Results for 'Historicizing Deduction'

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  1.  21
    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. 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. Inspired by Kant’s account of the intimate relation between intuition and concepts, McDowell (1996) has forcefully argued that the relation between sensible content and concepts is such that sensible content does not severally contribute to cognition but always only in conjunction with concepts. This view is known as conceptualism. Recently, Kantians Robert Hanna and Lucy Allais, among others, have brought against this view the charge that it neglects the (...)
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  3.  64
    The Proof Structure of Kant's A-Edition Objective Deduction.Corey W. Dyck - forthcoming - In Giuseppe Motta & Dennis Schulting (eds.), Kant’s Deduction From Apperception: An Essay on the Transcendental Deduction of the Categories. Berlin: DeGruyter.
    Kant's A-Edition objective deduction is naturally (and has traditionally been) divided into two arguments: an " argument from above" and one that proceeds " von unten auf." This would suggest a picture of Kant's procedure in the objective deduction as first descending and ascending the same ladder, the better, perhaps, to test its durability or to thoroughly convince the reader of its soundness. There are obvious obstacles to such a reading, however; and in this chapter I will argue (...)
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  4. 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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  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. 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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  7. 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 chapter, 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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  8. 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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  9. 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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  10. 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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  11. 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.  90
    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 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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  14. 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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  15. 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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  16.  70
    Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction.Moritz Cordes & Friedrich Reinmuth - 2017 - Logic and Logical Philosophy 26 (2).
    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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  17.  36
    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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  18. 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. (...)
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  19. 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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  20. 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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  21.  79
    The Shortest Way: Kant’s Rewriting of the Transcendental Deduction.Nathan Bauer - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-29.
    This work examines Kant’s remarkable decision to rewrite the core argument of the first Critique, the Transcendental Deduction of the Categories. I identify a two-part structure common to both versions: first establishing an essential role for the categories in unifying sensible intuitions; and then addressing a worry about how the connection between our faculties asserted in the first part is possible. I employ this structure to show how Kant rewrote the argument, focusing on Kant’s response to the concerns raised (...)
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  22.  60
    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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  23. 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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  24. Kant's Deduction From Apperception.Dennis Schulting - 2017 - In Kant's Radical Subjectivism. Perspectives on the Transcendental Deduction. London, UK: Palgrave. pp. 53-96.
  25. Liar-Type Paradoxes and Intuitionistic Natural Deduction Systems.Seungrak Choi - 2018 - Korean Journal of Logic 21 (1):59-96.
    It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (⊥). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ⊥. It is, however, not (...)
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  26. 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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  27.  41
    Kant’s Neglected Alternative and the Unavoidable Need for the Transcendental Deduction.Justin B. Shaddock - 2019 - Kantian Review 24 (1):127-152.
    The problem of Kant’s Neglected Alternative is that while his Aesthetic provides an argument that space and time are empirically real – in applying to all appearances – its argument seems to fall short of the conclusion that space and time are transcendentally ideal, in not applying to any things in themselves. By considering an overlooked passage in which Kant explains why his Transcendental Deduction is ‘unavoidably necessary’, I argue that it is not solely in his Aesthetic but more (...)
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  28. Fichte's Deduction of the Moral Law.Owen Ware - forthcoming - In Steven Hoeltzel (ed.), Palgrave Fichte Handbook. Palgrave.
    It is often assumed that Fichte's aim in Part I of the System of Ethics is to provide a deduction of the moral law, the very thing that Kant – after years of unsuccessful attempts – deemed impossible. On this familiar reading, what Kant eventually viewed as an underivable 'fact' (Factum), the authority of the moral law, is what Fichte traces to its highest ground in what he calls the principle of the 'I'. However, scholars have largely overlooked a (...)
     
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  29.  61
    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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  30. 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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  31. 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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  32. Kant's Radical Subjectivism. Perspectives on the Transcendental Deduction.Dennis Schulting - 2017 - London, UK: Palgrave-Macmillan.
  33.  60
    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.  46
    Kurt Gödel’s First Steps in Logic: Formal Proofs in Arithmetic and Set Theory Through a System of Natural Deduction.Jan von Plato - 2018 - Bulletin of Symbolic Logic 24 (3):319-335.
    What seem to be Kurt Gödel’s first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested by their inclusion in Hilbert and Ackermann’s logic book of 1928, the Grundzüge der theoretischen Logik. Such proofs are notoriously hard to construct within axiomatic logic. Gödel takes without further ado into use a linear system of natural deduction for the full language of higher-order logic, with (...)
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  35. 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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  36. 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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  37.  19
    Genealogy and Jurisprudence in Fichte’s Genetic Deduction of the Categories.G. Anthony Bruno - 2018 - History of Philosophy Quarterly 35 (1):77-96.
    Fichte argues that the conclusion of Kant’s transcendental deduction of the categories is correct yet lacks a crucial premise, given Kant’s admission that the metaphysical deduction locates an arbitrary origin for the categories. Fichte provides the missing premise by employing a new method: a genetic deduction of the categories from a first principle. Since Fichte claims to articulate the same view as Kant in a different, it is crucial to grasp genetic deduction in relation to the (...)
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  38. Instability, Modus Ponens and Uncertainty of Deduction.Huajie Liu - 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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  39. 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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  40. 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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  41.  37
    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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  42. 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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  43. Kant’s Deduction From Apperception: An Essay on the Transcendental Deduction of the Categories.Dennis Schulting - 2019 - Berlin, Germany: De Gruyter.
    In focusing on the systematic deduction of the categories from a principle, Schulting takes up anew the controversial project of the eminent German Kant scholar Klaus Reich, whose monograph “The Completeness of Kant's Table of Judgments” made the case that the logical functions of judgement can all be derived from the objective unity of apperception and can be shown to link up with one another systematically. -/- Common opinion among Kantians today has it that Kant did not mean to (...)
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  44. 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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  45.  41
    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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  46.  69
    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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  47.  26
    Translations From Natural Deduction to Sequent Calculus.Jan 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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  48.  81
    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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  49.  36
    Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics.Francesca Poggiolesi - 2016 - Studia Logica 104 (5):1003-1036.
    In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively (...)
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  50.  21
    Consistency of Heyting Arithmetic in Natural Deduction.Annika Kanckos - 2010 - Mathematical Logic Quarterly 56 (6):611-624.
    A proof of the consistency of Heyting arithmetic formulated in natural deduction is given. The proof is a reduction procedure for derivations of falsity and a vector assignment, such that each reduction reduces the vector. By an interpretation of the expressions of the vectors as ordinals each derivation of falsity is assigned an ordinal less than ε 0, thus proving termination of the procedure.
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