Results for 'triviality proof'

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  1.  8
    A Strictly Finitary Non-Triviality Proof for a Paraconsistent System of Set Theory Deductively Equivalent to Classical ZFC Minus Foundation.Arief Daynes - 2000 - Archive for Mathematical Logic 39 (8):581-598.
    The paraconsistent system CPQ-ZFC/F is defined. It is shown using strong non-finitary methods that the theorems of CPQ-ZFC/F are exactly the theorems of classical ZFC minus foundation. The proof presented in the paper uses the assumption that a strongly inaccessible cardinal exists. It is then shown using strictly finitary methods that CPQ-ZFC/F is non-trivial. CPQ-ZFC/F thus provides a formulation of set theory that has the same deductive power as the corresponding classical system but is more reliable in that non- (...) is provable by strictly finitary methods. This result does not contradict Gödel's incompleteness theorem because the proof of the deductive equivalence of the paraconsistent and classical systemss use non-finitary methods. (shrink)
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  2.  70
    The Simplest Lewis-Style Triviality Proof Yet?Peter Milne - 2003 - Analysis 63 (4):300–303.
  3.  7
    The Simplest Lewis-Style Triviality Proof Yet?P. Milne - 2003 - Analysis 63 (4):300-303.
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  4.  13
    Two More Characterizations of K-Triviality.Noam Greenberg, Joseph S. Miller, Benoit Monin & Daniel Turetsky - 2018 - Notre Dame Journal of Formal Logic 59 (2):189-195.
    We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is (...)
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  5. Desire-as-Belief Revisited.Richard Bradley & Christian List - 2009 - Analysis 69 (1):31-37.
    On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play very (...)
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  6. On the Triviality of Hume's Law: A Reply to Gerhard Schurz.Charles Pigden - 2010 - In Hume on Is and Ought. Palgrave-Macmillan. pp. 217-238.
    I argue that No-Ought-From-Is (in the sense that I believe it) is a relatively trivial affair. Of course, when people try to derive substantive or non-vacuous moral conclusions from non-moral premises, they are making a mistake. But No-Non-Vacuous-Ought-From-Is is meta-ethically inert. It tells us nothing about the nature of the moral concepts. It neither refutes naturalism nor supports non-cognitivism. And this is not very surprising since it is merely an instance of an updated version of the conservativeness of logic (in (...)
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  7.  29
    Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics.Peter Verdée - 2013 - Foundations of Science 18 (4):655-680.
    In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also (...)
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  8. Prove It! The Burden of Proof Game in Science Vs. Pseudoscience Disputes.Massimo Pigliucci & Maarten Boudry - 2014 - Philosophia 42 (2):487-502.
    The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue that burden of proof is often misapplied or used as a mere rhetorical gambit, with (...)
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  9.  44
    Proof: Its Nature and Significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.
    I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which we (...)
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  10.  65
    Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in (...)
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  11. Triviality For Restrictor Conditionals.Nate Charlow - 2016 - Noûs 50 (3):533-564.
    I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.
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  12. Legal Burdens of Proof and Statistical Evidence.Georgi Gardiner - forthcoming - In James Chase & David Coady (eds.), Routledge Handbook of Applied Epistemology. Routledge.
    In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases (...)
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  13. Nonexistence of Gods: An Inductive Proof.Christian Buth - manuscript
    I prove the nonexistence of gods. The proof is based on three axioms: Ockham’s razor (OR), religiosity is endogenous in humans, and, there are no miracles. The OR is formulated operationally, to remove improper postulates, such that it yields not only a plausible argument but truth. The validity of the second and the third axiom is established empirically by inductive reasoning relying on a thorough analysis of the psychiatric literature and skeptical publications. With these axioms I prove that gods (...)
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  14.  48
    Triviality Results and the Relationship Between Logical and Natural Languages.Justin Khoo & Matthew Mandelkern - forthcoming - Mind:fzy006.
    Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...)
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  15. Absolute Contradiction, Dialetheism, and Revenge.Francesco Berto - 2014 - Review of Symbolic Logic 7 (2):193-207.
    Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...)
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  16. Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kürbis - 2015 - Journal of Philosophical Logic 44 (6):713-727.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings (...)
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  17.  21
    The Proof by Cases Property and its Variants in Structural Consequence Relations.Petr Cintula & Carles Noguera - 2013 - Studia Logica 101 (4):713-747.
    This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this (...)
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  18.  21
    A Forest of Evidence: Third-Party Certification and Multiple Forms of Proof—a Case Study of Oil Palm Plantations in Indonesia. [REVIEW]Laura Silva-Castañeda - 2012 - Agriculture and Human Values 29 (3):361-370.
    In recent years, new forms of transnational regulation have emerged, filling the void created by the failure of governments and international institutions to effectively regulate transnational corporations. Among the variety of initiatives addressing social and environmental problems, a growing number of certification systems have appeared in various sectors, particularly agrifood. Most initiatives rely on independent third-party certification to verify compliance with a standard, as it is seen as the most credible route for certification. The effects of third-party audits, however, still (...)
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  19. Proof-Theoretic Semantics for a Natural Language Fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument (...)
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  20. The Dogmatist, Moore's Proof and Transmission Failure.Luca Moretti - 2014 - Analysis 74 (3):382-389.
    According to Jim Pryor’s dogmatism, if you have an experience as if P, you acquire immediate prima facie justification for believing P. Pryor contends that dogmatism validates Moore’s infamous proof of a material world. Against Pryor, I argue that if dogmatism is true, Moore’s proof turns out to be non-transmissive of justification according to one of the senses of non-transmissivity defined by Crispin Wright. This type of non-transmissivity doesn’t deprive dogmatism of its apparent antisceptical bite.
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  21.  38
    A Note on Gibbard's Proof.Justin Khoo - 2013 - Philosophical Studies 166 (S1):153-164.
    A proof by Allan Gibbard (Ifs: Conditionals, beliefs, decision, chance, time. Reidel, Dordrecht, 1981) seems to demonstrate that if indicative conditionals have truth conditions, they cannot be stronger than material implication. Angelika Kratzer's theory that conditionals do not denote two-place operators purports to escape this result [see Kratzer (Chic Linguist Soc 22(2):1–15, 1986, 2012)]. In this note, I raise some trouble for Kratzer’s proposed method of escape and then show that her semantics avoids this consequence of Gibbard’s proof (...)
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  22.  28
    Handbook of Proof Theory.Samuel R. Buss (ed.) - 1998 - Elsevier.
    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory (...)
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  23. Burdens of Proof and the Case for Unevenness.Imran Aijaz, Jonathan McKeown-Green & Aness Webster - 2013 - Argumentation 27 (3):259-282.
    How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to (...)
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  24.  31
    Proof Analysis: A Contribution to Hilbert's Last Problem.Sara Negri & Jan von Plato - 2011 - Cambridge University Press.
    Machine generated contents note: Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; (...)
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  25.  28
    Failure of Completeness in Proof-Theoretic Semantics.Thomas Piecha, Wagner de Campos Sanz & Peter Schroeder-Heister - 2015 - Journal of Philosophical Logic 44 (3):321-335.
    Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop’s (...)
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  26.  60
    The Burden of Proof and Its Role in Argumentation.Ulrike Hahn & Mike Oaksford - 2007 - Argumentation 21 (1):39-61.
    The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the latter case, it (...)
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  27.  9
    Burden of Proof in Bioethics.Julian J. Koplin & Michael J. Selgelid - 2015 - Bioethics 29 (9):597-603.
    A common strategy in bioethics is to posit a prima facie case in favour of one policy, and to then claim that the burden of proof falls on those with opposing views. If the burden of proof is not met, it is claimed, then the policy in question should be accepted. This article illustrates, and critically evaluates, examples of this strategy in debates about the sale of organs by living donors, human enhancement, and the precautionary principle. We highlight (...)
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  28. Conditionals, Indeterminacy, and Triviality.Justin Khoo - 2013 - Philosophical Perspectives 27 (1):260-287.
    This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of (...) is the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)
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  29. Putting the Burden of Proof in Its Place: When Are Differential Allocations Legitimate?Tim Dare & Justine Kingsbury - 2008 - Southern Journal of Philosophy 46 (4):503-518.
    To have the burden of proof is to be rationally required to argue for or provide evidence for your position. To have a heavier burden than an opponent is to be rationally required to provide better evidence or better arguments than they are required to provide. Many commentators suggest that differential or uneven distribution of the burden of proof is ubiquitous. In reasoned discourse, the idea goes, it is almost always the case that one party must prove the (...)
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  30. Knowledge of Mathematics Without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.
    Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show (...)
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  31. How to Read Moore's "Proof of an External World".Kevin Morris & Consuelo Preti - 2015 - Journal for the History of Analytical Philosophy 4 (1).
    We develop a reading of Moore’s “Proof of an External World” that emphasizes the connections between this paper and Moore’s earlier concerns and strategies. Our reading has the benefit of explaining why the claims that Moore advances in “Proof of an External World” would have been of interest to him, and avoids attributing to him arguments that are either trivial or wildly unsuccessful. Part of the evidence for our view comes from unpublished drafts which, we believe, contain important (...)
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  32. Moral Contextualism and the Problem of Triviality.Daan Evers - 2014 - Ethical Theory and Moral Practice 17 (2):285-297.
    Moral contextualism is the view that claims like ‘A ought to X’ are implicitly relative to some (contextually variable) standard. This leads to a problem: what are fundamental moral claims like ‘You ought to maximize happiness’ relative to? If this claim is relative to a utilitarian standard, then its truth conditions are trivial: ‘Relative to utilitarianism, you ought to maximize happiness’. But it certainly doesn’t seem trivial that you ought to maximize happiness (utilitarianism is a highly controversial position). Some people (...)
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  33. The Highest Good and Kant's Proof(s) of God's Existence.Courtney Fugate - 2014 - History of Philosophy Quarterly 31 (2).
    This paper explains a way of understanding Kant's proof of God's existence in the Critique of Practical Reason that has hitherto gone unnoticed and argues that this interpretation possesses several advantages over its rivals. By first looking at examples where Kant indicates the role that faith plays in moral life and then reconstructing the proof of the second Critique with this in view, I argue that, for Kant, we must adopt a certain conception of the highest good, and (...)
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  34.  64
    Triviality Pursuit.Alan Hájek - 2011 - Topoi 30 (1):3-15.
    The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I (...)
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  35.  20
    The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony.Peter Schroeder-Heister - 2014 - Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a canonical (...)
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  36.  15
    Proof-Theoretic Validity.Read Stephen & Stephen Read - 2015 - In Foundations of Logical Consequence. Oxford, UK: pp. 136-158.
    The idea of proof-theoretic validity originated in the work of Gentzen, when he suggested that the meaning of each logical expression was encapsulated in its introduction-rules. The idea was developed by Prawitz and Dummett, but came under attack by Prior under the soubriquet 'analytic validity'. Logical truths and logical consequences are deemed analytically valid by virtue of following, in a way which the present chapter clarifies, from the meaning of the logical constants. But different logics are based on different (...)
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  37.  53
    Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning.Peter Schroeder-Heister - 2012 - Topoi 31 (1):77-85.
    From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a (...)
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  38. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value.John Corcoran - 1971 - Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...)
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  39. What is Proof of Concept Research and How Does It Generate Epistemic and Ethical Categories for Future Scientific Practice?Catherine Elizabeth Kendig - 2016 - Science and Engineering Ethics 22 (3):735-753.
    Proof of concept” is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. I (...)
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  40.  39
    Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization.Ryo Takemura - 2013 - Studia Logica 101 (1):157-191.
    Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us (...)
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  41.  85
    Surviving Abduction.Walter Carnielli - 2006 - Logic Journal of the IGPL 14 (2):237-256.
    Abduction or retroduction, as introduced by C.S. Peirce in the double sense of searching for explanatory instances and providing an explanation is a kind of complement for usual argumentation. There is, however, an inferential step from the explanandum to the abductive explanans . Whether this inferential step can be captured by logical machinery depends upon a number of assumptions, but in any case it suffers in principle from the triviality objection: any time a singular contradictory explanans occurs, the system (...)
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  42.  48
    Conditionals and Theory Change: Revisions, Expansions, and Additions. [REVIEW]Hans Rott - 1989 - Synthese 81 (1):91-113.
    This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (additions) are to be equated with logical expansions. If negated or might conditionals are interpreted on the (...)
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  43.  64
    Presentism and the Triviality Objection.Takeshi Sakon - 2015 - Philosophia 43 (4):1089-1109.
    Presentism is usually understood as the thesis that only the present exists whereas the rival theory of eternalism is usually understood as the thesis that past, present, and future things are all equally real. The significance of this debate has been threatened by the so-called triviality objection, which allegedly shows that the presentist thesis is either trivially true or obviously false: Presentism is trivially true if it is read as saying that everything that exists now is present, and it (...)
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  44.  41
    Revisiting Dummett's Proof-Theoretic Justification Procedures.Hermógenes Oliveira - 2017 - In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016. London: College Publications. pp. 141-155.
    Dummett’s justification procedures are revisited. They are used as background for the discussion of some conceptual and technical issues in proof-theoretic semantics, especially the role played by assumptions in proof-theoretic definitions of validity.
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  45.  63
    The Strongest Possible Lewisian Triviality Result.Branden Fitelson - 2015 - Thought: A Journal of Philosophy 4 (2):69-74.
    The strongest possible Lewisian triviality result for the indicative conditional is proven.
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  46.  9
    Logics with Disjunction and Proof by Cases.San-min Wang & Petr Cintula - 2008 - Archive for Mathematical Logic 47 (5):435-446.
    This paper is a contribution to the general study of consequence relations which contain (definable) connective of “disjunction”. Our work is centered around the “proof by cases property”, we present several of its equivalent definitions, and show some interesting applications, namely in constructing axiomatic systems for intersections of logics and recognizing weakly implicative fuzzy logics among the weakly implicative ones.
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  47. Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal. [REVIEW]Jeffrey Bub - 2010 - Foundations of Physics 40 (9-10):1333-1340.
    Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was (...)
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  48.  34
    Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also (...)
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  49.  7
    Goal-Directed Proof Theory.Dov M. Gabbay - 2000 - Kluwer Academic.
    Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. (...)
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  50.  23
    Legal Stories and the Process of Proof.Floris Bex & Bart Verheij - 2013 - Artificial Intelligence and Law 21 (3):253-278.
    In this paper, we continue our research on a hybrid narrative-argumentative approach to evidential reasoning in the law by showing the interaction between factual reasoning (providing a proof for ‘what happened’ in a case) and legal reasoning (making a decision based on the proof). First we extend the hybrid theory by making the connection with reasoning towards legal consequences. We then emphasise the role of legal stories (as opposed to the factual stories of the hybrid theory). Legal stories (...)
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