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Logic, Metalogic and Neutrality

Erkenntnis 79 (2):211-231 (2013)

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  1. Ibn Sina’s Anticipation of Burdian and Barcan Formulas.Zia Movahed - 2006 - In Logic in Tehran. Cambridge: Cambridge University Press. pp. 248-255.
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  • Elements of Intuitionism.Michael Dummett - 1980 - British Journal for the Philosophy of Science 31 (3):299-301.
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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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  • VII*—Equivocation and Existence.Timothy Williamson - 1988 - Proceedings of the Aristotelian Society 88 (1):109-128.
    Timothy Williamson; VII*—Equivocation and Existence, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 109–128, https://doi.org/10.
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  • A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
    This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...)
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  • A Problem in Possible Worlds Semantics.David Kaplan - 1995 - In Walter Sinnott-Armstrong, Diana Raffman & Nicholas Asher (eds.), Modality, morality, and belief: essays in honor of Ruth Barcan Marcus. New York: Cambridge University Press. pp. 41-52.
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  • The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
    The second volume in the _Blackwell Brown Lectures in Philosophy_, this volume offers an original and provocative take on the nature and methodology of philosophy. Based on public lectures at Brown University, given by the pre-eminent philosopher, Timothy Williamson Rejects the ideology of the 'linguistic turn', the most distinctive trend of 20th century philosophy Explains the method of philosophy as a development from non-philosophical ways of thinking Suggests new ways of understanding what contemporary and past philosophers are doing.
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  • The Limits of Logic: Higher-order Logic and the Löwenheim-Skolem Theorem.Stewart Shapiro - 1996 - Routledge.
    The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.
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  • Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
    Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.
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  • Juxtaposition: A New Way to Combine Logics.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):560-606.
    This paper develops a new framework for combining propositional logics, called "juxtaposition". Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is (...)
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  • Equivocation And Existence.Timothy Williamson - 1988 - Proceedings of the Aristotelian Society 88:109-127.
    Timothy Williamson; VII*—Equivocation and Existence, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 109–128, https://doi.org/10.
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  • (2 other versions)A complete theory of everything: Satisfiability in the universal domain.Harvey M. Friedman - unknown
    Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.
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  • (2 other versions)Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
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  • Pluralism in logic.Hartry Field - 2009 - Review of Symbolic Logic 2 (2):342-359.
    There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...)
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  • The logic of common nouns: an investigation in quantified modal logic.Anil Gupta - 1980 - New Haven: Yale University Press.
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  • Saving truth from paradox.Hartry Field - 2008 - New York: Oxford University Press.
    A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.
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  • Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
    The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...)
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  • The concept of logical consequence.John Etchemendy - 1990 - Cambridge: Harvard University Press.
    Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.
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  • (1 other version)Philosophy of logic.Willard Van Orman Quine - 1986 - Cambridge: Harvard University Press. Edited by Simon Blackburn & Keith Simmons.
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  • Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.
    There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.
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  • Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • Logical pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  • Logical Pluralism.J. C. Beall & Greg Restall - 2005 - Oxford, GB: Oxford University Press. Edited by Greg Restall.
    Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.
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  • (2 other versions)Philosophy of Logic.W. V. Quine - 2005 - In José Medina & David Wood (eds.), Truth. Malden, MA: Blackwell.
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  • Oxford Handbook of Philosophy of Mathematics and Logic.Stewart Shapiro (ed.) - 2005 - Oxford and New York: Oxford University Press.
    This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a comprehensive (...)
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  • Vagueness.Timothy Williamson - 1994 - British Journal for the Philosophy of Science 46 (4):589-601.
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  • A critical appraisal of second-order logic.Ignacio Jané - 1993 - History and Philosophy of Logic 14 (1):67-86.
    Because of its capacity to characterize mathematical concepts and structures?a capacity which first-order languages clearly lack?second-order languages recommend themselves as a convenient framework for much of mathematics, including set theory. This paper is about the credentials of second-order logic:the reasons for it to be considered logic, its relations with set theory, and especially the efficacy with which it performs its role of the underlying logic of set theory.
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  • Truth, belief, and vagueness.Kenton F. Machina - 1976 - Journal of Philosophical Logic 5 (1):47-78.
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  • (1 other version)A completeness theorem for unrestricted first- order languages.Agustin Rayo & Timothy Williamson - 2003 - In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK. pp. 331-356.
    Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...)
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  • (1 other version)The Concept of Logical Consequence.John Etchemendy - 1994 - Erkenntnis 41 (2):281-284.
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  • (1 other version)The Concept of Logical Consequence.John Etchemendy - 1990 - Mind 100 (3):382-385.
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  • On How Logic Became First-Order.Matti Eklund - 1996 - Nordic Journal of Philosophical Logic 1 (2):147-67.
    Added by a category editor--not an official abstract. -/- Discusses the history (and reasons for the history) implicit in the title, as well as the author's view on same.
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  • (1 other version)Nominalist platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
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  • The tree of knowledge and other essays.G. H. Von Wright - 1993 - New York: E.J. Brill.
    Humanism, modernity, and scientific rationality are examined critically in these collected essays.
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  • (3 other versions)Précis of Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.
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  • Bare possibilia.Timothy Williamson - 1998 - Erkenntnis 48 (2-3):257--73.
    The theorems of the simplest and strongest sensible quantified modal logic include the Barcan Formula and its converse. Both formulas face strong intuitive objections. This paper develops a theory of possibilia to meet those objections.
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  • (2 other versions)Philosophy of Logic.Michael Jubien & W. V. Quine - 1988 - Journal of Symbolic Logic 53 (1):303.
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  • G. E. Hughes & M. J. Cresswell, A New Introduction to Modal Logic. [REVIEW]Paolo Crivelli & Timothy Williamson - 1998 - Philosophical Review 107 (3):471.
    This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.
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  • Bare possibilia.Timoti Vilijamson - 1998 - Theoria 41 (4):83-98.
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  • Universal Universal Quantification: Comments on Rayo and Williamson.Vann McGee - 2003 - In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK. pp. 357-364.
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  • (1 other version)A completeness theorem for unrestricted first- order languages.Agustin Rayo & Timothy Williamson - 2003 - In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK.
    Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...)
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  • Necessity and truth theories.Christopher Peacocke - 1978 - Journal of Philosophical Logic 7 (1):473 - 500.
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  • Our Knowledge of the external World as a field of scientific method in Philosophy.Bertrand Russell - 1914 - Revue Philosophique de la France Et de l'Etranger 81:306-308.
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  • Weak necessity and truth theories.Martin K. Davies - 1978 - Journal of Philosophical Logic 7 (1):415 - 439.
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  • (1 other version)Nominalist platonism.George Boolos - 1998 - In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press. pp. 73-87.
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  • On the Singularity Theory of Denotation.J. C. Beall - 2003 - In Liars and Heaps: New Essays on Paradox. Oxford, England: Oxford University Press UK.
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