Results for 'deduction'

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  1.  4
    Deduction.P. N. Johnson-Laird & R. M. J. Byrne - 1991 - Psychology Press.
    In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.
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  2. Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  3. Deductive Cogency, Understanding, and Acceptance.Finnur Dellsén - 2018 - Synthese 195 (7):3121-3141.
    Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...)
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  4.  22
    Malachi Hacohen Historicizing Deduction: Scientific Method, Critical Debate, and the Historian.Historicizing Deduction - 2004 - In Friedrich Stadler (ed.), Induction and Deduction in the Sciences. Springer. pp. 11--17.
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  5. Mark Siderits Deductive, Inductive, Both or Neither?Inductive Deductive - 2003 - Journal of Indian Philosophy 31:303-321.
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  6. The Deductive-Nomological Account of Metaphysical Explanation.Tobias Wilsch - 2016 - Australasian Journal of Philosophy 94 (1):1-23.
    The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I argue (...)
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  7. A Deductive-Nomological Model of Probabilistic Explanation.Peter Railton - 1978 - Philosophy of Science 45 (2):206-226.
    It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring in covering laws (...)
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  8. Non-Deductive Logic in Mathematics.James Franklin - 1987 - British Journal for the Philosophy of Science 38 (1):1-18.
    Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...)
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  9. Deductive Reasoning in the Structuralist Approach.Holger Andreas - 2013 - Studia Logica 101 (5):1093-1113.
    The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the (...)
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  10.  1
    A Deduction Model of Belief.Kurt Konolige - 1986 - Morgan Kaufmann Publishers.
  11. Communist Conventions for Deductive Reasoning.Sinan Dogramaci - 2015 - Noûs 49 (4):776-799.
    In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...)
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  12.  26
    Deductive Schemas with Uncertain Premises Using Qualitative Probability Expressions.Guy Politzer & Jean Baratgin - 2016 - Thinking and Reasoning 22 (1):78-98.
    ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained (...)
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  13.  52
    Relevant Deduction.Gerhard Schurz - 1991 - Erkenntnis 35 (1-3):391 - 437.
    This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of (...)
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  14.  27
    Deductive Reasoning.Philip Johnson-Laird - 1999 - Annual Review of Psychology 50 (1):109-135.
    This chapter describes the main accounts of deductive competence, which explain what is computed in carrying out deductions. It argues that people have a modicum of competence, which is useful in daily life and a prerequisite for acquiring logical expertise. It outlines the three main sorts of theory of deductive performance, which explain how people make deductions: They rely on factual knowledge, formal rules, or mental models. It reviews recent experimental studies of deductive reasoning in order to help readers to (...)
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  15. Against Deductive Closure.Paul D. Thorn - 2017 - Theoria 83 (2):103-119.
    The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.
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  16. Hypothetico-Deductive Confirmation.Jan Sprenger - 2011 - Philosophy Compass 6 (7):497-508.
    Hypothetico-deductive (H-D) confirmation builds on the idea that confirming evidence consists of successful predictions that deductively follow from the hypothesis under test. This article reviews scope, history and recent development of the venerable H-D account: First, we motivate the approach and clarify its relationship to Bayesian confirmation theory. Second, we explain and discuss the tacking paradoxes which exploit the fact that H-D confirmation gives no account of evidential relevance. Third, we review several recent proposals that aim at a sounder and (...)
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  17. 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 (...)
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  18.  61
    A Deductive-Nomological Model for Mathematical Scientific Explanation.Eduardo Castro - 2020 - Principia: An International Journal of Epistemology 24 (1):1-27.
    I propose a deductive-nomological model for mathematical scientific explanation. In this regard, I modify Hempel’s deductive-nomological model and test it against some of the following recent paradigmatic examples of the mathematical explanation of empirical facts: the seven bridges of Königsberg, the North American synchronized cicadas, and Hénon-Heiles Hamiltonian systems. I argue that mathematical scientific explanations that invoke laws of nature are qualitative explanations, and ordinary scientific explanations that employ mathematics are quantitative explanations. I analyse the repercussions of this deductivenomological model (...)
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  19.  52
    A Deduction From Apperception?Andrew Stephenson - 2014 - Studi Kantiani 27:77-86.
    I discuss three elements of Dennis Schulting’s new book on the transcendental deduction of the pure concepts of the understanding, or categories. First, that Schulting gives a detailed account of the role of each individual category. Second, Schulting’s insistence that the categories nevertheless apply ‘en bloc’. Third, Schulting’s defence of Kant’s so-called reciprocity thesis that subjective unity of consciousness and objectivity in the sense of cognition’s objective purport are necessary conditions for the possibility of one another. I endorse these (...)
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  20.  35
    Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
    The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no (...)
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  21. Natural Deduction in Connectionist Systems.William Bechtel - 1994 - Synthese 101 (3):433-463.
    The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from (...)
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  22.  10
    Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
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  23. Natural Deduction and Curry's Paradox.Susan Rogerson - 2007 - Journal of Philosophical Logic 36 (2):155 - 179.
    Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.
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  24. Does the Deduction Theorem Fail for Modal Logic?Raul Hakli & Sara Negri - 2012 - Synthese 187 (3):849-867.
    Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a (...)
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  25.  51
    Labelled Deductive Systems: Volume 1.Dov M. Gabbay - 1996 - Oxford, England: Oxford University Press.
    This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.
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  26. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and Any Other Truth-Functional Connective).Richard Zach - 2016 - Journal of Philosophical Logic 45 (2):183-197.
    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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  27.  69
    Natural Deduction for Dual-Intuitionistic Logic.Luca Tranchini - 2012 - Studia Logica 100 (3):631-648.
    We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.
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  28.  63
    Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order (...)
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  29. Uncertain Deductive Reasoning.Niki Pfeifer & G. D. Kleiter - 2011 - In K. Manktelow, D. E. Over & S. Elqayam (eds.), The Science of Reason: A Festschrift for Jonathan St B.T. Evans. Psychology Press. pp. 145--166.
    Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals). -/- This contribution consists of two parts. In the first part we discuss general features of reasoning systems including consequence relations, how uncertainty may enter argument forms, probability intervals, and probabilistic informativeness. These concepts are of (...)
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  30.  68
    Deductive and Inductive Conditional Inferences: Two Modes of Reasoning.Henrik Singmann & Karl Christoph Klauer - 2011 - Thinking and Reasoning 17 (3):247 - 281.
    A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions?namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. In two new (...)
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  31. Natural Deduction.Andrzej Indrzejczak - 2015
    Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.
     
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  32.  33
    Uncertain Deduction and Conditional Reasoning.Jonathan St B. T. Evans, Valerie A. Thompson & David E. Over - 2015 - Frontiers in Psychology 6.
  33. Aristotle's Natural Deduction System.John Corcoran - 1974 - In Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  34. Is Kant’s Transcendental Deduction of the Categories Fit for Purpose?Anil Gomes - 2010 - Kantian Review 15 (2):118-137.
    James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, (...)
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  35. The Justification of Deduction.Susan Haack - 1976 - Mind 85 (337):112-119.
    It is often taken for granted by writers who propose--and, for that matter, by writers who oppose--'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.
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  36.  44
    Inductive, Deductive.Perry Weddle - 1979 - Informal Logic 2 (1).
  37.  26
    Defining Deduction.Mark Vorobej - 1992 - Informal Logic 14 (2).
    This paper defends the view that the classification of an argument as being deductive ought to rest exclusively upon psychological considerations; specifically, upon whether the argument's author holds certain beliefs. This account is justified on theoretical and pedagogical grounds, and situated within a general taxonomy of competing proposals. Epistemological difficulties involved in the application of psychological definitions are recognized but claimed to be ineliminable from the praetice of argumentation. The paper concludes by discussing embryonic arguments where the author's relevant beliefs (...)
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  38.  9
    Deduction From Uncertain Premises.Rosemary J. Stevenson & David E. Over - 1995 - Quarterly Journal of Experimental Psychology Section A 48 (3):613-643.
    We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given (...)
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  39. Single Premise Deduction and Risk.Maria Lasonen-Aarnio - 2008 - Philosophical Studies 141 (2):157 - 173.
    It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry (...)
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  40.  21
    Local Deductions Theorems.Janusz Czelakowski - 1986 - Studia Logica 45 (4):377 - 391.
    The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).
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  41.  98
    Closure, Deduction and Hinge Commitments.Xiaoxing Zhang - 2021 - Synthese 198 (Suppl 15):3533-3551.
    Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from the fact that (...)
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  42.  28
    Deductive Cogency in Inductive Inference.Isaac Levi - 1965 - Journal of Philosophy 62 (3):68-77.
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  43. The Content of Deduction.Mark Jago - 2013 - Journal of Philosophical Logic 42 (2):317-334.
    For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...)
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  44.  15
    Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics.Yaroslav I. Petrukhin - 2017 - Logica Universalis 11 (4):525-532.
    In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
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  45.  73
    From Deduction to Deed: Kant's Grounding of the Moral Law.David Sussman - 2008 - Kantian Review 13 (1):52-81.
    In the Critique of Practical Reason, Kant presents the moral law as the sole ‘fact of pure reason’ that neither needs nor admits of a deduction to establish its authority. This claim may come as a surprise to many readers of his earlier Groundwork of the Metaphysics of Morals. In the last section of the Groundwork, Kant seemed to offer a sketch of just such a ‘deduction of the supreme principle of morality’ . Although notoriously obscure, this sketch (...)
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  46.  8
    Kant's Transcendental Deduction: An Analytic-Historical Commentary.Henry E. Allison - 2015 - Oxford University Press UK.
    Henry E. Allison presents an analytical and historical commentary on Kant`s transcendental deduction of the pure concepts of the understanding in the Critique of Pure Reason. He argues that, rather than providing a new solution to an old problem, it addresses a new problem, and he traces the line of thought that led Kant to the recognition of the significance of this problem in his 'pre-critical' period. In addition to the developmental nature of the account of Kant`s views presented (...)
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  47.  5
    The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning.Catarina Dutilh Novaes - 2020 - Cambridge University Press.
    This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and (...)
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  48.  55
    Natural Deduction Rules for a Logic of Vagueness.J. A. Burgess & I. L. Humberstone - 1987 - Erkenntnis 27 (2):197-229.
    Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.
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  49. The Deduction of Categories: The Metaphysical and Transcendental Deductions.Paul Guyer - 2010 - In The Cambridge Companion to Kant's Critique of Pure Reason. Cambridge University Press.
  50. Deduction and Novelty Again.Danny Frederick - 2014 - The Reasoner 8 (5):51-52.
    It is commonly claimed that the conclusion of a valid deductive argument is contained in its premises and says nothing new. In 'Deduction and Novelty,' in The Reasoner 5 (4), pp. 56-57, I refuted that claim. In The Reasoner, 8 (3), pp. 24-25, David McBride criticised my refutation. I show that McBride’s arguments are unsound.
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