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Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Jagiellonian University)
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  1. added 2016-05-04
    Bo Mou (forthcoming). How the Validity of the Parallel Inference is Possible: From the Ancient Mohist Diagnose to a Modern Logical Treatment of Its Semantic-Syntactic Structure. History and Philosophy of Logic:1-24.
    The purpose of this paper is to explore the issue of how the validity of the parallel inference is possible in view of its deep semantic-syntactic structure. I first present a philosophical interpretation of the ancient Mohist treatment of the parallel inference concerning its semantic-syntactic structure. Then, to formally and accurately capture the later Mohist point in this connection for the sake of giving a general condition for the validity of the parallel inference, I suggest a modern (...)
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  2. added 2016-05-04
    Urszula Wybraniec-Skardowska (forthcoming). Logical Squares for Classical Logic Sentences. Logica Universalis:1-20.
    In this paper, with reference to relationships of the traditional square of opposition, we establish all the relations of the square of opposition between complex sentences built from the 16 binary and four unary propositional connectives of the classical propositional calculus. We illustrate them by means of many squares of opposition and, corresponding to them—octagons, hexagons or other geometrical objects.
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  3. added 2016-05-03
    Alessandro Giordani (2016). A New Framework for Justification Logic. Journal of Applied Non-Classical Logics 25 (4):308-323.
    The logic of justification provides an in-depth analysis of the epistemic states of an agent. This paper aims at solving some of the problems to which the common interpretation of the operators of justification logic is subject by providing a framework in which a crucial distinction between potential and explicit justifiers is exploited. The paper is subdivided into three sections. The first section offers an introduction to a basic system LJ of justification logic and to the problems concerning its interpretation. (...)
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  4. added 2016-05-03
    Tim Button (2016). Knot and Tonk: Nasty Connectives on Many-Valued Truth-Tables for Classical Sentential Logic. Analysis 76 (1):7-19.
    Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...)
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  5. added 2016-05-03
    Imran Aijaz, Jonathan McKeown-Green & Aness Webster, Burdens of Proof and the Case for Unevenness.
    How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to some proposition (...)
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  6. added 2016-05-02
    Joshua D. K. Brown & James W. Garson (forthcoming). A New Semantics for Vagueness. Erkenntnis:1-21.
    Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...)
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  7. added 2016-05-01
    Luca Gili & Marco Sgarbi (eds.) (forthcoming). The Aftermath of Syllogism. Bloomsbury.
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  8. added 2016-04-27
    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.
  9. added 2016-04-27
    Matthew A. Benton (forthcoming). Lotteries and Prefaces. In Jonathan Jenkins Ichikawa (ed.), The Routledge Handbook of Epistemic Contextualism. Routledge
    The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...)
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  10. added 2016-04-27
    Corine Besson (2016). Trenton Merricks Propositions. [REVIEW] Notre Dame Philosophical Reviews 2016.
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  11. added 2016-04-27
    Frederique Janssen-Lauret, Making Room for Women in Our Tools forTeaching Logic: A Proposal for PromotingGender-Inclusiveness. Proceedings of the 4th International Conference on Tools for Teaching Logic.
    Logic is one of the most male-dominated areas within the already hugely male-dominated subject of philosophy. Popular hypotheses for this disparity include a preponderance of confident,mathematically-minded male students in the classroom, the historical association between logic and maleness, and the lack of female role-models for students, though to date none of these have been empirically tested. In this paper I discuss the effects of various attempts to address these potential causes whilst teaching second-year formal and philosophical logic courses at different (...)
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  12. added 2016-04-27
    Frederique Janssen-Lauret & Gary Kemp (eds.) (2015). Quine and His Place in History. Palgrave.
    Containing three previously unpublished papers by W.V. Quine as well as historical, exegetical, and critical papers by several leading Quine scholars including Hylton, Ebbs, and Ben-Menahem, this volume aims to remedy the comparative lack of historical investigation of Quine and his philosophical context.
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  13. added 2016-04-25
    Shawn Standefer (2016). Contraction and Revision. Australasian Journal of Logic 13 (3):58-77.
    An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.
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  14. added 2016-04-23
    David Ellerman, On Classical and Quantum Logical Entropy.
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  15. added 2016-04-23
    David Ellerman, The Quantum Logic of Direct-Sum Decompositions.
    Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) (...)
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  16. added 2016-04-23
    Bartosz Więckowski (forthcoming). Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity. Journal of Logic, Language and Information:1-54.
    A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...)
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  17. added 2016-04-22
    Michael Joseph Fitzgerald (forthcoming). Albert of Saxony's View of Complex Terms in Categorical Propositions and the ‘English-Rule’. History and Philosophy of Logic:1-28.
    The essay first makes some observations on the general interrelationship between the logical writings of Albert and Buridan. Second, it gives an account of a ‘semantic logical model’ for analyzing complex subject terms in some basic categorical propositions which is defended by Albert of Saxony, and briefly recounts Buridan's criticisms of that model. Finally, the essay maintains that the Albertian model is typically compatible with, and a further development of, what is called by a late-fourteenth century anonymous scholar ‘the English-Rule’ (...)
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  18. added 2016-04-21
    Tomoyuki Suzuki (forthcoming). The Distributivity on Bi-Approximation Semantics. Notre Dame Journal of Formal Logic.
    In this paper, we give a possible characterization of the distributivity on bi-approximation semantics. To this end, we introduce new notions of special elements on polarities and show that the distributivity is first-order definable on bi-approximation semantics. In addition, we investigate the dual representation of those structures and compare them with bi-approximation semantics for intuitionistic logic. We also discuss that two different methods to validate the distributivity—by the splitters and by the adjointness—can be explicated with the help of the axiom (...)
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  19. added 2016-04-21
    Joel David Hamkins & Cole Leahy (forthcoming). Algebraicity and Implicit Definability in Set Theory. Notre Dame Journal of Formal Logic.
    We analyze the effect of replacing several natural uses of definability in set theory by the weaker model-theoretic notion of algebraicity. We find, for example, that the class of hereditarily ordinal algebraic sets is the same as the class of hereditarily ordinal definable sets; that is, $\mathrm{HOA}=\mathrm{HOD}$. Moreover, we show that every algebraic model of $\mathrm{ZF}$ is actually pointwise definable. Finally, we consider the implicitly constructible universe $\mathrm{Imp}$—an algebraic analogue of the constructible universe—which is obtained by iteratively adding not only (...)
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  20. added 2016-04-21
    Jafar S. Eivazloo & Somayyeh Tari (forthcoming). SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures. Notre Dame Journal of Formal Logic.
    Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong CE-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has SCE-cell decomposition if and only if its canonical o-minimal extension has CE-cell decomposition. Then, we show that every weakly o-minimal structure with SCE-cell decomposition satisfies OCP. Our last result implies that every o-minimal structure in which every definable open (...)
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  21. added 2016-04-20
    Maciej Sendłak (forthcoming). Between the Actual and the Trivial World. Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 23 (2).
    The subject of this paper is the notion of similarity between the actual and impossible worlds. Many believe that this notion is governed by two rules. Ac-cording to the first rule, every non-trivial world is more similar to the actual world than the trivial world is. The second rule states that every possible world is more similar to the actual world than any impossible world is. The aim of this paper is to challenge both of these rules. We argue that (...)
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  22. added 2016-04-20
    H. Van Ditmarsch & P. Iliev (2016). The Succinctness of the Cover Modality. Journal of Applied Non-Classical Logics 25 (4):373-405.
    We prove that modal logic formulated in a language with the cover modality is exponentially more succinct than the usual box-and-diamond version. In contrast with this, we show that adding the so-called public announcement operator to the latter results in a modal system that is exponentially more succinct than the one based on the cover modality.
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  23. added 2016-04-19
    Kai Soerfjord, Kant's and Wittgenstein's Criterion-Integral of Validity is NOT the Presently Taught.
    I see no evidence that would lead me to deem it reasonable to charge Kant of such a blatant irrelevancy as it would necessarily be to compose lectures in logic that discuss the inherent reasonability of ‘logical truth’, unless he by ‘logical truth’ meant ‘reasonability-wise strength’ and saw that type of ‘strength’ to have the precise same pragmatic and philosophical relevance that theorizers now project onto the notion 'reasonability-wise validity’, logical (deductive) validity. It is the assumption of the irrelevancy constituted (...)
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  24. added 2016-04-19
    Hashem Morvarid (forthcoming). Hale on the Absoluteness of Logical Necessity. Acta Analytica:1-11.
    Hale has argued that logical necessities are absolute in the sense that there is no competing kind of modality under which they may be false. In this paper, I argue that there are competing kinds of modality, which I call “essentialist modalities,” under which logical necessities may be false. Since it is counter-intuitive to say that logical necessities are not absolute, my argument, if correct, shows that Hale’s characterization of absolute necessity does not adequately capture the intuitive (...)
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  25. added 2016-04-19
    Pawel Garbacz (2016). Conceptual Frames Revisited. Journal of Applied Non-Classical Logics 25 (4):287-307.
    The paper presents a logical framework formalising the main insights of the psychological theory of concepts developed by Lawrence Barsalou. The framework is established within the context of Common Logic as a logical theory in the axiomatic manner. Its semantic characterisation is provided and shown to be sound and incomplete with respect to the class of its models.
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  26. added 2016-04-18
    Herbert Roseman, Spinoza's Ethics as a Mathematical Object.
    Spinoza’s geometrical approach to his masterwork, the Ethics, can be represented by a digraph, a mathematical object whose properties have been extensively studied. The paper describes a project that developed a series of computer programs to analyze the Ethics as a digraph. The paper presents a statistical analysis of the distribution of the elements of the Ethics. It applies a network statistic, betweenness, to analyze the relative importance to Spinoza’s argument of the individual propositions. The paper finds that a small (...)
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  27. added 2016-04-18
    Ansten Klev (2016). A Proof‐Theoretic Account of the Miners Paradox. Theoria 82 (2).
    By maintaining that a conditional sentence can be taken to express the validity of a rule of inference, we offer a solution to the Miners Paradox that leaves both modus ponens and disjunction elimination intact. The solution draws on Sundholm's recently proposed account of Fitch's Paradox.
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  28. added 2016-04-17
    Michael Caie (forthcoming). Agreement Theorems for Self-Locating Belief. Review of Symbolic Logic.
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  29. added 2016-04-15
    Daniel Bonevac & Hans Kamp (forthcoming). Quantifiers Defined by Parametric Extensions. Journal of Philosophical Logic:1-45.
    This paper develops a metaphysically flexible theory of quantification broad enough to incorporate many distinct theories of objects. Quite different, mutually incompatible conceptions of the nature of objects and of reference find representation within it. Some conceptions yield classical first-order logic; some yield weaker logics. Yet others yield notions of validity that are proper extensions of classical logic.
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  30. added 2016-04-14
    Petra Murinová & Vilém Novák (forthcoming). Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic. Logica Universalis:1-19.
    In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.
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  31. added 2016-04-14
    Laureano Luna (forthcoming). Physicalism, Truth, and the Pinocchio Paradox. Mind and Matter.
    We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.
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  32. added 2016-04-14
    Nils Bulling & Wiebe Hoek (forthcoming). Special Issue on Logical Aspects of Multi-Agent Systems. Studia Logica:1-3.
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  33. added 2016-04-14
    Paul Tomassi (2010). Logic After Wittgenstein. Nordic Journal of Philosophical Logic 6 (1):43-70.
    Wittgenstein's later rejection of the externalist Tractarian picture of logic according to which all rationally analysable discourse is properly understood as truth-functional rules out any conception of logic as the study of universal features of discourse. Given later references to 'the logic of our language', some conception of logic appears to survive even on Wittgenstein's later view. However, given his rejection of any conception of philosophical theory as explanatory or hypothetical, Wittgenstein seems to be forced into descriptivism. Despite these constraints, (...)
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  34. added 2016-04-14
    Juan Barba (2010). Trees for Truth. Nordic Journal of Philosophical Logic 6 (1):71-99.
    This papers aims to analyse sentences of a self-referential language containing a truth-predicate by means of a Smullyan-style tableau system. Our analysis covers three variants of Kripke's partial-model semantics and three variants of the revision theory of truth.
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  35. added 2016-04-14
    Peter M. Schuster (2010). Too Simple Solutions of Hard Problems. Nordic Journal of Philosophical Logic 6 (2):138-146.
    Even after yet another grand conjecture has been proved or refuted, any omniscience principle that had trivially settled this question is just as little acceptable as before. The significance of the constructive enterprise is therefore not affected by any gain of knowledge. In particular, there is no need to adapt weak counterexamples to mathematical progress.
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  36. added 2016-04-14
    Neil Tennant (2010). Game Theory and Conventiont. Nordic Journal of Philosophical Logic 6 (1):3-19.
    This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; the alleged need for quantification over strategies when providing a game-theoretic semantics; and the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a new conjecture concerning the relationship among truth, (...)
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  37. added 2016-04-14
    Ahti Pietarinen (2010). Intentional Identity Revisited. Nordic Journal of Philosophical Logic 6 (2):147-188.
    The problem of intentional identity, as originally offered by Peter Geach, says that there can be an anaphoric link between an indefinite term and a pronoun across a sentential boundary and across propositional attitude contexts, where the actual existence of an individual for the indefinite term is not presupposed. In this paper, a semantic resolution to this elusive puzzle is suggested, based on a new quantified intensional logic and game-theoretic semantics of imperfect information. This constellation leads to an expressive intensional (...)
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  38. added 2016-04-14
    Mark Textor (2010). Does the Truth-Conditional Theory of Sense Work for Indexicals? Nordic Journal of Philosophical Logic 6 (2):119-137.
    The truth-conditional theory of sense holds that a theory of truth for a natural language can serve as a theory of sense: if knowledge of a theory of truth for a language L is sufficient for understanding utterance of L-sentences, the T-sentences of the theory 'show' the sense of the uttered object-language sentences. In this paper I aim to show that indexicals create a serious problem for this prima facie attractive theoretical option. The so-called 'instantiation problem' is that a truth-theory (...)
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  39. added 2016-04-14
    Stefano Pred Elli (2010). You Just Can't Tell: An Analysis of the Non-Specific Use of Indexicals. Nordic Journal of Philosophical Logic 6 (2):103-118.
    In this paper I provide a semantic analysis of non-specific uses of indexical expressions, such as "you" in typical utterances of "you just can't tell". My treatment employs independently motivated conceptual tools, such as the treatment of generics within Discourse Representation Theory, and the distinction between context of utterance and context of interpretation.
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  40. added 2016-04-12
    Greg Yang (2016). Computability of Validity and Satisfiability in Probability Logics Over Finite and Countable Models. Journal of Applied Non-Classical Logics 25 (4):324-372.
    The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. We (...)
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  41. added 2016-04-10
    Melvin Fitting (forthcoming). Modal Logics, Justification Logics, and Realization. Annals of Pure and Applied Logic.
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  42. added 2016-04-10
    Anubav Vasudevan (2013). On the a Priori and a Posteriori Assessment of Probabilities. Journal of Applied Logic 11 (4).
    We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these constraints inform (...)
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  43. added 2016-04-09
    Srećko Kovač (2013). Causation and Intensionality in Aristotelian Logic. Studia Philosophiae Christianae 49 (2):117-136.
    We want to show that Aristotle’s general conception of syllogism includes as its essential part the logical concept of necessity, which can be understood in a causal way. This logical conception of causality is more general then the conception of the causality in the Aristotelian theory of proof (“demonstrative syllogism”), which contains the causal account of knowledge and science outside formal logic. Aristotle’s syllogistic is described in a purely intensional way, without recourse to a set-theoretical formal semantics. It is shown (...)
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  44. added 2016-04-08
    Osvaldo Guzmán, Michael Hrušák & Arturo Martínez-Celis (forthcoming). Canjar Filters. Notre Dame Journal of Formal Logic.
    If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” models (...)
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  45. added 2016-04-08
    Bernard Anderson & Barbara Csima (forthcoming). Degrees That Are Not Degrees of Categoricity. Notre Dame Journal of Formal Logic.
    A computable structure $\mathcal {A}$ is $\mathbf {x}$-computably categorical for some Turing degree $\mathbf {x}$ if for every computable structure $\mathcal {B}\cong\mathcal {A}$ there is an isomorphism $f:\mathcal {B}\to\mathcal {A}$ with $f\leq_{T}\mathbf {x}$. A degree $\mathbf {x}$ is a degree of categoricity if there is a computable structure $\mathcal {A}$ such that $\mathcal {A}$ is $\mathbf {x}$-computably categorical, and for all $\mathbf {y}$, if $\mathcal {A}$ is $\mathbf {y}$-computably categorical, then $\mathbf {x}\leq_{T}\mathbf {y}$. We construct a (...)
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  46. added 2016-04-08
    Thomas Hofweber & Ralf Schindler (forthcoming). Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure. Notre Dame Journal of Formal Logic.
    We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.
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  47. added 2016-04-08
    Srećko Kovač (2015). Causality and Attribution in an Aristotelian Theory. In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziauvol. 1, Cham, Heidelberg, etc.: Springer-Birkhäuser. Springer-Birkhäuser 327-340.
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  48. added 2016-04-07
    Srećko Kovač & Kordula Świętorzecka (2015). Gödel's "Slingshot" Argument and His Onto-Theological System. In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper 123-162.
  49. added 2016-04-07
    Srećko Kovač (2015). Causal Interpretation of Gödel's Ontological Proof. In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper 163.201.
  50. added 2016-04-07
    Joseph P. Li Vecchi (2014). Logical Objectivity and Second Intentions. Angelicum 91 (4).
    The Fregean tradition promotes a conception of logic as being independent from all psychological acts of the knowing subject. Without questioning logic's status as a paradigm of objectivity the present essay rejects this conception, both on logical grounds and in light of the scholastic theory of intentionality. Finding fault with two key doctrines of the analytic movement, the linguistic turn and anti-psychologism, it reinterprets them to exclude only psychological acts that engender subjective interpretive variability. It then describes logic's dependence on (...)
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