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  1. Francine Abeles (2007). Lewis Carroll's Visual Logic. 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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  2. Francine Abeles (2005). Lewis Carroll's Formal Logic. 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 Then, using more recent publications and unpublished (...)
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  3. A. Abian (1972). Kategoryczność Przeliczalnych Bezatomowych Pierścieni Boole'a. Studia Logica 30 (1):68-68.
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  4. Tuomo Aho (1998). Frege and His Groups. History and Philosophy of Logic 19 (3):137-151.
    Frege's docent's dissertation Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen(1874) contains indications of a bold attempt to extend arithmetic. According to it, arithmetic means the science of magnitude, and magnitude must be understood structurally without intuitive support. The main thing is insight into the formal structure of the operation of ?addition?. It turns out that a general ?magnitude domain? coincides with a (commutative) group. This is an interesting connection with simultaneous developments in abstract algebra. As his main application, (...)
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  5. Ken Akiba (1996). Logic as Instrument: The Millian View on the Role of Logic. History and Philosophy of Logic 17 (1-2):73-83.
    I interpret Mill?s view on logic as the instrumentalist view that logical inferences, complex statements, and logical operators are not necessary for reasoning itself, but are useful only for our remembering and communicating the results of the reasoning. To defend this view, I first show that we can transform all the complex statements in the language of classical first-order logic into what I call material inference rules and reduce logical inferences to inferences which involve only atomic statements and the material (...)
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  6. Chiara Ambrosio (2009). La Teoria Delle Relazioni Nell'algebra Della Logica Schroderiana. History and Philosophy of Logic 30 (2):193-194.
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  7. Irving H. Anellis (2011). Peirce's Truth-Functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic 33 (1):87 - 97.
    We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...)
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  8. Irving H. Anellis (1992). Theology Against Logic: The Origins of Logic in Old Russia. History and Philosophy of Logic 13 (1):15-42.
    We consider the history of logic in pre-Petrine. Petrine. and immediate post-Pctrine Russia (from the 15th to the mid-18th centuries) and especially of the Petrine era from the late 17th to early 18th century. Throughout much of this time, the clergy evinced strong hostility towards logic. Nevertheless, a small number of academics and clerics such as Stefan Iavorskii and Fcofan Prokopovich kept Aristotelian logic alive during this period and provided the foundation for its development in the modern era.
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  9. Ignacio Angelelli (1967). On identity and interchangeability in Leibnitz and Frege. Notre Dame Journal of Formal Logic 8 (1-2):94-100.
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  10. Ignacio Angelelli & Terrell Ward Bynum (1966). Note on Frege's Begriffsschrift. Notre Dame Journal of Formal Logic 7 (4):369-370.
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  11. Marco Antonio Ruffino (1991). Context Principle, Fruitfulness of Logic and the Cognitive Value of Arithmetic in Frege. History and Philosophy of Logic 12 (2):185-194.
    I try to reconstruct how Frege thought to reconcile the cognitive value of arithmetic with its analytical nature. There is evidence in Frege's texts that the epistemological formulation of the context principle plays a decisive role; it provides a way of obtaining concepts which are truly fruitful and whose contents cannot be grasped beforehand. Taking the definitions presented in the Begriffsschrift,I shall illustrate how this schema is intended to work.
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  12. Michael Astroh, Ivor Grattan-Guinness & Stephen Read (2001). A Survey of the Life of Hugh MacColl (1837-1909). History and Philosophy of Logic 22 (2):81-98.
    The Scottish logician Hugh MacColl is well known for his innovative contributions to modal and nonclassical logics. However, until now little biographical information has been available about his academic and cultural background, his personal and professional situation, and his position in the scientific community of the Victorian era. The present article reports on a number of recent findings.
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  13. Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic. History and Philosophy of Logic 23 (1):1-30.
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  14. T. Spencer Baynes (1850/1971). An Essay on the New Analytic of Logical Forms. New York,B. Franklin.
    NEW ANALYTIC OF LOGICAL FORMS. THE main principle on which the new Analytic of Logical Forms proceeds is that of a thorough-going quantification of ...
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  15. Alessandro Bertinetto (2007). Die transzendentale Argumentation in der Transzendentalen Logik Fichtes. Fichte-Studien 31:255-265.
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  16. Alessandro Bertinetto (2003). Die Grundbeziehung von »Leben« und »Sehen« in der ersten Transzendentalen Logik Fichtes. Fichte-Studien 20:203-213.
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  17. Arianna Betti (2005). Propositions Et États de Choses Chez Twardowski. Dialogue 44 (3):469-492.
    Sur le contenu et l’objet des représentations (1894) de Kazimierz Twardowski est un des textes les plus influents de la tradition autrichienne. Le manuscrit Logik (1894-1895) complète ce dernier et nous permet entre autres de reconstruire la théorie du jugement de Twardowski. Ces textes soulèvent plusieurs questions, en particulier si Twardowski acceptait les notions de propositions et d’etats de choses, et si sa théorie est acceptable. Cet article presente la théorie de Twardowski, montre qu’il acceptait les états de choses, qu’il (...)
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  18. Arianna Betti & Maria van der Schaar (2004). The Road From Vienna to Lvov: Twardowski's Theory of Judgement Between 1894 and 1897. Grazer Philosophische Studien 67 (1):1-20.
    In several manuscripts, written between 1894 and 1897, Twardowski developed a new theory of judgement with two types of judgement: existential and relational judgements. In Zur Lehre he tried to stay within a Brentanian framework, although he introduced the distinction between content and object in the theory of judgement. The introduction of this distinction forced Twardowski to revise further Brentano'stheory.His changes concerned judgements about relations and about non-present objects. The latter are considered special cases of relational judgements. The existential judgements (...)
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  19. Terry Boswell (1995). A Note on John Venn as a Collector and Bibliographer of Works on Logic. History and Philosophy of Logic 16 (1):121-125.
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  20. Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...)
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  21. Dermot Cassidy (2007). Russell's Divine Ancestors. History and Philosophy of Logic 28 (2):123-132.
    Russell alleged that the version of the cosmological argument he debated with Copleston involved type confusions, but the definitions of plural descriptive functions and the ancestral in Principia Mathematica can be used to reformulate the argument in a type-safe way via a notion of causally self-sufficient classes. Although the argument depends on the assumption that the class of contingent things is not causally self-sufficient, if that assumption is weakened to say only that it may not be so, then a new (...)
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  22. Nino B. Cocciharella (1992). Cantor's Power-Set Theorem Versus Frege's Double-Correlation Thesis. History and Philosophy of Logic 13 (2):179-201.
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  23. John Corcoran (2003). Aristotle's Prior Analytics and Boole's Laws of Thought. 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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  24. Karin de Boer (2010). Hegel's Account of Contradiction in the Science of Logic Reconsidered. Journal of the History of Philosophy 48 (3):345-373.
    Hegel's Philosophy is notorious for its alleged claim that all things are contradictory. Whereas Marxists took this claim to support their view that the social-political world exhibits "real" contradictions, non-Hegelian philosophers of various breeds have used it to argue that Hegelian dialectic annihilates the very principle of scientific reasoning.1 Yet, even if it is granted that Hegel did not intend to violate the law of non-contradiction, the stakes of Hegel's account of contradiction in the Science of Logic are far from (...)
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  25. Oliver Deiser (2011). On the Development of the Notion of a Cardinal Number. History and Philosophy of Logic 31 (2):123-143.
    We discuss the concept of a cardinal number and its history, focussing on Cantor's work and its reception. J'ay fait icy peu pres comme Euclide, qui ne pouvant pas bien >faire< entendre absolument ce que c'est que raison prise dans le sens des Geometres, definit bien ce que c'est que memes raisons. (Leibniz) 1.
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  26. James Van Evra (2000). The Development of Logic as Reflected in the Fate of the Syllogism 1600–1900. 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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  27. Fernando Ferreira & Kai F. Wehmeier (2002). On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze. Journal of Philosophical Logic 31 (4):301-311.
    It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...)
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  28. J. Ferreiros (1996). Traditional Logic and the Early History of Sets, 1854-1908. Archive for History of Exact Sciences 50:5-71.
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  29. Gottlob Frege, P. T. Geach & Max Black (1951). On Concept and Object. Mind 60 (238):168-180.
  30. David M. Godden (2005). Psychologism in the Logic of John Stuart Mill: Mill on the Subject Matter and Foundations of Ratiocinative Logic. History and Philosophy of Logic 26 (2):115-143.
    This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's _System of Logic and his _Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it as a set of psychological (...)
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  31. I. Grattan-Guinness (1982). Psychology in the Foundations of Logic and Mathematics: The Cases of Boole, Cantor and Brouwer. History and Philosophy of Logic 3 (1):33-53.
    In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.
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  32. I. Grattan-Guinness (1980). Georg Cantor's Influence on Bertrand Russell. History and Philosophy of Logic 1 (1-2):61-93.
    This paper is concerned with the influence that the set theory of georg cantor (1845-1918) bore upon the mathematical logic of bertrand russell (1872-1970). In some respects the influence is positive, And stems directly from cantor's writings or through intermediary figures such as peano: but in various ways negative influence is evident, For russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, Six sections compare and contrast their views on matters of common (...)
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  33. Theodore Hailperin (1988). The Development of Probability Logic From Leibniz to Maccoll. History and Philosophy of Logic 9 (2):131-191.
    The introduction has a brief statement, sufficient for the purpose of this paper, which describes in general terms the notion of probability logic on which the paper is based. Contributions made in the eighteenth century by Leibniz, Jacob Bernoulli and Lambert, and in the nineteenth century by Bolzano, De Morgan, Boole, Peirce and MacColl are critically examined from a contemporary point of view. Historicity is maintained by liberal quotations from the original sources accompanied by interpretive explanation. Concluding the paper is (...)
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  34. Theodore Hailperin (1984). Boole's Abandoned Propositional Logic. History and Philosophy of Logic 5 (1):39-48.
    The approach used by Boole in Mathematical analysis of logic to develop propositional logic was based on the idea of ?cases? or ?conjunctures of circumstances?. But this was dropped in Laws of thought in favor of one which Boole considered to be more satisfactory, that of using the notion of ?time for which a proposition is true?. We show that, when suitable clarifications and corrections are made, the earlier approach? which accords with modern logic in eschewing the extraneous notion of (...)
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  35. Kevin J. Harrelson (2013). Logic and Ontology in Hegel's Theory of Predication. European Journal of Philosophy 21 (2).
    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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  36. Frans Hovens (1997). Lotze and Frege: The Dating of the'Kernsätze'∗. History and Philosophy of Logic 18 (1):17-31.
    Michael Dummett has shown that the fragment ?17 Kernsätze zur Logik? is evidence that Frege knew Lotze's Logik Dummett?s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege?s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ?Über die wissenschaftliche Berechtigung einer Begriffsschrift?, and veranlassenden Ursachen, from ?Logik?, certainly are borrowed from Lotze.Second, there are links between ?Booles rechnende Logik und die Begriffsschrift? and Lotze's (...)
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  37. Carlo Ierna (2008). Husserl's Critique of Double Judgments. In Filip Mattens (ed.), Meaning and Language: Phenomenological Perspectives. Springer. 49--73.
    In this paper I will discuss Edmund Husserl’s critique of Franz Brentano’s interpretation of categorical judgments as Double Judgments (Doppelurteile). This will be developed mostly as an internal critique, within the framework of the school of Brentano, and not through a direct contrast with Husserl’s own theory of judgment, as presented e.g. in the Fifth Investigation. Already during the 1890s Husserl overcame the psychologistic aspects of Brentano’s approach, advocating the importance of analysing the logical structure underlying language independently from psychology. (...)
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  38. Luis M. Laita (1980). Boolean Algebra and its Extra-Logical Sources: The Testimony of Mary Everest Boole. History and Philosophy of Logic 1 (1-2):37-60.
    Mary Everest, Boole's wife, claimed after the death of her husband that his logic had a psychological, pedagogical, and religious origin and aim rather than the mathematico-logical ones assigned to it by critics and scientists. It is the purpose of this paper to examine the validity of such a claim. The first section consists of an exposition of the claim without discussing its truthfulness; the discussion is left for the sections 2?4, in which some arguments provided by the examination of (...)
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  39. Karel Lambert (1983). Meinong and the Principle of Independence: Its Place in Meinong's Theory of Objects and its Significance in Contemporary Philosophical Logic. Cambridge University Press.
    As well as aiming to revive interest in Meinong's thought, this book challenges many of the most widespread assumptions of philosophical logic.
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  40. Robert Lane (1997). Peirce’s ‘Entanglement’ with the Principles of Excluded Middle and Contradiction. Transactions of the Charles S. Peirce Society 33 (3):680 - 703.
    Charles Peirce claimed that "anything is general in so far as the principle of excluded middle does not apply to it and is vague in so far as the principle of contradiction does not apply to it." This seems to imply that general propositions are neither true nor false and that vague propositions are both true and false. But this is not the case. I argue that Peirce's claim was intended to underscore relatively simple facts about quantification and negation, and (...)
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  41. Hugues Leblanc (1962). Boolean Algebra and the Propositional Calculus. Mind 71 (283):383-386.
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  42. Catherine Legg (2013). What is a Logical Diagram? In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. 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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  43. Catherine Legg (2008). The Problem of the Essential Icon. American Philosophical Quarterly 45 (3):207-232.
    Charles Peirce famously divided all signs into icons, indices and symbols. The past few decades have seen mainstream analytic philosophy broaden its traditional focus on symbols to recognise the so-called essential indexical. Can the moral now be extended to icons? Is there an “essential icon”? And if so, what exactly would be essential about it? It is argued that there is and it consists in logical form. Danielle Macbeth’s radical new “expressivist” interpretation of Frege’s logic and Charles Peirce’s existential graphs (...)
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  44. Albert C. Lewis (2004). The Unity of Logic, Pedagogy and Foundations in Grassmann's Mathematical Work. History and Philosophy of Logic 25 (1):15-36.
    Hermann Grassmann's Ausdehnungslehre of 1844 and his Lehrbuch der Arithmetik of 1861 are landmark works in mathematics; the former not only developed new mathematical fields but also both contributed to the setting of modern standards of rigor. Their very modernity, however, may obscure features of Grassmann's view of the foundations of mathematics that were not adopted since. Grassmann gave a key role to the learning of mathematics that affected his method of presentation, including his emphasis on making initial assumptions explicit. (...)
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  45. Yitzhak Y. Melamed (2012). “Omnis Determinatio Est Negatio” – Determination, Negation and Self-Negation in Spinoza, Kant, and Hegel. In Eckart Forster & Yitzhak Y. Melamed (eds.), Spinoza and German Idealism. Cambridge University Press.
    Spinoza’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza’s philosophy. It explains briefly the core of Spinoza’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious that matter in its totality, (...)
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  46. Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
    In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications (...)
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  47. Daniel D. Merrill (2005). Augustus De Morgan's Boolean Algebra. 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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  48. Dantel D. Merrill (1996). Making Sense of Solly's Syllogistic Symbolism. History and Philosophy of Logic 17 (1-2):199-207.
    This paper is an attempt to understand the method by which Thomas Solly (1816?1875), in his Syllabus of Logic (1839), provided a mathematical formulation of the traditional syllogism. The symbolism, in which analogues of multiplication, addition and subtraction are applied to term variables, is very puzzling at first. This paper provides a clear interpretation for this symbolism and explains why it works. It also addresses other notable features of the symbolism. The paper concludes by comparing the results which Solly obtained (...)
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  49. Gregory H. Moore (1999). Historians and Philosophers of Logic: Are They Compatible? The Bolzano-Weierstrass Theorem as a Case Study. History and Philosophy of Logic 20 (3-4):169-180.
    This paper combines personal reminiscences of the philosopher John Corcoran with a discussion of certain conflicts between historians of logic and philosophers of logic. Some mistaken claims about the history of the Bolzano-Weierstrass Theorem are analyzed in detail and corrected.
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  50. Shannon Nason (2011). Opposites, Contradictories, and Mediation in Kierkegaard's Critique of Hegel. Heythrop Journal 52 (6):24-36.
    In this paper I argue that Kierkegaard endorses Hegel's theory of mediation, the view that relative opposites are mediated. However, I show that Kierkegaard denies Hegel's thesis that there are all and only relative opposites. I develop two of his arguments against this thesis. The first is existential. This argument comes from the dramatic interplay between A, the often disagreeable aesthete of Either/Or I, and Judge William, the dutiful ethicist of Either/Or II. Judge William convincingly argues that the possibility of (...)
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