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  1. M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction. Studia Logica 92 (3):281 - 364.
    We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i , j =?. The method allows us to decide whether to declare a i , j = 0 or a i , j = 1 (...)
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  2. Jarosław Achinger & Andrzej W. Jankowski (1986). On Decidable Consequence Operators. Studia Logica 45 (4):415 - 424.
    The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
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  3. Wilhelm Ackermann (1956). Begründung Einer Strengen Implikation. Journal of Symbolic Logic 21 (2):113-128.
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  4. Ernest W. Adams (1996). Four Probability-Preserving Properties of Inferences. Journal of Philosophical Logic 25 (1):1 - 24.
    Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...)
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  5. Ernest W. Adams (1995). Remarks on a Theorem of McGee. Journal of Philosophical Logic 24 (4):343 - 348.
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  6. Leonard M. Adleman & M. Blum (1991). Inductive Inference and Unsolvability. Journal of Symbolic Logic 56 (3):891-900.
    It is shown that many different problems have the same degree of unsolvability. Among these problems are: THE INDUCTIVE INFERENCE PROBLEM. Infer in the limit an index for a recursive function f presented as f(0), f(1), f(2),.... THE RECURSIVE INDEX PROBLEM. Decide in the limit if i is the index of a total recursive function. THE ZERO NONVARIANT PROBLEM. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),... has value unequal to zero for infinitely many (...)
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  7. Kazimierz Ajdukiewicz (1956). Conditional Sentence and Material Implication. Studia Logica 4 (1):135-153.
  8. Ken Akiba (2000). Logic and Truth. Journal of Philosophical Research 25:101-123.
    It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning of the (...)
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  9. Natasha Alechina & Michiel van Lambalgen (1996). Generalized Quantification as Substructural Logic. Journal of Symbolic Logic 61 (3):1006-1044.
    We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of (...)
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  10. Patrick Allo & Edwin Mares (2012). Informational Semantics as a Third Alternative? Erkenntnis 77 (2):167-185.
    Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)
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  11. Alan Ross Anderson (1990). Entailment: The Logic of Relevance and Necessity. Princeton University Press.
  12. Alan Ross Anderson & Nuel D. Belnap Jr (1962). The Pure Calculus of Entailment. Journal of Symbolic Logic 27 (1):19-52.
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  13. Alan Ross Anderson & Nuel D. Belnap Jr (1959). Modalities in Ackermann's "Rigorous Implication". Journal of Symbolic Logic 24 (2):107-111.
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  14. Lee C. Archie (1979). A Simple Defense of Material Implication. Notre Dame Journal of Formal Logic 20 (2):412-414.
  15. Lee C. Archie, B. G. Hurdle & William Stewart Thomblison (1977). A Note on the Truth-Table for ``If $P$ Then $Q$''. Notre Dame Journal of Formal Logic 18 (4):596-598.
  16. E. J. Ashworth (1972). Strict and Material Implication in the Early Sixteenth Century. Notre Dame Journal of Formal Logic 13 (4):556-560.
  17. E. J. Ashworth (1968). Petrus Fonseca and Material Implication. Notre Dame Journal of Formal Logic 9 (3):227-228.
  18. Axel Arturo Barceló Aspeitia (2007). What Does '&' Mean? The Proceedings of the Twenty-First World Congress of Philosophy 5:45-50.
    Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is (...)
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  19. Arnon Avron (1986). On an Implication Connective of ${\Rm RM}$. Notre Dame Journal of Formal Logic 27 (2):201-209.
  20. Arnon Avron (1984). Relevant Entailment--Semantics and Formal Systems. Journal of Symbolic Logic 49 (2):334-342.
  21. Andrew Bacon (2013). Non-Classical Metatheory for Non-Classical Logics. Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)
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  22. John Robert Baker (1975). On Two Immediate Inferences by Limitation. Notre Dame Journal of Formal Logic 16 (4):496-500.
  23. Roberta Ballarin (2005). Validity and Necessity. Journal of Philosophical Logic 34 (3):275 - 303.
    In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...)
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  24. John A. Barker (1976). Presupposition and Entailment. Notre Dame Journal of Formal Logic 17 (2):272-278.
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  25. Eduardo Barrio (2007). Consecuencia lógica, modalidad y generalidad irrestricta. Manuscrito 30 (1).
    En este trabajo, me propongo discutir la plausibilidad de la tesis de que es posible captar las características modales del concepto intuitivo de consecuencia a través de un concepto de consecuencia definido generalizando sobre interpretaciones. Desde mi perspectiva, las argumentaciones que han ofrecido aquellos que, como Ray, quieren salvar el salto de lo general a lo modal, mostrando que hay suficientes interpretaciones como para representar las características modales de la noción preteórica de consecuencia, poseen un mismo tipo de limitación. La (...)
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  26. Jared Bates (2000). Comments on Foster's 'On Tarski's Theory of Logical Consequence--A Reply to Bates'. Southwest Philosophy Review 16 (2):191-194.
    In the present commentary, I argue that Foster has attacked an uncharitable reconstruction of Etchemendy's argument against Tarski's account of the logical properties. I provide an alternative, more charitable reconstruction of that argument that withstands Foster's objections.
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  27. Jared Bates (1999). Etchemendy, Tarski, and Logical Consequence. Southwest Philosophy Review 15 (1):47-54.
    John Etchemendy (1990) has argued that Tarski's definition of logical consequence fails as an adequate philosophical analysis. Since then, Greg Ray (1996) has defended Tarski's analysis against Etchemendy's criticisms. Here, I'll argue that--even given Ray's defense of Tarski's definition--we may nevertheless lay claim to the conditional conclusion that 'if' Tarski intended a conceptual analysis of logical consequence, 'then' it fails as such. Secondly, I'll give some reasons to think that Tarski 'did' intend a conceptual analysis of logical consequence.
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  28. Michael Baumgartner (2010). Informal Reasoning and Logical Formalization. In S. Conrad & S. Imhof (eds.), Ding und Begriff. Ontos.
    According to a prevalent view among philosophers formal logic is the philosopher’s main tool to assess the validity of arguments, i.e. the philosopher’s ars iudicandi. By drawing on a famous dispute between Russell and Strawson over the validity of a certain kind of argument – of arguments whose premises feature definite descriptions – this paper casts doubt on the accuracy of the ars iudicandi conception. Rather than settling the question whether the contentious arguments are valid or not, Russell and Strawson, (...)
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  29. Michael Baumgartner (2010). Shallow Analysis and the Slingshot Argument. Journal of Philosophical Logic 39 (5):531-556.
    According to the standard opinions in the literature, blocking the unacceptable consequences of the notorious slingshot argument requires imposing constraints on the metaphysics of facts or on theories of definite descriptions (or class abstracts). This paper argues that both of these well-known strategies to rebut the slingshot overshoot the mark. The slingshot, first and foremost, raises the question as to the adequate logical formalization of statements about facts, i.e. of factual contexts. It will be shown that a rigorous application of (...)
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  30. Michael Baumgartner & Timm Lampert (2008). Adequate Formalization. Synthese 164 (1):93-115.
    This article identifies problems with regard to providing criteria that regulate the matching of logical formulae and natural language. We then take on to solve these problems by defining a necessary and sufficient criterion of adequate formalization. On the basis of this criterion we argue that logic should not be seen as an ars iudicandi capable of evaluating the validity or invalidity of informal arguments, but as an ars explicandi that renders transparent the formal structure of informal reasoning.
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  31. Jc Beall & Julien Murzi (2013). Two Flavors of Curry Paradox. Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
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  32. Corine Besson (2009). Externalism, Internalism, and Logical Truth. Review of Symbolic Logic 2 (1):1-29.
    The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist-internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order logic (...)
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  33. Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
    Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...)
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  34. W. J. Blok & Bjarni Jónsson (2006). Equivalence of Consequence Operations. Studia Logica 83 (1-3):91 - 110.
    This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...)
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  35. W. J. Blok & J. G. Raftery (2004). Fragments of R-Mingle. Studia Logica 78 (1-2):59 - 106.
    The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...)
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  36. Susanne Bobzien (2002). The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century AD. Phronesis 47 (4):359-394.
    ABSTRACT: ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor (...)
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  37. Susanne Bobzien (1999). Logic: The Stoics (Part Two). In Keimpe Algra, Jonathan Barnes & et al (eds.), The Cambridge History of Hellenistic Philosophy. CUP.
    ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can be found (...)
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  38. Ivan Boh (1966). Propositional Connectives, Supposition, and Consequence in Paul of Pergola. Notre Dame Journal of Formal Logic 7 (1):109-128.
  39. R. T. Brady & P. A. Rush (2008). What is Wrong with Cantor's Diagonal Argument? Logique Et Analyse 51 (1):185-219..
    We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...)
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  40. Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...)
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  41. Andrew Brennan, Necessary and Sufficient Conditions. Stanford Encyclopedia of Philosophy.
    Describes the received theory of necessary and sufficient conditions, explains some standard objections to it, and lays out alternative ways of thinking about conditions and conditionals.
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  42. Constantin C. Brincus & Iulian D. Toader (2013). A Carnapian Approach to Counterexamples to Modus Ponens. Romanian Journal of Analytic Philosophy 7 (1):78-85.
    This paper proposes a Carnapian approach to known counterexamples to Modus Ponens (henceforth, MP). More specifically, it argues 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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  43. Eric M. Brown, Logic II: The Theory of Propositions.
    This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and modern logic using scholastic logic as the (...)
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  44. M. W. Bunder (1982). Deduction Theorems for Weak Implicational Logics. Studia Logica 41 (2-3):95 - 108.
    The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.In this paper we look in detail at special cases of the Gentzen rule for and show that various subsets of these in effect constitute deduction theorems determining all the theorems of many well known as well as not well (...)
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  45. Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'Ottaviano (2009). New Dimensions on Translations Between Logics. Logica Universalis 3 (1):1-18.
    After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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  46. Clive Cazeaux (2007). Metaphor and Continental Philosophy: From Kant to Derrida. Routledge.
    Kant and Heidegger on the creation of objectivity -- The power of judgment : metaphor in the structure of Kant's third Critique -- Sensation, categorization, and embodiment : Locke, Merleau-Ponty, and Lakoff and Johnson -- Heidegger and the senses -- Conflicting perspectives : epistemology and ontology in Nietzsche's will to power -- Cutting nature at the joints : metaphor and epistemology in the science wars -- Opening and belonging : between subject and object in Heidegger and Bachelard -- Metaphor and (...)
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  47. Samir Chopra & Eric Martin (2002). Generalized Logical Consequence: Making Room for Induction in the Logic of Science. [REVIEW] Journal of Philosophical Logic 31 (3):245-280.
    We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...)
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  48. Michael Clark (1980). Reply to Dale. Analysis 40 (1):12.
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  49. Michael Clark (1980). The Equivalence of Tautological and “Strict” Entailment: Proof of an Amended Conjecture of Lewy's. [REVIEW] Journal of Philosophical Logic 9 (1):9 - 15.
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  50. Michael Clark (1979). Lewy's Conjectures About Tautological Entailment. Analysis 39 (1):30 - 34.
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