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The concept of truth in formalized languages

In Logic, semantics, metamathematics. Oxford,: Clarendon Press. pp. 152--278 (1956)

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  1. Truth is Simple.Leon Horsten & Graham E. Leigh - 2016 - Mind:fzv184.
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  • Platonistic formalism.L. Horsten - 2001 - Erkenntnis 54 (2):173-194.
    The present paper discusses a proposal which says,roughly and with several qualifications, that thecollection of mathematical truths is identical withthe set of theorems of ZFC. It is argued that thisproposal is not as easily dismissed as outright falseor philosophically incoherent as one might think. Some morals of this are drawn for the concept ofmathematical knowledge.
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  • One Hundred Years of Semantic Paradox.Leon Horsten - 2015 - Journal of Philosophical Logic (6):1-15.
    This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.
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  • The Semantic Theory of Truth: Field’s Incompleteness Objection.Glen A. Hoffmann - 2007 - Philosophia 35 (2):161-170.
    According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints (...)
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  • Inferential Role and the Ideal of Deductive Logic.Thomas Hofweber - 209 - The Baltic International Yearbook of Cognition, Logic and Communication 5.
    Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely (...)
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  • Formal features of compositionality.Wilfrid Hodges - 2001 - Journal of Logic, Language and Information 10 (1):7-28.
    We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.
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  • Compositionality is not the problem.Wilfrid Hodges - 1998 - Logic and Logical Philosophy 6:7.
    The paper analyses what is said and what is presupposed by thePrinciple of Compositionality for semantics, as it is commonly stated. ThePrinciple of Compositionality is an axiom which some semantics satisfy andsome don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressionscontaining them. This is a sensible axiom only if one combines it with aconverse, that if two expressions make the same contribution to the meanings of sentences (...)
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  • Classical Logic I: First‐Order Logic.Wilfrid Hodges - 2017 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Oxford, UK: Blackwell. pp. 9–32.
    In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.
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  • Does the Traditional Treatment of Enthymemes Rest on a Mistake?David Hitchcock - 1998 - Argumentation 12 (1):15-37.
    In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that (...)
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  • A revolution in the foundations of mathematics?Jaakko Hintikka - 1997 - Synthese 111 (2):155-170.
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  • The Enhanced Indispensability Argument, the circularity problem, and the interpretability strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  • Mapping, meaning and metaphysics.Herbert Hochberg - 1975 - Philosophica 16 (1):191-211.
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  • The Birth of Semantics.Richard Kimberly Heck & Robert C. May - 2020 - Journal for the History of Analytical Philosophy 8 (6):1-31.
    We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...)
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  • Frege and semantics.Richard G. Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.
    In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantical notions such as reference and truth. I argue here Frege did make very serious use of semantical concepts. I argue, first, that Frege had reason to be interested in the question how the axioms and rules of his formal theory might be justified and, second, that he explicitly commits himself to offering a justification that appeals to the (...)
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  • The paradox of the believer.Sven Ove Hansson - 1991 - Philosophia 21 (1-2):25-30.
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  • Ray on Tarski on logical consequence.William H. Hanson - 1999 - Journal of Philosophical Logic 28 (6):605-616.
    In "Logical consequence: A defense of Tarski" (Journal of Philosophical Logic, vol. 25, 1996, pp. 617-677), Greg Ray defends Tarski's account of logical consequence against the criticisms of John Etchemendy. While Ray's defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger (...)
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  • Kant, truth and human nature.Robert Hanna - 2000 - British Journal for the History of Philosophy 8 (2):225 – 250.
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  • Truth and reduction.Volker Halbach - 2000 - Erkenntnis 53 (1-2):97-126.
    The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.
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  • Sense and Reference on the Web.Harry Halpin - 2011 - Minds and Machines 21 (2):153-178.
    We examine a crucial question for the World Wide Web: What does a Uniform Resource Identifier (URI) mean? Crucial for the next-generation Semantic Web, can it refer to things outside web-pages? The Web is a universal information space for naming and accessing information via URIs. However, the classical philosophical problems of meaning and reference that have been the source of debate within the philosophy of language return when the Web is given as the foundation for a knowledge representation with the (...)
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  • Some Uses of Logic in Rigorous Philosophy.Guillermo E. Rosado Haddock - 2010 - Axiomathes 20 (2-3):385-398.
    This paper is concerned with the use of logic to solve philosophical problems. Such use of logic goes counter to the prevailing empiricist tradition in analytic circles. Specifically, model-theoretic tools are applied to three fundamental issues in the philosophy of logic and mathematics, namely, to the issue of the existence of mathematical entities, to the dispute between first- and second-order logic and to the definition of analyticity.
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  • The Whole Truth and Nothing but the Truth.Susan Haack - 2008 - Midwest Studies in Philosophy 32 (1):20-35.
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  • The pragmatist theory of truth.Susan Haack - 1976 - British Journal for the Philosophy of Science 27 (3):231-249.
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  • Carnap's Contribution to Tarski's Truth.Monika Gruber - 2015 - Journal for the History of Analytical Philosophy 3 (10).
    In his seminal work “The Concept of Truth in Formalized Languages”, Alfred Tarski showed how to construct a formally correct and materially adequate definition of true sentence for certain formalized languages. These results have, eventually, been accepted and applauded by philosophers and logicians nearly in unison. Its Postscript, written two years later, however, has given rise to a considerable amount of controversy. There is an ongoing debate on what Tarski really said in the postscript. These discussions often regard Tarski as (...)
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  • Why Aristotle’s Sea-Battle Argument is Valid.Michael Groneberg - 2013 - History of Philosophy & Logical Analysis 16 (1):331-345.
    The paper tries to demonstrate the validity of Aristotle’s sea-battle argument, which is still considered as invalid by many authors. The first part presents the usual reconstruction of Aristotle’s argument and the reason for its rejection. It presents the late antique adoption of the argument as valid and strong by Ammonios and Boethius as well as its modern defence. In the second part, the elements that together assure the validity of the argument are combined and cast in the form of (...)
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  • Conceptual Marxism and Truth: Inquiry Symposium on Kevin Scharp’s Replacing Truth.Patrick Greenough - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (4):403-421.
    In Replacing Truth, Scharp takes the concept of truth to be fundamentally incoherent. As such, Scharp reckons it to be unsuited for systematic philosophical theorising and in need of replacement – at least for regions of thought and talk which permit liar sentences and their ilk to be formulated. This replacement methodology is radical because it not only recommends that the concept of truth be replaced, but that the word ‘true’ be replaced too. Only Tarski has attempted anything like it (...)
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  • The problem of logical constants.Mario Gómez-Torrente - 2002 - Bulletin of Symbolic Logic 8 (1):1-37.
    There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas and (...)
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  • Quotation revisited.Mario Gómez-Torrente - 2001 - Philosophical Studies 102 (2):123-153.
    The main aim of this paper is to point out that Davidsonian and Fregean theories of quotation do not accommodate certain facts about disquotation. A second aim is to dispel some errors of interpretation in a common Davidsonian reading of Tarski's claims about quotation. This allows a correct exegesis of Tarski's view, which is then seen not to be affected by the arguments usually adduced against the view wrongly attributed to Tarski. Finally, a Tarskian view is proposed of some problems (...)
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  • On quoting the empty expression.Mario Gómez-Torrente - 2010 - Philosophical Studies 148 (3):439 - 443.
    Roy Sorensen has argued that a certain technical use of quotation marks to name the empty string supports a revised version of Davidson’s theory of quotation. I point out that Sorensen’s considerations provide no support for Davidson’s original theory, and I show that at best they support the revised Davidsonian theory only to the same extent that they support a simpler revised version of a Tarskian theory.
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  • Logical truth and tarskian logical truth.Mario Gómez-Torrente - 1998 - Synthese 117 (3):375-408.
    This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress (...)
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  • A note on formality and logical consequence.Mario Gómez-Torrente - 2000 - Journal of Philosophical Logic 29 (5):529-539.
    Logic is formal in the sense that all arguments of the same form as logically valid arguments are also logically valid and hence truth-preserving. However, it is not known whether all arguments that are valid in the usual model-theoretic sense are truthpreserving. Tarski claimed that it could be proved that all arguments that are valid (in the sense of validity he contemplated in his 1936 paper on logical consequence) are truthpreserving. But he did not offer the proof. The question arises (...)
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  • Truth in the Tractatus.Hans Johann Https://Orcidorg909X Glock - 2006 - Synthese 148 (2):345-368.
    My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a (...)
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  • The liar in context.Michael Glanzberg - 2001 - Philosophical Studies 103 (3):217 - 251.
    About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of them have. Most papers on the Liar Paradox offer (...)
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  • Dynamical Phenomena and Their Models: Truth and Empirical Correctness.Marco Giunti - 2020 - Foundations of Science 28 (1):327-375.
    In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this (...)
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  • What is Tarski's Theory of Truth?Sher Gila - 1999 - Topoi 18 (2):149-166.
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  • Implicit complements: a dilemma for model theoretic semantics. [REVIEW]Brendan S. Gillon - 2012 - Linguistics and Philosophy 35 (4):313-359.
    I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that the (...)
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  • Ambiguity, generality, and indeterminacy: Tests and definitions. [REVIEW]Brendan S. Gillon - 1990 - Synthese 85 (3):391 - 416.
    The problem addressed is that of finding a sound characterization of ambiguity. Two kinds of characterizations are distinguished: tests and definitions. Various definitions of ambiguity are critically examined and contrasted with definitions of generality and indeterminacy, concepts with which ambiguity is sometimes confused. One definition of ambiguity is defended as being more theoretically adequate than others which have been suggested by both philosophers and linguists. It is also shown how this definition of ambiguity obviates a problem thought to be posed (...)
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  • Truth versus testability in quantum logic.Claudio Garola - 1992 - Erkenntnis 37 (2):197 - 222.
    We forward an epistemological perspective regarding non-classical logics which restores the universality of logic in accordance with the thesis of global pluralism. In this perspective every non-classical truth-theory is actually a theory of some metalinguistic concept which does not coincide with the concept of truth (described by Tarski's truth theory). We intend to apply this point of view to Quantum Logic (QL) in order to prove that its structure properties derive from properties of the metalinguistic concept of testability in Quantum (...)
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  • Truth as none and many.Will Gamester - 2023 - Synthese 202 (6):1-25.
    Truth pluralists say that there are many ways to be true. Aaron Cotnoir (“Pluralism and Paradox” in: Pedersen and Wright (eds) Truth and pluralism: current debates, Oxford University Press, Oxford, 2013) has suggested a “uniquely pluralist response to the liar”. The basic idea is to maintain that, if a sentence says of itself that it is not true in a certain way, then that sentence is not apt to be true in that way, but is instead apt to be true (...)
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  • Classes and truths in set theory.Kentaro Fujimoto - 2012 - Annals of Pure and Applied Logic 163 (11):1484-1523.
    This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, (...)
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  • Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities.Joel I. Friedman - 2005 - Journal of Philosophical Logic 34 (3):227-273.
    Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This (...)
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  • Non-Representational Mathematical Realism.María José Frápolli - 2015 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 30 (3):331-348.
    This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable. I will argue for the following (...)
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  • Prose versus proof: Wittgenstein on gödel, Tarski and Truth.Juliet Floyd - 2001 - Philosophia Mathematica 9 (3):280-307.
    A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g., Penrose; 3) Replies to an instructive criticism of my 1995 paper by Mark Steiner which assesses the importance of Tarski's semantical (...)
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  • The Protestant Ethic and the Spirit of Speculativism.Chris Fleming - 2022 - Derrida Today 15 (1):92-98.
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  • Omega-inconsistency without cuts and nonstandard models.Andreas Fjellstad - 2016 - Australasian Journal of Logic 13 (5).
    This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency (...)
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  • Axiomatizing semantic theories of truth?Martin Fischer, Volker Halbach, Jönne Kriener & Johannes Stern - 2015 - Review of Symbolic Logic 8 (2):257-278.
    We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.
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  • A challenge to the new metaphysics: deRosset, Priority, and explanation.David Fisher, Hao Hong & Timothy Perrine - 2021 - Synthese 198 (7):6403-6433.
    Priority Theory is an increasingly popular view in metaphysics. By seeing metaphysical questions as primarily concerned with what explains what, instead of merely what exists, it promises not only an interesting approach to traditional metaphysical issues but also the resolution of some outstanding disputes. In a recent paper, Louis deRosset argues that Priority Theory isn’t up to the task: Priority Theory is committed to there being explanations that violate a formal constraint on any adequate explanation. This paper critically examines deRosset’s (...)
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  • Semidisquotation and the infinitary function of truth.Camillo Fiore - 2021 - Erkenntnis 88 (2):851-866.
    The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to (...)
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  • Egocentric Content.Hartry Field - 2017 - Noûs 51 (3):521-546.
    The paper distinguishes two approaches to understanding the representational content of sentences and intentional states, and its role in describing people, predicting and explaining their behavior, and so forth. It sets forth the case for one of these approaches, the “egocentric” one, initially on the basis of its ability to explain the near‐indefeasibility of ascriptions of content to our own terms (“‘dogs’ as I use it means dogs”), but more generally on the basis of its providing an attractive overall picture (...)
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  • Compositional Principles vs. Schematic Reasoning.Hartry Field - 2006 - The Monist 89 (1):9-27.
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  • Tarskian Truth And The Correspondence Theory.Luis Fernández Moreno - 2001 - Synthese 126 (1-2):123-148.
    Tarski's theory of truth brings out the question of whether he intended his theory to be a correspondence theory of truth and whether, whatever his intentions, his theory is in fact a correspondence theory. The aim of this paper is to answer both questions. The answer to the first question depends on Tarski's relevant assertions on semantics and his conception of truth. In order to answer the second question Popper's and Davidson's interpretations of Tarski's truth theory are examined; to this (...)
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