Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic (...) pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of (...) class='Hi'>truth is not taken into account. The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

Arguments pro and contra convergent realism - underdetermination of theory by observational evidence and pessimistic meta-induction from past falsity- are considered. It is argued that, to meet the counter-arguments challenge, convergent realism should be considerably changed with a help of modification of the propositions from this meta-programme’s “hard core” and “protecting belt”. Maybe one of the ways out is to turn to the coherent theory of truth. Some of the works of Hegel (as interpreted by Merab Mamardashvili and Alexandre (...) Kojev), Husserl and Heidegger can help to dig still deeper into the background of this theory. Key words: Husserl, Heidegger, Hegel, convergent realism, internal realism, coherent theory of truth. -/- . (shrink)

The concept of truth is a fundamental philosophical inquiry that transcends time and cultural boundaries. This paper is aimed at illuminating the nature of truth and its intricate connection to the fabric of reality through an extensive bibliography. The reader will have at his disposal the most important references on the subject with a short abstract. The references are under the various theories of truth, even knowing the difficulties in classifying the authors under a label as (...) those proposed by the various theories of truth such as the correspondence, pragmatic, deflationary, constructivist, ontological, and semantic. (shrink)

One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that (...) Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth. (shrink)

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within (...) the constraints of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.

A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. (...) MTT is shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. (shrink)

The concept of truth and competing philosophical theories on what truth amounts to have an important place in contemporary philosophy. The aim of this chapter is to give a synopsis of different theories of truth and the particular philosophical issues related to the concept of truth. The literature on this topic is vast, and we must necessarily be rather selective and very brief about complex questions of interpretation of various philosophers. The focus of the (...) chapter is mainly on selected systematic issues and the most influential and well-established philosophical theories and key concepts. (shrink)

In 'On the nature of truth and falsehood' Russell offers both a multiple relation theory of judgment and a correspondence theory of truth. It has been a prevailing understanding of the Tractatus that Wittgenstein rejects Russell’s multiple relation idea but endorses the correspondence theory. Ramsey took the opposite view. In his 'Facts and Propositions', Ramsey endorses Russell’s multiple relation idea, rejects the correspondence theory, and then asserts that these moves are both due to Wittgenstein. This chapter will argue (...) that Ramsey’s ascriptions are both correct. The extent of the agreement between Ramsey and Wittgenstein will be argued, moreover, to count definitively against standard understandings of Ramsey as a redundancy theorist of truth. Wittgenstein is no correspondence theorist and Ramsey is no redundancy theorist; rather, both philosophers offer identity theories of truth. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: Adding a theory of truth to a finitely axiomatized theory T is more or (...) less equivalent to a kind of abstract consistency statement. A large part of the interest of the paper lies in the way syntactic theories are 'disentangled' from object theories. (shrink)

The topic of truth has long been thought to be connected to scientific realism and its opposition. In this essay, I discuss the various ways that truth might be related to realism. First, I consider how truth might be of use when defining scientific realism and its opposition. Second, I consider whether various stances regarding realism require specific stances on the nature of truth. I survey "neutralist" views that argue that one's stance on realism is independent (...) of one's view on truth, and partisan positions that claim that one's attitude on realism is, in part, determined by one's theory of truth. Though partisan views have been popular, and defended by seminal figures such as Thomas Kuhn, Richard Rorty, Hilary Putnam, and Arthur Fine, I raise a number of objections for them. (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model of knowledge. (...) 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

The article develops a correctness theory of truth (CTT) for semantic information. After the introduction, in section two, semantic information is shown to be translatable into propositional semantic information (i). In section three, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in section four, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + (...) A]. This completes the reduction of the truth of i to the correctness of A. In sections five and six, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates (in a Fregean sense) Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. The last section draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. (shrink)

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these (...) class='Hi'>theories meets the correspondence intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

Hannes Leitgeb formulated eight norms for theories of truth in his paper [5]: `What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms.

Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.

I argue that deflationary theories of truth reveal an important lesson for the broader theory of truth: although the notion of truthmaking has played an essential role in many traditional theories of truth, it can be separated from and survive the rejection of substantive theories of truth. I argue that many of the traditional substantive theories of truth are unified in defining truth in terms of the ontological grounds that are (...) needed to account for truth. Deflationists reject the idea that a theory of truth needs such metaphysical implications, but in so doing they need not rule out the possibility of developing an independently motivated theory of truthmaking. I argue that deflationists can and should embrace truthmaker theory, once it is shorn from its connection to the traditional project of defining truth. (shrink)

The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...) In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis. (shrink)

Minimalism is currently the received deflationary theory of truth. On minimalism, truth is a transparent concept and a deflated property of truth bearers. In this paper, I situate minimalism within current deflationary debate about truth by contrasting it with its main alternative―the redundancy theory of truth. I also outline three of the primary challenges facing minimalism, its formulation, explanatory adequacy and stability, and draw some lessons for the soundness of its conception of truth.

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated (...) for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)', by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. Main tools used in proofs are Zermelo-Fraenkel (ZF) set theory and classical logic. (shrink)

This book proposes a novel theory of truth and falsity. It argues that truth is a form of reference and falsity is a form of reference failure. -/- Most of the philosophical literature on truth concentrates on certain ontological and epistemic problems. This book focuses instead on language. By utilizing the Fregean idea that sentences are singular referring expressions, the author develops novel connections between the philosophical study of truth and falsity and the huge literature in (...) in the philosophy of language on the notion of reference. The first part of the book constructs the author’s theory and argues for it in length. Part II addresses the ways in which the theory relates to, and is different from, some of the basic theories of truth. Part III takes up how to account for the truth of sentences with logical operators and quantifiers. Finally, Part IV discusses the applications and implications of the theory for longstanding problems in philosophy of language, metaphysics, and epistemology. -/- A Referential Theory of Truth and Falsity will appeal to researchers and advanced students working in philosophy of language, epistemology, metaphysics, and linguistics. -/- . (shrink)

In Pragmatism, James promised his readers a theory of truth. However, many of his readers (even those sympathetic with other parts of James’s work) have concluded that James’s “theory” was little more than a tangle of mistakes. In this chapter, I offer an interpretation and defence of James’s theory of truth. I emphasize James’s truth pluralism.

Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that Tarski's only published remarks that (...) speak approvingly of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception (...) of paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata. (shrink)

This paper examines the work of Immanuel Kant in the light of a new theory on the nature of truth, knowledge and falsehood (the Inversion Theory of Truth). Kant’s idea that knowledge could be absolutely certain, and that its truth must correspond with reality, is discredited by a dissection of the Correspondence Theory of Truth. This examination of the nature of truth, as well as knowledge and falsehood, is conducted with reference to Sir Karl Popper’s (...) writings on regulative ideas, the criterion of demarcation and the principle of falsifiability. It is argued that if truth is to be regarded as certain, it should be used to describe objects and events in the objective (noumenal) state, and that subjective knowledge must contain (and is improved by) falsehood. Perceptions and knowledge are obtained by the biological and evolutionary process of Active Subjectivism. Ideas we have knowledge of can be metaphysical or scientific, according to Popper’s Criterion of Demarcation. Kant’s “Copernican revolution” claim that our intellect imposes absolutely true laws on nature could not allow for the possibility that ideas might be constructed from fallible perceptions, and hence that all knowledge is uncertain. Instead, he developed a Critique of Practical Reason in which religion, though not provable through logical reasoning, could be proved by our innate moral sense, giving us a Categorical Imperative that could lead to perverse results. By rejecting the absolute certainty of a priori knowledge, and admitting a degree of essential falsehood, we arrive at a more reasonable grounding for moral behavior. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the (...) nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

The paper presents Alfred Tarski’s debate with the semantic antinomies: the basic Liar Paradox, and its more sophisticated versions, which are currently discussed in philosophy: Strengthen Liar Paradox, Cyclical Liar Paradox, Contingent Liar Paradox, Correct Liar Paradox, Card Paradox, Yablo’s Paradox and a few others. Since Tarski, himself did not addressed these paradoxes—neither in his famous work published in 1933, nor in later papers in which he developed the Semantic Theory of Truth—therefore, We try to defend his concept of (...) truth against these antinomies. It is demonstrated that Tarskian theory of truth is resistant to the paradoxes and it is still the best solution to avoid the antinomies and remain within a classical logic, that is, accepting the laws of noncontradiction, excluded middle, and the principle of bivalence. Thus, the goal of the paper is double—firstly, to show that none of the versions of the Liar Paradox’s is a serious threat to Tarski’s concept of truth, and secondly, that Semantic Theory of Truth allows to remain within classical logic, and at the same time, avoid antinomies—which makes it the most attractive among classical theories of truth. (shrink)

By separating the general concept of truth into syntactic truth and semantic truth, this article proposes a new theory of truth to explain several paradoxes like the Liar paradox, Card paradox, Curry’s paradox, etc. By revealing the relationship between syntactic /semantic truth and being-nothing-becoming which are the core concepts of dialectical logic, it is able to formalize dialectical logic. It also provides a logical basis for complexity theory by transferring all reasoning into a directed (cyclic/acyclic) (...) graph which explains both paradoxical and paradox-free reasoning. The different structure between cyclic graphs and acyclic graphs is the key to understanding paradoxes. By explaining the immanent between logic, paradox, and cellular automata, it also illustrates dialectical logic as ontology. (shrink)

I want to show that truth is an important concept, and that it can be explained. However, we must deal with what are called ‘deflationist’ concepts of truth first. Deflationism is the view that there is nothing more to be said about truth once a semantic theory for the truth-predicate (such as Tarski's) has been provided.

Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued (...) that Horwich’s attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections. (shrink)

We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our (...) theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

Theodore de Laguna develops and argues for a deflationary view of truth well before the publication of what many have taken to be its source, or at least its inspiration, namely Frank P. Ramsey’s paper ‘Facts and Propositions’. I outline de Laguna’s view of truth and the arguments he offers for it; I also discuss its role in the history of twentieth-century philosophy. My outline and discussion serve as an introduction to de Laguna’s ‘A Nominalistic Interpretation of (...) class='Hi'>Truth’, a paper he originally wrote in English but which has hitherto only been published in French. (shrink)

In developing a theory of truth, as the main condition of knowledge, four issues are usually examined: definition or analysis of truth, truth bearer, truth-maker, and relation (in correspondence and coherence theories). A proper theory of truth is the one that affords the explanation of the truth of all types of propositions, and, at the same time, resists the liar paradox. The aim of this inquiry is to analyze Nasīr al-Dīn al-Tūsī’s theory of (...) truth one who is involved both in the liar paradox and in the explanation of the truth of the verity propositions and propositions that are made of intelligibles that have no instance in external world. This inquiry shows, with an analytical approach mostly systematic analysis, that he regards, against the difficulty of the lair paradox, propositions that are other than what they are about as the bearers of truth. Further, it shows that he, against the other difficulty, has two attitudes: first, he desists from the correspondence theory of truth and defines it as “ascription of an ideational thing to what, with its characteristic, is proper for it”; second, he considers the agent intellect to be the truth-maker. Although he regards the correspondence relation as an intentional relation, he does not discuss it much. One explanation could be that the issue of the correspondence relation does not play a serious part in the aforementioned difficulties. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? It turns out that, in a wide range of cases, we can get some nice answers to this question, but only if we work in a framework that is somewhat different from those usually employed (...) in discussions of axiomatic theories of truth. These results are then used to address a range of philosophical questions connected with truth, such as what Tarski meant by "essential richness" and the so-called conservativeness argument against deflationism. -/- This draft dates from about 2009, with some significant updates having been made around 2011. Around then, however, I decided that the paper was becoming unmanageable and that I was trying to do too many things in it. I have therefore exploded the paper into several pieces, which will be published separately. These include "Disquotationalism and the Compositional Principles", "The Logical Strength of Compositional Principles", "Consistency and the Theory of Truth", and "What Is Essential Richness?" You should probably read those instead, since this draft remains a bit of a mess. Terminology and notation are inconsistent, and some of the proofs aren't quite right. So, caveat lector. I make it public only because it has been cited in a few places now. (shrink)

Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's (...) paper 'What Theories of Truth Should be Like (but Cannot be)'. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

In this chapter, we defend the view that Davidson aimed not to replace the theory of meaning with the theory of truth, or to capture only certain features of the ordinary notion of meaning for certain theoretical purposes, but rather to pursue the traditional project of explaining in the broadest terms “what it is for words to mean what they do” through a clever bit of indirection, namely, by exploiting the recursive structure of a Tarskian‐style truth theory, which (...) meets certain constraints in an illuminating way, to generate theorems that give truth conditions for object language sentences that at the same time provide interpretations of them. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation (...) in inquisitive semantics: truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

A few years ago, Krzysztof Czerniawski published the book Three Ver- sions of the Epistemic Theory of Truth: Dummett, Putnam, Wright. It at- tracted my attention, as while there are many works which are concerned with the philosophical problem of truth, there are just a few compara- tive studies of different ideas concerning the theory of truth. The author in question focuses on the so-called Epistemic Theory of Truth, which as- sumes, according to the characterization of (...) Wolfgang Künne, that being true depends to some extent on our judgement. It is clear that many other philosophers have understood truth in similar terms: e.g. Pierce, Brenta- no and Neurath. However, Czerniawski concentrates on the most recent history of the Epistemic Theory, and does not seek to take account of the philosophies of either Habermas or Gadamer, whose ideas on truth stand in a somewhat more complex relationship both to this line of development and to the analytical tradition from which it has mostly emerged. Thus, he chooses Michael Dummett, Hilary Putnam and Crispin Wright—three analytical philosophers who have significantly contributed to the devel- opment of “epistemic” approaches to the problem of truth. (shrink)

Truth is the degree of accuracy when representing reality. We postulate three cognitive stages: the psychon, produced by perception; the construct, produced by intellection; and the speech act, produced by communication. Truth lies in the second; only constructs are alethic. Truth is a quality which takes place in degrees. Certainty is the unreachable perfect tip of this gradation, so it is an ideal concept. A thesis is deemed true if its alethical degree is acceptably efficacious, otherwise the (...) thesis is deemed false. Put in other words, we deem true any thesis not having enough fails to deem it false. (shrink)

This paper by Theodore de Laguna presents and argues for the deflationary theory of truth. The paper was first published in French in 1922. The version published here is the original, English version of the paper and has been edited by Joel Katzav.

Truthmaker theory begins with the idea that truth depends upon reality. When a truth-bearer is true, that is because something or other in the world makes it true. My dissertation offers a theory of truthmakers that shows how we should flesh out this thought while avoiding the contentious metaphysical commitments that are built into other truthmaker theories. Because of these commitments, many philosophers have come to view truthmaker theory as being essentially tied to correspondence theories of (...) truth, and to metaphysical realism. I argue that, quite to the contrary, truthmaker theory is distinct from correspondence theory, and that the former actually undermines the motivation for the latter. In fact, truthmaker theory can be used to argue for a particular kind of deflationism about truth. I also argue that debates about realism and anti-realism are best viewed through the lens of truthmaker theory, which is not—contrary to what many have thought—an essentially realist approach to metaphysics. Anti-realists of various stripes can also make use of truthmakers. The anti-realism of such views depends upon either the nature of the truthmakers they use, or the nature of the truthmaking relation itself. (shrink)

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)

A preliminary statement of the formal theory of the truthmaker relation advanced in the paper “Truth-makers” (Mulligan, Simons and Smith) in 1984. Correspondence theories of truth have. I give a brief account of some more or less obvious formal characteristics of this almost forgotten basic truthmaker relation. I then attempt to show how this account may be extended to provide elements of a theory of truth which is in keeping with the spirit of Wittgenstein’s Tractatus.