Results for 'syllogism'

198 found
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  1. Division, Syllogistic, and Science in Prior Analytics I.31.Justin Vlasits - forthcoming - Ergo: An Open Access Journal of Philosophy.
    In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...)
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  2. Stoic Syllogistic.Susanne Bobzien - 1996 - Oxford Studies in Ancient Philosophy 14:133-92.
    ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental (...)
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  3. Conditionals, Modals, and Hypothetical Syllogism.Lee Walters - 2014 - Thought: A Journal of Philosophy 3 (1):90-97.
    Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.
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  4. What Is a Perfect Syllogism in Aristotelian Syllogistic?Theodor Ebert - 2015 - Ancient Philosophy 35 (2):351-374.
    The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status (...)
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  5. Syllogistic reasoning as a ground for the content of judgment: A line of thought from Kant through Hegel to Peirce.Preston Stovall - 2020 - European Journal of Philosophy 29 (4):864-886.
    European Journal of Philosophy, Volume 29, Issue 4, Page 864-886, December 2021.
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  6. Why Hypothetical Syllogism is Invalid for Indicative Conditionals.Moti Mizrahi - 2013 - Thought: A Journal of Philosophy 2 (1):40-43.
    In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism with indicative conditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicative conditionals.
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  7. Aristotle’s assertoric syllogistic and modern relevance logic.Philipp Steinkrüger - 2015 - Synthese 192 (5):1413-1444.
    This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises (...)
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  8. Material cause and syllogistic necessity in posterior analytics II 11.Paolo Fait - 2019 - Manuscrito 42 (4):282-322.
    The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula ‘given what things, is it necessary for this to be’ [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that (...)
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  9. Against Hypothetical Syllogism.Lee Walters - 2014 - Journal of Philosophical Logic 43 (5):979-997.
    The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical (...)
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  10. (1 other version)Pre-Stoic Hypothetical Syllogistic in Galen.Susanne Bobzien - 2002 - The Bulletin of the Institute of Classical Studies:57-72.
    ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.
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  11. Aristotle’s Syllogistic and Core Logic.Neil Tennant - 2014 - History and Philosophy of Logic 35 (2):120-147.
    I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is (...)
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  12. Aristotle's syllogism as simple as ABC by new transformed Raval's notations.Ravinder Kumar Singh - manuscript
    Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S (...)
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  13. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  14. The Dialectical Syllogism in Aristotle’s Topics.Fernando Martins Mendonça - 2023 - Archai: Revista de Estudos Sobre as Origens Do Pensamento Ocidental 33:1-34.
    The purpose of this paper is an attempt to delimitate what the dialectical syllogism looks like in Aristotle’s Topics. Aristotle never gave an example of a dialectical syllogism, but we have some clues spread over books I and VIII of the Topics which make it possible to understand at least what within a dialectical debate is a dialectical syllogism. The interpretation advanced here distinguishes the logical order of the dialectical argumentation from the order of the debate. This (...)
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  15. Aristotle's Theory of the Assertoric Syllogism.Stephen Read - manuscript
    Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was (...)
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  16. From Syllogism to Predicate Calculus.Thomas J. McQuade - 1994 - Teaching Philosophy 17 (4):293-309.
    The purpose of this paper is to outline an alternative approach to introductory logic courses. Traditional logic courses usually focus on the method of natural deduction or introduce predicate calculus as a system. These approaches complicate the process of learning different techniques for dealing with categorical and hypothetical syllogisms such as alternate notations or alternate forms of analyzing syllogisms. The author's approach takes up observations made by Dijkstrata and assimilates them into a reasoning process based on modified notations. The author's (...)
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  17. Aristotle's definition of syllogism in Prior Analytics 24b18-20.Lucas Angioni - manuscript
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  18. Aristotle’s Akrasia: The Role of Potential Knowledge and Practical Syllogism.Imge Oranli - 2018 - Proceedings of the XXIII World Congress of Philosophy 2 (2):233-238.
    In Nicomachean Ethics VII Aristotle describes akrasia as a disposition. Taking into account that it is a disposition, I argue that akrasia cannot be understood on an epistemological basis alone, i.e., it is not merely a problem of knowledge that the akratic person acts the ways he does, but rather one is akratic due to a certain kind of habituation, where the person is not able to activate the potential knowledge s/he possesses. To stress this point, I focus on the (...)
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  19. Remarks on Axiomatic Rejection in Aristotle’s Syllogistic.Piotr Kulicki - 2002 - Studies in Logic and Theory of Knowledge 5:231-236.
    In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show that any (...)
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  20. The Normalization Theorem for the First-Order Classical Natural Deduction with Disjunctive Syllogism.Seungrak Choi - 2021 - Korean Journal of Logic 2 (24):143-168.
    In the present paper, we prove the normalization theorem and the consistency of the first-order classical logic with disjunctive syllogism. First, we propose the natural deduction system SCD for classical propositional logic having rules for conjunction, implication, negation, and disjunction. The rules for disjunctive syllogism are regarded as the rules for disjunction. After we prove the normalization theorem and the consistency of SCD, we extend SCD to the system SPCD for the first-order classical logic with disjunctive syllogism. (...)
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  21. Aristotle’s Modal Syllogistic. [REVIEW]Lucas Angioni - 2018 - Ancient Philosophy 38 (1):211-216.
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  22. Review: Aristotle’s Syllogistic Underlying Logic: His Model with His Proofs of Soundness and Completeness. [REVIEW]C. G. King - 2023 - History and Philosophy of Logic (4):1–3.
    This book presents a (new) attempt to apply the notion of an underlying logic to Aristotle’s Organon and certain passages of the Metaphysics. The author situates his approach as part of a ‘deductio...
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  23. Aristotle's Syllogistic Model of Knowledge and the Biological Sciences: Demonstrating Natural Processes.Mariska Leunissen - 2010 - Apeiron 43 (2-3):31-60.
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  24.  65
    A Study of the Metatheory of Assertoric Syllogistic.Maristela Rocha - 2023 - Logica Universalis 17 (3):347-371.
    We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a calculus of natural deduction. (...)
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  25. Mereology in Aristotle's Assertoric Syllogistic.Justin Vlasits - 2019 - 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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  26. Review of Marko Malink, Aristotle's Modal Syllogistic[REVIEW]Jacob Rosen - 2014 - Notre Dame Philosophical Reviews.
    Malink’s interpretation is designed to validate Aristotle’s claims of validity and invalidity of syllogistic-style arguments, as well as his conversion claims. The remaining sorts of claims in Aristotle's text are allowed to fall out as they may. Thus, not all of Aristotle’s examples turn out correct: on some occasions, Aristotle claims that a given pair of terms yields a true (false) sentence of a given type although, under Malink’s interpretation, the sentence in question is false (true). Similarly, some of Aristotle’s (...)
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  27. On a Minimal System of Aristotle’s Syllogistic.Piotr Kulicki - 2011 - Bulletin of the Section of Logic 40 (3/4):129-145.
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  28. Opuscula logica. 2. The tripropositional bivalent level (3L2) and its relationship with the aristotelic syllogistic.Gabriel Garduño-Soto - 2008 - Mexico, DF, MEXICO: Author's edition.
    In this fragment of Opuscula Logica it is displayed an arithmetical treatment of the aristotelic syllogisms upon the previous interpretations of Christine Ladd-Franklin and Jean Piaget. For the first time, the whole deductive corpus for each syllogism is presented in the two innovative modalities first proposed by Hugo Padilla Chacón. A. The Projection method (all the possible expressions that can be deduced through the conditional from a logical expression) and B. The Retrojection method (all the possible valid antecedents or (...)
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  29. Three-membered domains for Aristotle's syllogistic.Fred Johnson - 1991 - Studia Logica 50 (2):181 - 187.
    The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.
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  30.  87
    Aristotle on Hypothetical Arguments and the Completeness of the Syllogistic.Tal Glezer - 2007 - Ancient Philosophy 27 (2):323-334.
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  31. A Critical Examination of Ibn-Sina’s Theory of the Conditional Syllogism.Zia Movahed - 2009 - Sophia Perennis 1:5-22.
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  32. Cartesian analyticity.Jesús A. Díaz - 1988 - Southern Journal of Philosophy 26 (1):47-55.
    The syllogism and the predicate calculus cannot account for an ontological argument in Descartes' Fifth Meditation and related texts. Descartes' notion of god relies on the analytic-synthetic distinction, which Descartes had identified before Leibniz and Kant did. I describe how the syllogism and the predicate calculus cannot explain Descartes' ontological argument; then I apply the analytic-synthetic distinction to Descartes’ idea of god.
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  33. The objective Bayesian conceptualisation of proof and reference class problems.James Franklin - 2011 - Sydney Law Review 33 (3):545-561.
    The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...)
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  34. Aristotle's Many-sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...)
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  35. Aristotle on “dunatos” as a label for imperfect syllogisms.Lucas Angioni - forthcoming - In Graziana Ciola & Milo Crimi (eds.), Validity Throughout History. Philosophia Verlag.
    This paper discusses the following question: why was the term “dunatos” (“possible”) employed by Aristotle as an alternative label for imperfect syllogisms in his discussion of assertoric syllogistic? My answer ascribes to Aristotle a bottom up perspective, in which he stresses what is necessary in the premise-pairs to attain target conclusions of a given form within a given figure. I argue that “dunatos” is employed by Aristotle to stress that an imperfect syllogism is always one of the possible options (...)
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  36. Causation and intensionality in Aristotelian Logic.Srećko Kovač - 2013 - Studia Philosophiae Christianae 49 (2):117-136.
    We want to show that Aristotle’s general conception of syllogism includes as its essential part the logical concept of necessity, which can be understood in a causal way. This logical conception of causality is more general then the conception of the causality in the Aristotelian theory of proof (“demonstrative syllogism”), which contains the causal account of knowledge and science outside formal logic. Aristotle’s syllogistic is described in a purely intensional way, without recourse to a set-theoretical formal semantics. It (...)
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  37. Systemy sylogistyki dowodowej.Piotr Kulicki - 2010 - Roczniki Filozoficzne 58 (1):139-154.
    Aristotle in Analytica Posteriora presented a notion of proof as a special case of syllogism. In the present paper the remarks of Aristotle on the subject are used as an inspiration for developing formal systems of demonstrative syllogistic, which are supposed to formalize syllogisms that are proofs. We build our systems in the style of J. Łukasiewicz as theories based on classical propositional logic. The difference between our systems and systems of syllogistic known from the literature lays in the (...)
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  38. Zur Formulierung prädikativer Aussagen in den logischen Schriften des Aristoteles.Theodor Ebert - 1977 - Phronesis 22 (2):123 - 145.
    Why does Aristotle not use the copulative wording for categorical propositions, but instead the clumsier terminological formulations (e. g. the B belongs to every A) in his syllogistic? The proposed explanations by Alexander, Lukasiewicz and Patzig: Aristotle wants to make clear the difference between subject and predicate, seems to be insufficient. In quantified categorical propositions, this difference is always sufficiently clear by the use of the pronouns going with the subject expressions. Aristotle opts for the terminological wording because in premiss (...)
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  39. On the Origin of Venn Diagrams.Amirouche Moktefi & Jens Lemanski - 2022 - Axiomathes 32 (3):887-900.
    In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came (...)
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  40. Demonstração, silogismo e causalidade.Lucas Angioni - 2014 - In Lógica e Ciência em Aristóteles. Phi. pp. 61-120.
    This chapter argues in favour of three interrelated points. First, I argue that demonstration (as expression of scientific knowledge) is fundamentally defined as knowledge of the appropriate cause for a given explanandum: to have scientific knowledge of the explanandum is to explain it through its fully appropriate cause. Secondly, I stress that Aristotle’s notion of cause has a “triadic” structure, which fundamentally depends on the predicative formulation (or “regimentation”) of the explanandum. Thirdly, I argue that what has motivated Aristotle to (...)
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  41. Platonic Division and the Origins of Aristotelian Logic.Justin Vlasits - 2017 - Dissertation, University of California, Berkeley
    Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was (...)
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  42.  58
    Proofs of valid categorical syllogisms in one diagrammatic and two symbolic axiomatic systems.Antonielly Garcia Rodrigues & Eduardo Mario Dias - manuscript
    Gottfried Leibniz embarked on a research program to prove all the Aristotelic categorical syllogisms by diagrammatic and algebraic methods. He succeeded in proving them by means of Euler diagrams, but didn’t produce a manuscript with their algebraic proofs. We demonstrate how key excerpts scattered across various Leibniz’s drafts on logic contained sufficient ingredients to prove them by an algebraic method –which we call the Leibniz-Cayley (LC) system– without having to make use of the more expressive and complex machinery of first-order (...)
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  43. New Remarks on the Concept in Logical Use.Nijaz Ibrulj - 2021 - The Logical Foresight 1 (1):72-85.
    The main thesis of this paper is directed against the traditional (cognitivetheoretical) definition of the concept which claims that the concept is the '' thought about the essence of the object being thought'', i.e. that it is “a set of essential features or essential characteristics of an object''. But the '' set of essential features or essential characteristics of an object of thought'' is a '' content’’ of the thought. The thought about the essence of an object is definition and (...)
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  44. Some Characteristics of the Referential and Inferential Predication in Classical Logic.Nijaz Ibrulj - 2021 - The Logical Foresight 1 (1):1-27.
    In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the treatment of (...)
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  45. Legal Mind - from an ethical point of view.Yusuke Kaneko - 2009 - Journal of Applied Ethics and Philosophy 1:41-55.
    Although written in Japanese, 法的思考(Legal Mind)pursues a good explanation of how we can apply the so-called practical syllogism to the legal manner of thought.
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  46. Las reglas de Irving Copi y Carl Cohen son una condición necesaria y suficiente de la validez en los silogismos categóricos de forma estándar.Franklin Galindo & Kris Martins - 2005 - Episteme 25 (1):123-148.
    Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...)
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  47. Fichte’s Formal Logic.Jens Lemanski & Andrew Schumann - 2023 - Synthese 202 (1):1-27.
    Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to correctly (...)
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  48. A Mereological Reading of the Dictum de Omni et Nullo.Phil Corkum - forthcoming - Archiv für Geschichte der Philosophie.
    When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the (...)
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  49. A Cláusula Final da Definição Geral do Silogismo e suas funções na silogística e nos Primeiros Analíticos I de Aristóteles.Felipe Weinmann - 2014 - Dissertation, University of Campinas
    Aristotle's General Definition of the Syllogism may be taken as consisting of two parts: the Inferential Conditions and the Final Clause. Although this distinction is well known, traditional interpretations neglect the Final Clause and its influence on syllogistic. Instead, the aforementioned tradition focuses on the Inferential Conditions only. We intend to show that this neglect has severe consequences not just on syllogistic but on the whole exegesis of Aristotle's Prior Analytics I. Due to these consequences, our objective is to (...)
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  50. Aristotle's demonstrative logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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