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  1. JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.John Corcoran - manuscript
    JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...)
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  2. Aristotle on Logical Consequence.Phil Corkum - manuscript
    Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...)
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  3. A Dialogue with I ! حوار مع أنا.Salah Osman - manuscript
    هل يمكن إذن أن أكون أنا لست أنا بانطباعات الزمان على جسدي وفكري؟ أليس لي جوهرٌ ثابتٌ تتبدل عليه الأعراض من حين إلى آخر، ومن ثم لا أفقد هويتي الحقيقية؟ لقد وُلدت منذ سنوات خلت، وتعلمت وعلمت أنني هو أنا، ويعلم المحيطون بي أنني هو أنا، بل يستطيع العلم المعاصر أن يُثبت أن لي تركيبًا جينيًا وراثيًا يميزني عن غيري، وأن لي بصمات أصابع وبصمة صوت لا تتطابق مع بصمات غيري، وسيحاسبني ربي يوم العرض عليه بوصفي شخصًا واحدًا هو أنا؛ (...)
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  4. Probability Semantics for Aristotelian Syllogisms.Niki Pfeifer & Giuseppe Sanfilippo - manuscript
    We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms (...)
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  5. How We Naturally Reason.Fred Sommers - manuscript
    In the 17th century, Hobbes stated that we reason by addition and subtraction. Historians of logic note that Hobbes thought of reasoning as “a ‘species of computation’” but point out that “his writing contains in fact no attempt to work out such a project.” Though Leibniz mentions the plus/minus character of the positive and negative copulas, neither he nor Hobbes say anything about a plus/minus character of other common logical words that drive our deductive judgments, words like ‘some’, ‘all’, ‘if’, (...)
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  6. Are Information, Cognition and the Principle of Existence Intrinsically Structured in the Quantum Model of Reality?Elio Conte - forthcoming - Open Systems and Information Dynamics.
    The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum and hydrogen atom.
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  7. Is Aristotle's Syllogistic a Logic?Phil Corkum - forthcoming - History and Philosophy of Logic.
    Much of the last fifty years of scholarship on Aristotle’s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory or formal ontology, a system concerned with general features of the world. In this paper, I will argue that this a misleading interpretative framework. The syllogistic is something sui generis: by our lights, it is neither clearly a logic, nor clearly a theory, but rather exhibits certain (...)
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  8. Dialectic After Plato and Aristotle.O. Yu Goncharko - forthcoming - History and Philosophy of Logic:1-6.
    The general content of the book is dedicated to the dialectical practices and their logical tools and techniques developed after Plato and Aristotle within the philosophical schools of the Hellenis...
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  9. Connexive Principles After a ‘Classical’ Turn in Medieval Logic.Spencer C. Johnston - forthcoming - History and Philosophy of Logic:1-13.
    The aim of this paper is to look at the arguments advanced by three Parisian arts masters about how to understand Prior Analytics II 4 and the more general discussion that medieval authors situate...
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  10. Kilwardby's 55th Lesson.Wolfgang Lenzen - forthcoming - Logic and Logical Philosophy:1.
    In “Lectio 55” of his Notule libri Priorum, Robert Kilwardby discussed various objections that had been raised against Aristotle’s Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, ∼p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (∼p → p) would be “absurd”. (...)
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  11. Analysis in Prior Analytics I.45.Igor Martinjak - forthcoming - History and Philosophy of Logic:1-25.
    I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetri...
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  12. Gersonides and Spinoza on God’s Knowledge of Universals and Particulars.Yitzhak Melamed - forthcoming - In Gad Freudenthal, David Wirmer & Ofer Elior (eds.), Gersonides Through the Ages.
  13. Exploring the Landscape of Relational Syllogistic Logics.Alex Kruckman & Lawrence S. Moss - 2021 - Review of Symbolic Logic 14 (3):728-765.
    This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences.
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  14. Extended Syllogistics in Calculus CL.Jens Lemanski - 2021 - Journal of Applied Logics 8 (2):557-577.
    Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...)
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  15. The Aftermath of Syllogism. Aristotelian Logical Argument From Avicenna to Hegel.J. Mendelsohn - 2021 - History and Philosophy of Logic 42 (2):189-191.
    This volume brings together nine previously unpublished, historically focused papers covering syllogistic logic and the notion of the syllogism. The book’s purpose, according to the editors, is ‘to...
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  16. Computability of Diagrammatic Theories for Normative Positions.Matteo Pascucci & Giovanni Sileno - 2021 - In Erich Schweighofer (ed.), Proceedings of JURIX 2021: 34th International Conference on Legal Knowledge and Information Systems. IOS Press. pp. 171-180.
    Normative positions are sometimes illustrated in diagrams, in particular in didactic contexts. Traditional examples are the Aristotelian polygons of opposition for deontic modalities (squares, triangles, hexagons, etc.), and the Hohfeldian squares for obligative and potestative concepts. Relying on previous work, we show that Hohfeld’s framework can be used as a basis for developing several Aristotelian polygons and more complex diagrams. Then, we illustrate how logical theories of increasing strength can be built based on these diagrams, and how those theories enable (...)
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  17. The Cretan Square.Jean-Yves Beziau & Jens Lemanski - 2020 - Logica Universalis 14 (1):1-5.
    This special issue is related to the 6th World Congress on the Square of Opposition which took place at the Orthodox Academy of Crete in November 2018. In this introductory paper we explain the context of the event and the topics discussed.
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  18. The Power of Logic, 6th Edition.Daniel Howard-Snyder, Frances Howard-Snyder & Ryan Wasserman - 2020 - New York: McGraw-Hill.
    This is a basic logic text for first-time logic students. Custom-made texts from the chapters is an option as well. And there is a website to go with text too.
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  19. Proof by Assumption of the Possible in Prior Analytics, 1.15; How Not to Blend Modal Frameworks.Doukas Kapantais & George Karamanolis - 2020 - History and Philosophy of Logic 41 (3):203-216.
    The present paper aims to show that the reconstruction of the formal framework of the proofs in Pr. An. 1.15, as proposed by Malink and Rosen 2013 (‘Proof by Assumption of the Possible in Prior Analytics 1.15’, Mind, 122, 953-85) is due to affront a double impasse. Malink and Rosen argue convincingly that Aristotle operates with two different modal frameworks, one as found in the system of modal logic presented in Prior Analytics 1.3 and 8-22, and one occurring in many (...)
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  20. Arthur Schopenhauer on Naturalness in Logic.Jens Lemanski & Hubert Martin Schüler - 2020 - In Language, Logic, and Mathematics in Schopenhauer. Cham, Schweiz: pp. 145-165.
    The question of naturalness in logic is widely discussed in today’s research literature. On the one hand, naturalness in the systems of natural deduction is intensively discussed on the basis of Aristotelian syllogistics. On the other hand, research on “natural logic” is concerned with the implicitly existing logical laws of natural language, and is therefore also interested in the naturalness of syllogistics. In both research areas, the question arises what naturalness exactly means, in logic as well as in language. We (...)
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  21. The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms.Marko Malink & Anubav Vasudevan - 2020 - Review of Symbolic Logic 13 (1):141-205.
    Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...)
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  22. Syllogistic Logic with Cardinality Comparisons, on Infinite Sets.Lawrence S. Moss & Selçuk Topal - 2020 - Review of Symbolic Logic 13 (1):1-22.
    This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: All x are y and Some x are y, There are at least as many x as y, and There are more x than y. Here x and y range over subsets of a given infinite set. Moreover, x and y may appear complemented, with the natural meaning. We formulate (...)
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  23. A Cube of Opposition for Predicate Logic.Jørgen Fischer Nilsson - 2020 - Logica Universalis 14 (1):103-114.
    The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.
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  24. Swyneshed, Aristotle and the Rule of Contradictory Pairs.Stephen Read - 2020 - Logica Universalis 14 (1):27-50.
    Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...)
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  25. 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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  26. A Class-Room Introduction to Logic.Desh Raj Sirswal - 2020 - Pehowa(Kurukshetra): CPPIS.
    This book is an outcome of my wordpress page “A Class-Room Introduction to Logic” This was prepared for the students of the paper entitled “Principles of Logic” in the Diploma-in-Reasoning Course of Department of Philosophy, Kurukshetra University, Kurukshetra, where I taught in the Diploma about four years and presently have an experience of teaching logic about 15 years. This book is beneficial for graduate students who have elementary logic course in their syllabus as well as for the general reader of (...)
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  27. Existential Import, Aristotelian Logic, and its Generalizations.Corina Strößner - 2020 - Logica Universalis 14 (1):69-102.
    The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal (...)
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  28. On the Historical Transformations of the Square of Opposition as Semiotic Object.Ioannis M. Vandoulakis & Tatiana Yu Denisova - 2020 - Logica Universalis 14 (1):7-26.
    In this paper, we would show how the logical object “square of opposition”, viewed as semiotic object, has been historically transformed since its appearance in Aristotle’s texts until the works of Vasiliev. These transformations were accompanied each time with a new understanding and interpretation of Aristotle’s original text and, in the last case, with a transformation of its geometric configuration. The initial textual codification of the theory of opposition in Aristotle’s works is transformed into a diagrammatic one, based on a (...)
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  29. What is the O-Corner Interpretation and Does It Save the Traditional Square of Opposition?Yavuz Recep Başoğlu - 2019 - Felsefe Arkivi - Archives of Philosophy 1 (51):37-59.
    To salvage traditional logic and traditional square of opposition from the problem of existential import, logicians have been offering solutions for centuries. In this paper, firstly it will be argued that as far as we know, the historically first solution proposed by Abelard in 11th century and by Seuren in 2002 is actually a version of the O-Corner Interpretation of traditional logic, which is generally attributed to the 14th-century logician Ockham. Secondly, it will be advocated that two systems of Abelard (...)
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  30. Aristotle’s Argument From Truth in Metaphysics Γ 4.Graham Clay - 2019 - Analysis 79 (1):17-24.
    Some of Aristotle’s statements about the indemonstrability of the Principle of Non-Contradiction (PNC) in Metaphysics Γ 4 merit more attention. The consensus seems to be that Aristotle provides two arguments against the demonstrability of the PNC, with one located in Γ 3 and the other found in the first paragraph of Γ 4. In this article, I argue that Aristotle also relies upon a third argument for the same conclusion: the argument from truth. Although Aristotle does not explicitly state this (...)
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  31. Dialectic, the Dictum de Omni and Ecthesis.Michel Crubellier, Mathieu Marion, Zoe McConaughey & Shahid Rahman - 2019 - History and Philosophy of Logic 40 (3):207-233.
    In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...)
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  32. Indirect Proof and Inversions of Syllogisms.Roy Dyckhoff - 2019 - Bulletin of Symbolic Logic 25 (2):196-207.
    By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.
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  33. Internal Negation and the Principles of Non-Contradiction and of Excluded Middle in Aristotle.Christopher Izgin - 2019 - History and Philosophy of Logic 41 (1):1-15.
    It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of (...)
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  34. Em direção a uma tradicão inferencialmente expressivista da silogística.Aislan Pereira - 2019 - Dissertation, UFPB, Brazil
    The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...)
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  35. Probability Propagation in Selected Aristotelian Syllogisms.Niki Pfeifer - 2019 - In G. Kern-Isberner & Zoran Ognjanović (eds.), ECSQARU 2019: Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Cham: Springer. pp. 419-431.
    This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set {.
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  36. Trespassers and Existential Import.Kai‐Yee Wong & Chi‐Ho Hung - 2019 - Thought: A Journal of Philosophy 8 (1):57-62.
    It is a received view of the post-Fregean predicate logic that a universal statement has no existential import and thus does not entail its particular (existential) counterpart. This paper takes issue with the view by discussing the trespasser case, which has widely been employed for supporting the view. The trespasser case in fact involves a shift of context. Properly understood, the case provides no support for the received view but rather suggests that we rethink the ‘quantity view’ of the existential (...)
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  37. Why Does Aristotle Defend the Principle of Non‐Contradiction Against its Contrary?Daniel Coren - 2018 - Philosophical Forum 49 (1):39-59.
    In his Metaphysics Γ.4, Aristotle defends the principle of non-contradiction (PNC). The PNC says that all contradictions are false. So if some contradictions are true, then PNC is false. Even if PNC’s contrary is false, PNC’s contradictory might still be true. But it’s been noted in the literature for over a century that Aristotle seems to be exclusively interested in attacking PNC’s contrary (‘All contradictions are true’) rather than PNC’s contradictory (‘Some contradictions are true’). So his defense of PNC seems (...)
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  38. Combinatorial Bitstring Semantics for Arbitrary Logical Fragments.Lorenz6 Demey & Hans5 Smessaert - 2018 - Journal of Philosophical Logic 47 (2):325-363.
    Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...)
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  39. Probabilistic Semantics for Categorical Syllogisms of Figure II.Niki Pfeifer & Giuseppe Sanfilippo - 2018 - In D. Ciucci, G. Pasi & B. Vantaggi (eds.), Scalable Uncertainty Management. Cham, Switzerland: pp. 196-211.
    A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is not informative, (...)
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  40. 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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  41. Rejection in Łukasiewicz's and Słupecki's Sense.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...)
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  42. Rejection in Łukasiewicz's and Słupecki' Sense.Urszula Wybraniec-Skardowska - 2018 - Lvov-Warsaw School. Past and Present.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...)
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  43. New Dimensions of the Square of Opposition.Jean-Yves Béziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently (...)
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  44. Using Syllogistics to Teach Metalogic.Lorenz Demey - 2017 - Metaphilosophy 48 (4):575-590.
    This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...)
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  45. De Logische Geometrie van Johannes Buridanus' Modale Achthoek.Lorenz Demey & Philipp Steinkrüger - 2017 - Tijdschrift Voor Filosofie 79 (2):217-238.
    In order to elucidate his logical analysis of modal quantified propositions (e.g. ‘all men are necessarily mortal’), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that Buridan’s modal octagon precisely captures (...)
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  46. Is There A Logic of the Ineffable? Or, How Is It Possible to Talk About the Unsayable?Stephen R. Palmquist - 2017 - In Nahum Brown & J. Aaron Simmons (eds.), Contemporary Debates in Negative Theology and Philosophy. Springer. pp. 71-80.
    This chapter defends a single, fixed, definite answer to the question: Is there a logic that governs the unsayable? The proposed answer is: “Yes, and no. Or yes-but-not-yes. And/or yes-no.” Each component of this answer is examined and used to generate three laws of what I call “synthetic logic”, which correspond directly to the laws of classical (Aristotelian) logic: the law of contradiction (“A=-A”), the law of non-identity (“A≠A”), and the law of the included middle (“-(Av-A)”). We can talk about (...)
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  47. Square of Opposition Under Coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, Alessandro Giordani, B. Vantaggi, M. Gagolewski, M. Á Gil, P. Grzegorzewski & O. Hryniewicz (eds.), Soft Methods for Data Science. Cham, Switzerland: pp. 407-414.
    Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...)
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  48. The Square of Opposition: A Cornerstone of Thought.Jean-Yves Beziau & Gianfranco Basti (eds.) - 2016 - Basel, Switzerland: Birkhäuser.
    This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.
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  49. Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
    In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...)
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  50. The Interaction Between Logic and Geometry in Aristotelian Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Diagrammatic Representation and Inference, Diagrams 9781:67 - 82.
    © Springer International Publishing Switzerland 2016. We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation and to all Aristotelian families of 6-formula fragments that are closed under negation.
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