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  1. added 2020-07-01
    On Logical and Scientific Strength.Luca Incurvati & Carlo Nicolai - manuscript
    The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.
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  2. added 2020-06-10
    On Representations of Intended Structures in Foundational Theories.Neil Barton, Moritz Müller & Mihai Prunescu - manuscript
    Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...)
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  3. added 2020-05-17
    Some Logical Notations for Pragmatic Assertions.Massimiliano Carrara, Daniele Chiffi & Ahti-Veikko Pietarinen - forthcoming - Logique Et Analyse.
    The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these (...)
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  4. added 2020-04-11
    A Classification System for Argumentation Schemes.Douglas Walton & Fabrizio Macagno - 2016 - Argument and Computation 6 (3):219-245.
    This paper explains the importance of classifying argumentation schemes, and outlines how schemes are being used in current research in artificial intelligence and computational linguistics on argument mining. It provides a survey of the literature on scheme classification. What are so far generally taken to represent a set of the most widely useful defeasible argumentation schemes are surveyed and explained systematically, including some that are difficult to classify. A new classification system covering these centrally important schemes is built.
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  5. added 2020-03-08
    Structural Relativity and Informal Rigour.Neil Barton - forthcoming - In Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...)
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  6. added 2020-02-01
    Papineau's Philosophical Devices [Review]. [REVIEW]Matheus Silva - 2012 - Fundamento 5:147-150.
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  7. added 2019-12-05
    Prior's Puzzle Generalized.Justin D'Ambrosio - manuscript
    Prior's puzzle is the puzzle of why, given the assumption that that-clauses denote propositions, substitution of "the proposition that P" for "that P" within the complements of many propositional attitude verbs is invalid. I show that there are two variants on Prior's puzzle---a quantificational variant and a pronominal variant---that have the same source and warrant the same solution as the original puzzle. I then show that neither the original puzzle nor its variants are specific to that-clauses or propositional attitude verbs. (...)
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  8. added 2019-11-26
    A Toothful of Concepts: Towards a Theory of Weighted Concept Combination.Daniele Porello, Oliver Kutz, Guendalina Righetti, Nicolas Troquard, Pietro Galliani & Claudio Masolo - 2019 - In Mantas Simkus & Grant E. Weddell (eds.), Proceedings of the 32nd International Workshop on Description Logics, Oslo, Norway, June 18-21, 2019.
    We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some (...)
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  9. added 2019-10-24
    A Conspiracy of Theories.Steve Brewer - 2016 - Philosophy Now 114:57-58.
    A dialogue in which Freya argues that conspiracy theories are illogical, but Orin is not so sure!
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  10. added 2019-09-19
    Kant on Proving Aristotle’s Logic as Complete.Huaping Lu-Adler - 2016 - Kantian Review 21 (1):1-26.
    Kant claims that Aristotles logic as complete, explain the historical and philosophical considerations that commit him to proving the completeness claim and sketch the proof based on materials from his logic corpus. The proof will turn out to be an integral part of Kant’s larger reform of formal logic in response to a foundational crisis facing it.
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  11. added 2019-09-17
    Exposing Fake Logic.Avi Sion - 2018, 2019 - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    Exposing Fake Logic by Avi Sion is a collection of essays written after publication of his book A Fortiori Logic, in which he critically responds to derivative work by other authors who claim to know better. This is more than just polemics; but allows further clarifications of a fortiori logic and of general logic. This collection includes essays on: a fortiori argument (in general and in Judaism); Luis Duarte D’Almeida; Mahmoud Zeraatpishe; Michael Avraham (et al.); an anonymous reviewer of BDD (...)
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  12. added 2019-07-14
    On Quine's Ontology: Quantification, Extensionality and Naturalism (or From Commitment to Indifference).Daniel Durante Pereira Alves - 2019 - Proceedings of Ther 3rd Filomena Workshop.
    Much of the ontology made in the analytic tradition of philosophy nowadays is founded on some of Quine’s proposals. His naturalism and the binding between existence and quantification are respectively two of his very influential metaphilosophical and methodological theses. Nevertheless, many of his specific claims are quite controversial and contemporaneously have few followers. Some of them are: (a) his rejection of higher-order logic; (b) his resistance in accepting the intensionality of ontological commitments; (c) his rejection of first-order modal logic; and (...)
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  13. added 2019-07-12
    Non-Normative Logical Pluralism and the Revenge of the Normativity Objection.Erik Stei - 2020 - Philosophical Quarterly 70 (278):162–177.
    Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that L1 and L2 are correct logics that coincide except for the argument from Γ to φ, which is valid in L1 but invalid in L2. If you accept (...)
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  14. added 2019-07-03
    Relevant Logics, Counterfactual Worlds, and the Understanding of Narrative.Luis Galván - 2019 - In Matei Chihaia & Katharina Rennhak (eds.), Relevance and Narrative Research. Lanham, USA / London: Lexington Books. pp. 37-60.
    The aim of this paper is to explore what insights relevant logics may provide for the understanding of literary fictional narrative. To date, hardly anyone has reflected on the intersection of relevant logics and narratology, and some could think that there is good reason for it. On the one hand, relevance has been a prominent issue in pragmatics, in the tradition of Grice, and Sperber and Wilson; thus framed, relevance is highly context-sensitive, so it seems unsuitable for formal analysis. On (...)
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  15. added 2019-07-02
    Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and their interpretation. (...)
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  16. added 2019-06-06
    Future Contingents and Aristotle’s Fantasy.Andrea Iacona - 2007 - Critica 39 (117):45-60.
    This paper deals with the problem of future contingents, and focuses on two classical logical principles, excluded middle and bivalence. One may think that different attitudes are to be adopted towards these two principles in order to solve the problem. According to what seems to be a widely held hypothesis, excluded middle must be accepted while bivalence must be rejected. The paper goes against that line of thought. In the first place, it shows how the rejection of bivalence leads to (...)
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  17. added 2019-05-03
    Em direção a uma tradicão inferencialmente expressivista da silogística.Aislan Pereira - 2019 - Dissertation, UFPB, Brazil
    The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...)
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  18. added 2019-04-10
    Consequences and Design in General and Transcendental Logic.Elena G. Dragalina-Chernaya - 2018 - Kantian Journal 37 (1):25-39.
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  19. added 2019-02-04
    Content Recarving as Subject Matter Restriction.Vincenzo Ciccarelli - forthcoming - Manuscrito: Revista Internacional de Filosofía 42 (1).
    In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based (...)
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  20. added 2019-01-04
    Many-Valued And Fuzzy Logic Systems From The Viewpoint Of Classical Logic.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):624 - 657.
    The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist at (...)
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  21. added 2018-10-31
    What Isn’T Obvious About ‘Obvious’: A Data-Driven Approach to Philosophy of Logic.Moti Mizrahi - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Press. pp. 201-224.
    It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...)
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  22. added 2018-09-21
    A Perverse Case of the Contingent A Priori: On the Logic of Emasculating Language.Adèle Mercier - 1995 - Philosophical Topics 23 (2):221-259.
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  23. added 2018-09-20
    Epistemic Friction: An Essay on Knowledge, Truth, and Logic.Gila Sher - 2016 - Oxford: Oxford University Press UK.
    Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...)
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  24. added 2018-09-04
    On the Justification of Deduction and Induction.Franz Huber - 2017 - European Journal for Philosophy of Science 7 (3):507-534.
    The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...)
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  25. added 2018-08-30
    Logic and Gambling.Stephen Spielman - manuscript
    This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of logical (...)
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  26. added 2018-06-04
    Existential Instantiation, Arbitrary Reference and Supposition.Wylie Breckenridge - manuscript
    Existential instantiation is a rule of inference that allows us infer, from the proposition that there are some p things, the proposition that a is a p thing. What role does 'a' play here? According to one account, recently defended by Breckenridge and Magidor, we use 'a' to refer to a p thing. I argue that this cannot be right. I propose an alternative account, according to which we use 'a' to refer to a supposedly p thing.
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  27. added 2018-05-30
    (Master Thesis) Of Madness and Many-Valuedness: An Investigation Into Suszko's Thesis.Sanderson Molick - 2015 - Dissertation, UFRN
    Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undeter- mined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value (...)
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  28. added 2018-03-24
    Syllogisms Diagrammed: OOA to OOO.Mark Andrews - manuscript
    This document diagrams the forms OOA, OOE, OOI, and OOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a system in (...)
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  29. added 2018-03-12
    Exploring Randomness.Panu Raatikainen - 2001 - Notices of the AMS 48 (9):992-6.
    Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.
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  30. added 2018-02-20
    Defining a Decidability Decider.Pete Olcott - manuscript
    By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...)
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  31. added 2018-02-20
    The Basics of Display Calculi.Tim Lyon, Christian Ittner, Timo Eckhardt & Norbert Gratzl - 2017 - Kriterion - Journal of Philosophy 31 (2):55-100.
    The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.
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  32. added 2018-02-19
    How Gödelian Ontological Arguments Fail.Matthew Parker - manuscript
    Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer scrutiny are not. The premises have modal import that is required for the arguments but is not immediately grasped on inspection, and which ultimately undermines the simpler logical intuitions that make the premises seem plausible. Furthermore, the notion of necessity that they involve goes unspecified, and yet must go beyond standard varieties of logical necessity. This leaves us little reason (...)
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  33. added 2018-02-16
    A Computational Theory of Perspective and Reference in Narrative.Janyce M. Wiebe & William J. Rapaport - 1988 - In Proceedings of the 26th Annual Meeting of the Association for Computational Linguistics. Association for Computational Linguistics. pp. 131-138.
    Narrative passages told from a character's perspective convey the character's thoughts and perceptions. We present a discourse process that recognizes characters'.
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  34. added 2018-02-11
    On Knowing What to Say: Planning Speech Acts.Philip Raymond Cohen - 1978 - Dissertation, University of Toronto
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  35. added 2018-01-02
    Natural Deduction for Diagonal Operators.Fabio Lampert - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Cham: Birkhäuser. pp. 39-51.
    We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...)
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  36. added 2017-10-28
    The AGM Theory and Inconsistent Belief Change.Koji Tanaka - 2005 - Logique Et Analyse 48 (189-192):113-150.
    The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...)
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  37. added 2017-07-20
    Revisiting Dummett's Proof-Theoretic Justification Procedures.Hermógenes Oliveira - 2017 - In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016. London: College Publications. pp. 141-155.
    Dummett’s justification procedures are revisited. They are used as background for the discussion of some conceptual and technical issues in proof-theoretic semantics, especially the role played by assumptions in proof-theoretic definitions of validity.
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  38. added 2017-07-03
    Didactic-Reflexive Form Errors, Full Initial MANUSCRIPT, May 2017.Kai Soerfjord - manuscript
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  39. added 2017-06-06
    The Role of Reflexivity in Understanding Human Understanding.Steven James Bartlett - 1992 - In Steven J. Bartlett (ed.), Reflexivity: A Source-Book in Self-Reference. Amsterdam, Netherlands: Distributors for the U.S. And Canada, Elsevier Science Pub. Co.. pp. 3--18.
    The Introduction to the collection of papers, _Reflexivity: A Source-book in Self-reference_. The Introduction studies the limits of our understanding that we carry unavoidably with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and (...)
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  40. added 2017-01-30
    On Tracy Lupher’s “A Logical Choice".Klaus Ladstaetter - 2012 - Southwest Philosophy Review 28 (2):101-106.
    In his essay Tracy Lupher (henceforth, TL) is concerned with Robert Kane's (1984) version of the modal ontological argument (MOA). As he correctly points out, Kane's argument is valid only if the accessibility relation between possible worlds is assumed to be symmetric. TL's remarks pave the way to thinking that the MOA is intended to establish the existence of a perfect being as a matter of logical necessity. Moreover, given TL's undisputed supposition (even shared by Kane) that S5 - in (...)
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  41. added 2017-01-14
    Proceedings of the 26th Annual Meeting of the Association for Computational Linguistics (SUNY Buffalo).Janyce M. Wiebe & William J. Rapaport (eds.) - 1988 - Assoc for computational linguistics.
    Narrative passages told from a character's perspective convey the character's thoughts and perceptions. We present a discourse process that recognizes characters' thoughts and perceptions in third-person narrative. An effect of perspective on reference In narrative is addressed: references in passages told from the perspective of a character reflect the character's beliefs. An algorithm that uses the results of our discourse process to understand references with respect to an appropriate set of beliefs is presented.
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  42. added 2017-01-08
    What Makes Logical Truths True?Constantin C. Brîncuș - 2016 - Logos and Episteme 7 (3): 249-272.
    The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these principles also regulate and control (...)
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  43. added 2017-01-06
    Deontic ‘Cocktail’ According to E. Mally’s Receipt.Lisanyuk Elena - 2013 - Logical Investigations 19:5-27.
    In 1926, Ernst Mally, an Austrian logician, has introduced a system of deontic logic in which he has proposed three fundamental distinctions which proved to be important in the context of the further development of the logic of norms. It is argued that in his philosophical considerations Mally has introduced a number of important distinctions concerning the very concept of norm, but by getting them confused in introducing the subsequent formalisms he failed to formally preserve them. In some of his (...)
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  44. added 2016-12-08
    The Logic of Qualia.Merriam Paul - manuscript
    We indicate how to construct a logic of qualia.
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  45. added 2016-12-08
    Deviant Logic, Fuzzy Logic: Beyond the Formalism.Achille C. Varzi & Susan Haack - 1998 - Philosophical Review 107 (3):468.
    This book has three main parts. The first, longer, part is a reprint of the author's Deviant Logic, which initially appeared as a book by itself in 1974. The second and third parts include reprints of five papers originally published between 1973 and 1980. Three of them focus on the nature and justification of deductive reasoning, which are also a major concern of Deviant Logic. The other two are on fuzzy logic, and make up for a major omission of Deviant (...)
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  46. added 2016-10-29
    DLEAC: A Dialetheic Logic with Exclusive Assumptions and Conclusions.Massimiliano Carrara & Enrico Martino - 2019 - Topoi 38 (2):379-388.
    This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...)
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  47. added 2016-10-23
    On Rules of Inference and the Meanings of Logical Constants.Panu Raatikainen - 2008 - Analysis 68 (4):282-287.
    In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett and (...)
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  48. added 2016-08-23
    Definite Descriptions and Indeterminate Identity (Extended Abstract).Derek von Barandy - 2016 - Logiko-Filosofskie Studii 13 (2):111-112.
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  49. added 2016-05-07
    Uma Abordagem sobre a Concepção de Proposição da Teoria Intuicionista de Tipos.Bruno Rigonato Mundim - 2013 - Dissertation, Universidade Federal de Goiás
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  50. added 2016-02-19
    Metáforas del pensamiento en Peirce.Eduardo Dib - 2015 - In Hugo Aguilar & Marisa Moyano (eds.), Sentido y performatividad V - La norma social como matriz ideológica del poder ISBN 978-987-46031-2-8. Ediciones Cántaro de Piedra. pp. 311-324.
    Las «metáforas», «analogías» o «alegorías» tienen un lugar bien ganado en la tradición filosófica. Han sido atacadas por dar lugar a una interpretación poco rigurosa de las nociones que describen, pues permite asociarles propiedades que originalmente no se había pensado (ni resulta deseable) que formen parte de su concepto. Sin embargo, a pesar del reclamo en favor de procedimientos estrictos de definición, el uso de una imagen apropiada suele ser el mejor modo de explicar esas cuestiones que cada siglo escapan (...)
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