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  1. (4 other versions)Naming and Necessity.Saul Kripke - 1980 - Philosophy 56 (217):431-433.
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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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  • The Epsilon-Reconstruction of Theories and Scientific Structuralism.Georg Schiemer & Norbert Gratzl - 2016 - Erkenntnis 81 (2):407-432.
    Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...)
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  • The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.
    The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe (...)
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  • The Significance of Complex Numbers for Frege's Philosophy of Mathematics.Robert Brandom - 1996 - Proceedings of the Aristotelian Society 96 (1):293 - 315.
    Robert Brandom; XII*—The Significance of Complex Numbers for Frege's Philosophy of Mathematics1, Proceedings of the Aristotelian Society, Volume 96, Issue 1, 1.
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  • Arbitrary reference.Wylie Breckenridge & Ofra Magidor - 2012 - Philosophical Studies 158 (3):377-400.
    Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. Which one? We do (...)
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  • (1 other version)Psychophysical and theoretical identifications.David K. Lewis - 1972 - Australasian Journal of Philosophy 50 (3):249-258.
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  • Paraconsistent vagueness: a positive argument.Pablo Cobreros - 2011 - Synthese 183 (2):211-227.
    Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...)
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  • (1 other version)Truth, Ramsification, and the Pluralist's Revenge.Cory Wright - 2010 - Australasian Journal of Philosophy 88 (2):265–283.
    Functionalists about truth employ Ramsification to produce an implicit definition of the theoretical term _true_, but doing so requires determining that the theory introducing that term is itself true. A variety of putative dissolutions to this problem of epistemic circularity are shown to be unsatisfactory. One solution is offered on functionalists' behalf, though it has the upshot that they must tread on their anti-pluralist commitments.
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  • (1 other version)Can there be vague objects?Gareth Evans - 1978 - Analysis 38 (4):208.
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  • Platonism and aristotelianism in mathematics.Richard Pettigrew - 2008 - Philosophia Mathematica 16 (3):310-332.
    Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic (...)
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  • Identity, indiscernibility, and Ante Rem structuralism: The tale of I and –I.Stewart Shapiro - 2008 - Philosophia Mathematica 16 (3):285-309.
    Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...)
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  • Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.
    On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carry-on baggage? Probably not. In ordinary language, ‘everything’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’, ...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs’ is true as uttered in a (...)
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  • Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
    This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.
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  • (1 other version)How to define theoretical terms.David Lewis - 1970 - Journal of Philosophy 67 (13):427-446.
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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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  • Theory change and the indeterminacy of reference.Hartry Field - 1973 - Journal of Philosophy 70 (14):462-481.
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  • (1 other version)The meaning of 'meaning'.Hilary Putnam - 1975 - Minnesota Studies in the Philosophy of Science 7:131-193.
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  • (1 other version)Definiteness and Knowability.Timothy Williamson - 1995 - Southern Journal of Philosophy 33 (S1):171-192.
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  • Indeterminate Identities, Supervaluationism, and Quantifiers.Achille C. Varzi - 2020 - Analytic Philosophy 61 (3):218-235.
    I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it comes out true on some admissible ways of precisifying the semantics of the relevant vocabulary and false on others. In this paper, I focus on the special case of identity statements. I take it that such statements, too, may occasionally suffer a truth-value gap, including philosophically significant instances. Yet there is a potentially devastating objection that can be raised against the supervaluationist treatment (...)
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  • (2 other versions)Vagueness and Ignorance.Timothy Williamson & Peter Simons - 1992 - Aristotelian Society Supplementary Volume 66 (1):145-178.
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  • On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
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  • On the coherence of vague predicates.Crispin Wright - 1975 - Synthese 30 (3-4):325--65.
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  • Singular terms, truth-value gaps, and free logic.Bas C. van Fraassen - 1966 - Journal of Philosophy 63 (17):481-495.
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  • Reply to McGee and McLaughlin.Timothy Williamson - 2004 - Linguistics and Philosophy 27 (1):113-122.
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  • (1 other version)Timothy Williamson, vagueness: London and new York: 1994. [REVIEW]Vann McGee & Brian McLaughlin - 1998 - Linguistics and Philosophy 21 (2):221-235.
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  • (1 other version)Timothy Williamson, Vagueness: London and New York: 1994. [REVIEW]Vann McGee - 1998 - Linguistics and Philosophy 21 (2):221-235.
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  • Logical commitment and semantic indeterminacy: A reply to Williamson.Vann Mcgee & Brian P. Mclaughlin - 2004 - Linguistics and Philosophy 27 (1):123-136.
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  • From heaps and gaps to heaps of gluts.Dominic Hyde - 1997 - Mind 106 (424):641-660.
    One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...)
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  • Hilbert's ɛ-operator and classical logic.J. L. Bell - 1993 - Journal of Philosophical Logic 22 (1):1 - 18.
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  • The Logical Foundations of Probability. [REVIEW]Rudolf Carnap - 1950 - Journal of Philosophy 60 (13):362-364.
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  • Critical Notices.Rosanna Keefe - 2003 - Philosophy and Phenomenological Research 67 (2):491-500.
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  • Truth, Vagueness, and Paradox. An Essay on the Logic of Truth.Vann Mcgee & Giovanni Sommaruga-Rosolemos - 1993 - Critica 25 (73):83-108.
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  • X*—What Is “Realism”?Hilary Putnam - 1976 - Proceedings of the Aristotelian Society 76 (1):177-194.
    Hilary Putnam; X*—What Is “Realism”?, Proceedings of the Aristotelian Society, Volume 76, Issue 1, 1 June 1976, Pages 177–194, https://doi.org/10.1093/aristotel.
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  • My Basic Conceptions of Probability and Induction, PA Schilpp ed.Rudolf Carnap - 1963 - In Paul Arthur Schilpp (ed.), The philosophy of Rudolf Carnap. La Salle, Ill.,: Open Court.
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  • Semantic Sovereignty.Stephen Kearns & Ofra Magidor - 2012 - Philosophy and Phenomenological Research 85 (2):322-350.
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  • Précis of Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.
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  • Mathematics as a science of patterns. [REVIEW]Mark Steiner - 2000 - Philosophical Review 109 (1):115-118.
    For the past hundred years, mathematics, for its own reasons, has been shifting away from the study of “mathematical objects” and towards the study of “structures”. One would have expected philosophers to jump onto the bandwagon, as in many other cases, to proclaim that this shift is no accident, since mathematics is “essentially” about structures, not objects. In fact, structuralism has not been a very popular philosophy of mathematics, probably because of the hostility of Frege and other influential logicists, and (...)
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  • Vagueness and Contradiction.Roy Sorensen - 2005 - Philosophy and Phenomenological Research 71 (3):695-703.
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  • Vagueness in Context. [REVIEW]Stewart Shapiro - 2008 - Philosophy and Phenomenological Research 76 (2):471-483.
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  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.
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  • An “I” for an I: Singular terms, uniqueness, and reference.Stewart Shapiro - 2012 - Review of Symbolic Logic 5 (3):380-415.
    There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...)
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  • Philosophical Foundations of Physics. An Introduction to the Philosophy of Science.Rudolf Carnap & Martin Gardner - 1966 - Synthese 17 (1):366-367.
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  • On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part B†.Hannes Leitgeb - 2021 - Philosophia Mathematica 29 (1):64-87.
    This is Part B of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A motivated an understanding of unlabeled graphs as structures sui generis and developed a corresponding axiomatic theory of unlabeled graphs. Part B turns to the philosophical interpretation and assessment of the theory: it points out how the theory avoids well-known problems concerning identity, objecthood, and reference that have been attributed to non-eliminative structuralism. The part (...)
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  • Introduction to Logic.Roland Hall - 1960 - Philosophical Quarterly 10 (40):287-288.
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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 Jáskowski and Halldén were presented as logics of vagueness. One possible explanation for this is that, despite initial (...)
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  • Der logische Aufbau der Welt.Rudolf Carnap - 1928 - Annalen der Philosophie Und Philosophischen Kritik 8:106-107.
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  • What cannot be evaluated cannot be evaluated and it cannot be supervalued either.Jerry A. Fodor & Ernest Lepore - 1996 - Journal of Philosophy 93 (1):516--35.
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  • Supervaluationism and Logical Consequence: A Third Way.Pablo Cobreros - 2008 - Studia Logica 90 (3):291-312.
    It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist (...)
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  • On the Use of Hilbert's ε-Operator in Scientific Theories.Rudolf Carnap - 1961 - In Bar-Hillel, Yehoshua & [From Old Catalog] (eds.), Essays on the Foundations of Mathematics. Jerusalem,: Magnes Press. pp. 156--164.
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