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  1. Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
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  • Hobbes's Laws of Nature in Leviathan as a Synthetic Demonstration: Thought Experiments and Knowing the Causes.Marcus P. Adams - 2019 - Philosophers' Imprint 19.
    The status of the laws of nature in Hobbes’s Leviathan has been a continual point of disagreement among scholars. Many agree that since Hobbes claims that civil philosophy is a science, the answer lies in an understanding of the nature of Hobbesian science more generally. In this paper, I argue that Hobbes’s view of the construction of geometrical figures sheds light upon the status of the laws of nature. In short, I claim that the laws play the same role as (...)
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  • The Interactivist Model.Mark H. Bickhard - 2009 - Synthese 166 (3):547 - 591.
    A shift from a metaphysical framework of substance to one of process enables an integrated account of the emergence of normative phenomena. I show how substance assumptions block genuine ontological emergence, especially the emergence of normativity, and how a process framework permits a thermodynamic-based account of normative emergence. The focus is on two foundational forms of normativity, that of normative function and of representation as emergent in a particular kind of function. This process model of representation, called interactivism, compels changes (...)
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  • The Beginnings of Formal Logic: Deduction in Aristotle’s Topics Vs. Prior Analytics.Marko Malink - 2015 - Phronesis 60 (3):267-309.
  • Argumentation Schemes and Communities of Argumentational Practice.Andrew Aberdein - 2009 - In Juho Ritola (ed.), Argument Cultures: Proceedings of OSSA 2009. OSSA.
    Is it possible to distinguish communities of arguers by tracking the argumentation schemes they employ? There are many ways of relating schemes to communities, but not all are productive. Attention must be paid not only to the admissibility of schemes within a community of argumentational practice, but also to their comparative frequency. Two examples are discussed: informal mathematics, a convenient source of well-documented argumentational practice, and anthropological evidence of nonstandard reasoning.
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  • Logic, Logics, and Logicism.Solomon Feferman - 1999 - Notre Dame Journal of Formal Logic 40 (1):31-54.
    The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized similarly is a natural generalization of Tarski’s thesis, due to Sher, in terms of bijections between domains. My main (...)
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  • Remarks on Operators and Modalities.María-Luisa Rivero - 1972 - Foundations of Language 9 (2):209-241.
  • Preadolescents Solve Natural Syllogisms Proficiently.Guy Politzer, Christelle Bosc-Miné & Emmanuel Sander - 2017 - Cognitive Science 41 (S5):1031-1061.
    “Natural syllogisms” are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy and an operational use of the concept of inclusion, it was hypothesized that these syllogisms would be within the grasp of non-adult participants, provided they have acquired the notion of deductive (...)
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  • Kant’s Conception of Analytic Judgment.Ian Proops - 2005 - Philosophy and Phenomenological Research 70 (3):588–612.
    In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of “containment,” a second time in terms of “identity,” a third time in terms of the explicative–ampliative contrast, and a fourth time in terms of the notion of “cognizability in accordance with the principle of contradiction.” The paper asks: Which of these characterizations—or apparent characterizations—best captures Kant’s conception of analyticity in the first Critique? It suggests: “the second.” It argues, further, that (...)
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  • What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
    In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic (...)
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  • Reason, Causation and Compatibility with the Phenomena.Basil Evangelidis - forthcoming - Wilmington, Delaware, USA: Vernon Press.
    'Reason, Causation and Compatibility with the Phenomena' strives to give answers to the philosophical problem of the interplay between realism, explanation and experience. This book is a compilation of essays that recollect significant conceptions of rival terms such as determinism and freedom, reason and appearance, power and knowledge. This title discusses the progress made in epistemology and natural philosophy, especially the steps that led from the ancient theory of atomism to the modern quantum theory, and from mathematization to analytic philosophy. (...)
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  • Stoic Sequent Logic and Proof Theory.Susanne Bobzien - forthcoming - History and Philosophy of Logic:1-32.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...)
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  • Epicureans and the Present Past.James Warren - 2006 - Phronesis 51 (4):362-387.
    This essay offers a reading of a difficult passage in the first book of Lucretius' "De Rerum Natura" in which the poet first explains the Epicurean account of time and then responds to a worry about the status of the past (1.459-82). It identifies two possible readings of the passage, one of which is compatible with the claim that the Epicureans were presentists about the past. Other evidence, particularly from Cicero "De Fato", suggests that the Epicureans maintained that all true (...)
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  • On the Difference Between the Two Barbaras.Živilė Pabijutaitė - 2018 - Problemos 93.
    [full article, abstract in English; only abstract in Lithuanian] The paper deals with the problem of the “two Barbaras” in the Aristotelian modal syllogistic. The problem consists in Aristotle’s differing views on two at a first sight similar in nature syllogisms of mixed assertoric and necessary premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held (...)
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  • The Psychology of Uncertainty and Three-Valued Truth Tables.Jean Baratgin, Guy Politzer, David E. Over & Tatsuji Takahashi - 2018 - Frontiers in Psychology 9.
    Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...)
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  • The Basic Slippery Slope Argument.Douglas Walton - 2015 - Informal Logic 35 (3):273-311.
    Although studies have yielded a detailed taxonomy of types of slippery slope arguments, they have failed to identify a basic argumentation scheme that applies to all. Therefore, there is no way of telling whether a given argument is a slippery slope argument or not. This paper solves the problem by providing a basic argumentation scheme. The scheme is shown to fit a clear and easily comprehensible example of a slippery slope argument that strongly appears to be reasonable, something that has (...)
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  • Analyticity, Truthmaking and Mathematics.Adrian Heathcote - 2018 - Open Journal of Philosophy 8 (3):243-261.
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  • Is Logic All in Our Heads? From Naturalism to Psychologism.Francis J. Pelletier, Renée Elio & Philip Hanson - 2008 - Studia Logica 88 (1):3-66.
    Psychologism in logic is the doctrine that the semantic content of logical terms is in some way a feature of human psychology. We consider the historically influential version of the doctrine, Psychological Individualism, and the many counter-arguments to it. We then propose and assess various modifications to the doctrine that might allow it to avoid the classical objections. We call these Psychological Descriptivism, Teleological Cognitive Architecture, and Ideal Cognizers. These characterizations give some order to the wide range of modern views (...)
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  • Human Rationality: Misleading Linguistic Analogies.Geoffrey Sampson - 1981 - Behavioral and Brain Sciences 4 (3):350-351.
  • Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like.Ahti-Veikko Pietarinen - 2011 - History and Philosophy of Logic 32 (3):265-281.
    This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ?moving pictures of thought?. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...)
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  • Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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  • The Persistence of Cognitive Illusions.Persi Diaconis & David Freedman - 1981 - Behavioral and Brain Sciences 4 (3):333-334.
  • Mental Probability Logic.Niki Pfeifer & Gernot D. Kleiter - 2009 - Behavioral and Brain Sciences 32 (1):98-99.
    We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.
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  • Logical Machines: Peirce on Psychologism.Majid Amini - 2008 - Disputatio 2 (24):1 - 14.
    This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem.
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  • The Role of Discrete Terms in the Theory of the Properties of Terms.Julie Brumberg-Chaumont - 2013 - Vivarium 51 (1-4):169-204.
    Discrete supposition occurs whenever a discrete term, such as ‘Socrates‘, is the subject of a given proposition. I propose to examine this apparently simple notion. I shall draw attention to the incongruity, within a general theory of the semantic variation of terms in a propositional context, of the notion of discrete supposition, in which a term usually has a single semantic correlate. The incongruity comes to the fore in those treatises that attempt to describe discrete supposition as a sort of (...)
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  • The Road to Modern Logic—An Interpretation.José Ferreirós - 2001 - Bulletin of Symbolic Logic 7 (4):441-484.
    This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order-Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of (...)
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  • The First Rule of Stoic Logic and its Relationship with the Indemonstrables.Miguel López Astorga - 2016 - Tópicos: Revista de Filosofía 50:9-23.
    Además de los indemostrables, la lógica estoica incluye varias reglas de reducción. En este trabajo, analizo la primera de ellas con el fin de comprobar si fue derivada formalmente a partir de los indemostrables o los estoicos pudieron plantearla a partir del uso de sus capacidades naturales de razonamiento. De esta manera, trato de mostrar que tenemos razones para apoyar ambas posibilidades y, basándome en un enfoque semántico como el de la teoría de los modelos mentales, de ofrecer argumentos al (...)
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  • Verdad, metafísica y epistemología. Observaciones sobre la neutralidad de la verdad.José Andrés Forero Mora - 2015 - Universitas Philosophica 32 (64):283.
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  • Vorprung Durch Logik: The German Analytic Tradition: Hans-Johann Glock.Hans-Johann Glock - 1999 - Royal Institute of Philosophy Supplement 44:137-166.
    Although at present analytic philosophy is practiced mainly in the English-speaking world, it is to a considerable part the invention of German speakers. Its emergence owes much to Russell, Moore, and American Pragmatism, but even more to Frege, Wittgenstein, and the logical positivists of the Vienna Circle. No one would think of analytic philosophy as a specifically Anglophone phenomenon, if the Nazis had not driven many of its pioneers out of central Europe.
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  • Hδυν-Αλυπον.Tjitte H. Janssen - 1990 - Journal of Hellenic Studies 110:186-188.
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  • A Critique of Anxious Identity.James D. Marshall - 2006 - Educational Philosophy and Theory 38 (5):693–705.
  • Barbara Thayer‐Bacon on Knowers and the Known.Jim McKenzie - 2002 - Educational Philosophy and Theory 34 (3):301-319.
  • A Reconstruction of Aristotle's Modal Syllogistic.Marko Malink - 2006 - History and Philosophy of Logic 27 (2):95-141.
    Ever since ?ukasiewicz, it has been opinio communis that Aristotle's modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle's syllogistic is a pure term logic that does not recognize an extra syntactic category of individual symbols besides syllogistic terms and, second, (...)
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  • Term Kinds and the Formality of Aristotelian Modal Logic.Joshua Mendelsohn - 2017 - History and Philosophy of Logic 38 (2):99-126.
    Recent formalizations of Aristotle's modal syllogistic have made use of an interpretative assumption with precedent in traditional commentary: That Aristotle implicitly relies on a distinction between two classes of terms. I argue that the way Rini employs this distinction undermines her attempt to show that Aristotle gives valid proofs of his modal syllogisms. Rini does not establish that Aristotle gives valid proofs of the arguments which she takes to best represent Aristotle's modal syllogisms, nor that Aristotle's modal syllogisms are instances (...)
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  • Dialectic and Logic in Aristotle and His Tradition.Matthew Duncombe & Catarina Dutilh Novaes - 2016 - History and Philosophy of Logic 37 (1):1-8.
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  • Dialectical Contradictions and Classical Formal Logic.Inoue Kazumi - 2014 - International Studies in the Philosophy of Science 28 (2):113-132.
    A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.
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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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  • Problems for Logical Pluralism.Owen Griffiths - 2013 - History and Philosophy of Logic 34 (2):170 - 182.
    I argue that Beall and Restall's logical pluralism fails. Beall?Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ?settled core? of consequence: they believe that truth-preservation, necessity, formality and normativity are ?settled? features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their (...)
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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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  • Erhard Weigel's Contributions to the Formation of Symbolic Logic.Maarten Bullynck - 2013 - History and Philosophy of Logic 34 (1):25-34.
    The aspects of Erhard Weigel's Analysis Aristotelica ex Euclide restituta that foreshadowed and helped form some characteristics of symbolic logic are highlighted: first, the idea of a pure form of a logical syllogism or of a mathematical proof and, second, a tentative arithmetisation of some aspects of logic. Also, Weigel's emphasis on the role of symbols and figures in the process of mathematical proof is discussed.
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  • Charles Peirce's Reading of Richard Whately's Elements of Logic.Charles Seibert - 2005 - History and Philosophy of Logic 26 (1):1-32.
    Charles S. Peirce frequently mentioned reading Richard Whately's Elements of Logic when he was 12 years old. Throughout his life, Peirce emphasized the importance of that experience. This valorization of Whately is puzzling at first. Early in his career Peirce rejected Whately's central logical doctrines. What valuable insight concerning logic was robust enough to survive these specific rejections? Peirce recommended a biographical approach to understanding his philosophy. This essay follows that suggestion by considering Peirce's reading of Whately in a larger (...)
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  • Lewis Carroll's Formal Logic.Francine Abeles - 2005 - History and Philosophy of Logic 26 (1):33-46.
    Charles L. Dodgson's reputation as a significant figure in nineteenth-century logic was firmly established when the philosopher and historian of philosophy William Warren Bartley, III published Dodgson's ?lost? book of logic, Part II of Symbolic Logic, in 1977. Bartley's commentary and annotations confirm that Dodgson was a superb technical innovator. In this paper, I closely examine Dodgson's methods and their evolution in the two parts of Symbolic Logic to clarify and justify Bartley's claims. Then, using more recent publications and unpublished (...)
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  • The Development of Modern Logic.John P. Burgess - 2011 - History and Philosophy of Logic 32 (2):187 - 191.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 187-191, May 2011.
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  • La Métalangue d'Une Syntaxe Inscriptionnelle.Paula Quinon - 2011 - History and Philosophy of Logic 32 (2):191 - 193.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 191-193, May 2011.
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  • The Reception of Frege in Poland.Jan Woleński - 2004 - History and Philosophy of Logic 25 (1):37-51.
    This paper examines how the work of Frege was known and received in Poland in the period 1910?1935 (with one exception concerning the later work of Suszko). The main thesis is that Frege's reception in Poland was perhaps faster and deeper than in other countries, except England, due to works of Russell and Jourdain. The works of ?ukasiewicz, Le?niewski and Cze?owski are described.
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  • ‘Everybody Makes Errors’: The Intersection of De Morgan's Logic and Probability, 1837 – 1847.Adrian Rice - 2003 - History and Philosophy of Logic 24 (4):289-305.
    For Ivor Grattan-Guinness on the occasion of his retirement. The work of Augustus De Morgan on symbolic logic in the mid-nineteenth century is familiar to historians of logic and mathematics alike. What is less well known is his work on probability and, more specifically, the use of probabilistic ideas and methods in his logic. The majority of De Morgan's work on probability was undertaken around 1837???1838, with his earliest publications on logic appearing from 1839, a period which culminated with the (...)
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  • Augustus De Morgan's Boolean Algebra.Daniel D. Merrill - 2005 - History and Philosophy of Logic 26 (2):75-91.
    De Morgan's Formal Logic, which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic, contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that it is a (...)
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  • Lewis Carroll's Visual Logic.Francine F. Abeles - 2007 - History and Philosophy of Logic 28 (1):1-17.
    John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...)
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  • The Doctrine of Distribution.Terence Parsons - 2006 - History and Philosophy of Logic 27 (1):59-74.
    Peter Geach describes the ?doctrine of distribution? as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...)
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  • William Stanley Jevons and the Extent of Meaning in Logic and Economics.Bert Mosselmans - 1998 - History and Philosophy of Logic 19 (2):83-99.
    This paper shows that William Stanley Jevons was not precursor of logical positivism despite his attempt to build up a unified science. His mechanical reductionism was directed towards this project, and Jevons tried to found mathematics on logic through the development of a theory of number. We show that his attempts were unsuccessful, and that his errors remain visible within the totality of his mechanical system, including his economics. We argue that both his logic and his economics are comprehensible only (...)
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