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  1. added 2015-05-24
    John Corcoran & Sriram Nambiar (2014). De Morgan on Euclid’s Fourth Postulate. Journal of Symbolic Logic 20:250-1.
    This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...)
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  2. added 2015-05-23
    Gilbert Plumer (2013). Commentary On: Chiara Pollaroli's "T(R)Opical Patterns in Advertising". In D. Mohammed M. Lewiński (ed.), Virtues of Argumentation. Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation [CD-ROM]. Centre for Research in Reasoning, Argumentation and Rhetoric, and the University of Windsor. 1-5.
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  3. added 2015-05-23
    John Corcoran (2006). George Boole. In Encyclopedia of Philosophy. 2nd edition. macmillan.
    2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...)
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  4. added 2015-05-23
    Gilbert E. Plumer (2000). A Review of the LSAT Using Literature on Legal Reasoning. Law School Admission Council Computerized Testing Report 97 (8):1-19.
    Research using current literature on legal reasoning was conducted with the goals of (a) determining what skills are most important in good legal reasoning according to such literature, (b) determining the extent to which existing Law School Admission Test item types and subtypes are designed to assess those skills, and (c) suggesting test specifications or new or refined item types and formats that could be developed in the future to assess any important skills that appear [by (a) and (b)] to (...)
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  5. added 2015-05-23
    John Corcoran (1987). Three Rules of Distribution: One Counterexample. Journal of Symbolic Logic 52:886-887.
    This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...)
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  6. added 2015-05-22
    Massimiliano Carrara & Enrico Martino (forthcoming). The Mereological Foundation of Megethology. Journal of Philosophical Logic:1-9.
    In Mathematics is megethology . Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non (...)
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  7. added 2015-05-22
    John Corcoran (2009). Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic. In W. A. Carnielli (ed.), The Many Sides of Logic. College Publications. 71-103.
    The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...)
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  8. added 2015-05-21
    Prem Kumar Singh & Abdullah Gani (forthcoming). Fuzzy Concept Lattice Reduction Using Shannon Entropy and Huffman Coding. Journal of Applied Non-Classical Logics:1-19.
    In the last decade, formal concept analysis in a fuzzy setting has received more attention for knowledge processing tasks in various fields. The hierarchical order visualisation of generated formal concepts is a major concern for the practical application of FCA. In this process, a major issue is the huge number of formal concepts generated from ‘a large context’, and another problem is their ‘storage’ complexity. To deal with these issues a method is proposed in this paper based on Shannon entropy (...)
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  9. added 2015-05-20
    Francesco Berto (2015). The Firmest of All Principles. In Channa van Dijk, Eva van der Graaf, Michiel den Haan, Rosa de Jong, Christiaan Roodenburgh, Dyane Til & Deva Waal (eds.), Under Influence - Philosophical Festival Drift (2014). 82-93.
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  10. added 2015-05-18
    Matteo Bianchi & Franco Montagna (forthcoming). Trakhtenbrot Theorem and First-Order Axiomatic Extensions of MTL. Studia Logica:1-19.
    In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. Hájek generalized this result to the first-order versions of Łukasiewicz, Gödel and Product logics, w.r.t. their standard algebras. In this paper we extend the analysis to the first-order versions of axiomatic extensions of MTL. Our main result is the following. Let \ be a class of MTL-chains. Then the set of all first-order tautologies associated to the finite models (...)
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  11. added 2015-05-16
    Alfredo Storck (forthcoming). The Meanings of ‘Logic’ in the Thirteenth Century. Logica Universalis:1-22.
    The goal of this article is to call attention to different ways in which logic was understood in the thirteenth century. Thus, it will recall some relevant historical facts related to the problem of classifying logic among scientific disciplines. This problem involved methodological questions linked to the form of presenting both the scientific disciplines and the books by which they were transmitted. Next, it will stress the contexts that led Medievals to raise questions about the nature of logic and why (...)
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  12. added 2015-05-15
    George Barmpalias, Mingzhong Cai, Steffen Lempp & Theodore A. Slaman (forthcoming). On the Existence of a Strong Minimal Pair. Journal of Mathematical Logic:150513211853004.
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  13. added 2015-05-15
    Jessica Leech (2015). Logic and the Laws of Thought. Philosophers' Imprint 15 (12).
    An approach to explaining the nature and source of logic and its laws with a rich historical tradition takes the laws of logic to be laws of thought. This view seems intuitively compelling, after all, logic seems to be intimately related with how we think. But how exactly should we understand it? And what arguments can we give in favour? I will propose one line of argument for the claim that the laws of logic are laws of thought. I will (...)
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  14. added 2015-05-13
    Marcus Rossberg And Philip A. Ebert J. J. Green (2015). The Convenience of the Typesetter; Notation and Typography in Frege's "Grundgesetze der Arithmetik. Bulletin of Symbolic Logic 21 (1):15-30,.
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  15. added 2015-05-13
    Solomon Feferman and Vladimir Lifschitz (2015). In Memoriam: Grigori E. Mints 1939-2014. Bulletin of Symbolic Logic 21 (1):31-33,.
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  16. added 2015-05-13
    John Corcoran And Hassan Masoud (2015). Existential-Import Mathematics. Bulletin of Symbolic Logic 21 (1):1-14,.
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  17. added 2015-05-12
    Richard Zach (forthcoming). Natural Deduction for the Sheffer Stroke and Peirce’s Arrow. Journal of Philosophical Logic:1-15.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow . The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions (...)
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  18. added 2015-05-11
    Sam Buss (forthcoming). Book Review: Matthias Baaz and Alexander Leitsch, Methods of Cut-Elimination. [REVIEW] Studia Logica:1-5.
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  19. added 2015-05-11
    Kazem Sadegh-Zadeh (2nd ed. 2015). Fuzzy Logic. In Handbook of Analytic Philosophy of Medicine. Springer Netherlands.
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  20. added 2015-05-11
    Cezar Augusto Mortari (2001). Introdução à Lógica. Editora Unesp.
  21. added 2015-05-09
    Rutger Kuyper (forthcoming). First-Order Logic in the Medvedev Lattice. Studia Logica:1-40.
    Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal quantifier. We extend the work of Medvedev to first-order logic, using the notion of a first-order hyperdoctrine from categorical logic, to a structure which we will call the hyperdoctrine (...)
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  22. added 2015-05-09
    Yan Zhang & Kai Li (forthcoming). Decidability of Logics Based on an Indeterministic Metric Tense Logic. Studia Logica:1-40.
    This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique.
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  23. added 2015-05-08
    Rosalie Iemhoff (forthcoming). On Rules. Journal of Philosophical Logic:1-15.
    This paper contains a brief overview of the area of admissible rules with an emphasis on results about intermediate and modal propositional logics. No proofs are given but many references to the literature are provided.
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  24. added 2015-05-04
    Terence Rajivan Edward, Another Solution to the Surprise Exam Paradox.
    I identify an assumption that the students should not rely on. Even if students are entitled to assume that the teacher was sincere at the time of giving the exam announcement, there is a reason against them assuming the following: if the teacher believes that the exam will not be a surprise on a certain day, the teacher will not give the exam on that day. The reason I present does not involve doubting the moral goodness of the teacher.
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  25. added 2015-05-01
    Pierre-Jean Renaudie (forthcoming). La Question de la Logique Dans l'Idéalisme Allemand. History and Philosophy of Logic:1-4.
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  26. added 2015-04-30
    Gil Sagi (2014). Formality in Logic: From Logical Terms to Semantic Constraints. Logique Et Analyse 57 (227).
    In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no longer (...)
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  27. added 2015-04-27
    Peter Anstey (2015). Francis Bacon and the Laws of Ramus. Hopos: The Journal of the International Society for the History of Philosophy of Science 5 (1):1-23.
    This article assesses the role of the laws of the French logician and educational reformer Petrus Ramus in the writings of Francis Bacon. The laws of Ramus derive from Aristotle’s grounds for necessary propositions. Necessary propositions, according to Aristotle, Ramus, and Bacon, are required for the premises of scientific syllogisms. It is argued that in Bacon’s Advancement of Learning and De augmentis scientiarum the only role for these laws is in the transmission of knowledge that has already been acquired. However, (...)
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  28. added 2015-04-26
    D. M. Gabbay & O. Rodrigues (forthcoming). Probabilistic Argumentation: An Equational Approach. Logica Universalis:1-38.
    There is a generic way to add any new feature to a system. It involves identifying the basic units which build up the system and introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: the nature of the arguments involved; the membership relation in the set S of arguments; the attack relation; and the choice of extensions. Generically to (...)
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  29. added 2015-04-26
    D. M. Gabbay & O. Rodrigues (forthcoming). Equilibrium States in Numerical Argumentation Networks. Logica Universalis:1-63.
    Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed (...)
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  30. added 2015-04-26
    Alexandru Baltag & Sonja Smets (forthcoming). Logics of Informational Interactions. Journal of Philosophical Logic:1-13.
    The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions between subsystems of a global physical system. Similarly, epistemic (...)
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  31. added 2015-04-26
    Dale Jacquette (2014). Against Logically Possible World-Relativized Existence. Metaphysica 15 (1).
    The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept of world-relativized existence is examined in Alvin Plantinga’s formal development and explanation of modal semantic relations. Despite proposing an attractive unified semantics of alethic modality, Plantinga’s argument is rejected on formal grounds as (...)
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  32. added 2015-04-25
    Gary Ebbs (forthcoming). Satisfying Predicates: Kleene's Proof of the Hilbert–Bernays Theorem. History and Philosophy of Logic:1-21.
    The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for (...)
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  33. added 2015-04-22
    Alberto Gatto (forthcoming). Axiomatization of a Branching Time Logic with Indistinguishability Relations. Journal of Philosophical Logic:1-28.
    Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.
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  34. added 2015-04-19
    Max Gottschlich (forthcoming). Logik und Selbsterkenntnis. Perspektiven der Philosophie.
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  35. added 2015-04-19
    John Corcoran (2014). Truth-Preserving and Consequence-Preserving Deduction Rules”,. Bulletin of Symbolic Logic 20:130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...)
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  36. added 2015-04-19
    John Corcoran (2001). Second-Order Logic. In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER. 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...)
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  37. added 2015-04-18
    Harold T. Hodes (2015). Why Ramify? Notre Dame Journal of Formal Logic 56 (2):379-415.
    This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...)
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  38. added 2015-04-18
    Takahiro Seki (2015). Halldén Completeness for Relevant Modal Logics. Notre Dame Journal of Formal Logic 56 (2):333-350.
    Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.
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  39. added 2015-04-18
    Hsing-Chien Tsai (2015). On the Decidability of Axiomatized Mereotopological Theories. Notre Dame Journal of Formal Logic 56 (2):287-306.
    The signature of the formal language of mereotopology contains two predicates $P$ and $C$, which stand for “being a part of” and “contact,” respectively. This paper will deal with the decidability issue of the mereotopological theories which can be formed by the axioms found in the literature. Three main results to be given are as follows: all axiomatized mereotopological theories are separable; all mereotopological theories up to $\mathbf{ACEMT}$, $\mathbf{SACEMT}$, or $\mathbf{SACEMT}^{\prime}$ are finitely inseparable; all axiomatized mereotopological theories except $\mathbf{SAX}$, $\mathbf{SAX}^{\prime}$, (...)
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  40. added 2015-04-18
    David R. Belanger (2015). Weak Truth Table Degrees of Structures. Notre Dame Journal of Formal Logic 56 (2):263-285.
    We study the weak truth table degree spectra of first-order relational structures. We prove a dichotomy among the possible wtt degree spectra along the lines of Knight’s upward-closure theorem for Turing degree spectra. We prove new results contrasting the wtt degree spectra of finite- and infinite-signature structures. We show that, as a method of defining classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than the Turing degree spectrum.
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  41. added 2015-04-18
    Tapani Hyttinen (2015). Forking in Finite Models. Notre Dame Journal of Formal Logic 56 (2):307-320.
    We study properties of forking in the classes of all finite models of a complete theory in a finite variable logic. We also study model constructions under the assumption that forking is trivial.
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  42. added 2015-04-18
    Andrea Sorbi & Sebastiaan A. Terwijn (2015). Generalizations of the Weak Law of the Excluded Middle. Notre Dame Journal of Formal Logic 56 (2):321-331.
    We study a class of formulas generalizing the weak law of the excluded middle and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice.
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  43. added 2015-04-18
    George Voutsadakis (2015). Categorical Abstract Algebraic Logic: Truth-Equational $Pi$-Institutions. Notre Dame Journal of Formal Logic 56 (2):351-378.
    Finitely algebraizable deductive systems were introduced by Blok and Pigozzi to capture the essential properties of those deductive systems that are very tightly connected to quasivarieties of universal algebras. They include the equivalential logics of Czelakowski. Based on Blok and Pigozzi’s work, Herrmann defined algebraizable deductive systems. These are the equivalential deductive systems that are also truth-equational, in the sense that the truth predicate of the class of their reduced matrix models is explicitly definable by some set of unary equations. (...)
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  44. added 2015-04-18
    Paolo Mancosu (2014). Grundlagen, Section 64: Frege's Discussion of Definitions by Abstraction in Historical Context. History and Philosophy of Logic 36 (1):62-89.
    I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools . In addition, I put Frege's considerations in the context of a widespread debate in Germany (...)
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  45. added 2015-04-17
    Terence Rajivan Edward, A Solution to the Surprise Exam Paradox.
    The students’ argument against the possibility of a surprise exam assumes that the following would not occur: the teacher decides to give the exam on a certain day, the exam would not be a surprise on that day, but the teacher does not realize this. I give a reason to reject this assumption, and I point out that an attempt to reformulate the surprise exam paradox in order to allow for the assumption does not result in an acceptable argument.
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  46. added 2015-04-17
    Marc Champagne, Reply to My Commentator. Argument Cultures: Proceedings of the Ontario Society for the Study of Argumentation.
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  47. added 2015-04-15
    Sébastien Gandon (forthcoming). The Logical Must: Wittgensein on Logic. History and Philosophy of Logic:1-3.
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  48. added 2015-04-14
    Katrin Schulz (forthcoming). Conditionals From a Linguistic Point of View: Two Case Studies. Journal of Philosophical Logic:1-12.
    IntroductionThe meaning of conditional sentences bears an intrinsic relation to a number of central philosophical problems, like the nature of reasoning, the possibility of knowledge, and the status of laws of nature. This has incited philosophers to spend a lot of time working on conditionals and to fill countless bookshelves with inspiring and sophisticated theories on their meaning. However, the overall question of how to approach the meaning of conditionals is still open. There are many different theories on the market, (...)
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  49. added 2015-04-11
    Andreas Herzig (2015). Letter From the Editor. Journal of Applied Non-Classical Logics 25 (1):1-1.
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  50. added 2015-04-10
    Stanislav Kikot (forthcoming). A Dichotomy for Some Elementarily Generated Modal Logics. Studia Logica:1-31.
    In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form \ . We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.
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