Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.

I argue that there is no metaphysically substantive property of truth. Although many take this thesis to be central to deflationism about truth, it is sometimes left unclear what a metaphysically substantive property of truth is supposed to be. I offer a precise account by relying on the distinction between the property and concept of truth. Metaphysical substantivism is the view that the property of truth is a sparse property, regardless of how one understands the nature of sparse properties. I (...) then offer two new arguments against metaphysical substantivism that employ ideas involving recombination and truthmaking. First, I argue that there are no theoretically compelling reasons to posit the existence of a metaphysically substantive property of truth. Secondly, I argue that if we do posit the existence of such a property, then we end up with a view that is either contradictory or unmotivated. What we’re left with is a metaphysically deflationary account of the property of truth that fully respects the metaphysical ambitions of truthmaker theory, and that is consistent with both the view that truth is a deflated, explanatorily impotent concept and the view that truth is an explanatorily powerful concept. (shrink)

One of the many ways that ‘deflationary’ and ‘inflationary’ theories of truth are said to differ is in their attitude towards truth qua property. This difference used to be very easy to delineate, with deflationists denying, and inflationists asserting, that truth is a property, but more recently the debate has become a lot more complicated, owing primarily to the fact that many contemporary deflationists often do allow for truth to be considered a property. Anxious to avoid inflation, however, these deflationists (...) are at pains to point out that the truth property, on their view, is not a property of any significant interest. Correspondingly, inflationists have seen this as an opportunity to refine what kind of property they think truth is, which—according to them—moves their views beyond deflationism. The upshot of this is that there are number of different accounts in the literature of what distinguishes an inflationary truth property from a deflationary one, or—as it is sometimes put—what distinguishes a ‘substantive’ property from an ‘insubstantive’ one. This has made it hard to pin down exactly what is at issue at the metaphysical level between deflationists and inflationists, which makes it increasingly hard to see how debates between them are properly phrased. Given that these positions represent the two central attitudes towards truth in contemporary debates, this makes for a serious obstacle for the project of discerning the correct theory of truth. The aim of this paper is to discern the best way to distinguish between substantive and insubstantive properties, and thus to restore some focus to these debates. I argue that the three central distinctions in the literature fail, and offer what I take to be a more promising distinction in terms of a graded distinction between abundant and sparse properties. (shrink)

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called ‘conservativeness argument’ against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show that the problems confronting the deflationist are in fact more basic: even the observation that logic is true is beyond his reach. This seems to conflict (...) with the deflationary characterization of the role of the truth predicate in proving generalizations. However, in the final section we propose a way out for the deflationist — a solution that permits him to accept a strong theory, having important truth-theoretical generalizations as its theorems. (shrink)

Cieslinski has given an interesting response to Shapiro 1998 and Ketland 1999, which argued that deflationary truth theories are inadequate, since they lack the property of ‘reflective adequacy’. Cieslinski’s response, following Tennant (2002, 2005), aims to explain, without a detour using truth axioms, why someone who accepts the axioms of a theory should also accept its reflection principles. The argument is formulated very clearly (in fact, to justify a different reflection principle), and involves a couple of important assumptions, the crucial (...) one being that the reflection scheme for a theory ‘expresses’ the acceptance of its theorems. I argue that this assumption is incorrect. For if the reflection principle for a theory expresses the claim that one is ready to accept its theorems, this latter claim should imply the reflection principle. But it does not. So, I conclude, the response fails to yield the required ‘truth-free’ method for proving or justifying reflection principles. (shrink)

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of (...) Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic. (shrink)

For many, the paradigm of a deflationary theory of truth is the redundancy theory, which is typically taken to consist of two claims: namely (i) that sentences containing the truth predicate are synonymous with sentences not containing the truth predicate (and so the truth predicate is redundant) and (ii) that there is no property of truth.1 The redundancy theory is not an attractive theory of truth since neither of its claims is particularly plausible on its own, and the combination of (...) the two claims is, if not actually inconsistent, at least uncomfortable.2 Very few deflationists nowadays endorse either part of the theory. (shrink)

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Truth is one of the most debated topics in philosophy; Wolfgang Kunne presents a comprehensive critical examination of all major theories, from Aristotle to the present day. He argues that it is possible to give a satisfactory 'modest' account of truth without invoking problematic notions like correspondence, fact, or meaning. The clarity of exposition and the wealth of examples will make Conceptions of Truth an invaluable and stimulating guide for advanced students and scholars.

Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...) -- Reflection -- Ontological reduction -- Applying theories of truth. (shrink)

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.

According to the disquotationalist theory of truth, the Tarskian equivalences, conceived as axioms, yield all there is to say about truth. Several authors have claimed that the expression of infinite conjunctions and disjunctions is the only purpose of the disquotationalist truth predicate. The way in which infinite conjunctions can be expressed by an axiomatized truth predicate is explored and it is considered whether the disquotationalist truth predicate is adequate for this purpose.

What would something unlike us--a chimpanzee, say, or a computer--have to be able to do to qualify as a possible knower, like us? To answer this question at the very heart of our sense of ourselves, philosophers have long focused on intentionality and have looked to language as a key to this condition. Making It Explicit is an investigation into the nature of language--the social practices that distinguish us as rational, logical creatures--that revises the very terms of this inquiry. Where (...) accounts of the relation between language and mind have traditionally rested on the concept of representation, this book sets out an alternate approach based on inference, and on a conception of certain kinds of implicit assessment that become explicit in language. Making It Explicit is the first attempt to work out in detail a theory that renders linguistic meaning in terms of use--in short, to explain how semantic content can be conferred on expressions and attitudes that are suitably caught up in social practices. -/- At the center of this enterprise is a notion of discursive commitment. Being able to talk--and so in the fullest sense being able to think--is a matter of mastering the practices that govern such commitments, being able to keep track of one’s own commitments and those of others. Assessing the pragmatic significance of speech acts is a matter of explaining the explicit in terms of the implicit. As he traces the inferential structure of the social practices within which things can be made conceptually explicit, the author defines the distinctively expressive role of logical vocabulary. This expressive account of language, mind, and logic is, finally, an account of who we are. (shrink)

An irrealist conception of a given region of discourse is the view that no real properties answer to the central predicates of the region in question. Any such conception emerges, invariably, as the result of the interaction of two forces. An account of the meaning of the central predicates, along with a conception of the sorts of property the world may contain, conspire to show that, if the predicates of the region are taken to express properties, their extensions would have (...) to be deemed uniformly empty. The question then becomes whether the predicates are best understood as expressing properties, and hence as founded on error, or whether they ought to be understood along non-factualist lines.z Historically, irrealist models were developed primarily in connection with evaluative discourse, although as physicalism has flourished and as reductionist programs have failed, their application has been extended to many other domains. Indeed, it is one of the more influential suggestions in contemporary philosophy of mind that they apply even to ordinary belief/desire psychology. A correct understanding of the semantics and metaphysics of content-based psychology leaves us, so the proponents of the in-. (shrink)

Jamin Asay's book offers a fresh and daring perspective on the age-old question 'What is truth?', with a comprehensive articulation and defence of primitivism, the view that truth is a fundamental and indefinable concept. Often associated with Frege and the early Russell and Moore, primitivism has been largely absent from the larger conversation surrounding the nature of truth. Asay defends primitivism by drawing on a range of arguments from metaphysics, philosophy of language and philosophy of logic, and navigates between correspondence (...) theory and deflationism by reviving analytic philosophy's first theory of truth. In its exploration of the role that truth plays in our cognitive and linguistic lives, The Primitivist Theory of Truth offers an account of not just the nature of truth, but the foundational role that truth plays in our conceptual scheme. It will be valuable for students and scholars of philosophy of language and of metaphysics. (shrink)

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...) conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

Any consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...) the deflationist has at his disposal such extended methods-methods which make no use or mention of a truth-predicate. This consideration leads us to reassess arguments recently advanced-one by Shapiro and another by Ketland-against the deflationist's account of truth. Their main point of agreement is this: they both adduce the Gödel phenomena as motivating a 'thick' notion of truth, rather than the deflationist's 'thin' notion. But the so-called 'semantical argument', which appears to involve a 'thick' notion of truth, does not really have to be semantical at all. It is, rather, a reflective argument. And the reflections upon a system that are contained therein are deflationarily licit, expressible without explicit use or mention of a truth-predicate. Thus it would appear that this anti-deflationist objection fails to establish that there has to be more to truth than mere conformity to the disquotational T-schema. (shrink)

An introduction to the developments of nonstandard models. Beginning with Godel's incompleteness theorem, it covers the prime models, cofinal extensions, and extensions, Gaifman's construction of a definable type, Tennenbaum's theorem and Friedman's theorem on indicators, ending with a chapter on recursive saturation and resplendency.

In this article, the prospects of deflationism about the concept of truth are investigated. A new version of deflationism, called inferential deflationism, is articulated and defended. It is argued that it avoids the pitfalls of earlier deflationist views such as Horwich’s minimalist theory of truth and Field’s version of deflationism.

It is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain (...) hold that the combination has a circular explanation of the ideas or concepts of meaning and truth. I show that these arguments identify a genuine, but acceptable, circularity. (shrink)

The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory - a theory which is conservative over its base, but can't be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the deflationist (...) still needs some additional principles, which would permit him to construct his preferred theory of truth. (shrink)

consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called ‘semantical argument’ for the truth of the Gödel sentence. We are concerned to show that the (...) deflationist has at his disposal such extended methods—methods which make no use or mention of a truth-predicate. This consideration leads us to reassess arguments recently advanced—one by Shapiro and another by Ketland—against the deflationist's account of truth. Their main point of agreement is this: they both adduce the Gödel phenomena as motivating a ‘thick’ notion of truth, rather than the deflationist's ‘thin’ notion. But the so-called ‘semantical argument’, which appears to involve a ‘thick’ notion of truth, does not really have to be semantical at all. It is, rather, a reflective argument. And the reflections upon a system that are contained therein are deflationarily licit, expressible without explicit use or mention of a truth-predicate. Thus it would appear that this anti-deflationist objection fails to establish that there has to be more to truth than mere conformity to the disquotational T-schema. (shrink)

Following recent developments in the literature on axiomatic theories of truth, we investigate an alternative to the widespread habit of formalizing the syntax of the object-language into the object-language itself. We first argue for the proposed revision, elaborating philosophical evidences in favor of it. Secondly, we present a general framework for axiomatic theories of truth with theories of syntax. Different choices of the object theory O will be considered. Moreover, some strengthenings of these theories will be introduced: we will consider (...) extending the theories by the addition of coding axioms or by extending the schemas of O, if present, to the entire vocabulary of our theory of truth. Finally, we touch on the philosophical consequences that the theories described can have on the debate about the metaphysical status of the truth predicate and on the formalization of our informal metatheoretic reasoning. (shrink)

Any (1-)consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a nontrivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...) the deflationist has at his disposal such extended methods--methods which make no use or mention of a truth-predicate. (edited). (shrink)

Deflationists have argued that truth is an ontologically thin property which has only an expressive function to perform, that is, it makes possible to express semantic generalizations like 'All the theorems are true', 'Everything Peter said is true', etc. Some of the deflationists have also argued that although truth is ontologically thin, it suffices in conjunctions with other facts not involving truth to explain all the facts about truth. The purpose of this paper is to show that in the case (...) of arithmetic, it is difficult to combine the expressive with the explanatory function of truth if the latter is understood in a deflationist way. We will make our point by investigating several logical systems: first-order logic, full second-order logic, and existential second-order (?11-) logic. (shrink)

At the end of the nineties some authors (Leon Horsten, Stewart Shapiro and Jeffrey Ketland) worked out a fairly technical argument against deflationary theories of truth. In a nutshell, deflationism, it was argued, is committed to conservativeness by the the claim that truth is not a substantial notion, a conservative theory (under the light of certain logico-mathematical facts) can not be an adequate theory of truth, therefore deflationism is an inadequate theory of truth. Beside the apparent simplicity of this argument, (...) it hides a lot of subtle questions and problems and it is a very sophisticated argument. Deflationists attempted to reply in different ways to the argument but the general impression is that, so far, they have not been able to find a good solution. Deflationism does really seem to be condemned to be an inadequate theory. This work is divided in three main parts. The first part is a very general survey where the study of the notion of truth is introduced. In Chapter One we sketch philosophical theories of truth comparing more traditional approaches to deflationism; we briefly survey the history of deflationism and then we try to find a general characterization of it. In the second Chapter the notion of truth is considered under a formal approach and some important and simple axiomatic theories of truth are sketched. The second part join the philosophical and the formal approach to truth together into the debate over deflationism and conservativeness. In Chapter Three we introduce the notion of conservativeness and we give some example of its application both to logical and to philosophical matters. Then we spell out the argument from conservativeness and we discuss it in order to get a precise requirement that deflationary theories are supposed to satisfy. In Chapter Four we focus on deflationist replies to the argument from conservativeness and we discuss each solution. The third and last part is the core of the work, it consists in a more technical study of some presuppositions of the debate: we want to take a step backward and to compare the two major claims of deflationism - the centrality of T-sentences and the logical function of the truth predicate - with conservativeness. Many of the results used here are due to other logicians and philosophers and are available in literature yet, the originality consists in a critical consideration of such results under the light of the conservativeness of truth. More original reflections can be found in Chapter Seven and in particular in the conclusive Chapter Eight, where the proposal is completely new, at least as far as I know. In Chapter Five we compare T-sentences with the empty base theory and in Chapter Six we analyse in what measure a deflationary theory can be really conservative over a theory of syntax. The result would be quite serious for a deflationist. In Chapter Seven we compare conservativeness with the logical function of the truth predicate. We will get the unpleasant result that the truth predicate is not able to serve the logical function in no sense without loosing conservativeness at the same time. In Chapter Eight we draw some conclusion and we sketch a reformulation of the conservativeness requirement. This new requirement, we will argue, makes justice to the claim of the unsubstantiality of truth and at the same time it does not condemn deflationism to death. In this way, we will be able also to clarify what is the exact role of truth in sentential quantification, showing that this role is really innocent and unsubstantial. The unsubstantiality of deflationary truth, though, will not force deflationism into an inadequate theory of truth. (shrink)

In Bertrand Russell’s The Principles of Mathematics and related works, the notion of a proposition plays an important role; it is by analyzing propositions, showing what kinds of constituents they have, that Russell arrives at his core logical concepts. At this time, his conception of proposition contains both a conventional and an unconventional part. The former is the view that propositions are the ultimate truth-bearers; the latter is the view that the constituents of propositions are “worldly” entities. In the latter (...) respect, Russellian propositions are akin to states-of-affairs on some robust understanding of these entities. The idea of Russellian propositions is well known, at least in outline. Not so well known is his treatment of truth, which nevertheless grows directly out of this notion of proposition. For the early Russell, the import of truth is primarily metaphysical, rather than semantic; reversing the usual direction of explanation, he holds that truth is explanatory of what is the case rather than vice versa. That is, what properties a thing has and what relations it bears to other things is determined, metaphysically speaking, by there being a suitable array of true and false propositions. In the present paper, this doctrine is examined for its content and motivation. To show that it plays a genuine role in Russell’s early metaphysics and logic, I examine its consequences for the possibility of truth-definitions and the problem of the unity of the proposition. I shall draw a few somewhat tentative conclusions about where Russell stood vis-à-vis his metaphysics of propositions, suggesting a possible source of dissatisfaction that may have played a role in his eventual rejection of his early notion of proposition. (shrink)

The founder of modern logic and grandfather of analytic philosophy was 70 years old when he published his paper 'Der Gedanke' (The Thought ) in 1918. This essay contains some of Gottlob Frege's deepest and most provocative reflections on the concept of truth, and it will play a prominent role in my lectures. The plan for my lectures is as follows. What is it that is (primarily) true or false? 'Thoughts', is Frege's answer. In §1, I shall explain and defend (...) this answer. In §2, I shall briefly consider his enthymematic argument for the conclusion that the word 'true' resists any attempt at defining it. In §3, I shall discuss his thesis that the thought that things are thus and so is identical with the thought that it is true that things are thus and so. The reasons we are offered for this thesis will be found wanting. In §4, I shall comment extensively on Frege's claim that, in a non-formal language like the one I am currently trying to speak, we can say whatever we want to say without ever using the word 'true' or any of its synonyms. I will reject the propositional-redundancy claim, endorse the assertive-redundancy claim and deny the connection Frege ascribes to them. In his classic 1892 paper 'Über Sinn und Bedeutung' (On Sense and Signification) Frege argues that truth-values are objects. In §5, I shall scrutinize his argument. In §6, I will show that in Frege's ideography (Begriffsschrift) truth, far from being redundant, is omnipresent. The final §7 is again on truth-bearers, this time as a topic in the theory of intentionality and in metaphysics. In the course of discussing Frege's views on the objecthood, the objectivity of thoughts and the timelessness of truth(s), I will plead for a somewhat mitigated Platonism. (shrink)