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  1. Fred Ablondi (2002). A Note on Hahn's Philosophy of Logic. History and Philosophy of Logic 23 (1):37-42.
    Hans Hahn, mathematician, philosopher and co-founder of the Vienna Circle, attempted to reconcile the validity and applicability of both logic and mathematics with a strict empiricism. This article begins with a review of this attempt, focusing on his view of the relation of language to logic and his answer to the question of why we need logic. I then turn to some recent work by Stephen Yablo in an attempt to show that Yablo's fictionalism, and in particular his use of (...)
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  2. Hans Richard Ackermann (1983). Aus Dem Briefwechsel Wilhelm Ackermanns. History and Philosophy of Logic 4 (1-2):181-202.
    A selection from the correspondence of the logician Wilhelm Ackermann (1896?1962) is presented in this article. The most significant letters were exchanged with Bernays, Scholz and Lorenzen, from which extensive passages are transcribed. Some remarks from other letters, with quotations, are also included.
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  3. 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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  4. Enrique Alonso & Maria Manzano (2005). Diagonalisation and Church's Thesis: Kleene's Homework. History and Philosophy of Logic 26 (2):93-113.
    In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1?In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the ??definable functions. But, quickly realizing that the diagonalization cannot be (...)
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  5. Irving H. Anellis (2009). Russell and His Sources for Non-Classical Logics. Logica Universalis 3 (2):153-218.
    My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...)
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  6. 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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  7. Irving H. Anellis (1987). Mathematical Logic in the Soviet Union, 1917–1980. History and Philosophy of Logic 8 (1):71-76.
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  8. Irving H. Anellis (1987). The Heritage of S. A. Janovskaja. History and Philosophy of Logic 8 (1):45-56.
    A survey is provided of the Soviet-Russian logician and historian Sof'ja A. Janovskaya (1896?1966). She wrote survey articles on logic, and also historical and philosophical essays on logic and on mathematics. A selected bibliography of her writings is appended.
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  9. Aldo Antonelli, Frege: Fra Estensionalismo E Logicismo.
    Due programmi diversi si intersecano nel lavoro di Frege sui fondamenti dell’aritmetica: • Logicismo: l’aritmetica `e riducibile alla logica; • Estensionalismo: l’aritmetica `e riducibile a una teoria delle estensioni. Sia nei Fondamenti che nei Principi, Frege articola l’idea che l’aritmetica sia riducibile a una teoria logica delle estensioni.
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  10. G. Aldo Antonelli & Robert C. May (2005). Frege's Other Program. Notre Dame Journal of Formal Logic 46 (1):1-17.
    Frege’s logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the “neo-logicist” approach of Hale & Wright. Less attention has been given to Frege’s extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of (...)
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  11. G. Aldo Antonelli & Robert C. May (2000). Frege's New Science. Notre Dame Journal of Formal Logic 41 (3):242-270.
    In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege’s debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege’s critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be (...)
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  12. D. M. Armstrong (1992). Book Review: Raymond Bradley. The Nature of All Being: A Study of Wittgenstein's Modal Atomism. [REVIEW] Notre Dame Journal of Formal Logic 34 (1):150-156.
  13. S. Arpaia (2006). On Magari's Concept of General Calculus: Notes on the History of Tarski's Methodology of Deductive Sciences. History and Philosophy of Logic 27 (1):9-41.
    This paper is an historical study of Tarski's methodology of deductive sciences (in which a logic S is identified with an operator Cn S , called the consequence operator, on a given set of expressions), from its appearance in 1930 to the end of the 1970s, focusing on the work done in the field by Roberto Magari, Piero Mangani and by some of their pupils between 1965 and 1974, and comparing it with the results achieved by Tarski and the Polish (...)
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  14. F. G. Asenjo (1977). Leśniewski's Work and Nonclassical Set Theories. Studia Logica 36 (4):249-255.
  15. Jeremy Avigad & Richard Zach (2008). The Epsilon Calculus. Stanford Encyclopedia of Philosophy.
    The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term..
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  16. 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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  17. Steve Awodey & Erich H. Reck, Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic.
    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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  18. Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics. History and Philosophy of Logic 23 (2):77-94.
    This paper is the second 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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  19. Francesco Barone & Ludovico Geymonat (1992). Omaggio a Ludovico Geymonat. Saggi e Testimonianze. Franco Muzzio Editore.
    Il volume comprende i saggi dei seguenti autori: Corrado Mangione, Enrico Bellone, Giulio Giorello, Marco Mondadori, Gabriele Lolli, Silvano Tagliagambe, Francesco Barone, Umberto Bottazzini, Vincenzo Cappelletti, Domenico Costantini, Piero Mangani, Carlos Minguez, Alberto Pasquinelli, Rossano Pancaldi, Mario Servi.
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  20. Tomás Barrero (2004). Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação). Dissertation, Universidade Estadual de Campinas
    This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...)
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  21. O. Bradley Bassler (2006). Book Review: Mark van Atten. On Brouwer. [REVIEW] Notre Dame Journal of Formal Logic 47 (4):581-599.
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  22. T. Batóg (1968). Problems of Traditional Logic in the Works of Adam Wiegner. Studia Logica 23 (1):147-147.
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  23. James E. Baumgartner (1997). In Memoriam: Paul Erdös, 1913-1996. Bulletin of Symbolic Logic 3 (1):70-72.
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  24. Timothy Bays (2000). The Fruits of Logicism. Notre Dame Journal of Formal Logic 41 (4):415-421.
    You’ll be pleased to know that I don’t intend to use these remarks to comment on all of the papers presented at this conference. I won’t try to show that one paper was right about this topic, that another was wrong was about that topic, or that several of our conference participants were talking past one another. Nor will I try to adjudicate any of the discussions which took place in between our sessions. Instead, I’ll use these remarks to make (...)
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  25. Valentin A. Bazhanov (2008). Non-Classical Stems From Classical: N. A. Vasiliev's Approach to Logic and His Reassessment of the Square of Opposition. [REVIEW] Logica Universalis 2 (1):71-76.
    . In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880–1940) noted this opposition and stressed that the way for the novel – non-Aristotelian – logic was already paved. He made an attempt to construct non-Aristotelian logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What reasons forced him to reassess the status of particular propositions and to replace the square of opposition by (...)
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  26. Enrico Bellone, Corrado Mangione, Giulio Giorello, Marco Mondadori, Gabriele Lolli, Silvano Tagliagambe, Francesco Barone, Umberto Bottazzini, Vincenzo Cappelletti, Domenico Costantini, Piero Mangani, Carlos Minguez, Alberto Pasquinelli, Rossano Pancaldi & Mario Servi (1992). Omaggio a Ludovico Geymonat. Franco Muzzio Editore.
  27. J. Berg (1987). Is Russell's Antinomy Derivable in Bolzano's Logic? In Bolzano-Studien. Philosophia Naturalis 24 (4):406-413.
  28. Corine Besson (forthcoming). Norms, Reasons and Reasoning: A Guide Through Lewis Carroll’s Regress Argument. In Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity.
  29. A. Betti, Łukasiewicz and Leśniewski on Contradiction.
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  30. A. Betti, The Strange Case of Savonarola and the Painted Fish. On the Bolzanization of Polish Thought.
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  31. Arianna Betti (2010). Leśniewski's Characteristica Universalis. Synthese 174 (2):295-314.
    Leśniewski’s systems deviate greatly from standard logic in some basic features. The deviant aspects are rather well known, and often cited among the reasons why Leśniewski’s work enjoys little recognition. This paper is an attempt to explain why those aspects should be there at all. Leśniewski built his systems inspired by a dream close to Leibniz’s characteristica universalis: a perfect system of deductive theories encoding our knowledge of the world, based on a perfect language. My main claim is that Leśniewski (...)
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  32. Arianna Betti (2004). Lesniewski's Early Liar, Tarski and Natural Language. Annals of Pure and Applied Logic 127 (1-3):267-287.
    This paper is a contribution to the reconstruction of Tarski’s semantic background in the light of the ideas of his master, Stanislaw Lesniewski. Although in his 1933 monograph Tarski credits Lesniewski with crucial negative results on the semantics of natural language, the conceptual relationship between the two logicians has never been investigated in a thorough manner. This paper shows that it was not Tarski, but Lesniewski who first avowed the impossibility of giving a satisfactory theory of truth for ordinary language, (...)
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  33. Patricia Blanchette (2007). The Frege-Hilbert Controversy. The Stanford Encyclopedia of Philosophy.
    In the early years of the twentieth century, Gottlob Frege and David Hilbert, two titans of mathematical logic, engaged in a controversy regarding the correct understanding of the role of axioms in mathematical theories, and the correct way to demonstrate consistency and independence results for such axioms. The controversy touches on a number of difficult questions in logic and the philosophy of logic, and marks an important turning-point in the development of modern logic. This entry gives an overview of that (...)
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  34. Andrés Bobenrieth M. (2011). The Origins of the Use of the Argument of Trivialization in the Twentieth Century. History and Philosophy of Logic 31 (2):111-121.
    The origin of paraconsistent logic is closely related with the argument, 'from the assertion of two mutually contradictory statements any other statement can be deduced'; this can be referred to as ex contradictione sequitur quodlibet (ECSQ). Despite its medieval origin, only by the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this article is to study what happened earlier: from Principia Mathematica to that time, when it became well (...)
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  35. David Bostock (2009). Russell's Early Theory of Denoting. History and Philosophy of Logic 30 (1):49-67.
    The article concerns the treatment of the so-called denoting phrases, of the forms ?every A?, ?any A?, ?an A? and ?some A?, in Russell's Principles of Mathematics. An initially attractive interpretation of what Russell's theory was has been proposed by P.T. Geach, in his Reference and Generality (1962). A different interpretation has been proposed by P. Dau (Notre Dame Journal, 1986). The article argues that neither of these is correct, because both credit Russell with a more thought-out theory than he (...)
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  36. Manuel Bremer (2010). Universality in Set Theories. Ontos.
    The book discusses the fate of universality and a universal set in several set theories.
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  37. Constantin C. Brîncuș & Iulian D. Toader (2013). A Carnapian Approach to Counterexamples to Modus Ponens. Romanian Journal of Analytic Philosophy 7:78-85.
    This paper defends a Carnapian approach to known counterexamples to Modus Ponens (MP). More specifically, it proposes that instead of rejecting MP as invalid in certain interpretations, one should regard the interpretations themselves as non-normal, in Carnap’s sense.
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  38. William Brooke & Andrew Aberdein (2011). The Formal Failure and Social Success of Logic. In Frank Zenker (ed.), Argumentation: Cognition & community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18–21, 2011. OSSA
    Is formal logic a failure? It may be, if we accept the context-independent limits imposed by Russell, Frege, and others. In response to difficulties arising from such limitations I present a Toulmin-esque social recontextualization of formal logic. The results of my project provide a positive view of formal logic as a success while simultaneously reaffirming the social and contextual concerns of argumentation theorists, critical thinking scholars, and rhetoricians.
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  39. Hans-Christoph Schmidt Am Busch & Kai Wehmeier (2007). On the Relations Between Heinrich Scholz and Jan Łukasiewicz. History and Philosophy of Logic 28 (1):67-81.
    The aim of the present study is (1) to show, on the basis of a number of unpublished documents, how Heinrich Scholz supported his Warsaw colleague Jan ?ukasiewicz, the Polish logician, during World War II, and (2) to discuss the efforts he made in order to enable Jan ?ukasiewicz and his wife Regina to move from Warsaw to Münster under life-threatening circumstances. In the first section, we explain how Scholz provided financial help to ?ukasiewicz, and we also adduce evidence of (...)
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  40. Paola Cantù & De Zan Mauro (2009). Life and Works of Giovanni Vailati. In Arrighi Claudia, Cantù Paola, De Zan Mauro & Suppes Patrick (eds.), Life and Works of Giovanni Vailati. CSLI Publications
    The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a form of pragmatism is not a faithful interpretation of Peano’s (...)
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  41. P. Cassou-Nogues (2009). Gödel's Introduction to Logic in 1939. History and Philosophy of Logic 30 (1):69-90.
    This article presents three extracts from the introductory course in mathematical logic that Gödel gave at the University of Notre Dame in 1939. The lectures include a few digressions, which give insight into Gödel's views on logic prior to his philosophical papers of the 1940s. The first extract is Gödel's first lecture. It gives the flavour of Gödel's leisurely style in this course. It also includes a curious definition of logic and a discussion of implication in logic and natural language. (...)
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  42. Carlo Cellucci (1998). The Scope of Logic: Deduction, Abduction, Analogy. Theoria 64 (2-3):217-242.
    The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. (...)
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  43. Stefania Centrone (2006). Husserl on the 'Totality of All Conceivable Arithmetical Operations'. History and Philosophy of Logic 27 (3):211-228.
    In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is ? as far as we know ? the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate ? (...)
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  44. Arkadiusz Chrudzimski & Dariusz Łukasiewicz (eds.) (2006). Actions, Products, and Things: Brentano and Polish Philosophy. Ontos.
    This volume is devoted to Brentano's influence on the Polish Analytic Philosophy better known under the name of: Lvov-Warsaw School.
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  45. Alonzo Church (1976). Review: Douglas Lackey, Bertrand Russell, Essays in Analysis by Bertrand Russell. [REVIEW] Journal of Symbolic Logic 41 (3):700-702.
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  46. Cezary Cieśliński (2015). How Tarski Defined the Undefinable. European Review 23 (01):139 - 149.
    This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept.
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  47. B. Jack Copeland (2006). Meredith, Prior, and the History of Possible Worlds Semantics. Synthese 150 (3):373 - 397.
    This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.
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  48. John Corcoran, LOGIC TEACHING IN THE 21ST CENTURY.
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...)
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  49. John Corcoran (forthcoming). Tarski’s Convention T: Condition Beta. SOUTH AMERICAN JOURNAL OF LOGIC 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  50. John Corcoran (2016). LOGIC TEACHING IN THE 21ST CENTURY. Quadripartita Ratio: Revista de Argumentación y Retórica 1 (1):1-34.
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...)
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