Results for 'indirect deduction'

998 found
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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.  28
    Indirect-Deduction Theorems.S. J. Surma - 1967 - Studia Logica 20 (1):164-166.
    By indirect-deduction theorems introduced in the present paper we mean the theorems that allow to formalize indirect reasonings occurring in deductive practice in general and in mathematics in particular. We discuss the relationship between the introduced theorems and some logical calculi being virtually confined to propositional calculi with implication and negation. It is worth to notice that the above theorems are very handy and effective in proving logical theses.
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  3.  15
    Stoic “Undemonstrables” and Indirect-Deduction Theorems.Grzegorz Bryll & Zofia Kostrzycka - 1994 - Bulletin of the Section of Logic 23 (2):53-60.
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  4.  24
    A Note on Indirect Deduction Theorems Valid in Łukasiewicz's Finitely-Valued Propositional Calculi.S. J. Surma - 1973 - Studia Logica 31 (1):142-142.
  5.  26
    Beth E. W.. I Fondamenti Logici Della Matematica. Italian Translation by Casari Ettore of XXV 269. Feltrinelli Editore, Milan 1963, XIII + 335 Pp.Casari Ettore. Prefazione Del Traduttore. Therein, Pp. VII–XIII.Beth E. W.. Osservazioni Sulla Deduzione Naturale. Italian Translation by Casari Ettore of XXII 360. Therein, Pp. 255–259.Beth E. W.. Considerazioni Euristiche Sui Metodi di Deduzione Per Sequenze. Italian Translation by Ettore Casari of Considérations Heuristiques Sur les Méthodes de Déduction Par Séquences. Therein, Pp. 260–267.Beth E. W.. Osservazioni a Proposito Del Ragionamento Indiretto. Italian Translation by Ettore Casari of Observations au Sujet du Raisonnement Indirect. Therein, Pp. 268–276.Beth E. W.. Risultati di Completezza Per Sistemi Formali. Italian Translation by Casari Ettore of XXVII 110. Therein, Pp. 277–285.Casari Ettore. I Calcoli N E L di Gentzen. Therein, Pp. 287–294. [REVIEW]Giorgio Sandri - 1971 - Journal of Symbolic Logic 36 (2):325.
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  6. 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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  7.  56
    Aristotelian Syllogisms: Valid Arguments or True Universalized Conditionals?John Corcoran - 1974 - Mind 83 (330):278-281.
    Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed (...)
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  8.  10
    Argumentative Aspects of Indirect Proof.James Gasser - 1992 - Argumentation 6 (1):41-49.
    While direct proof is widely considered the paradigm of the acquisition of knowledge by deductive means, indirect proof has traditionally been criticized as showing merely ‘that’ its conclusion is true and not ‘why’ it is true. This paper accounts for the traditional objection by emphasizing the argumentative role in indirect proof of logical principles such as excluded middle and non-contradiction.
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  9. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  10.  26
    Tichý's Two-Dimensional Conception of Inference.Ivo Pezlar - 2013 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (2):54-65.
    In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling or simply (...)
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  11. Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is (...)
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  12.  45
    Integrating Induction and Deduction for Finding Evidence of Discrimination.Salvatore Ruggieri, Dino Pedreschi & Franco Turini - 2010 - Artificial Intelligence and Law 18 (1):1-43.
    We present a reference model for finding evidence of discrimination in datasets of historical decision records in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. We formalize the process of direct and indirect discrimination discovery in a rule-based framework, by modelling protected-by-law groups, such as minorities or disadvantaged segments, and contexts where discrimination occurs. Classification rules, extracted from the historical records, allow for unveiling contexts of unlawful discrimination, where the degree of burden over (...)
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  13.  42
    Teaching the PARC System of Natural Deduction.Daryl Close - 2015 - American Association of Philosophy Teachers Studies in Pedagogy 1:201-218.
    PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can (...)
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  14. JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.John Corcoran - manuscript
    JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...)
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  15. Review of Striker Translation of Aristotle's PRIOR ANALYTICS. [REVIEW]John Corcoran - 2010 - Notre Dame Philosophical Reviews:1-13.
    This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...)
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  16.  79
    Normal Derivability in Classical Natural Deduction.Jan Von Plato & Annika Siders - 2012 - Review of Symbolic Logic 5 (2):205-211.
    A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.
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  17. Dialectic and Indirect Proof.Clark Butler - 1991 - The Monist 74 (3):422-437.
    Contends that Hegel's reconstruction of valid logic leads to a conception of indirect proof and syllogisms. Clarification of the concept of indirect proof; Reference to previous papers on the subject; Indirect proof as the natural form of deduction.
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  18. REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
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  19.  23
    Propositions in Prepositional Logic Provable Only by Indirect Proofs.Jan Ekman - 1998 - Mathematical Logic Quarterly 44 (1):69-91.
    In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in prepositional logic makes prepositional logic non-normalizable. From this follows that some provable propositions in prepositional logic has no direct proof.
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  20. The Founding of Logic.John Corcoran - 1994 - Ancient Philosophy 14 (S1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  21. Can Kants Deduction of Judgments of Taste Be Saved?Miles Rind - 2002 - Archiv für Geschichte der Philosophie 84 (1):20-45.
    Kant’s argument in § 38 of the *Critique of Judgment* is subject to a dilemma: if the subjective condition of cognition is the sufficient condition of the pleasure of taste, then every object of experience must produce that pleasure; if not, then the universal communicability of cognition does not entail the universal communicability of the pleasure. Kant’s use of an additional premise in § 21 may get him out of this difficulty, but the premises themselves hang in the air and (...)
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  22.  96
    Identity Logics.John Corcoran & Stanley Ziewacz - 1979 - Notre Dame Journal of Formal Logic 20 (4):777-784.
    In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...)
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  23.  14
    Aristotle’s Theory of Deduction and Paraconsistency.Evandro Luís Gomes & Itala M. Loffredo D'Ottaviano - 2010 - Principia: An International Journal of Epistemology 14 (1):71-97.
    In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises studied by the (...)
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  24.  78
    Aristotle’s “Whenever Three Terms”.John Corcoran - 2013 - Bulletin of Symbolic Logic 19 (3):234-235.
    The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...)
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  25.  66
    The Unity of Cognition and the Subjectivist Vs. 'Transformative' Approaches to the B-Deduction, or, How to Read the Leitfaden (A79).Dennis Schulting - manuscript
    In this article, I discuss one of the most important essays on Kant's Transcendental Deduction recently published, by James Conant, addressing important themes such as the unity of cognition, the guiding thread passage in the Metaphysical Deduction, the two-step procedure of the Transcendental Deduction, the precise nature of a priori synthesis, and the role of transcendental apperception.
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  26. 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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  27.  69
    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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  28. Must . . . Stay . . . Strong!Kai von Fintel & Anthony S. Gillies - 2010 - Natural Language Semantics 18 (4):351-383.
    It is a recurring mantra that epistemic must creates a statement that is weaker than the corresponding flat-footed assertion: It must be raining vs. It’s raining. Contrary to classic discussions of the phenomenon such as by Karttunen, Kratzer, and Veltman, we argue that instead of having a weak semantics, must presupposes the presence of an indirect inference or deduction rather than of a direct observation. This is independent of the strength of the claim being made. Epistemic must is (...)
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  29. 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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  30. 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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  31. Quotation and Unquotation in Free Indirect Discourse.Emar Maier - 2015 - Mind and Language 30 (3):345-373.
    I argue that free indirect discourse should be analyzed as a species of direct discourse rather than indirect discourse. More specifically, I argue against the emerging consensus among semanticists, who analyze it in terms of context shifting. Instead, I apply the semantic mechanisms of mixed quotation and unquotation to offer an alternative analysis where free indirect discourse is essentially a quotation of an utterance or thought, but with unquoted tenses and pronouns.
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  32. 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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  33. 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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  34. 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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  35.  34
    The Case for Valuing Non-Health and Indirect Benefits.Govind Persad & Jessica du Toit - 2020 - In Ole F. Norheim, Ezekiel J. Emanuel & Joseph Millum (eds.), Global Health Priority-Setting: Beyond Cost-Effectiveness. New York, NY, USA: pp. 207-222.
    Health policy is only one part of social policy. Although spending administered by the health sector constitutes a sizeable fraction of total state spending in most countries, other sectors such as education and transportation also represent major portions of national budgets. Additionally, though health is one important aspect of economic and social activity, people pursue many other goals in their social and economic lives. Similarly, direct benefits—those that are immediate results of health policy choices—are only a small portion of the (...)
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  36. 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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  37. 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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  38. On Choosing Between Deterministic and Indeterministic Models: Underdetermination and Indirect Evidence.Charlotte Werndl - 2013 - Synthese 190 (12):2243-2265.
    There are results which show that measure-theoretic deterministic models and stochastic models are observationally equivalent. Thus there is a choice between a deterministic and an indeterministic model and the question arises: Which model is preferable relative to evidence? If the evidence equally supports both models, there is underdetermination. This paper first distinguishes between different kinds of choice and clarifies the possible resulting types of underdetermination. Then a new answer is presented: the focus is on the choice between a Newtonian deterministic (...)
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  39.  92
    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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  40. 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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  41. 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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  42. Structural Correspondence, Indirect Reference, and Partial Truth: Phlogiston Theory and Newtonian Mechanics.Gerhard Schurz - 2011 - Synthese 180 (2):103-120.
    This paper elaborates on the following correspondence theorem (which has been defended and formally proved elsewhere): if theory T has been empirically successful in a domain of applications A, but was superseded later on by a different theory T* which was likewise successful in A, then under natural conditions T contains theoretical expressions which were responsible for T’s success and correspond (in A) to certain theoretical expressions of T*. I illustrate this theorem at hand of the phlogiston versus oxygen theories (...)
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  43. 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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  44. A Reconsideration of Indirect Duties Regarding Non-Human Organisms.Toby Svoboda - 2014 - Ethical Theory and Moral Practice 17 (2):311-323.
    According to indirect duty views, human beings lack direct moral duties to non-human organisms, but our direct duties to ourselves and other humans give rise to indirect duties regarding non-humans. On the orthodox interpretation of Kant’s account of indirect duties, one should abstain from treating organisms in ways that render one more likely to violate direct duties to humans. This indirect duty view is subject to several damaging objections, such as that it misidentifies the moral reasons (...)
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  45. The Puzzle of Free Indirect Discourse.Yael Sharvit - 2008 - Linguistics and Philosophy 31 (3):353-395.
    The purpose of this paper is to shed some light on the familiar puzzle of free indirect discourse (FID). FID shares some properties with standard indirect discourse and with direct discourse, but there is currently no known theory that can accommodate such a hybrid. Based on the observation that FID has ‘de se’ pronouns, I argue that it is a kind of an attitude report.
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  46. 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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  47.  73
    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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  48.  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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  49. 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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  50. Skepticism: The Hard Problem for Indirect Sensitivity Accounts.Guido Melchior - 2014 - Erkenntnis 79 (1):45-54.
    Keith DeRose’s solution to the skeptical problem is based on his indirect sensitivity account. Sensitivity is not a necessary condition for any kind of knowledge, as direct sensitivity accounts claim, but the insensitivity of our beliefs that the skeptical hypotheses are false explains why we tend to judge that we do not know them. The orthodox objection line against any kind of sensitivity account of knowledge is to present instances of insensitive beliefs that we still judge to constitute knowledge. (...)
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