04 Jim Hutchinson
It is widely recognized that Frege's systematic conception of science has a major impact on his work. I argue that central to this conception and its impact is Frege's Simplicity Requirement that a...
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A Deductive System for Boole’s ‘The Mathematical Analysis of Logic’ and Its Application to Aristotle’s Deductions History and Philosophy of Logic (IF 0.5) Pub Date : 2023-11-29 G. A. Kyriazis
George Boole published the pamphlet The Mathematical Analysis of Logic in 1847. He believed that logic should belong to a universal mathematics that would cover both quantitative and nonquantitativ...
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Review Article History and Philosophy of Logic (IF 0.5) Pub Date : 2023-11-20 E. Ficara
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Belief and Counterfactuals: A Study in Means-end Philosophy History and Philosophy of Logic (IF 0.5) Pub Date : 2023-11-16 G. Haas
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Cavaillès on Gentzen ‘dans son poêle’: A Brief Historical Note History and Philosophy of Logic (IF 0.5) Pub Date : 2023-09-20 Peter Milne
In a letter to Lautman, Cavaillès speaks of Gentzen ‘dans son poêle’ in Göttingen. The translators of the English edition of Menzler-Trott's biography of Gentzen miss the allusion to Descartes.
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Aristotle’s Syllogistic Underlying Logic: His Model with His Proofs of Soundness and Completeness History and Philosophy of Logic (IF 0.5) Pub Date : 2023-09-15 C. G. King
Published in History and Philosophy of Logic (Vol. 44, No. 4, 2023)
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Timpler, Clemens. Logicae systema methodicum Libris V. comprehensum, in quo universus bene disserendi et sciendi modus, tam generatim, quam speciatim, per praecepta et quaestiones breviter ac dilucide explicatur & probatur History and Philosophy of Logic (IF 0.5) Pub Date : 2023-09-05 M. Walter
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Hegel’s Logic and Metaphysics History and Philosophy of Logic (IF 0.5) Pub Date : 2023-08-30 C. Yang
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Logic in Question. Talks from the Annual Sorbonne Logic Workshop (2011–2019) History and Philosophy of Logic (IF 0.5) Pub Date : 2023-08-30 G. Guibert, B. Sauzay
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Aristotle's Proofs Through the Impossible in Prior Analytics 1.15 History and Philosophy of Logic (IF 0.5) Pub Date : 2023-08-17 Riccardo Zanichelli
In Prior Analytics 1.15, Aristotle attempts to give a proof through the impossible of Barbara, Celarent, Darii, and Ferio with an assertoric first premiss, a contingent second premiss, and a possib...
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Arthur Prior's Proofs of the Necessities of Identity and Difference History and Philosophy of Logic (IF 0.5) Pub Date : 2023-08-11 Nils Kürbis
This paper draws attention to a proof of the necessity of identity given by Arthur Prior. In its simplicity, it is comparable to a proof of Quine's, popularised by Kripke, but it is slightly different. Prior's Polish notation is transcribed into a more familiar idiom. Prior's proof is followed by a proof of the necessity of difference, possibly the first such proof in the literature, which is also
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An Enhanced Account of Relative Identity: Double-Reference Starting Point and Dual-Track Feature History and Philosophy of Logic (IF 0.5) Pub Date : 2023-07-26 Bo Mou
This article gives a holistic re-examination of the semantic content and syntactic structure of the concept of relative identity: it suggests and explains an expanded and enhanced dual-track characterization of relative identity. It is expanded in this sense: its due coverage is not narrowly restricted to the equal-status case of identity statements (the symmetric case for identity simplex) but also
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Logicism and Principle of Tolerance: Carnap’s Philosophy of Logic and Mathematics* History and Philosophy of Logic (IF 0.5) Pub Date : 2023-07-27 Stefano Domingues Stival
In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such dev...
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Connexivity in Aristotle’s Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2023-07-11 Fabian Ruge
At APr 2.4 57a36–13, Aristotle presents a notorious reductio argument in which he derives the claim ‘If B is not large, B is large’ and calls that result impossible. Aristotle is thus committed to ...
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An Axiomatic System Based on Ladd-Franklin's Antilogism History and Philosophy of Logic (IF 0.5) Pub Date : 2023-07-06 Fangzhou Xu
This paper sketches the antilogism of Christine Ladd-Franklin and historical advancement about antilogism, mainly constructs an axiomatic system Atl based on first-order logic with equality and the wholly-exclusion and not-wholly-exclusion relations abstracted from the algebra of Ladd-Franklin, with soundness and completeness of Atl proved, providing a simple and convenient tool on syllogistic reasoning
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Brouwer's Intuition of Twoity and Constructions in Separable Mathematics History and Philosophy of Logic (IF 0.5) Pub Date : 2023-06-05 Bruno Bentzen
ABSTRACT My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's
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Dashtakī's Solution to the Liar Paradox: A Synthesis of the Earlier Solutions Proposed by Ṭūsī and Samarqandī History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-29 Mohammad Saleh Zarepour
Ṣadr al-Dīn al-Dashtakī (d. 1498) has proposed a solution to the liar paradox according to which the liar sentence is a self-referential sentence in which the predicate ‘false’ is iterated. Discussing the conditions for the truth-aptness of the sentences with nested and iterated instances of the predicates ‘true’ and/or ‘false’, Dashtakī argued that the liar sentence is not truth-apt at all. In the
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Arthur N. Prior on the Labours of Ł3 Conjunctions History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-25 Jeremiah Joven Joaquin, Peter Eldridge-Smith
ABSTRACT In ‘Many-valued Logics’, a lecture broadcast over New Zealand's public radio in 1957, Arthur N. Prior (1914–1969) complained that conjunctions are put ‘to something like forced labour’ in Łukasiewicz's three-valued semantics, Ł3. In this paper, we discuss what Prior might have meant by this.
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John Eliot's Logick Primer: A Bilingual English-Massachusett Logic Textbook History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-18 Sara L. Uckelman
In 1672 John Eliot, English Puritan educator and missionary to New England, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof (Eliot 1672) The Logick Primer: Some Logical Notions to Initiate the INDIANS in the Knowledge of the Rule of Reason; and to Know How to Make Use Thereof , Cambridge, MA: Marmaduke
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Form, Formality, Formalism in Hegel’s Dialectic-Speculative Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Angelica Nuzzo
This essay addresses the general systematic question underlying any project of ‘formalization’ of Hegel’s dialectic-speculative logic, namely, the question concerning the peculiar concept of logical ‘form’ and the connected type of ‘formalism’ at stake in a logic that is, programmatically and innovatively within the historical tradition, a ‘dialectic-speculative’ logic.
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Introduction: The Formalization of Dialectics History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Elena Ficara, Graham Priest
The idea at the basis of this special issue is that reopening the old debate about the logical status of Hegel's dialectics is extremely interesting, for various reasons. The first reason is that a new Hegel is circulating, nowadays, in the philosophical literature, with specific reference to Hegel's dialectical logic and its relation to the history and philosophy of logic. This development deserves
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Hegelian Conjunction, Hegelian Contradiction History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Jc Beall, Elena Ficara
Understanding what is the strictly formal import of Hegel's view is something on which few analytic philosophers have seen time worth spending. Still in our view there is enough in Hegel's work to suggest that a formal account of his dialectial process might be profitable both for better understanding Hegel's ideas and for introducing a new sort of glutty logic. The focus of our analysis is Hegel's
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Hegel’s Interpretation of the Sorites History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Franca d’Agostini
ABSTRACT Hegel’s approach to soritical arguments (as well as to paradoxes in general) can be read as a kind of conjunctive paraconsistency: the ‘explosive’ effect of contradictions is avoided by assuming ‘the unity of the opposites’, so that contradictory conjunctions are not simplifiable. The paper reconsiders what Hegel says about the Sorites and justifies the conjunctive interpretation. The first
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Hegel’s Logic of Self-Predication History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Gregory S. Moss
ABSTRACT Hegel’s Doctrine of the Concept advances a theory of conceptual determinacy. As I will demonstrate, Hegel’s theory of conceptual determinacy leads him to endorse self-predication and existential implication as features endemic to conceptual content. I first demonstrate some features of this logic, and some of its entailments. Following the reconstruction of Hegel’s logic of self-predication
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A Lack of Form in Hegel’s Logic? Hegel and the Trans-classical Logic of Gotthard Günther History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Valentin Pluder
Gotthard Günther's early work is inspired by Hegel's logic. Both share the view that the forms of ‘classical logic’ are insufficient to capture essential aspects of thought. However, while Hegel rules out formalization for his dialectical logic, Günther attributes this to the fact that Hegel's thought itself is still bound to the forms of a classical logic. Günther thus develops a trans-classical logic
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Intuitionist and Classical Dimensions of Hegel’s Hybrid Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2023-05-15 Paul Redding
Hegel interpreters commonly reject attempts to situate Hegel’s logic in relation to modern movements. Appealing to his criticisms of the logic of Verstand or mere understanding with its fixed logical structure, Hegel’s logic, it is pointed out, was a logic of Vernunft or reason—a logic more at home in the thought of Plato and Aristotle than in modern mathematical forms. Contesting this implied dichotomy
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The Logical Writings of Karl Popper History and Philosophy of Logic (IF 0.5) Pub Date : 2023-04-26 Constantin C. Brîncuş
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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The Arithmetical dictum History and Philosophy of Logic (IF 0.5) Pub Date : 2023-04-04 Paolo Maffezioli, Riccardo Zanichelli
Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the r...
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Tractatus 6 Reconsidered: An Algorithmic Alternative to Wittgenstein's Trade-Off History and Philosophy of Logic (IF 0.5) Pub Date : 2023-03-21 A. Roman, J. Gomułka
Wittgenstein's conception of the general form of a truth function given in thesis 6 can be presented as a sort of a trade-off: the author of the Tractatus is unable to reconcile the simplicity of his original idea of a series of forms with the simplicity of his generalisation of Sheffer's stroke; therefore, he is forced to sacrifice one of them. As we argue in this paper, the choice he makes – to weaken
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Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism History and Philosophy of Logic (IF 0.5) Pub Date : 2023-03-17 M. Rescorla
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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The Modal Logic of John Fabri of Valenciennes (c. 1500). A Study in Token-Based Semantics History and Philosophy of Logic (IF 0.5) Pub Date : 2023-03-01 Ana María Mora-Márquez
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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A Formal Explication of Blanchette's Conception of Fregean Consequence History and Philosophy of Logic (IF 0.5) Pub Date : 2023-03-01 Günther Eder
Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is ‘semantically laden’ and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas
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Language, Logic, and Mathematics in Schopenhauer History and Philosophy of Logic (IF 0.5) Pub Date : 2023-02-06 Christopher Ryan
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Anthologie de la calculabilité History and Philosophy of Logic (IF 0.5) Pub Date : 2023-02-06 P. Cantù
Published in History and Philosophy of Logic (Ahead of Print, 2023)
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Leśniewskian Ontology with Many-argument Predication History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-30 Jacek Paśniczek
ABSTRACT Leśniewskian Ontology (LO) is a system in which the basic subject-predicate formula takes the form of a ϵϵ b and express one-argument predication, e.g. John is a student. In LO’s language, there is no many-argument form of predication given that would allow for the structural expression of, for example, the sentence John is Anne’s son. In this article, a simple and natural extension of LO
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Burhān al-dīn Nasafī as the Author of Al-Manṭiq al-kabīr (MS Aḥmad iii, no. 3401) History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-24 Asadollah Fallahi
Recently, in ‘An inquiry on Fakhr al-Dīn Rāzī’s authorship of Al-manṭiq al-kab ι¯r (MS Aḥmad iii, no. 3401)’, we refuted the quite common view among historians of Arabic logic as to attribute Al-manṭiq al-kab ι¯r (Major [book on] logic) to Fakhr al-dīn Rāzī; however, in that paper, we could not identify the real author of the book. In this paper, we try to show that Al-manṭiq al-kab ι¯r was written
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Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-18 Amirouche Moktefi, Fabien Schang
The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show...
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Wahrheit und logisches Schließen History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-12 W. Stelzner
Published in History and Philosophy of Logic (Vol. 44, No. 4, 2023)
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Carnapian Lessons for Anti-Exceptionalism about Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-11 Jonas Rafael Becker Arenhart, Ivan Ferreira da Cunha
This paper aims at disentangling two distinct problems in present philosophy of logic: the a priori/a posteriori divide and the theory choice problem. A confusion of these problems is present in the heart of current anti-exceptionalism about logic, as the use of a posteriori methods is identified with theory choice. We illustrate how the division may be preserved in a version of anti-exceptionalism
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A. Benitez, La Silogística de Aristóteles History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-11 M. Dahlquist
Published in History and Philosophy of Logic (Vol. 44, No. 4, 2023)
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Forms of Carroll’s Paradox in Post-Classical Arabic Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2023-01-04 Dustin D. Klinger
Arabic logicians in the thirteenth century discussed a set of arguments raised by the theologian Fakhr al-Dīn al-Rāzī (d. 1210) that in some respects closely resembles Carroll’s paradox. Roughly, the paradox states that we can never reach a conclusion from a set of premises without incurring an infinite regress. The present article presents and discusses Rāzī’s formulation of the problem with syllogistic
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Bolzano on Bolzano: A Hitherto Unknown Announcement of Bolzano’s Beyträge History and Philosophy of Logic (IF 0.5) Pub Date : 2022-12-28 Elías Fuentes Guillén
In 1817, in the preface to his Rein analytischer Beweis, Bernard Bolzano revealed that he had decided to postpone the publication of any subsequent instalment of his Beyträge zu einer begründeteren...
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Note on the Negative Approach of al-Shahīd al-Thānī Towards Logic in al-Iqtiṣād wa al-Irshād History and Philosophy of Logic (IF 0.5) Pub Date : 2022-12-21 Mahmood Zeraatpisheh
Aversion towards logic is a characteristic feature of the Islamic traditionalists. There is in fact a history of opposition to logic in Islam. As any other areas of history, here also the correct picture will not be achieved unless all of the pieces are put together. In what follows, I am going to shed light on a chapter written by Zayn al-Dīn al-ʿĀmilī (d. 966/1558), the Twelver Shīʿī Scholar better
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Prior’s big Y and the Idea of Branching Time History and Philosophy of Logic (IF 0.5) Pub Date : 2022-12-19 Peter Øhrstrøm, Manuel González
In his famous letter to A. N. Prior dated 3 September 1958, Saul Kripke suggested the use of branching time in temporal logic. In this paper, however, it is argued that Prior worked with an idea close to the notion of branching time (‘the big Y’) already the year before he received Kripke’s letter. It is likely that Prior’s findings based on this early study can explain why Prior so quickly accepted
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Russell Contra Sense/Reference, the ‘Mont Blanc’ Correspondence History and Philosophy of Logic (IF 0.5) Pub Date : 2022-12-12 Clare Hay
It is argued that Russell before 1905 saw no value in Frege's sense/reference distinction. This is clearest in the Mont Blanc correspondence. It is argued that Russell and Frege failed to engage be...
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How to Distinguish Simple Objectless Ideas History and Philosophy of Logic (IF 0.5) Pub Date : 2022-12-09 Jan Claas
Bernard Bolzano offers a criterion of individuation for ideas, according to which ideas are distinct if and only if they represent different objects or are composed differently. It fails to individ...
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John von Neumann’s Discovery of the 2nd Incompleteness Theorem History and Philosophy of Logic (IF 0.5) Pub Date : 2022-11-28 Giambattista Formica
ABSTRACT Shortly after Kurt Gödel had announced an early version of the 1st incompleteness theorem, John von Neumann wrote a letter to inform him of a remarkable discovery, i.e. that the consistency of a formal system containing arithmetic is unprovable, now known as the 2nd incompleteness theorem. Although today von Neumann’s proof of the theorem is considered lost, recent literature has explored
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Kant’s Die falsche Spitzfindigkeit and Proof-theoretic Semantics History and Philosophy of Logic (IF 0.5) Pub Date : 2022-11-17 Tiago Rezende de Castro Alves
According to Schroeder-Heister 2018, proof-theoretic semantics is ‘an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof
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Lvov-Warsaw School. Past and Present Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2022-09-19 K. Gan-Krzywoszyńska, P. Leśniewski
Published in History and Philosophy of Logic (Vol. 44, No. 3, 2023)
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Ramsey's Lost Counterfactual History and Philosophy of Logic (IF 0.5) Pub Date : 2022-09-19 Caterina Sisti
In contemporary works on conditionals, the Ramsey test is a procedure for the evaluation of conditional sentences. There are several versions of the test, all inspired by a footnote by the British philosopher and mathematician Frank Ramsey, in his General Propositions and Causality. However, no study on Ramsey's own account of conditionals has been put forth so far. Furthermore, the footnote seems
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Modal Homotopy Type Theory. The Prospect of a New Logic for Philosophy History and Philosophy of Logic (IF 0.5) Pub Date : 2022-09-05 A. Klev, C. Zwanziger
Published in History and Philosophy of Logic (Vol. 44, No. 3, 2023)
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A Logic for Aristotle's Modal Syllogistic History and Philosophy of Logic (IF 0.5) Pub Date : 2022-08-26 Clarence Lewis Protin
ABSTRACT We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic, it is also a logic of terms that admits a (sound) extensional semantics involving possible states-of-affairs in a given world. Applied to the analysis of Aristotle's modal syllogistic as found in the Prior Analytics
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The Bounds of Transcendental Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2022-07-27 S. Kovač
Published in History and Philosophy of Logic (Vol. 44, No. 1, 2023)
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Knowledge and the Philosophy of Number History and Philosophy of Logic (IF 0.5) Pub Date : 2022-07-06 Richard Lawrence
Published in History and Philosophy of Logic (Vol. 43, No. 4, 2022)
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Psychology and Time in Boole’s Logic History and Philosophy of Logic (IF 0.5) Pub Date : 2022-07-05 Andrew Stone
In the Laws of Thought, Boole establishes a theory of secondary propositions based upon the notion of time. This temporal interpretation of secondary propositions has historically been met with wide disapproval and is usually dismissed in the modern literature as a philosophical non-starter. What was Boole thinking? This paper attempts to give an answer to this question. Specifically, it provides an