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  1. Is Every Deductively Valid Argument Circular?Danny Frederick - manuscript
    David Miller claims that every valid deductive argument begs the question. Other philosophers and logicians have made similar claims. I show that the claim is false. Its appeal depends on the existence of logical terminology, particularly concerning what a proposition 'contains' or its 'logical content,' that is best understood as metaphoric and that, given its aptness to mislead, would be better eschewed. I show how the terminology appears to derive from early modern theories of the nature of mind, ideas and (...)
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  2. Hegel and the Problem of Beginning.Robb Dunphy - forthcoming - Hegel Bulletin:1-24.
    In this article I develop an interpretation of the opening passages of Hegel's essay ‘With what must the beginning of science be made?’ I suggest firstly that Hegel is engaging there with a distinctive problem, the overcoming of which he understands to be necessary in order to guarantee the scientific character of the derivation of the fundamental categories of thought which he undertakes in the Science of Logic. I refer to this as ‘the problem of beginning’. I proceed to clarify (...)
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  3. Frege and Peano on Definitions.Edoardo Rivello - forthcoming - In Proceedings of the "Frege: Freunde und Feinde" conference, held in Wismar, May 12-15, 2013.
    Frege and Peano started in 1896 a debate where they contrasted the respective conceptions on the theory and practice of mathematical definitions. Which was (if any) the influence of the Frege-Peano debate on the conceptions by the two authors on the theme of defining in mathematics and which was the role played by this debate in the broader context of their scientific interaction?
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  4. Proceedings of the 11th International Kant Congress.Clinton Tolley - forthcoming - De Gruyter.
  5. Adaptive Fregean Set Theory.Diderik Batens - 2020 - Studia Logica 108 (5):903-939.
    This paper defines provably non-trivial theories that characterize Frege’s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.
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  6. Frege's Intellectual Life As a Logicist Project. [REVIEW]Joan Bertran-San Millán - 2020 - Teorema: International Journal of Philosophy 39:127-138.
    I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.
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  7. ¿Es posible entender la determinación de un concepto como una relación de orden en la lógica dialéctica de Hegel?Eduardo Dib - 2020 - Zenodo Profile by Eduardo Dib.
    By the beginning of the 19th century Hegel's dialectic turn contradiction (conceived as unity of a concept with its determined negation) into distinguished inference. In the course of 20th century a family of systems known as "paraconsistent" formalized dialectical logic according to the contemporary paradigm of inference, oriented to truth-preserving, and not powered anymore solely by contradiction. In this way, nevertheless, Hegel's idea of logic as unfolding of concepts ordered by degree of "determination" reached at every step of the process, (...)
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  8. “Always Mixed Together”: Notation, Language, and the Pedagogy of Frege's Begriffsschrift.David E. Dunning - 2020 - Modern Intellectual History 17 (4):1099-1131.
    Gottlob Frege is considered a founder of analytic philosophy and mathematical logic, but the traditions that claim Frege as a forebear never embraced his Begriffsschrift, or “conceptual notation”—the invention he considered his most important accomplishment. Frege believed that his notation rendered logic visually observable. Rejecting the linearity of written language, he claimed Begriffsschrift exhibited a structure endogenous to logic itself. But Frege struggled to convince others to use his notation, as his frustrated pedagogical efforts at the University of Jena illustrate. (...)
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  9. Frege: A Philosophical Biography: Dale Jacquette, Cambridge: Cambridge University Press, 2019. Xiv + 667 Pp. Hardcover $45.00. ISBN: 978-0-521-86327-8. Ebook $36.00, ISBN 978-1-108-36504-8. [REVIEW]Wolfgang Kienzler - 2020 - History and Philosophy of Logic 41 (2):199-202.
    Volume 41, Issue 2, May 2020, Page 199-202.
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  10. Russell on Negative Judgement.Anssi Korhonen - 2020 - Topoi 39 (3):727-742.
    This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell put forth at different times: a dual relation theory ; a multiple relation theory ; a psychological theory of judgement. Four issues are singled out for a more detailed discussion: quality dualism versus quality monism, that is, the question whether judgement comes in two kinds, acceptance and rejection, or whether there is only one judgement-quality ; the (...)
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  11. 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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  12. The Venn-MacColl Dispute in Nature.Lukas M. Verburgt - 2020 - History and Philosophy of Logic 41 (3):244-251.
    During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about ‘symbolical logic’. The letters to the editor shed interesting light on the early reception of MacColl’s contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of the development of (...)
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  13. Indicating a Translation for ‘Bedeutung’.Karen Green - 2019 - History and Philosophy of Logic 41 (2):114-127.
    The translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and (...)
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  14. Review of Sandra Lapointe (Ed) "Logic From Kant to Russell: Laying the Foundations of Analytic Philosophy". [REVIEW]James Pearson - 2019 - Notre Dame Philosophical Reviews.
  15. New Essays on Frege: Between Science and Literature.Gisela Bengtsson, Simo Säätelä & Alois Pichler (eds.) - 2018 - Springer.
    This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place of (...)
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  16. Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over.Woosuk Park - 2018 - Springer Verlag.
    This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...)
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  17. Laws of Thought and Laws of Logic After Kant.Lydia Patton - 2018 - In Sandra Lapointe (ed.), Logic from Kant to Russell. New York: Routledge. pp. 123-137.
    George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire (...)
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  18. El Comienzo de la Existencia en Hegel y Kierkegaard.Gabriel Leiva Rubio - 2018 - Eikasia. Revista de Filosofía 83:265-280.
    This text aims to contrast the metaphysical beginnings of the philosophies of Hegel and Kierkegaard. For this task, the notion of Being Pure of the Hegel of Logic will be used in relation with the concept of Irony that Kierkegaard expresses in his Concept of irony. The need for this "contrast of beginnings" seeks to clarify, from a “metaphysical awakening”, the evident theoretical courtship that has so far distanced by the dominant historiographical traditions of continental philosophy.
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  19. MANY 1 - A Transversal Imaginative Journey Across the Realm of Mathematics.Jean-Yves Beziau - 2017 - Journal of Indian Council of Philosophical Research 34 (2):259-287.
    We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behaviour as a neutral element and finally its role as a truth-value in logic.
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  20. Frege on Thinking and Its Epistemic Significance. [REVIEW]Carlo Cellucci - 2017 - History and Philosophy of Logic 38 (1):92-95.
  21. Mill on Logic.David Godden - 2017 - In Dale E. Miller & Christopher Macleod (eds.), A companion to Mill. Hoboken, NJ: John Wiley & Sons. pp. 175-191.
    Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference that is (...)
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  22. Frege's Begriffsschrift is Indeed First-Order Complete.Yang Liu - 2017 - History and Philosophy of Logic 38 (4):342-344.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is (...)
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  23. Bolzano's Conception of Grounding.Stefan Roski - 2017 - Frankfurt am Main: Klostermann Verlag.
    Not all truths are on a par. The realm of truths is structured: some propositions are only true because others are. The relation that endows the realm of truths with this structure is often called grounding. Grounding has achieved much attention in 21st century metaphysics, but the topic is arguably as old as philosophy itself. -/- This becomes apparent when investigating the works of the 19th-century philosopher Bernard Bolzano, who developed what is perhaps the first comprehensive theory of grounding, drawing (...)
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  24. Stefan Roski, Bolzano’s Conception of Grounding. [REVIEW]Petter Sandstad - 2017 - Phenomenological Reviews.
    I review Stefan Roski's "Bolzano's Conception of Grounding".
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  25. The Sign of Consequence.Francesco Bellucci - 2016 - The Commens Encyclopedia: The Digital Encyclopedia of Peirce Studies.
    The “sign of consequence” is a notation for propositional logic that Peirce invented in 1886 and used at least until 1894. It substituted the “copula of inclusion” which he had been using since 1870.
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  26. La Lógica de Gottlob Frege: 1879-1903.Joan Bertran-San Millán - 2016 - Dissertation, Universitat de Barcelona
    In this dissertation I offer a global and detailed reconstruction of the logic developed by Gottlob Frege throughout his career. Even though Frege's logic suffered profound modifications from his initial formulation in Begriffsschrift to its revised version in Grundgesetze, the significant differences between these two works have been rarely taken at face value. I not only argue that these differences exist, but I also explain how they should be understood in the light of the evolution of Frege's thought. First, I (...)
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  27. 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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  28. The Philosophical Significance of Carroll's Regress.Pascal Engel - 2016 - Carrollian: The Lewis Carroll Journal 28.
  29. Frege the Carnapian and Carnap the Fregean.Gregory Lavers - 2016 - In Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag. pp. 353--373.
    In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not the metaphysical realist that he is standardly taken to be. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proved (...)
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  30. Charles Sanders Peirce on Necessity.Catherine Legg & Cheryl Misak - 2016 - In Adriane Rini, Edwin Mares & Max Cresswell (eds.), Logical Modalities from Aristotle to Carnap: The Story of Necessity. Cambridge, UK: Cambridge University Press. pp. 256-278.
    Necessity is a touchstone issue in the thought of Charles Peirce, not least because his pragmatist account of meaning relies upon modal terms. We here offer an overview of Peirce’s highly original and multi-faceted take on the matter. We begin by considering how a self-avowed pragmatist and fallibilist can even talk about necessary truth. We then outline the source of Peirce’s theory of representation in his three categories of Firstness, Secondness and Thirdness, (monadic, dyadic and triadic relations). These have modal (...)
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  31. 'What the Tortoise Said to Achilles': Lewis Carroll's Paradox of Inference.Amirouche Moktefi & Francine F. Abeles (eds.) - 2016 - London: The Lewis Carroll Society.
    Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.
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  32. Logik. Wiener Logikkolleg 1894/95.Kazimierz Twardowski (ed.) - 2016 - De Gruyter.
    This book presents the long-awaited critical edition of an unpublished manuscript of 277 pages containing Twardowski’s lecture notes on logic given in German at the University of Vienna. As to length, language and topic, this text is unique among the works of the author, who is renowned for his Zur Lehre vom Inhalt und Gegenstand der Vorstellungen (1894), an influential but short book that has been out of stock for a long time already. In Logik Twardowski’s ideas are exposed in (...)
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  33. Logic and Ontology in Hegel's Theory of Predication.Kevin J. Harrelson - 2015 - European Journal of Philosophy 23 (4):1259-1280.
    In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. The second concern (...)
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  34. Review of Danielle Macbeth, "Realizing Reason: A Narrative of Truth and Knowing". [REVIEW]Catherine Legg - 2015 - Notre Dame Philosophical Reviews:online.
  35. Logic Gallery.David Marans - 2015 - Great Britan: HUMBOX.
  36. On the Social Utility of Symbolic Logic: Lewis Carroll Against ‘The Logicians’.Amirouche Moktefi - 2015 - Studia Metodologiczne 35:133-150.
    Symbolic logic faced great difficulties in its early stage of development in order to acquire recognition of its utility for the needs of science and society. The aim of this paper is to discuss an early attempt by the British logician Lewis Carroll (1832–1898) to promote symbolic logic as a social good. This examination is achieved in three phases: first, Carroll’s belief in the social utility of logic, broadly understood, is demonstrated by his numerous interventions to fight fallacious reasoning in (...)
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  37. Functions and Generality of Logic.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.) - 2015 - Springer Verlag.
    Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.
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  38. Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338.John Corcoran - 2014 - MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud if (...)
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  39. Mill's System of Logic.David Godden - 2014 - In W. J. Mander (ed.), Oxford handbook of British philosophy in the nineteenth century. Oxford University Press. pp. 44-70.
    This chapter situates Mill’s System of Logic (1843/1872) in the context of some of the meta-logical themes and disputes characteristic of the 19th century as well as Mill’s empiricism. Particularly, by placing the Logic in relation to Whately’s (1827) Elements of Logic and Mill’s response to the “great paradox” of the informativeness of syllogistic reasoning, the chapter explores the development of Mill’s views on the foundation, function, and the relation between ratiocination and induction. It provides a survey of the Mill-Whewell (...)
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  40. Fregean Quantification Theory.Saul A. Kripke - 2014 - Journal of Philosophical Logic 43 (5):879-881.
    Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.
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  41. Bolzano and the Analytical Tradition.Sandra Lapointe - 2014 - Philosophy Compass 9 (2):96-111.
    In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...)
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  42. “Logic, Ethics and the Ethics of Logic”,.Catherine Legg - 2014 - In T. Thellefsen B. Sorensen (ed.), Charles Sanders Peirce in His Own Words. pp. 271-278.
    An exposition of the following quote from Charles Peirce (1902), ". . . the main reason logic is unsettled is that thirteen different opinions are current as to the true aim of the science. Now this is not a logical difficulty, but an ethical difficulty; for ethics is the science of aims. Secondly, it is true that ethics has been, and always must be, a theatre of discussion for the reason that its study consists in the gradual development of a (...)
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  43. Propositional Function.Edwin Mares - 2014 - Stanford Encyclopedia of Philosophy.
  44. La Logique Symbolique En Débat À Oxford À la Fin du XIXe Siècle : Les Disputes Logiques de Lewis Carroll Et John Cook Wilson.Mathieu Marion & Amirouche Moktefi - 2014 - Revue D’Histoire des Sciences 67 (2):185-205.
    The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who (...)
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  45. Remarks on the Idealist and Empiricist Interpretation of Frequentism: Robert Leslie Ellis Versus John Venn.Lukas M. Verburgt - 2014 - BSHM Bulletin: Journal of the British Society for the History of Mathematics 29 (3):184-195.
    The goal of this paper is to correct a widespread misconception about the work of Robert Leslie Ellis and John Venn, namely that it can be considered as the ‘British empiricist’ reaction against the traditional theory of probability. It is argued, instead, that there was no unified ‘British school’ of frequentism during the nineteenth century. Where Ellis arrived at frequentism from a metaphysical idealist transformation of probability theory’s mathematical calculations, Venn did so on the basis of an empiricist critique of (...)
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  46. The Horn Theory of Boole's Partial Algebras.Stanley N. Burris & H. P. Sankappanavar - 2013 - Bulletin of Symbolic Logic 19 (1):97-105.
    This paper augments Hailperin's substantial efforts to place Boole's algebra of logic on a solid footing. Namely Horn sentences are used to give a modern formulation of the principle that Boole adopted in 1854 as the foundation for his algebra of logic—we call this principle The Rule of 0 and 1.
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  47. Gottlob Frege: Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford, UK: Oxford University Press.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.
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  48. The Varieties of Rigorous Experience.Juliet Floyd - 2013 - In Michael Beaney (ed.), The Oxford Handbook of the History of Analytic Philosophy. Oxford University Press.
  49. Singular Terms, Predicates and the Spurious ‘Is’ of Identity.Danny Frederick - 2013 - Dialectica 67 (3):325-343.
    Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill's account of predication, connotation and denotation. I show that singular terms may be (...)
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  50. What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. pp. 1-18.
    Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does (...)
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