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  1. Logical Foundations and Kant's Principles of Formal Logic.Srećko Kovač - 2019 - History and Philosophy of Logic 41 (1):48-70.
    The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort of (...)
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  • Deductions and Reductions Decoding Syllogistic Mnemonics.John Corcoran, Daniel Novotný & Kevin Tracy - 2018 - Entelekya Logico-Metaphysical Review 2 (1):5-39.
    The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it (...)
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  • Ancestor Worship in The Logic of Games. How Foundational Were Aristotle's Contributions?John Woods - 2013 - The Baltic International Yearbook of Cognition, Logic and Communication 8 (1).
    Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: "Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?'' A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational (...)
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  • On Logics of Transitive Verbs With and Without Intersective Adjectives.Selçuk Topal - 2018 - Studia Humana 7 (1):31-43.
    The purpose of this paper is to contribute to the natural logic program which invents logics in natural language. This study presents two logics: a logical system called d R containing transitive verbs and a more expressive logical system R containing both transitive verbs and intersective adjectives. The paper offers three different set-theoretic semantics which are equivalent for the logics.
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  • 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 Mar...
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  • Preface.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):1-8.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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  • Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW]Catarina Dutilh Novaes & Edgar Andrade-Lotero - 2012 - Journal of Philosophical Logic 41 (2):387 - 418.
    We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...)
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  • The Syllogistic with Unity.Ian Pratt-Hartmann - 2013 - Journal of Philosophical Logic 42 (2):391-407.
    We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.
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  • The Hamiltonian Syllogistic.Ian Pratt-Hartmann - 2011 - Journal of Logic, Language and Information 20 (4):445-474.
    This paper undertakes a re-examination of Sir William Hamilton’s doctrine of the quantification of the predicate . Hamilton’s doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit existential quantifiers, so that, for example, All p is q is to be understood as All p is some q . Second, these implicit quantifiers can be meaningfully dualized to yield novel sentence-forms, such as, for example, All p is all q . Hamilton attempted to provide a deductive system (...)
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  • Syllogisms in Rudimentary Linear Logic, Diagrammatically.Ruggero Pagnan - 2013 - Journal of Logic, Language and Information 22 (1):71-113.
    We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...)
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  • Acerca dos concomitantes per se em Aristóteles.Breno Andrade Zuppolini - 2015 - Filosofia Grega E Helenística (Coleção XVI Encontro Anpof).
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  • Mereology in Aristotle's Assertoric Syllogistic.Justin Vlasits - 2018 - History and Philosophy of Logic 40 (1):1-11.
    How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness and completeness (...)
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  • 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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  • 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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  • 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 analyse (...)
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  • O expressivismo lógico de Aristóteles segundo Lucas Angioni: um breve e introdutório quadro teórico.Aislan Fernandes Pereira - 2017 - Books of Abstracts (3rd FILOMENA Workshop).
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  • Aristoteles’ in izahat Yöntemi Hakkindaki Yorumlar.Murat Kelikli - 2014 - Kutadgubilig Felsefe-Bilim Araştırmaları Dergisi 25:115-127.
    There is very little information about the proving by Aristotle’s ecthesis method both in Aristotle’s and his commentators’ articles. Researches on ecthesis which were made by recent commentators are only on expository term. In our study, comments have been evaluated, points that are subject to contradiction have been determined, and opinions about ecthesis have been cited by giving proofs obtained by the ecthesis method.
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  • Štyri antické argumenty o budúcich nahodnostiach (Four Ancient Arguments on Future Contingencies).Vladimir Marko - 2017 - Bratislava, Slovakia: Univerzita Komenského.
    Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument.
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  • Necessidade, mediação e o papel do 'toi tauta einai' nos Primeiros Analíticos I.4 e I.7 de Aristóteles.Felipe Weinmann - 2013 - Revista Do Seminário Dos Alunos Do PPGLM/UFRJ 4 (1):70-87.
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  • Selected Bibliography on Aristotle's Theory of Categorical Syllogism.Raul Corazzon - unknown
    "However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..
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  • Aristotelian Assertoric Syllogistic.Mohamed A. Amer - manuscript
    Abstract. Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. These approaches (with few exceptions) are here discussed, developed and interrelated. Among other things, di-erent facets of soundness, completeness, decidability and independence are investigated. Speci/cally arithmetization (Leibniz), algebraization (Leibniz and Boole), and Venn models (Euler and Venn) are closely examined. All proofs are simple. In particular (...)
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  • Completeness of an Ecthetic Syllogistic.Robin Smith - 1983 - Notre Dame Journal of Formal Logic 24 (2):224-232.
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  • Existential-Import Mathematics.John Corcoran & Hassan Masoud - 2015 - Bulletin of Symbolic Logic 21 (1):1-14.
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  • 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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  • Aristotle on Universal Quantification: A Study From the Point of View of Game Semantics.M. Marion & H. Rückert - 2016 - History and Philosophy of Logic 37 (3):201-229.
    In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...)
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  • Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions.John Corcoran & Hassan Masoud - 2015 - History and Philosophy of Logic 36 (1):39-61.
    Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...)
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  • The Principle of Contradiction and Ecthesis in Aristotle's Syllogistic.Pierre Joray - 2014 - History and Philosophy of Logic 35 (3):219-236.
    In his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction . He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic vis-à-vis PC is nevertheless true. For that purpose, we first establish that there (...)
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  • Distributive Terms, Truth, and the Port Royal Logic.John N. Martin - 2013 - History and Philosophy of Logic 34 (2):133-154.
    The paper shows that in the Art of Thinking Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do not require the introduction (...)
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  • Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...)
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  • Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic.Edgar Jose Andrade & Edward Samuel Becerra - 2008 - History and Philosophy of Logic 29 (4):309-325.
    This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon the same properties (...)
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  • Logic and Metaphor.James Gasser - 1999 - History and Philosophy of Logic 20 (3-4):227-238.
    In this work, attention is drawn to the abundant use of metaphor and analogy in works of logic. I argue that pervasiveness of figurative language is to be counted among the features that characterize logic and distinguish it from other sciences. This characteristic feature reflects the creativity that is inherent in logic and indeed has been demonstrated to be a necessary part of logic. The goal of this paper, in short, is to provide specific examples of figurative language used in (...)
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  • The Development of Logic as Reflected in the Fate of the Syllogism 1600–1900.James Van Evra - 2000 - History and Philosophy of Logic 21 (2):115-134.
    One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...)
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  • 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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  • Completion, Reduction and Analysis: Three Proof-Theoretic Processes in Aristotle’s Prior Analytics.George Boger - 1998 - History and Philosophy of Logic 19 (4):187-226.
    Three distinctly different interpretations of Aristotle?s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle?s remarkable degree of metalogical (...)
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  • Aristotle'S Natural Deduction Reconsidered.John M. Martin - 1997 - History and Philosophy of Logic 18 (1):1-15.
    John Corcoran?s natural deduction system for Aristotle?s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz?s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz (...)
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  • Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  • Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
    The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio (...)
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  • An Intensional Leibniz Semantics for Aristotelian Logic.Klaus Glashoff - 2010 - Review of Symbolic Logic 3 (2):262-272.
    Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.
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  • What Is Aristotelian Ecthesis?Robin Smith - 1982 - History and Philosophy of Logic 3 (2):113-127.
    I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...)
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  • Aristotle’s Prototype Rule-Based Underlying Logic.John Corcoran - 2018 - Logica Universalis 12 (1-2):9-35.
    This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...)
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  • Termos singulares, transcategoriais e Summa Genera na lógica de Aristóteles.Wellington Damasceno de Almeida - 2013 - Manuscrito 36 (1):5-48.
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  • Equivalential Structures for Binary and Ternary Syllogistics.Selçuk Topal - 2018 - Journal of Logic, Language and Information 27 (1):79-93.
    The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \ \) and \ \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics of (...)
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  • On Finding Compactness in Aristotle.Michael Scanlan - 1983 - History and Philosophy of Logic 4 (1&2):1-8.
    Jonathan Lear has suggested that Aristotle attempts to demonstrate a proof-theoretic analogue of a compactness theorem in Posterior analyticsI, chs. 19?22. Aristotle argues in these chapters that there cannot be in finite series of predications of terms. Lear's analysis of Aristotle's arguments are shown to be based on confusions about the nature of infinite orderings. Three distinct confusions are identified. In final remarks, it is suggested that a compactness claim is irrelevant to the issues which motivate Aristotle's arguments.
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  • The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms.Marko Malink & Anubav Vasudevan - forthcoming - Review of Symbolic Logic:1-65.
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