Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles (...) and principles of mathematical and transfinite induction as well as the status of the latter with respect to various foundational characterizations of number theory. (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)

One of the popular explications of the deflationary tenet of ‘thinness’ of truth is the conservativeness demand: the declaration that a deflationary truth theory should be conservative over its base. This paper contains a critical discussion and assessment of this demand. We ask and answer the question of whether conservativity forms a part of deflationary doctrines.

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It (...) turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic). (shrink)

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)

It is widely believed that deflationary truth has no explanatory power. I will argue that it does. Specifically, I will consider some objections to deflationary truth having explanatory power, and argue that they fail. The position which will emerge is that the deflationary concept of truth is analogous to the concept of an average. Scientists take averages to be explanatory, and I will argue that the concept of deflationary truth is explanatory in the same way. I then argue that this (...) deflationary _concept_ of truth motivates a theory of the _property_ of truth which is metaphysically disunified, but that this is no obstacle to explanation. This leads to a way of understanding the deflationary/substantive distinction in terms of grounding. (shrink)

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...) based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

A new approach to truth is offered which dispenses with the truth predicate, and replaces it with a special kind of quantifier which simultaneously binds variables in sentential and nominal positions. The resulting theory of truth for a (first-order) language is shown to be able to handle blind truth ascriptions, and is shown to be compatible with a characterization of the semantic and syntactic principles governing that language. Comparisons with other approaches to truth are drawn. An axiomatization of AU-quantifiers and (...) a model theory for them is given, and an appendix contains a completeness proof. (shrink)

It is argued that the blind ascriptive role for the word true, its use, that is, in conjunction with descriptions of classes of sentences or with proper names of sentences (but not quote-names), is one which applies indiscriminately to sentences regardless of whether these are in languages we speak, can understand, or can translate into sentences that we do speak (and understand). Formal analogues of the ordinary word true as they arise in Tarskis seminal work, and in others, cannot replicate (...) this essential role of the ordinary word true. (shrink)

In this paper, I address some of the chief challenges, or problems, for Deflationary Theories of Truth, viz., the Generalization Problem, the Conservativeness Argument, and the Success Argument.

What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of compositional and Tarskian theories concern descriptive theories only. -/- Second, two requirements (...) that any deflationist truth theory intended to serve a logical purpose must satisfy are put forward. These requirements, it is argued, suggest that (i) many well-known compositional and Tarskian theories are acceptable from a deflationist standpoint (including CT); (ii) certain other popular theories of truth (including KF and FS) are not similarly acceptable; (iii) there are no conclusive reasons to impose a conservativeness requirement on deflationary theories of truth. (shrink)

It's often said that according to deflationary theories of truth, truth is not a ‘substantial’ property. While this is a fine slogan, it is far from transparent what deflationists mean (or ought to mean) in saying that truth is ‘insubstantial’. Focusing so intently upon the concept of truth and the word ‘true’, I argue, deflationists and their critics have been insufficiently attentive to a host of metaphysical complexities that arise for deflationists in connection with the property of truth. My aim (...) is to correct several misunderstandings as to what deflationists are after here—including some harboured by deflationists themselves—and to offer an account of the commitments about truth's nature that they ought to undertake. In developing this account, I focus particularly upon the issue of what metaphysics of truth a Horwichian minimalist ought to adopt. (shrink)

Many philosophers believe that a deflationist theory of truth must conservatively extend any base theory to which it is added. But when applied to arithmetic, it's argued, the imposition of a conservativeness requirement leads to a serious objection to deflationism: for the Gödel sentence for Peano Arithmetic is not a theorem of PA, but becomes one when PA is extended by adding plausible principles governing truth. This paper argues that no such objection succeeds. The issue turns on how we understand (...) the notion of logical consequence implicit in any conservativeness requirement, and whether we possess a categorical conception of the natural numbers. I offer a disjunctive response: if we possess a categorical conception of arithmetic, then deflationists have principled reason to accept a rich notion of logical consequence according to which the Gödel sentence follows from PA. But if we do not, then the reasons for requiring the derivation of the Gödel sentence lapse, and deflationists are free to accept a conservativeness requirement stated proof-theoretically. Either way, deflationism is in the clear. (shrink)

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. -/- (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.). (shrink)

In recent decades deflationary theories of truth have been challenged with a technical argument based on the notion of conservativeness. In this paper, I shall stress that conservative extensions of theories and expandability of their models are not equivalent notions. Then, I shall argue that the deflationary thesis of the unsubstantiality of truth is better understood as leveraging on the stronger notion of expandability of models. Once expandability is involved in the argument, some notable consequences follow: the strategy proposed by (...) Hartry Field in response to the conservativeness objection is strongly undermined and even simpler proposals (such as theories based on standard t-sentences) are shown to be quite problematical. (shrink)

The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most, if not all, conceptions of harmony can already be found in Michael Dummett's seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the (...) notion of harmony, we do well to start here. Unfortunately, however, Dummett's discussion is not always easy to follow. The following is an attempt to disentangle the main strands of Dummett's treatment of harmony. The different variants of harmony as well as their interrelations are clarified and their individual shortcomings qua interpretations of harmony are demonstrated. Though no attempt is made to give a detailed alternative account of harmony here, it is hoped that our discussion will lay the ground for an adequate rigorous treatment of this central notion. (shrink)

Remarks on the Foundations of Mathematics, Wittgenstein, despite his official 'mathematical nonrevisionism', slips into attempting to refute Gödel's theorem. Actually, Wittgenstein could have used Gödel's theorem to good effect, to support his view that proof, and even truth, are 'family resemblance' concepts. The reason that Wittgenstein did not see all this is that Gödel's theorem had become an icon of mathematical realism, and he was blinded by his own ideology. The essay is a reply to Juliet Floyd's work on Gödel: (...) what she says Wittgenstein said, I say he should have said, but didn't (couldn't). (shrink)

Two central themes of Douglas Edwards’s The Metaphysics of Truth are anti-deflationism and substantial pluralism. In Part I of this paper I discuss Edwards’s grounds for rejecting deflationism and suggest a few additional grounds. In Part II I discuss Edward's truth-pluralism and respond to his criticism of my correspondence-pluralism. While these pluralisms share significant features, their differences also raise several important questions.

Substantivism is a general philosophical methodology advocating a substantive approach to philosophical theorizing. In this article, I present an overview of this methodology with a special emphasis on the field of truth. I begin with a framework for understanding what is at stake in the substantivist–deflationist debate and describe the substantivist critique of deflationism. I then proceed to discuss contemporary substantivism as a positive methodology, present examples of recent substantivist theories of truth, delineate several principles of philosophical substantivism, and connect (...) it to contemporary thought about the nature and methods of philosophy. Due to limitations of space, I am unable to discuss all the forms contemporary substantivism has taken. But I try to give a clear sense of the central principles, challenges, and promise of this methodology. (shrink)

The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)

In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain (...) some recursion- and proof-theoretic results about Kripke-style fixed-point theories of truth. Section 5 shows how to derive full second-order arithmetic from principles of truth. Section 6 investigates the proof-theoretic strength of disquotation without an arithmetical base theory. (shrink)

This article examines Kevin Scharp’s formal solution to the alethic paradoxes, ADT, which stands for ascending and descending truth. One of the main supposed benefits of ADT over its competitors is that it alone can validate the uses of truth concepts in theoretical contexts, such as truth-theoretic semantics. The appendixes contain a new consistency proof for ADT, and additionally show that it is conservative. As a result of its conservativity, the article argues that ADT faces a problem in accounting for (...) certain mathematical uses of truth. Thus, Scharp’s theory needs to be amended in order to fulfill its aim of replicating all substantive uses of truth. (shrink)

Tarski’s Convention T is often taken to claim that it is both sufficient and necessary for adequacy in a definition of truth that it imply instances of the T-schema where the embedded sentence translates the mentioned sentence. However, arguments against the necessity claim have recently appeared, and, furthermore, the necessity claim is actually not required for the indefinability results for which Tarski is justly famous; indeed, Tarski’s own presentation of the results in the later Undecidable Theories makes no mention of (...) an assumption to the effect that the definition of truth implies the biconditionals. This raises a question: was Tarski in fact committed to the necessity claim in the important papers of the 1930s and 40s? I argue that he was not. The discussion of this apparently esoteric interpretive issue in fact gets to the heart of many important questions about truth, and in the final sections of the paper I discuss the importance of the T-biconditionals in the theory of meaning and the relation of deflationary and inflationary theories of truth to the semantic paradoxes. (shrink)

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...) in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories. (shrink)

Truth-theoretic deflationism holds that truth is simple, and yet that it can fulfil many useful logico-linguistic roles. Deflationism focuses on axioms for truth: there is no reduction of the notion of truth to more fundamental ones such as sets or higher-order quantifiers. In this paper I argue that the fundamental properties of reasonable, primitive truth predicates are at odds with the core tenets of classical truth-theoretic deflationism that I call fix, express, and quantify. Truth may be regarded as a broadly (...) logical, sui generis notion. However, this has little to do with the original aims of the deflationary theory of truth. (shrink)

Deflationists argue that ‘true’ is merely a logico-linguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be non-conservative and that, for this reason, truth cannot be deflationary :493–521, (...) 1998; Ketland in Mind 108:69–94, 1999). We consider two defences of conservative deflationism, respectively proposed by Waxman :429–463, 2017) and Tennant :551–582, 2002), and argue that they are both unsuccessful. In Waxman’s hands, deflationists are committed either to a non-purely expressive notion of truth, or to a conception of mathematics that does not allow them to justifiably exclude non-conservative theories of truth. Tennant’s conservative deflationism fares no better: if deflationist truth must be conservative over arithmetic, it can be shown to collapse into a non-conservative variety of deflationism. (shrink)

El deflacionismo en torno a la verdad afirma que una teoría completa de esta noción no debe atender a una naturaleza subyacente a la misma, sino al uso que se hace de ella. Pero la viabilidad de esta postura filosófica ha sido puesta en duda en la literatura por el “argumento de la conservatividad” avanzado originalmente por Shapiro. El presente trabajo propone una respuesta a dicho argumento, en términos de la defensa de un deflacionismo compatible con la no-conservatividad de una (...) teoría formal de la verdad. (shrink)

Recent work on formal theories of truth has revived an approach, due originally to Tarski, on which syntax and truth theories are sharply distinguished—‘disentangled’—from mathematical base theories. In this paper, we defend a novel philosophical constraint on disentangled theories. We argue that these theories must be epistemically stable: they must possess an intrinsic motivation justifying no strictly stronger theory. In a disentangled setting, even if the base and the syntax theory are individually stable, they may be jointly unstable. We contend (...) that this flaw afflicts many proposals discussed in the literature; we defend a new, stable disentangled theory, double second-order arithmetic. (shrink)

Niniejsza praca stanowi przegląd niedawnych wyników, zarówno opublikowanych, jak i jeszcze czekających na publikację, dotyczących różnych pojęć słabości i siły pojęcia prawdy, a także próbę ich systematyzacji i ukazania na tle szerszego nurtu badań. Omawiamy pojęcie granicy Tarskiego oddzielającej słabe i silne teorie prawdy. Omawiamy znane twierdzenia dotyczące niekonserwatywnych rozszerzeń podstawowej kompozycyjnej teorii prawdy oraz opisujemy pewną naturalną silną teorię prawdy, którą można scharakteryzować wieloma pozornie ze sobą niezwiązanymi układami aksjomatów. Na koniec przytaczamy inne możliwe eksplikacje pojęcia „siły” aksjomatycznych teorii (...) prawdy. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (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.

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)

Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory thinks that is empirically correct, and furthermore is a realist about the ‘structural content’ of . But what exactly is ‘structural content’? One proposal is that the ‘structural content’ of a scientific theory may be associated with its Ramsey sentence (). However, Demopoulos and Friedman have argued, using ideas drawn from Newman's earlier criticism of (...) Russell's structuralism, that this move fails to achieve an interesting intermediate position between realism and anti-realism. Rather, () adds little content beyond the instrumentalistically acceptable claim that the theory is empirically adequate. Here, I formulate carefully the crucial claim of Demopoulos and Friedman, and show that the Ramsey sentence () is true just in case possesses a full model which is empirically correct and satisfies a certain cardinality condition on its theoretical domain. This suggests that structural realism is not a position significantly different from the anti-realism it attempts to distinguish itself from. Introduction Technical framework Ramsification Empirical adequacy Ramsification empirical adequacy + cardinality constraint Conclusion. (shrink)

Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as Bays (...) rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)

Certain translational T-schemes of the form True « f, where f can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.

Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can (...) then be strengthened to the conclusion that infinitely many things exist. Those things are not just all Gödel codes of sentences but rather all natural numbers. Against this background inclusive negative free logic collapses into noninclusive free logic, which collapses into classical logic. The consequences for ontological deflationism with respect to truth are discussed. (shrink)

A common objection against deflationist theories of truth is that they cannot do justice to the correspondence intuition, i.e. the intuition that there is an explanatory relationship between, for instance, the truth of ‘Snow is white’ and snow's being white. We scrutinize two attempts to meet this objection and argue that both fail. We then propose a new response to the objection which, first, sheds doubt on the correctness of the correspondence intuition and, second, seeks to explain how we may (...) nonetheless have come to have that intuition. (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)

I argue that a popular brand of deflationism about truth, disquotationalism, does not adequately account for some central varieties of truth ascription. For example, given Boyle’s Law is “The product of pressure and volume is exactly a constant for an ideal gas”, disquotationalism does not explain why the blind ascription “Boyle’s Law is true” implies that the product of pressure and volume is exactly a constant for an ideal gas, and given Washington said only “Birds sing”, disquotationalism does not explain (...) why the existentially quantified ascription “Something Washington said is true” implies that birds sing. Thus disquotationalism fails to account for all the facts about truth. (shrink)

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.

This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for a first-order language, taken (...) together, have substantial logical strength, amounting to a kind of abstract consistency statement. (shrink)

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...) schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF, and thus of ramified analysis up to go. (shrink)

It has been argued in the literature that the deflationists’ thesis about the dispensability of truth as an explanatory notion forces them to adopt a conservative theory of truth. I suggest that the deflationists’ claim that the notion of truth is akin to a logical notion should be taken more seriously. This claim casts some doubts on the adequacy of the conservativity requirement, while it also calls for further investigation to assess its philosophical plausibility.