Results for 'Deduction'

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  1.  11
    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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  2.  68
    Kant's Deduction From Apperception.Dennis Schulting - 2017 - In Kant's Radical Subjectivism. Perspectives on the Transcendental Deduction. London, UK: Palgrave. pp. 53-96.
    In this article, I consider critical arguments levelled against central elements of my view, expounded in my book Kant’s Deduction and Apperception (Schulting 2012b; KDA), that the categories are derived a priori from the principle of apperception, the ‘I think’. This view goes back to a much earlier, and more famous attempt by Klaus Reich, first proposed in 1932 (see Reich 2001), to argue that the functions of thought are ultimately and a priori derivable from the objective unity of (...)
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  3. On Hegel's Critique of Kant's Subjectivism in the Transcendental Deduction.Dennis Schulting - 2017 - In Kant's Radical Subjectivism. Perspectives on the Transcendental Deduction. London: Palgrave. pp. 341-370.
    In this article, I expound Hegel’s critique of Kant, which he first and most elaborately presented in his early essay "Faith and Knowledge" (1802), by focusing on the criticism that Hegel levelled against Kant’s (supposedly) arbitrary subjectivism about the categories. This relates to the restriction thesis of Kant’s transcendental idealism: categorially governed empirical knowledge only applies to appearances, not to things in themselves, and so does not reach objective reality, according to Hegel. Hegel claims that this restriction of knowledge to (...)
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  4.  7
    Problems of Kantian Nonconceptualism and the Transcendental Deduction.Dennis Schulting - 2017 - In Kant's Radical Subjectivism. Perspectives on the Transcendental Deduction. London, UK: Palgrave. pp. 195-255.
    In this paper, I discuss the debate on Kant and nonconceptual content in the context of the main argument of the B-Deduction. Kantian conceptualists (Bowman 2011; Griffith 2012; Gomes 2014) have responded to the recent nonconceptualist offensive, with reference to A89ff./B122ff. (§13)—which, confusingly, the nonconceptualists also cite as evidence for their contrary reading—by arguing that the nonconceptualist view conflicts with the central goal of TD, namely, to argue that all intuitions are subject to the categories. I contend that the (...)
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  5. 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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  6. 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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  7. Kant on Perception: Naive Realism, Non-Conceptualism, and the B-Deduction.Anil Gomes - 2014 - Philosophical Quarterly 64 (254):1-19.
    According to non-conceptualist interpretations, Kant held that the application of concepts is not necessary for perceptual experience. Some have motivated non-conceptualism by noting the affinities between Kant's account of perception and contemporary relational theories of perception. In this paper I argue (i) that non-conceptualism cannot provide an account of the Transcendental Deduction and thus ought to be rejected; and (ii) that this has no bearing on the issue of whether Kant endorsed a relational account of perceptual experience.
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  8.  54
    On the Justification of Deduction and Induction.Franz Huber - forthcoming - European Journal for the Philosophy of Science.
    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 (1739; 1748)'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 (1963; 1968) and Goodman (1954), as well as praise Reichenbach (1938; 1940)'s approach. -/- Some of these (...)
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  9. Natural Deduction Systems for Some Non-Commutative Logics.Norihiro Kamide & Motohiko Mouri - 2007 - Logic and Logical Philosophy 16 (2-3):105-146.
    Varieties of natural deduction systems are introduced for Wansing’s paraconsistent non-commutative substructural logic, called a constructive sequential propositional logic (COSPL), and its fragments. Normalization, strong normalization and Church-Rosser theorems are proved for these systems. These results include some new results on full Lambek logic (FL) and its fragments, because FL is a fragment of COSPL.
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  10. Kant's Transcendental Deduction: An Analytical‐Historical Commentary, by Henry Allison. Oxford University Press, 2015, 496 Pp. ISBN 13: 978‐0‐19‐872485‐8 Hb £75.00. [REVIEW]Colin McLear - 2017 - European Journal of Philosophy 25 (2):546-554.
  11.  52
    Why the Transcendental Deduction is Compatible with Nonconceptualism.Sacha Golob - 2016 - In Dennis Schulting (ed.), Kantian Nonconceptualism. Palgrave-Macmillan. pp. 27-52.
    One of the strongest motivations for conceptualist readings of Kant is the belief that the Transcendental Deduction is incompatible with nonconceptualism. In this article, I argue that this belief is simply false: the Deduction and nonconceptualism are compatible at both an exegetical and a philosophical level. Placing particular emphasis on the case of non-human animals, I discuss in detail how and why my reading diverges from those of Ginsborg, Allais, Gomes and others. I suggest ultimately that it is (...)
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  12.  59
    Nonconceptualist Readings of Kant and the Transcendental Deduction.Thomas Land - 2015 - Kantian Review 20 (1):25-51.
    I give an argument against nonconceptualist readings of Kants claim that intuitions and concepts constitute two distinct kinds of representation than is assumed by proponents of nonconceptualist readings. I present such an interpretation and outline the alternative reading of the Deduction that results.
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  13. Kant's Deduction From Apperception: A Reply to My Critics.Dennis Schulting - 2014 - Studi Kantiani 27:95-115.
    In my reply to the respective critiques by Corey Dyck, Marcel Quarfood and Andrew Stephenson of my book Kant’s Deduction and Apperception: Explaining the Categories (Palgrave 2012), I go over some of the main planks of my interpretation of the first step of the B-Deduction. In response to Dyck, I explain that there are several reasons why I believe that the deduction of the categories must indeed be seen as a logical derivation from the unity of apperception, (...)
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  14. 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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  15. 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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  16. 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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  17. Kant's Legal Metaphor and the Nature of a Deduction.Ian Proops - 2003 - Journal of the History of Philosophy 41 (2):209-229.
    This essay partly builds on and partly criticizes a striking idea of Dieter Henrich. Henrich argues that Kant's distinction in the first Critique between the question of fact (quid facti) and the question of law (quid juris) provides clues to the argumentative structure of a philosophical "Deduction". Henrich suggests that the unity of apperception plays a role analogous to a legal factum. By contrast, I argue, first, that the question of fact in the first Critique is settled by the (...)
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  18.  41
    Mind Critical Notice of Kant's Transcendental Deduction, by Henry Allison.Golob Sacha - 2017 - Mind 126 (501):278-289.
    Critical Notice of Kant's Transcendental Deduction, by Henry Allison. Oxford: Oxford University Press, 2015. Pp. Xv + 477.
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  19.  44
    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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  20. Empirical Cognition in the Transcendental Deduction: Kant’s Starting Point and His Humean Problem.Curtis Sommerlatte - 2016 - Kantian Review 21 (3):437-463.
    In this paper, I argue that in the sense of greatest epistemological concern for Kant, empirical cognition is “rational sensory discrimination”: the identification or differentiation of sensory objects from each other, occurring through a capacity to become aware of and express judgments. With this account of empirical cognition, I show how the transcendental deduction of the first Critique is most plausibly read as having as its fundamental assumption the thesis that we have empirical cognition, and I provide evidence that (...)
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  21. Kant's Subjective Deduction.Nathan Bauer - 2010 - British Journal for the History of Philosophy 18 (3):433-460.
    In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof (...)
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  22. On 'Deduction' and the Inductive/Deductive Distinction.Jeffrey Goodman & Daniel Flage - 2012 - Studies in Logic 5 (3).
    The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We (...)
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  23. 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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  24. A Speech Act Calculus. A Pragmatised Natural Deduction Calculus and its Meta-Theory.Moritz Cordes & Friedrich Reinmuth - manuscript
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e. a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs. (Translation of our German paper (...)
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  25. Instability, Modus Ponens and Uncertainty of Deduction.Liu Huajie - 2006 - Frontiers of Philosophy in China 1 (4):658-674.
    Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validity of reasoning sequences in the real physical world, and similar results cannot necessarily be obtained from similar causes. Some kind of stability hypothesis should be added in order to draw meaningful conclusions. Hence, the uncertainty of deductive inference appears to be like that of inductive inference, and the asymmetry between deduction and induction becomes unrecognizable such as to undermine the (...)
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  26.  5
    The Unity of Cognition and the Subjectivist Vs. "Transformative Approaches to the B-Deduction. Comments on James Conant.Dennis Schulting - 2017 - Critique:00-00.
    In an illuminating new essay ‘Die Einheit des Erkenntnisvermögens bei Kant’ (Conant 2016/2017), James Conant critically addresses what he argues is a widespread assumption in modern philosophy, namely, the assumption that our rational capacity to know is a capacity that is somehow “added” or tacked on to the capacity that we humans share with other animals, that is, our receptive capacity for sensations, our sensibility. This is the so-called “additive” theory of cognition, more specifically of the relation between sensibility and (...)
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  27.  26
    Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect (...)
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  28.  23
    Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation of classical logic are formulated.
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  29. Kant on the Transcendental Deduction of Space and Time: An Essay on the Philosophical Resources of the Transcendental Aesthetic.Melissa McBay Merritt - 2010 - Kantian Review 14 (2):1-37.
    I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment to (...)
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  30.  45
    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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  31.  36
    The New Riddle of Induction and the New Riddle of Deduction.Gal Yehezkel - 2016 - Acta Analytica 31 (1):31-41.
    Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy between induction and (...) in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)
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  32. Kant’s Transcendental Idealism and His Transcendental Deduction.Justin B. Shaddock - 2015 - Kantian Review 20 (2):265-288.
    I argue for a novel, non-subjectivist interpretation of Kant’s transcendental idealism. Kant’s idealism is often interpreted as specifying how we must experience objects or how objects must appear to us. I argue to the contrary by appealing to Kant’s Transcendental Deduction. Kant’s Deduction is the proof that the categories are not merely subjectively necessary conditions we need for our cognition, but objectively valid conditions necessary for objects to be appearances. My interpretation centres on two claims. First, Kant’s method (...)
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  33.  41
    What Were Kant's Aims in the Deduction?Gary Hatfield - 2003 - Philosophical Topics 31 (1/2):165-198.
    This article argues that many (often Anglophone) interpreters of the Deduction have mistakenly identified Kant's aim as vindicating ordinary knowledge of objects and as refuting Hume's (alleged) skepticism about such knowledge. Instead, the article contends that Kant's aims were primarily negative. His primary mission (in the Deduction) was not to justify application of the categories to experience, but to show that any use beyond the domain of experience could not be justified. To do this, he needed to show (...)
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  34.  22
    Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW]Torben Braüner - 2004 - Journal of Logic, Language and Information 13 (1):1-23.
    In this paper two different natural deduction systems forhybrid logic are compared and contrasted.One of the systems was originally given by the author of the presentpaper whereasthe other system under consideration is a modifiedversion of a natural deductionsystem given by Jerry Seligman.We give translations in both directions between the systems,and moreover, we devise a set of reduction rules forthe latter system bytranslation of already known reduction rules for the former system.
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  35. Natural Deduction in Connectionist Systems.William P. 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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  36.  89
    “Truth-Preserving and Consequence-Preserving Deduction Rules”,.John Corcoran - 2014 - Bulletin of Symbolic Logic 20:130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized (...)
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  37. Remarks on Stoic Deduction.John Corcoran - 1974 - In Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 169--181.
    This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.
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  38.  8
    Natural Deduction for Diagonal Operators.Fabio Lampert - forthcoming - In Proceedings of the Canadian Society for History and Philosophy of Mathematics. Springer.
    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 eval- uation (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 (...)
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  39.  14
    Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction.Moritz Cordes & Friedrich Reinmuth - forthcoming - Logic and Logical Philosophy.
    We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the original proof. (...)
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  40.  92
    The Subjective Deduction and the Search for a Fundamental Force.Corey W. Dyck - 2008 - Kant-Studien 99 (2):152-179.
    In this paper, I claim that Kant’s subjective deduction in the first edition of the KrV is to be understood in terms of an investigation of the fundamental force(s) (Grundkraft) of the soul, an investigation essential to Wolffian psychology and much debated throughout Germany in the second half of the 1700’s. I argue that the subjective deduction is indeed presented by means of the exposition of the three-fold syntheses but only insofar as these syntheses are employed as pointers (...)
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  41.  7
    Contextual Deduction Theorems.J. G. Raftery - 2011 - Studia Logica 99 (1-3):279-319.
    Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a (...)
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  42. Kant's Deduction and Apperception. Explaining the Categories.Dennis Schulting - 2012 - Palgrave-Macmillan.
    Dennis Schulting offers a thoroughgoing, analytic account of the first half of the Transcendental Deduction of the Categories in the B-edition of Kant’s Critique of Pure Reason that is different from existing interpretations in at least one important aspect: its central claim is that each of the 12 categories is wholly derivable from the principle of apperception, which goes against the current view that the Deduction is not a proof in a strict philosophical sense and the standard reading (...)
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  43.  80
    The Conclusion of the Deduction of Taste in the Dialectic of Aesthetic Power of Judgment in Kant.Manuel Sánchez Rodríguez - 2013 - Trans/Form/Ação 36 (2):45-62.
    In this paper, it is argued that only in the section on dialectic in the Critique of Judgment does Kant reach a definitive and conclusive version of deduction, after discovering the concept of the supersensible. In the section on the deduction of pure aesthetic judgments, Kant does not satisfactorily explain the critical distinction between the sensible nature of humanity and the supersensible nature of human reason presupposed in the concept of universal communicability. While the concept of the supersensible (...)
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  44.  78
    The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative?Marcello D'Agostino & Luciano Floridi - 2009 - Synthese 167 (2):271 - 315.
    Deductive inference is usually regarded as being "tautological" or "analytical": the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...)
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  45.  27
    A Nonconceptualist Reading of the B-Deduction.Roberto Horácio de Sá Pereira - 2017 - Philosophical Studies 174 (2):425-442.
    In this paper, I propose a new nonconceptual reading of the B-Deduction. As Hanna correctly remarks :399–415, 2011: 405), the word “cognition” has in both editions of the first Critique a wide sense, meaning nonconceptual cognition, and a narrow meaning, in Kant’s own words “an objective perception”. To be sure, Kant assumes the first meaning to account for why the Deduction is unavoidable. And if we take this meaning as a premise of the B-Deduction, then there is (...)
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  46.  29
    The Method of Scientific Discovery in Peirce's Philosophy: Deduction, Induction, and Abduction. [REVIEW]Cassiano Terra Rodrigues - 2011 - Logica Universalis 5 (1):127-164.
    In this paper we will show Peirce’s distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce’s originality on this, we show Peirce’s distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, (...)
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  47.  63
    Natural Deduction for Modal Logic with a Backtracking Operator.Jonathan Payne - 2015 - Journal of Philosophical Logic 44 (3):237-258.
    Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. (...)
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  48.  13
    Translations From Natural Deduction to Sequent Calculus.J. Von Plato - 2003 - Mathematical Logic Quarterly 49 (5):435.
    Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut-free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut-free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts (...)
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  49.  60
    Cogito, ergo sum : induction et déduction.Vilmer Jean-Baptiste Jeangène - 2004 - Archives de Philosophie 67 (1):51-63.
    Le « cogito, ergo sum » cartésien apparaît depuis quarante ans comme « inférence et performance » (J. Hintikka). Mais de quelle inférence s'agit-il précisément ? Pour le savoir, cet article poursuit deux objectifs : d'abord, montrer que la question pertinente à laquelle il s'agit de répondre ne concerne pas la relation logique interne qui lie le cogito au sum, et qui est une intuition, mais celle, externe, qui lie le « cogito, ergo sum » tout entier au « quicquid (...)
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  50.  8
    Note on Deduction Theorems in Contraction‐Free Logics.Karel Chvalovský & Petr Cintula - 2012 - Mathematical Logic Quarterly 58 (3):236-243.
    This paper provides a finer analysis of the well-known form of the Local Deduction Theorem in contraction-free logics . An infinite hierarchy of its natural strengthenings is introduced and studied. The main results are the separation of its initial four members and the subsequent collapse of the hierarchy.
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