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Wittgenstein on Incompleteness Makes Paraconsistent Sense

In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 257--276 (2012)

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  1. (1 other version)Entailment: The Logic of Relevance and Necessity, Vol. 1.A. Anderson & N. Belnap (eds.) - 1975 - Princeton, NJ, USA: Princeton University Press.
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  • (1 other version)Information.Luciano Floridi - 2005 - In Carl Mitcham (ed.), Encyclopedia of Science, Technology, and Ethics (ESTE).
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  • (1 other version)On the Plenitude of Truth. A Defense of Trivialism. [REVIEW]Claudia Olmedo-García & Luis Estrada-González - unknown
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  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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  • A Note on Wittgenstein’s “Notorious Paragraph” About the Gödel Theorem.Juliet Floyd & Hilary Putnam - 2000 - Journal of Philosophy 97 (11):624-632.
    A look at Wittgenstein's comments on the incompleteness theorem with an inter-pretation that is consistent with what Gödel proved.
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  • (2 other versions)Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.
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  • (4 other versions)Doubt Truth to Be a Liar.Graham Priest - 2007 - Studia Logica 87 (1):129-134.
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  • The preservation of coherence.R. E. Jennings & P. K. Schotch - 1984 - Studia Logica 43:89.
    It is argued that the preservation of truth by an inference relation is of little interest when premiss sets are contradictory. The notion of a level of coherence is introduced and the utility of modal logics in the semantic representation of sets of higher coherence levels is noted. It is shown that this representative role cannot be transferred to first order logic via frame theory since the modal formulae expressing coherence level restrictions are not first order definable. Finally, an inference (...)
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  • Bridges from Classical to Nonmonotonic Logic.David Makinson - 2008 - Studia Logica 89 (3):437-439.
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  • (1 other version)New Foundations for Lewis Modal Systems.E. J. Lemmon - 1958 - Journal of Symbolic Logic 23 (3):346-347.
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • Paraconsistent Vagueness: Why Not?Dominic Hyde & Mark Colyvan - 2008 - Australasian Journal of Logic 6:107-121.
    The idea that the phenomenon of vagueness might be modelled by a paraconsistent logic has been little discussed in contemporary work on vagueness, just as the idea that paraconsistent logics might be fruitfully applied to the phenomenon of vagueness has been little discussed in contemporary work on paraconsistency. This is prima facie surprising given that the earliest formalisations of paraconsistent logics presented in Jaśkowski(1948) and Halldén(1949) were presented as logics of vagueness. One possible explanation for this is that, despite initial (...)
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  • Vagueness.Timothy Williamson - 1994 - British Journal for the Philosophy of Science 46 (4):589-601.
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  • (1 other version)The Development of Logic.William Calvert Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press. Edited by Martha Kneale.
    This book traces the development of formal logic from its origins inancient Greece to the present day. The authors first discuss the work oflogicians from Aristotle to Frege, showing how they were influenced by thephilosophical or mathematical ideas of their time. They then examinedevelopments in the present century.
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  • Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
    This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.
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  • Theories of Vagueness.Rosanna Keefe - 2000 - New York: Cambridge University Press.
    Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this book, first published in 2000, Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories (...)
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  • General information in relevant logic.Edwin D. Mares - 2009 - Synthese 167 (2):343-362.
    This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.
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  • Beyond the Limits of Thought.Graham Priest - 1995 - Cambridge, England: Cambridge University Press.
    This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new interpretations of Berkeley's (...)
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  • Relevant Logic: A Philosophical Interpretation.Edwin Mares - 2004 - New York: Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...)
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  • An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - New York: Cambridge University Press.
    This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...)
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  • (1 other version)Literal Meaning.François Récanati - 2002 - New York: Cambridge University Press.
    According to the dominant position among philosophers of language today, we can legitimately ascribe determinate contents to natural language sentences, independently of what the speaker actually means. This view contrasts with that held by ordinary language philosophers fifty years ago: according to them, speech acts, not sentences, are the primary bearers of content. François Recanati argues for the relevance of this controversy to the current debate about semantics and pragmatics. Is 'what is said' determined by linguistic conventions, or is it (...)
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  • Supervaluationism and Its Logics.Achille C. Varzi - 2007 - Mind 116 (463):633-676.
    What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...)
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  • Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
    According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...)
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  • Vagueness in Context.Stewart Shapiro - 2006 - Oxford, England: Oxford University Press UK.
    Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature (...)
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  • INFORMATION-THEORETIC LOGIC.John Corcoran - 1998 - In C. Martínez U. Rivas & L. Villegas-Forero (eds.), Truth in Perspective edited by C. Martínez, U. Rivas, L. Villegas-Forero, Ashgate Publishing Limited, Aldershot, England (1998) 113-135. ASHGATE. pp. 113-135.
    Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...)
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  • Hyper-contradictions.G. Priest - 1984 - Logique Et Analyse 27 (7):237.
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  • Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.
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  • Beginning Logic.Sarah Stebbins - 1965 - London, England: Hackett Publishing.
    "One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic.... The emphasis throughout is on natural deduction derivations, and the text's deductive systems are its greatest strength. Lemmon's unusual procedure of presenting derivations before truth tables is very effective." --Sarah Stebbins, The (...)
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  • Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
    Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...)
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  • (1 other version)Exploring Meinong's Jungle and Beyond.Richard Routley - 1983 - Journal of Philosophy 80 (3):173-179.
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  • (1 other version)Relevant arithmetic.Robert Meyer - 1976 - Bulletin of the Section of Logic 5 (4):133-135.
    This is a republication of R.K. Meyer's "Relevant Arithmetic", which originally appeared in the Bulletin of the Section of Logic 5. It sets out the problems that Meyer was to work on for the next decade concerning his system, R#.
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  • (1 other version)There Are No Ordinary Things.Peter Unger - 1994 - In Delia Graff & Timothy Williamson (eds.), Vagueness. London and New York: Ashgate. pp. 117-154.
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  • Relevant Logics.Edwin D. Mares & Robert K. Meyer - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 280–308.
    Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...)
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  • Wittgenstein's Philosophy of Mathematics'.Reuben Louis Goodstein - 1972 - In Alice Ambrose (ed.), Ludwig Wittgenstein: Philosophy and Language. New York,: Routledge.
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  • The AGM theory and inconsistent belief change.Koji Tanaka - 2005 - Logique Et Analyse 48 (189-192):113-150.
    The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...)
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  • What is Wrong with Cantor's Diagonal Argument?R. T. Brady & P. A. Rush - 2008 - Logique Et Analyse 51 (1):185-219..
    We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...)
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  • Bayesian Rationality: The Probabilistic Approach to Human Reasoning.Mike Oaksford & Nick Chater - 2007 - Oxford University Press.
    Are people rational? This question was central to Greek thought and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus (...)
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  • Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  • Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
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  • A Theory of Conditionals.Robert Stalnaker - 1968 - In Nicholas Rescher (ed.), Studies in Logical Theory. Oxford,: Blackwell. pp. 98-112.
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  • The SNePS Family.Stuart C. Shapiro & William J. Rapaport - 1992 - Computers and Mathematics with Applications 23:243-275.
    SNePS, the Semantic Network Processing System 45, 54], has been designed to be a system for representing the beliefs of a natural-language-using intelligent system (a \cognitive agent"). It has always been the intention that a SNePS-based \knowledge base" would ultimatelybe built, not by a programmeror knowledge engineer entering representations of knowledge in some formallanguage or data entry system, but by a human informing it using a natural language (NL) (generally supposed to be English), or by the system reading books or (...)
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  • Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
    Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.
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  • Information flow and relevant logics.Greg Restall - 1996 - In Jerry Seligman & Dag Westerstahl (eds.), Logic, Language and Computation. Center for the Study of Language and Inf. pp. 463–477.
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  • Sylvan's Box: A Short Story and Ten Morals.Graham Priest - 1997 - Notre Dame Journal of Formal Logic 38 (4):573-582.
    The paper contains a short story which is inconsistent, essentially so, but perfectly intelligible. The existence of such a story is used to establish various views about truth in fiction and impossible worlds.
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  • Modal Logics in the Vicinity of S.Brian F. Chellas & Krister Segerberg - 1996 - Notre Dame Journal of Formal Logic 37 (1):1-24.
    We define prenormal modal logics and show that S1, S1, S0.9, and S0.9 are Lewis versions of certain prenormal logics, determination and decidability for which are immediate. At the end we characterize Cresswell logics and ponder C. I. Lewis's idea of strict implication in S1.
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  • Russell's Mathematical Logic.Kurt Gödel - 1944 - In The Philosophy of Bertrand Russell. Northwestern University Press. pp. 123-154.
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  • A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
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  • Transfinite numbers in paraconsistent set theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
    This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...)
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  • Contradictions at the borders.David Ripley - 2011 - In Rick Nouwen, Robert van Rooij, Uli Sauerland & Hans-Christian Schmitz (eds.), Vagueness in Communication. Springer. pp. 169--188.
    The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories (...)
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  • How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency.Francesco Berto - 2007 - College Publications.
    There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...)
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