All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s use (...) of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox. (shrink)

In this paper I critically evaluate a number of current "consistent inconsistency theories" and then briefly motivate a rival position. The rival position challenges a consistent inconsistency theory, by sharing many of its basic commitments without suffering the problems that such a theory appears to face.

Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have (...) broader bite, afflicting both consistent and inconsistent proposals for resolving semantic pathology. Thus, while our primary goal is to uncover some important connections between dialetheism, semantic pathology, and other, more general issues, the problem that we pose might be a worry for anyone who aims to resolve semantic pathology - consistently or not. (shrink)

ETUDES DE PHILOLOGIE 38 ETD'HISTOIRE JEANETTE MA BEER Narrative Conventions of Truth in the Middle Ages GENEVE ...

In his presidential address to the APA, ‘‘How to be an Anti-realist’’ (1982, 64–66), Alvin Plantinga argues that the only sensible way to be an antirealist is to be a theist.1 Anti-realism (AR) in this context is the epistemic analysis of truth that says, (AR) necessarily, a statement is true if and only if it would be believed by an ideally [or sufficiently] rational agent/community in ideal [or sufficiently good] epistemic circumstances. Plantinga demonstrates, with modest modal resources, that AR entails (...) that necessarily, ideal epistemic circumstances obtain. It is a contingent matter whether ideal epistemic circumstances obtain for worldly agents and communities. Hence, the lesson, according to Plantinga, is that an anti-realist should be a theist. In the present paper we evaluate whether anti-realism entails that necessarily ideal epistemic circumstances obtain. A more careful analysis of Plantinga’s argument appears in section 1. We notice that Plantinga’s interpretation of anti-realism harbors an ambiguity of quantifier scope and that only on the less plausible placement of the quantifiers does AR obviously entail that necessarily ideal epistemic circumstances obtain. In section 2 we evaluate an alternative version of Plantinga’s argument developed by Michael Rea. Rea’s argument gets the quantifiers straight, but depends on logical resources that the anti-realist has independent reason to reject. After evaluating Rea’s argument we conclude that an anti-realist need not be a theist and is not committed to the necessary existence of.. (shrink)

Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...) logic.2 The only other principle in play in Dummett’s discussion is (+) A iff Tr(A), which, as he notes, the anti-realist is likely to accept. (shrink)

The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into paraconsistent logic (...) in order to avoid strengthened liar paradoxes. (shrink)

the background. In this case (and I have in mind Kant's "On the Supposed Right to Lie because of Philanthropic Concerns"1), the commitment to truth ...

§§3-4 of the Begriffsschrift present Frege’s objections to a dominant if murky nineteenth-century semantic picture. I sketch a minimalist variant of the pre-Fregean picture which escapes Frege’s criticisms by positing a thin notion of semantic content which then interacts with a multiplicity of kinds of truth to account for phenomena such as modality. After exploring several ways in which we can understand the existence of multiple truth properties, I discuss the roles of pointwise and setwise truth properties in modal logic. (...) I argue that thinking of supertruth and determinate truth as setwise truth properties allows an understanding of supervaluationist approaches to vagueness which escapes both Williamson’s objections to and a needless metalinguistic orientation of traditional supervaluationism. (shrink)

This book argues that correspondence theories of truth fail because the relation that holds between a true thought and a fact is that of identity, not correspondence. Facts are not complexes of worldly entities which make thoughts true they are merely true thoughts. According to Julian Dodd, the resulting modest identity theory , while not defining truth, correctly diagnoses the failure of correspondence theories, and thereby prepares the ground for a defensible deflation of the concept of truth.

In this short, lucid, rich book, Sir Michael Dummett, perhaps the most eminent living British philosopher, sets out his views about some of the deepest questions in philosophy. The fundamental question of metaphysics is: what does reality consist of? Dummett puts forward his controversial view of reality as indeterminate: there may be no fact of the matter about whether an object does or does not have a given property.

I elaborate and defend the inconsistency view on vagueness I have earlier argued for in my (2002) and (forthcoming). In rough outline, the view is that the sorites paradox arises because tolerance principles, despite their inconsistency, are meaning-constitutive for vague expressions. Toward the end of the paper I discuss other inconsistency views on vagueness that have been proposed, and compare them to the view I favor.

In my ‘Deep Inconsistency’ (2002a) (henceforth DI), I criticized Graham Priest’s dialetheism by unfavorably comparing it to my preferred view on the liar paradox, a view I will here call the meaning–inconsistency view. Perhaps the main claim in Jc Beall and Priest’s reply (henceforth B&P)1 is that I am guilty of an ignoratio: in DI, I argue that Priest (1987) fails to establish the analyticity of certain principles, but, B&P say, Priest (1987) isn’t concerned to argue for the analyticity of (...) these principles. Among other criticisms B&P level against DI can be mentioned especially the following: (i) Since I do not in fact defend a particular theory of truth I am ‘out of the game’, not really participating in the debate which others participate in; (ii) I lack—for principled reasons—an account of in virtue of what principles are meaning–constitutive. Here is what I will do in this reply. First I will briefly rehearse the main elements of both my own view and the criticisms of dialetheism raised in DI. Then I will respond to the charges listed from B&P. Lastly I will make some remarks on the strengthened liar. (shrink)

Two Experiments demonstrate the existence of a “collapse illusion”, in which reasoners evaluate Truthteller-type propositions (“I am telling the truth”) as if they were simply true, whereas Liar-type propositions (“I am lying”) tend to be evaluated as neither true nor false. The second Experiment also demonstrates an individual differences pattern, in which shallow reasoners are more susceptible to the illusion. The collapse illusion is congruent with philosophical semantic truth theories such as Kripke's (1975), and with hypothetical thinking theory's principle of (...) satisficing, but can only be partially accounted for by the model theory principle of truth. Pragmatic effects related to sentence cohesion further reinforce hypothetical thinking theory interpretation of the data, although the illusion and cohesion data could also be accounted for within a modified mental model theory. (shrink)

Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...) and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A (...) within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language. (shrink)

Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...) we reject excluded middle, with special emphasis on the conditional. There is also discussion of higher order indeterminacy (in several different senses) and of penumbral connections; and there is a suggested definition of determinateness in terms of the conditional and a discussion of the extent to which the notion of determinateness is objective. And there are suggestions about a unified treatment of vagueness and the semantic paradoxes. (shrink)

... ou im- plicitement lie ä un ensemble de categories mentales et d'autres enonces (la simple affirmation: Napoleon est mort ä Sainte-Helene implique dans ...

∗Thanks to J. C. Beall, Alex Byrne, Jason Decker, Tyler Doggett, Paul Elbourne, Adam Elga, Warren Goldfarb, Delia Graff, Richard Heck, Charles Parsons, Mark Richard, Susanna Siegel, Jason Stanley, Judith Thomson, Carol Voeller, Brian Weatherson, Ralph Wedgwood, Steve Yablo, Cheryl Zoll, and an anonymous referee for valuable comments and discussions. Versions of this material were presented in my seminar at MIT in the Fall of 2000, and at the University of Maryland, Baltimore County. Parts of this paper also derive from (...) my comments on a paper of Scott Soames at the ‘Liars and Heaps’ conference at the University of Connecticut in the Fall of 2002. I am grateful for the help of these audiences, and especially to Prof. Soames. (shrink)

The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the ‘nature’, if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes.

Truth is one of the central subjects in philosophy. It is also one of the largest. Truth has been a topic of discussion in its own right for thousands of years. Moreover, a huge variety of issues in philosophy relate to truth, either by relying on theses about truth, or implying theses about truth.

A common objection to hierarchical approaches to truth is that they fragment the concept of truth. This paper defends hierarchical approaches in general against the objection of fragmentation. It argues that the fragmentation required is familiar and unprob-lematic, via a comparison with mathematical proof. Furthermore, it offers an explanation of the source and nature of the fragmentation of truth. Fragmentation arises because the concept exhibits a kind of failure of closure under reflection. This paper offers a more precise characterization of (...) the reflection involved, first in the setting of formal theories of truth, and then in a more general setting. (shrink)

• Suppose we try to “solve” the sorites paradox (i.e., say either why the premises aren’t both true or why the reasoning isn’t valid reasoning) by denying the sorites premise: by saying that it’s *not* the case that any man 1mm shorter than a tall man is tall (for a man).

Relativism is one of the most tenacious theories about truth, with a pedigree as old as philosophy itself. Nearly as ancient is the chief criticism of relativism, namely the charge that the theory is self-refuting. This paper develops a logic of relativism that (1) illuminates the classic self-refutation charge and shows how to escape it; (2) makes rigorous the ideas of truth as relative and truth as absolute, and shows the relations between them; (3) develops an intensional logic for relativism; (...) (4) provides a framework in which relativists can consistently promote ethical, mathematical, scientific, religious, and political truths (among others) as being relative; (5) argues that the notion of incommensurability is far less troubling than is commonly thought; and (6) argues that the concept of a perspective as needed by the theory is not prey to Davidson's well-known critique of conceptual schemes. The paper will not defend relativism as the correct theory of truth, nor will it provide a fully satisfying theory about the nature of a perspective. The logic of relativism is primarily meant to provide a formal framework in which relativists can consistently develop their theories. This alone is a considerable step forward, since the debate about relativism often founders upon the rock of self-refutation. It is argued that while 'everything is relative' is inconsistent, 'everything true is relatively true' is not. The latter is all a relativist really needs. (shrink)

(i) It is propositions, not sentences, that are true or false. It is true ‘Dogs bark’ does not make sense. It is true that dogs bark does. (ii) and (iii) Davidson wrong about ‘that’. (iv) The difference between ‘implies’ and ‘if ... then ...’. (v), (vi), (vii) and (viii) Russell, not Quine, right about the subject matter of logic. (ix) The objectual and substitutional interpretations of quantifiers compatible. (x), (xi), (xii), (xiii), (xiv), (xv) and (xvi) Implications for well-known theories of (...) truth; truth correspondence. (xvii), (xviii) and (xix) and (xx) Implications for the principle of bivalence, the law of excluded middle, and the principle of non-contradiction. (xxi) Recapitulation. (xxii) ‘That’ and entailment. (xxiii) Propositions not entities, subsistent or otherwise. Footnotes1 This article was stimulated by some remarks by J. J. C. Smart in criticism of a piece of work (God, Freedom and Immortality, Ashgate, 1999) that he was kind enough to read for me. I am greatly indebted to my friend David Rees for correcting the manuscript, and making some valuable suggestions concerning its content. (shrink)

This is a book that every logician will want to read. The well-worn topics of self-reference and the paradoxes have been given new life in these papers by a distinguished group of logicians.

Focusing on Truth explores the question of what truth is, balancing historical with issue-orientated discussion. The book offers a comprehensive survey of all the major theories of truth. Lawrence Johnson investigates a number of closely related matters of truth in his inquiry, such as: What sorts of things are true or false? What is attributed to them when they are said to be true or false? What do facts have to do with truth? What can we learn from previous theories? (...) The book opens with an analysis of the coherence theory of truth and then the correspondence theory of truth, as developed by Moore, Russell and Wittgenstein. Through a study of the semantic conceptions of truth, the author reveals that an adequate theory of truth must take account of the pragmatics of person, purpose, and circumstance. A full understanding of facts and truth bearers is considered central to Johnson's criticism of the opposing truth theories of J. L. Austin and P. F. Strawson. Drawing on the merits of these theories and others, while identifying their deficiencies, Johnson presents a new account of truth, based on the correlation of referential foci and the use of linguistic conventions. This account is defended as being adequate to meet the legitimate demands made on a theory of truth. Johnson argues that the account leaves scope for statements of many different sorts to be true in their own widely varying ways, without the existence of a need to posit fundamentally different kinds of truth. (shrink)

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...) consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived. (shrink)