Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.

This document presents a Gentzen-style deductive calculus and proves that it is complete with respect to a 3-valued semantics for a language with quantifiers. The semantics resembles the strong Kleene semantics with respect to conjunction, disjunction and negation. The completeness proof for the sentential fragment fills in the details of a proof sketched in Arnon Avron (2003). The extension to quantifiers is original but uses standard techniques.

Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...) and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable. (shrink)

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must be different in several nontrivial ways. I explore what an axiomatic (...) theory of truth would look like. Because Horwich’s is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel’s incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory. (shrink)

There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...) dubious assumption about the linguistic expression of concepts. Successful revenge would require that there be a notion other than truth that plays the same role with respect to concept-expression that truth is naturally thought to play before we are confronted with the Liar paradox. (shrink)

This paper spells out the positive theory sketched at the end of "Against Stepping Back".): According to deflationists, [p] is true is in some sense equivalent to p. The problem that the semantic paradoxes pose for the deflationist is to explicate this equivalence without relying on a semantics grounded in the sort of real reference relations that a deflationist thinks do not exist. More generally, the deflationist is challenged to give an account of logical validity that does not force us (...) to countenance such relations. (The usual model-theoretic definition seems to presuppose that there is some special interpretation, the intended interpretation, such that truth simpliciter is truth on that intended interpretation. So if the deflationist adopts this sort of definition, the deflationist will be challenged to identify the intended interpretation without positing real reference relations.) Fortunately, a precise semantics compatible with the deflationist philosophy can be had as follows: First, we define a context as a certain sort of set constructed from a basis of literals (atomic sentences and negations of atomic sentences). This formal account of contexts has to be supplemented with an account of the conditions under which a structure satisfying the formal definition is the structure of that kind pertinent ot a given conversation. For each syntactic type of sentence, we define the conditions under which a sentence of that type is assertible relative to a context. In particular, we define the conditions under which sentences of the form " [p] is true" are assertible in a context, and we define the conditions under which sentences of the form "[p] is assertible in context G" are assertible in a context. Finally, logical validity is defined as preservation of assertibility in a context. It is demonstrated that this approach to semantics resists the semantic paradoxes. (shrink)

According to the deflationary theory of truth, to assert that a statement is true is just to assert the statement itself. For example, to say that ‘snow is white’ is true, or that it is true that snow is white, is equivalent to saying simply that snow is white, and this, according to the deflationary theory, is all that can be said significantly about the truth of ‘snow is white’.

In his recent article Christopher Gauker (2001) has presented a thoughtprovoking argument against deflationist theories of truth. More exactly, he attacks what he calls ‘T-schema deflationism’, that is, the claim that a theory of truth can simply take the form of certain instances of the T-schema.

It is well known that Tarski proved a result which can be stated roughly as: no sufficiently rich, consistent, classical language can contain its own truth definition. Tarski's way around this problem is to deal with two languages at a time, an object language for which we are defining truth and a metalanguage in which the definition occurs. An obvious question then is: under what conditions can we construct a definition of truth for a given object language. Tarski claims that (...) it is necessary and sufficient that the metalanguage be "essentially richer". Our contention, put bluntly, is that this claim deserves more scrutiny from philosophers than it usually gets and in fact is false unless "essentially richer" means nothing else than "sufficient to contain a truth definition for the object language.". (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)

A historically popular response to the liar paradox (“this sentence is false”) is to say that the liar sentence is meaningless (or semantically defective, or malfunctions, or…). Unfortunately, like all other supposed solutions to the liar, this approach faces a revenge challenge. Consider the revenge liar sentence, “this sentence is either meaningless or false”. If it is true, then it is either meaningless or false, so not true. And if it is not true, then it can’t be either meaningless or (...) false, so it must be true. Either way, we are back in a paradox. This paper provides a detailed and exhaustive discussion of the options for responding to revenge on behalf of “meaningless” theories. Though I attempt to discuss all of the options fairly, I will ultimately opt for one specific response and discuss some of its challenges. Various technical and logical matters will be discussed throughout the paper, but my focus will be philosophical, throughout. My overall conclusion is that the “meaningless” strategy is at least as well off in the face of revenge as any other approach to the liar and related paradoxes. (shrink)

We introduce and analyze a new axiomatic theory $\mathsf {CD}$ of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that $\mathsf {CD}$ is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances (...) of the T-schema are restricted to determinate sentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of $\mathsf {CD}$ are analyzed. (shrink)

If we want to retain classical logic and standard syntax in light of the liar, we are forced to restrict the T-schema. The traditional philosophical justification for this is sentential – liar sentences somehow malfunction. But the standard formal way of implementing this is conditional, our T-sentences tell us that if “p” does not malfunction, then “p” is true if and only if p. Recently Bacon and others have pointed out that conditional T-restrictions like this flirt with incoherence. If we (...) want to keep the “malfunction” motivation, our only other option is to non-conditionally restrict the T-schema, but Field and others have given powerful philosophical and technical arguments against this kind of approach. Here I argue that if we really take the philosophical motivation for restricting T-sentences seriously, we can explain why conditional restrictions fail, answer Field's argument, and reason in a coherent way about truth using a non-conditional restriction strategy. This cracks the door open for a fully classical response to the liar and related paradoxes. In closing, I argue that, when properly understood, this kind of “restriction” is not really a restriction at all. If this is right, then the holy grail of liar studies (classical logic, naïve truth, and standard syntax) may yet be attainable. (Note for readers: when this paper was first put online, the typesetters had changed some instances of corners to brackets, leading to confusion. The paper has now been corrected online by PPR, so please make sure you have the corrected version before reading or citing.). (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in the informal introduction of Gödel’s classic (1931) and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, that particular (...) informal argument plays no rôle in Gödel’s technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e., those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems—a debate which goes back to Dummett (1963). (shrink)

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)

We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi [21]: we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.

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)

Cook regards Sorenson’s so-called ‘the no-no paradox’ as only a kind of ‘meta-paradox’ or ‘quasi-paradox’ because the symmetry principle that Sorenson imposes on the paradox is meta-theoretic. He rebuilds this paradox at the object-language level by replacing the symmetry principle with some ‘background principles governing the truth predicate’. He thus argues that the no-no paradox is a ‘new type of paradox’ in that its paradoxicality depends on these principles. This paper shows that any theory is inconsistent with the T-schema instances (...) for the no-no sentences, plus the T-schema instance for a Curry sentence associated with the symmetry of the no-no sentences. It turns out that the no-no paradox still depends on the problematic instances of the T-schema in a way that the liar paradox does. What distinguishes the no-no paradox is the T-schema instance for the above Curry sentence, which encodes Sorensen’s symmetry principle at the object-language level. (shrink)

It is not uncommon among theorists favoring a deviant logic on account of the semantic paradoxes to subscribe to an idea that has come to be known as ‘classical recapture’. The main thought underpinning it is that non-classical logicians are justified in endorsing many instances of the classically valid principles that they reject. Classical recapture promises to yield an appealing pair of views: one can attain naivety for semantic concepts while retaining classicality in ordinary domains such as mathematics. However, Julien (...) Murzi and Lorenzo Rossi have recently suggested that revisionary approaches to truth breed revenge paradoxes when they are coupled with the thought that classical reasoning can be recaptured in certain circumstances. What’s novel about the paradoxes they put forward is that they cannot be dismissed so easily. The concepts used to generate these paradoxes—those of paradoxicality and unparadoxicality—are concepts that non-classical theorists need in order to offer a diagnosis of the truth-theoretic paradoxes. My goal in this paper is to argue that non-classical theorists can represent the concept of paradoxicality without falling prey to revenge paradoxes. In particular, I will show how to provide a formal fixed-point semantics for a language extended with a paradoxicality predicate that adequately expresses the non-classical logician’s notion of paradoxicality. (shrink)

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

A raft of new philosophical problems concerning truth have recently been discovered by several theorists. These problems concern the question of how ascriptions of truth are to be grounded. Most previous commentators have taken the problems to shed light on the theory of ground. In this paper, I argue that they also shed light on the theory of truth. In particular, I argue that the notion of ground can be deployed to clearly articulate one strand of deflationary thinking about truth, (...) according to which truth is “metaphysically lightweight.” I offer a ground-theoretic explication of the lightness of truth and show how it yields a novel solution to the problems concerning how truth is grounded. So, the theory of truth and the theory of ground interact fruitfully: we can apply the notion of ground to offer a clear explication of the deflationist claim that truth is “metaphysically lightweight” that both captures the motivations for that claim and solves the problems. (shrink)

The idea of classical recapture has played a prominent role for non-classical logicians. In the specific case of non-classical theories of truth, although we know that it is not possible to retain classical logic for every statement involving the truth predicate, it is clear that for many such statements this is in principle feasible, and even desirable. What is not entirely obvious or well-known is how far this idea can be pushed. Can the non-classical theorist retain classical logic for every (...) non-paradoxical statement? If not, is she forced to settle for a very weak form of Classical Recapture, or are there robust versions of classical recapture available to her? These are the main questions that I will address in this paper. As a test case I will consider a paracomplete account of the truth-theoretic paradoxes and I will argue for two claims. First, that it is not possible to retain the law of excluded middle for every non-paradoxical statement. Secondly, that there are no robust versions of classical recapture available to the paracomplete logician. (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)

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)

The main aim of our paper was to present three formal tools for comparing various axiomatic theories of truth. In Section 2 we aimed at showing that there are indeed many different approaches to defining a set of axioms for the notion of truth. In Section 3 we introduced three different \measures of strength" of axiomatic theories of truth, i.e. three reflexive and transitive relations on the set of axiomatic theories of truth. We have explained the intuition behind each of (...) them. The three relations were called : Fujimoto definability, model-theoretical strength, proof-theoretical strength. Then in the last section we described how they order the truth theories introduced in Section 2. We observed that theories made equivalent by the coarser relation can be strictly ordered by the next one. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...) It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide proof-theoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.

Deflationists claim that the truth predicate was introduced into our language merely to full a certain logico-linguistic function. Oddly enough, the question what this function exactly consists in has received little attention. We argue that the best way of understanding the function of the truth predicate is as enabling us to mimic higher-order quantification in a first-order framework. Indeed, one can show that the full simple theory of types is reducible to disquotational principles of truth. Our analysis has important consequences (...) for our understanding of truth. In this paper, we can only touch on one of them: we will argue that the insubstantiality of truth does not imply a conservativity requirement on our best theories of truth. (shrink)

In this paper I introduce Horwich’s deflationary theory of truth, called ‘Minimalism’, and I present his proposal of how to cope with the Liar Paradox. The proposal proceeds by restricting the T-schema and, as a consequence of that, it needs a constructive specification of which instances of the T-schema are to be excluded from Minimalism. Horwich has presented, in an informal way, one construction that specifies the Minimalist theory. The main aim of the paper is to present and scrutinize some (...) formal versions of Horwich’s construction. (shrink)

A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...) instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)

Horwich proposes a solution to the liar paradox that relies on a particular notion of grounding—one that, unlike Kripke’s notion of grounding, does not invoke any “Tarski-style compositional principles”. In this short note, we will formalize Horwich’s construction and argue that his solution to the liar paradox does not justify certain generalizations about truth that he endorses. We argue that this situation is not resolved even if one appeals to the \-rule. In the final section, we briefly discuss how Horwich (...) might respond to the situation. (shrink)

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More generally, I argue (...) that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike. (shrink)

The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of reference. To do this, we first give sound and arithmetically simple notions of reference, self-reference, and well-foundedness for the language of first-order arithmetic extended with a truth predicate; a task that has been so far elusive in the literature. Then, we use the new notions to restrict the T-schema to sentences that exhibit "safe" reference patterns, confirming the widely accepted but never (...) worked out idea that paradoxes can be characterised in terms of their underlying reference patterns. This results in a strong, ω-consistent, and well-motivated system of disquotational truth, as required by minimalism. (shrink)

Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema -/- <p> is true iff p. -/- My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to the paradoxes.

There has been much debate recently as to whether the notion of truth, as applied to one's home language, is metaphysically neutral, the interesting metaphysical questions arising elsewhere (in relation to such notions as mind-independence or objectivity or existence). ' On one side, the minimalists, as they have come to be known, favour deflationary accounts of truth such as the redundancy or disquotational theories and conclude that the notion of truth is applicable to declarative sentences in general - at least (...) where there are fairly definite standards of appropriateness for the assertion or denial of such sentences - irrespective of the metaphysical commitments of the propositions the sentences express. Opponents have criticized the minimalist account of truth or denied that it follows from this account that truth is metaphysically neutral. My sympathies in this debate lie with the minimalist but I wish to focus on a serious problem for the minimalist - that posed by the Liar paradox. This problem has featured very little in the recent debate but seems to me to yield the strongest objection to minimalism. I develop the objection in the next section, in §2 sketching what I feel to be the minimalist's best response, namely developing the position not in terms of Tarskian classical biconditionals but rather in terms of the naive rules for truth. It emerges, then, that the minimalist will be forced to repudiate classical logic. The last section, §3, deals with objections to the strategy of §2. (shrink)

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of (...) Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

Vann McGee has argued against solutions to the liar paradox that simply restrict the scope of the T sentences as little as possible. This argument is often taken to disprove Paul Horwich’s preferred solution to the liar paradox for his Minimal Theory of truth. I argue that Horwich’s theory is different enough from the theory McGee criticized that these criticisms do not apply to Horwich’s theory. On the basis of this, I argue that propositional theories, like MT, cannot be evaluated (...) using the same methods as sentential theories. (shrink)

T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors ) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus (...) spelling doom to deflationist and minimalist truth theories in particular. The situation is indeed worrisome as formal theories of minimalist truth are missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In the present article, we will show how to find safe instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong. (shrink)

In this paper, we investigate the phenomenon ofspeed-upin the context of theories of truth. We focus on axiomatic theories of truth extending Peano arithmetic. We are particularly interested on whether conservative extensions of PA have speed-up and on how this relates to a deflationist account. We show that disquotational theories have no significant speed-up, in contrast to some compositional theories, and we briefly assess the philosophical implications of these results.

Che cos'è la verità? A questa domanda le teorie deflazioniste rispondono in modo sorprendente: niente, o quasi. Secondo il deflazionismo la verità, come proprietà, semplicemente non esiste o è priva di qualsiasi sostanza. In questo contributo presenterò tale posizione offrendo un breve resoconto critico dell'evoluzione della proposta e una disamina delle sue tesi centrali.

Suppose our ordinary notion of truth is ‘inconsistent’ in the sense that its meaning is partly given by principles that classically entail a logical contradiction. Should we replace the notion with a consistent surrogate? This paper begins by defusing various arguments in favor of this revisionary proposal, including Kevin Scharp’s contention that we need to replace truth for the purposes of semantic theorizing . Borrowing a certain conservative metasemantic principle from Matti Eklund, the article goes on to build a positive (...) case for the opposite policy: retaining truth as-is. The thought is basically that bivalence for the bulk of what we say in the course of ordinary, scientific, and philosophical inquiry should suffice to justify keeping ‘true’. Two versions of the story are told: one more philosophical, drawing on an analogy to Lewis’ response to Putnam’s paradox; the other more technical, invoking a deviant stran.. (shrink)

Recently, Paul Horwich has developed the minimalist theory of truth, according to which the truth predicate does not express a substantive property, though it may be used as a grammatical expedient. Minimalism shares these claims with Quine’s disquotationalism; it differs from disquotationalism primarily in holding that truth-bearers are propositions, rather than sentences. Despite potential ontological worries, allowing that propositions bear truth gives Horwich a prima facie response to several important objections to disquotationalism. In section I of this paper, disquotationalism is (...) given a careful exegesis, in which seven known objections are traced to the disquotational schema, and two new objections are raised. A version of disquotationalism which avoids two of the seven known objections is recommended. In section II, an examination of minimalism shows that it faces eight of the nine objections facing disquotationalism, plus a new objection. In section III, a finite formulation of minimalism proposed by Ernest Sosa is shown to meet five of the nine objections facing disquotationalism as well as the objection new to minimalism, though it faces another new objection. (shrink)