DOCSLIB.ORG

Truth, Semantic Closure, and Conditionals

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Truth, Semantic Closure, and Conditionals View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by D-Scholarship@Pitt TRUTH, SEMANTIC CLOSURE, AND CONDITIONALS by Shawn Standefer B.A., Stanford, 2006 M.A., Stanford, 2006 Submitted to the Graduate Faculty of the Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2013 UNIVERSITY OF PITTSBURGH KENNETH P. DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Shawn Standefer It was defended on August 20, 2013 and approved by Anil Gupta, Department of Philosophy, University of Pittsburgh Nuel Belnap, Department of Philosophy, University of Pittsburgh Robert Brandom, Department of Philosophy, University of Pittsburgh James Shaw, Department of Philosophy, University of Pittsburgh Jeremy Avigad, Department of Philosophy, Carnegie Mellon University Dissertation Director: Anil Gupta, Department of Philosophy, University of Pittsburgh ii Copyright c by Shawn Standefer 2013 iii TRUTH, SEMANTIC CLOSURE, AND CONDITIONALS Shawn Standefer, PhD University of Pittsburgh, 2013 Almost all theories of truth place limits on the expressive power of languages containing truth predicates. Such theories have been criticized as inadequate on the grounds that these limitations are illegitimate. These criticisms set up several requirements on theories of truth. My initial focus is on the criticisms and why their requirements should be accepted. I argue that an adequate theory of truth should validate intuitive arguments involving truth and respect intuitive evaluations of the semantic statuses of sentences. From this starting point, I analyze the arguments in favor of several common requirements on theories of truth and formulate some minimal requirements on theories of truth. One is a logic neutrality requirement that says that a theory must be compatible with a range of logical resources, such as different negations. Another is the requirement that the theory validate certain laws governing truth, such as the T-sentences. These two requirements rule out many theories of truth. The main problem is that many theories lack an adequate conditional, the addition of which is, in fact, precluded by those theories. I argue that the revision theory of truth can satisfy my criteria when augmented with a pair of conditionals, which are defined using a modification of the framework of circular definitions of the revision theory. I distinguish two roles for conditionals in theories of truth and argue that the conditionals of the proposed theory fill those roles well. The conditionals are interdefinable with a modal operator. I prove a completeness theorem for the calculus C0 of The Revision Theory of Truth modified with rules for this operator. I examine the modal logic of this operator and prove a Solovay-type completeness theorem linking the modal logic and a certain class of circular definitions. iv I conclude by examining Field's recent theory of truth with its new conditional. I argue that Field's theory does not meet my requirements and that it fails to vindicate some of Field's own philosophical views. I close by proposing a framework for studying Field's conditional apart from his canonical models. v TABLE OF CONTENTS 1.0 THE PROBLEM OF SEMANTIC CLOSURE ..............1 1.1 Introduction..................................1 1.2 Three approaches to truth..........................5 1.3 Appeals to Semantic Closure........................ 12 1.4 Problems................................... 17 1.5 Projects.................................... 18 1.6 Languages and semantics.......................... 22 1.7 Hierarchies.................................. 25 1.7.1 Arithmetic.............................. 26 1.7.2 Sets.................................. 28 1.7.3 Semantics.............................. 29 1.8 Self-sufficiency................................ 32 1.8.1 First argument............................ 35 1.8.2 Second argument.......................... 36 1.8.3 Third argument........................... 36 1.8.4 Conclusions on semantic self-sufficiency.............. 37 1.9 Chapter summary.............................. 38 2.0 VERSIONS OF SEMANTIC CLOSURE .................. 39 2.1 Universality.................................. 39 2.1.1 Expressibility............................ 40 2.1.2 Extensibility............................. 42 2.1.3 Logic neutrality........................... 44 vi 2.1.4 Conclusions on universality..................... 47 2.2 Closure.................................... 47 2.2.1 Syntactic closure........................... 48 2.2.2 Semantic closure........................... 49 2.2.3 Predicates.............................. 51 2.2.4 Conclusions on closure....................... 53 2.3 Classification................................. 53 2.3.1 Kripke................................ 54 2.3.2 Field................................. 56 2.3.3 Beall................................. 58 2.3.4 Diagnosis............................... 60 2.3.5 Conclusions on classification.................... 63 2.4 Metalanguages................................ 64 2.4.1 Reinhardt.............................. 65 2.4.2 Priest on metalanguages...................... 66 2.4.3 No Richer Metalanguages...................... 67 2.4.4 Conclusions on metalanguages................... 71 2.5 Laws...................................... 71 2.6 Conclusions.................................. 75 3.0 CONDITIONALS AND REVISION THEORY .............. 77 3.1 Background.................................. 78 3.2 Connectives.................................. 80 3.2.1 Conditionals............................. 80 3.2.2 Box.................................. 84 3.2.3 Features............................... 85 3.3 Validity and related concepts........................ 92 3.4 Discussion................................... 94 3.4.1 Intersubstitutivity.......................... 95 3.4.2 Arguments.............................. 99 3.4.3 Inadequacy.............................. 101 vii 3.4.4 Neutrality.............................. 104 3.5 Determinateness............................... 106 3.6 Conclusion.................................. 112 4.0 EXPANDING THE REVISION THEORY ................ 114 4.1 Foundations.................................. 114 4.1.1 Similarity, hypotheses, and correspondence............ 115 4.1.2 Falling under hypotheses and the semantics of box........ 122 4.1.3 Extensions.............................. 123 4.1.4 Equality............................... 124 4.1.5 Revision............................... 126 4.1.6 Semantic substitution........................ 130 4.1.7 Definitions for revision theory................... 131 4.2 Soundness................................... 132 4.3 Completeness................................. 134 4.4 Finite definitions............................... 139 4.5 Revision indices................................ 144 5.0 THE MODAL LOGIC OF REVISION ................... 151 5.1 Modal logic.................................. 151 5.2 Solovay-type theorems............................ 169 5.2.1 Propositional Solovay-type theorem................ 170 5.2.2 First-order Solovay-type theorem.................. 176 5.2.3 Variations of Solovay-type theorems................ 180 6.0 FIELD'S THEORY ............................... 184 6.1 Background.................................. 184 6.2 Overview of Field's conditional....................... 188 6.2.1 General logic............................. 190 6.3 Negative features of Field's logic...................... 197 6.3.1 Responding to Gupta's criticisms................. 198 6.3.2 Artifacts and deflationism..................... 202 6.3.3 Truth-preservation.......................... 208 viii 6.4 Field's propositional logic.......................... 211 6.4.1 Short sequences........................... 218 6.4.2 Longer sequences.......................... 220 6.4.3 Even longer sequences........................ 221 6.5 Conclusions.................................. 224 7.0 CONCLUDING THOUGHTS ........................ 225 8.0 BIBLIOGRAPHY ................................ 229 ix LIST OF TABLES 1 Pattern of truth values across revisions..................... 173 2 Pattern of satisfaction across revisions...................... 174 3 Pattern of truth values across revisions..................... 175 4 Pattern of extensions for predicates across worlds................ 178 5 Pattern of extensions assigned by hypotheses.................. 178 6 Pattern of sets satisfied by hypotheses...................... 179 x LIST OF FIGURES 1 Corollary1..................................... 119 2 Lemma5...................................... 119 3 Lemma8...................................... 121 4 Lemma 10..................................... 121 5 Proof strategy for Solovay-type theorems.................... 171 xi 1.0 THE PROBLEM OF SEMANTIC CLOSURE 1.1 INTRODUCTION Truth seems to be a simple concept, one that is governed by principles of the form, pAq is true if and only if A where pAq is a name of the sentence A. These principles have come to be called T-sentences, or Tarski biconditionals. The collection of T-sentences for a language, together with classical logic and some modest syntactic resources results in triviality, so the set of naively interpreted T-sentences alone cannot be an adequate account of truth. There is a need to develop a theory of truth, an account of the logical and semantic features of truth. Truth easily gives rise to paradoxes, such as the liar paradox. A liar sentence is a sentence that says of itself that
Load more

Recommended publications
  • Limits in the Revision Theory More Than Just Definite Verdicts
    Journal of Philosophical Logic https://doi.org/10.1007/s10992-018-9477-y Limits in the Revision Theory More Than Just Definite Verdicts Catrin Campbell-Moore1 Received: 28 July 2016 / Accepted: 11 December 2016 / © The Author(s) 2018 Abstract We present a new proposal for what to do at limits in the revision theory. The usual criterion for a limit stage is that it should agree with any definite verdicts that have been brought about before that stage. We suggest that one should not only consider definite verdicts that have been brought about but also more general properties; in fact any closed property can be considered. This more general framework is required if we move to considering revision theories for concepts that are concerned with real numbers, but also has consequences for more traditional revision theories such as the revision theory of truth. Keywords Revision theory · Self-reference · Circular definitions · Taking limits · Probability 1 Introduction The revision theory is an influential method of working with concepts that are charac- terised by circular definitions, i.e. definitions that refer to that very notion. The most widely studied instance of the revision theory is the revision theory of truth, which was initially developed by Herzberger and Gupta (independently) to study truth in a way that can account for the liar paradox: a sentence which says of itself that it is not true. They take the equivalence “ϕ is true” if and only if ϕ to be one of definition. To apply the definition one starts with a hypothesis about the interpretation of ‘true’ and then revises this hypothesis in accordance with the definition to determine a new This work was done partly while at the Munich Center for Mathematical Philosophy, funded by the Alexander von Humboldt Foundation, and partly while at Corpus Christi College, Cambridge, funded by the college.
    [Show full text]
  • Contraction and Revision
    CORE Metadata, citation and similar papers at core.ac.uk Provided by PhilPapers Australasian Journal of Logic Contraction and revision Shawn Standefer The University of Melbourne Abstract An important question for proponents of non-contractive approaches to paradox is why contraction fails. One non-contractive theorist, Elia Zardini, offers the answer that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally mo- tivates failure of many principles that non-contractive theorists want to maintain. 1 Introduction Non-contractive logics are receiving increased attention as ways of responding to the semantic and set-theoretic paradoxes.1 These logics are often presented in a proof-theoretic form, characterized by their rejection of the structural rules of contraction, (W `) and (` W ). X; A; A; Z ` Y X ` Y; A; A; Z (W `) (` W ) X; A; Z ` Y X ` Y; A; Z There is a philosophical question of why contraction fails. One prominent non-contractive theorist, Elia Zardini, justifies the failure of contraction by an appeal to unstable states of affairs, using some ideas from revision theory.2 1See Petersen[2000], Zardini[2011], Shapiro[2011], Beall and Murzi[2013], Mares and Paoli[2014], and Murzi and Shapiro[2015], among others. See French and Ripley [2015] for a good overview of the area. There are other approaches that reject forms of contraction for the conditional but maintain the structural rule of contraction, e.g. Brady [2006], Field[2008, 2014, 2016], Beall[2009], and Bacon[2013]. My focus will be on the approaches that reject the structural rule.
    [Show full text]
  • Anil Gupta, Fellow of the American Academy of Arts and Sciences: Biographical Bibliometric Fact Sheets
    Anil Gupta, Fellow of the American Academy of Arts and Sciences: Biographical Bibliometric Fact Sheets E. R. Prakasan and V. L. Kalyane Scientific Information Resource Division, Knowledge Management Group, Bhabha Atomic Research Centre, Trombay, Mumbai, India – 400 085 *e-mail: [email protected] Anil Gupta, Distinguished Professor Logic, Philosophy of Language, Metaphysics, Epistemology PhD, Pittsburgh, 1977 [email protected] Anil Gupta is Distinguished Professor of Philosophy, professor of History and Philosophy of Science, and a fellow of the Center for Philosophy of Science. He is also a fellow of the American Academy of Arts and Sciences. Before joining the department in 2001, he taught at Indiana, Illinois at Chicago, and McGill [1]. Materials and Methods Standard bibliometric methods were used [2-70] for the analysis of the Bibliography (see Appendix) of Anil Gupta [71-117]. Results He is the author of The Logic of Common Nouns (Yale, 1980) and Empiricism and Experience (Oxford, 2006), and a co-author (with Nuel Belnap) of The Revision Theory of Truth (MIT, 1993). Gupta has received fellowships from the NEH and the ACLS, and he was a fellow at the Center for Advanced Study in the Behavioral Sciences, Stanford, in 1998-99. Gupta’s main research interests lie in logic, philosophy of language, metaphysics, and epistemology. Topics that are of special interest to him include definitions, truth, meaning, and perception. 50 7 Number of publications 45 Cumulative Number of Publications 6 40 ations c i 35 ons ubl 5 P cati 30 of 4 25 publi
    [Show full text]
  • Conditionals in Theories of Truth⋆
    Noname manuscript No. (will be inserted by the editor) Conditionals in Theories of Truth? Anil Gupta · Shawn Standefer Received: date / Accepted: date Abstract We argue that distinct conditionals|conditionals that are gov- erned by different logics|are needed to formalize the rules of Truth Intro- duction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field. Keywords Truth, paradox, revision theory, conditionals, circular definitions ? This is a near-final version of our paper published in the Journal of Philosophical Logic. Small differences may exist, so please cite the published version, available at http: //dx.doi.org/10.1007/s10992-015-9393-3. Anil Gupta University of Pittsburgh E-mail: [email protected] Shawn Standefer University of Melbourne E-mail: [email protected] 2 Anil Gupta, Shawn Standefer 1 Introduction The conditionals we will be concerned with are those used in stating the rules for truth, Truth Introduction (TI) and Truth Elimination (TE): (TI) If A, then `A' is true; and (TE) If `A' is true, then A. We will argue that the two conditionals here are different: they do not mean the same; they are not governed by the same logic. In outline, our argument will be as follows. We will take it that (TI) and (TE) are the best formulations we have of the principal rules governing truth. Aristotle suggested these rules in the Categories; the medievals called them `Aristotle's Rules'; and at least on this bit of logic no one has improved on Aristotle.
    [Show full text]
  • Truth & Paradox
    c Toby Meadows Online v0.7 Truth & Paradox Draft Toby Meadows c Toby Meadows Online v0.7 Draft 3 READ ME: These notes are still drafts: • there will be typos; • there may be errors; and • I plan to augment them. That said, they should be complete enough to be useful and I hope you find them so. I plan to update this document on my website: https://sites.google.com/site/tobymeadows/. Unless you’ve already come from there, it could be worth looking there for a more recent version of Toby Meadows c this document. Draft Also, if you do spot any problems or there’s something you don’t like or understand, I’d like to hear about it. Please drop me an email at: [email protected]. Online v0.7 Contents Chapter 1. om liar sentences to Kripke’s construction 5 1.1. The Liar Paradox 6 1.2. Getting formal 11 1.3. What should we do? 21 1.4. Tarski’s solution 22 Chapter 2. Kripke’s construction, its cousins & what you can do with them 29 2.1. Kripke’s solution 30 2.2. Contemporary research in formal theories of truth 40 2.3. Consistency & non-triviality 41 Bibliography 44 Toby Meadows c Draft Online v0.7 4 CHAPTER 1 om liar sentences to Kripke’s construction This week, we’re going to build up some of the technical basics involved in understanding the liar paradox and some of the contemporary approaches to it on the market. We’ll run through the following sections: (1) The liar paradox - we’ll develop the basic ingredients of the paradox, investigate some problematic solutions and in so doing make things more precise.
    [Show full text]
  • Rethinking Revision
    Welch, P. D. (2018). Rethinking Revision. Journal of Philosophical Logic, 1-18. https://doi.org/10.1007/s10992-018-9482-1 Publisher's PDF, also known as Version of record License (if available): CC BY Link to published version (if available): 10.1007/s10992-018-9482-1 Link to publication record in Explore Bristol Research PDF-document This is the final published version of the article (version of record). It first appeared online via Springer at https://link.springer.com/article/10.1007%2Fs10992-018-9482-1 . Please refer to any applicable terms of use of the publisher. University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/ Journal of Philosophical Logic https://doi.org/10.1007/s10992-018-9482-1 Rethinking Revision P. D. Welch1 Received: 28 October 2016 / Accepted: 9 March 2017 / © The Author(s) 2018 Abstract We sketch a broadening of the Gupta-Belnap notion of a circular or revision theoretic definition into that of a more generalized form incorporating ideas of Kleene’s gener- alized or higher type recursion. This thereby connects the philosophically motivated, and derived, notion of a circular definition with an older form of definition by recur- sion using functionals, that is functions of functions, as oracles. We note that Gupta and Belnap’s notion of ‘categorical in L’ can be formulated in at least one of these schemes.
    [Show full text]
  • Gupta's Gambit
    Gupta’s Gambit The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Berker, Ahmet Selim. 2011. Gupta’s gambit. Philosophical Studies 152(1): 17-39. Published Version doi:10.1007/s11098-009-9435-1 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:4391333 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Gupta’s Gambit Selim Berker Harvard University [email protected] [forthcoming in a symposium on Anil Gupta’s Empiricism and Experience in Philosophical Studies; please cite that version] I. Introduction Anil Gupta’s Empiricism and Experience1 is a tour de force: inspired by his work with Nuel Belnap on the revision theory of truth, Gupta presents a brilliant new approach to perceptual justification that aims to embrace the epistemic interdependence of our perceptual judgments and background beliefs without succumbing to skepticism. Gupta sees his project as a continuation of the empiricist tradition, and his overarching goal is to preserve the genuine insights that can be found in classical empiricism while avoiding the assumptions that force most classical empiricists to renounce (or at least radically reinterpret) our commonsense view of the world. There is much to be admired in Gupta’s book: several elements in his theory are strikingly original, his use of technical machinery to achieve epistemological results is masterful, and his critical discussions of Quine, Sellars, Davidson, and others are sharp and incisive.
    [Show full text]
  • Probability for the Revision Theory of Truth
    Journal of Philosophical Logic (2019) 48: 87–112 https://doi.org/10.1007/s10992-018-9475-0 Probability for the Revision Theory of Truth Catrin Campbell-Moore1 · Leon Horsten1 · Hannes Leitgeb2 Received: 13 September 2016 / Accepted: 24 May 2017 / Published online: 13 September 2018 © The Author(s) 2018 Abstract We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfi- nite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the resulting probability function. One such property is Leitgeb’s Probabilistic Con- vention T, which says that the probability of ϕ equals the probability that ϕ is true. Keywords Liar paradox · Semantic paradox · Revision theory of truth · Probabilistic convention T 1 Introduction The revision theory of truth is an influential way to account for a type-free truth predicate. This theory constructs a series of hypotheses, or extensions, of the truth predicate. In this process one ‘revises’, or moves from one hypothesis to the next, by an application of Tarski biconditionals. After some sufficiently long initial sequence one can look back at the revision sequence and draw certain conclusions about the semantic status of different sentences. The sentence T0 = 0, for example, settles down on being true, whereas the liar sentence (which says of itself that it is not true) will have its truth value continuing to switch throughout the revision sequence.
    [Show full text]
  • Prosentence, Revision, Truth and Paradox
    Philosophy and Phenomenological Research Vol. LXXIII, No. 3, November 2006 Prosentence, Revision, Truth, and Paradox NUEL BELNAP University of Pittsburgh Tim Maudlin’s Truth and Paradox (Maudlin 2004, cited here as T&P), a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993 (The Revision Theory of Truth, henceforth RTT).’ There is no discussion of either theory, nor even any mention of them in the list of references. I offer a pair of quotes chosen from among a number of T&P generalizations that Maudlin would doubtless have modified if RTT had been on his mind at the time of composition of T&P. (1) “...every acceptable account of truth seems to imply that the TInferences must be valid” (p. 15). My response is that the revision theory of truth is built on an explicit denial of this. Rather than taking them as “valid,” RTT takes the T-Inferences as stage-of-revision-shifting revision principles in the context of a definitional account of truth. (2) “...most discussions of the Liar paradox and related paradoxes ...do not address [such questions as]... where [T&P’s] Proof Lambda and Proof Gamma go wrong” (p. 20). In fact, RTT is not open to this criticism. It’s simple natural-deduction calculus C, addresses exactly such questions. 1 Tarski’s strategy as normative Now, given the thousands of pages on truth, that T&P omits discussion of two of my favorite theories is thoroughly understandable.
    [Show full text]
  • Revision Without Revision Sequences: Self-Referential Truth
    Journal of Philosophical Logic manuscript No. (will be inserted by the editor) Revision without revision sequences: Self-referential truth Edoardo Rivello Received: date / Accepted: date Abstract The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical in- sights of Gupta and Belnap's Revision Theory of Truth into the formal frame- work of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defin- ing a monotone operator through a variant of van Fraassen's supervaluation scheme which is simply based on !-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of \grounded" true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. Keywords Self-referential truth · Revision · Supervaluation 1 Introduction The revision-theoretic method was introduced in the field of semantic theories of self-referential truth by Herzberger [15] and by Gupta [7], independently of each other.
    [Show full text]
  • A Structuralist Theory of Belief Revision
    A Structuralist Theory of Belief Revision Holger Andreas April 1, 2011 Abstract The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present inves- tigation, a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and non- trivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scien- tific knowledge. Keywords: Abduction, Belief Bases, Belief Revision, Default Logic, Defeasible Reasoning, Epistemic Ranking, Structuralist Theory of Science. 1 Introduction The present paper aims to integrate the Sneed formalism known as the struc- turalist theory of science into belief revision theory. Among other things, this integration allows for a substantial simplification of the ranking information that is necessary to define revisions and contractions in a unique manner. In classi- cal belief revision theory, some form of ranking is needed that orders any item of the belief set. Standard concepts to introduce this ranking are the relation of epistemic entrenchment (Gärdenfors 1988) and Spohn’s ordinal conditional ranking functions (Spohn 1988). In the hybrid system of the present paper, by contrast, it is only theory-elements, i.e., pieces of background theories, that 1 need to have a ranking.
    [Show full text]
  • What Theories of Truth Should Be Like (But Cannot Be) Hannes Leitgeb* University of Bristol
    Philosophy Compass 2/2 (2007): 276–290, 10.1111/j.1747-9991.2007.00070.x What Theories of Truth Should be Like (but Cannot be) Hannes Leitgeb* University of Bristol Abstract This article outlines what a formal theory of truth should be like, at least at first glance. As not all of the stated constraints can be satisfied at the same time, in view of notorious semantic paradoxes such as the Liar paradox, we consider the maximal consistent combinations of these desiderata and compare their relative advantages and disadvantages. Formal theories of truth originated with Alfred Tarski (‘Der Wahrheits- begriff’; ‘Semantic Conception of Truth’). They turned again into a hot topic of philosophical logic after Kripke, as well as Martin and Woodruff, had published their seminal pieces in 1975. In the meantime the number of contributions in this area has become legion; consequently, it is difficult to keep track of the aims that have shaped the field or may do so in the future. The plan of this article is to outline what a formal theory of truth should be like, at least at first glance, i.e. the prima facie goals that we ought to reach for when we set up a theory of truth. We will see that not all of our intentions can be satisfied at the same time, so we are led to consider the maximal consistent combinations of these and compare their relative advantages and disadvantages. Sometimes a distinction is made between philosophical theories of truth and formal or logical theories of truth. If such a distinction is granted at all, then this article should certainly be regarded as focusing on the latter.
    [Show full text]