It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. (...) Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories. (shrink)

I identify an inconsistency in Jago’s theory of truth. I show that Jago is committed to the identity of the proposition that the proposition that A is true and the proposition that A. I show that Jago is committed to the proposition that A being true because A if the proposition that A is true. I show that these two commitments, given the rest of Jago’s theory, entail a contradiction. I show that while the latter commitment (...) follows from Jago’s theory of truth, even by Jago’s own lights he should not be committed to the identity of the proposition that the proposition that A is true and the proposition that A. (shrink)

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing (...) it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth. (shrink)

While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. (...) Thus, with little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections. (shrink)

One of the most intuitive concepts of truth is the classical correspondence theory of truth. Aside from the theoretical cogency and plausibility, this truth theory has two fundamental problems. I shall explore both of these problems. This will not be to reveal the problematic nature of the classical correspondence theory of truth itself, but to demonstrate the implications it has on Islam. I shall establish that the problems of this truth theory (...) contribute in the failure to determine the truth of a particular notion of an Islamic God. Consequently this truth theory would prove inconsistent with a particular notion of God within the Islamic tradition. (shrink)

The main argument of the book under review, 'Theories of Truth in Chinese Philosophy,' is to show that one can find a pluralistic theory of shí 實 in the Lunheng, “prepared” by a range of sources in the Warring States Period in China. This argument is not convincing because of small inconsistencies and major unsupported stipulations. Nevertheless the book contains many perceptive and suggestive remarks concerning the texts discussed.

The main argument of the book under review, 'Theories of Truth in Chinese Philosophy,' is to show that one can find a pluralistic theory of shí 實 in the Lunheng, “prepared” by a range of sources in the Warring States Period in China. This argument is not convincing because of small inconsistencies and major unsupported stipulations. Nevertheless the book contains many perceptive and suggestive remarks concerning the texts discussed.

It is easy to fall for a conceptual beauty and simplicity of the coherence theory of truth. But the texts in which its foundations were for the first time explicitly developed are rich in subtleties, defying a consistent interpretation and inviting various forms of criticism. That is why the following study will take one more look at the writings of Harold H. Joachim and Brand Blanshard, in order to prove that in the analyses which they proposed there is (...) an additional, so far unrecognised element – namely the process of translation – which plays a crucial role in making their accounts valid and complete. Initially then, the article will specify how the notion of translation should be here understood. Next, key postulates of both theories will be recalled, with an indication of several potential inconsistencies which they might entail. Finally, the analysis exposes translative ground of each reconstructed model. What will be thereby underscored, is not only the interpretative depth of Joachim’s and Blanshard’s legacy, but also significance of translation for the philosophical enquiry into the nature of truth. (shrink)

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)

This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while (...) on a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in “Understanding the Liar” and other papers. (shrink)

The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? (...) What are the proof-theoretic strengths of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of ${\Sigma^1_1}$ dependent choice. (shrink)

In this paper I present three problems for Simmons' singularity theory of truth as he presents it in Universality and the Liar. I begin with a brief overview of the theory and then present the three problems I see for it. The first problem shows that the singularity theory is in conflict with our ordinary notion of truth. I present a set of sentences that the singularity theory evaluates differently than does our pretheoretic concept (...) of truth. The second problem shows that Simmons' theory is incomplete, in the sense that there are sentences of its object language of which it does not have the resources to evaluate. The third problem suggests that Simmons theory does not, contrary to the claim of the book, allow for semantic universality. I consider Simmons' extension of the singularity theory to accommodate truth-in-a-context and show that it is inconsistent with his basic theory. Specifically I present a sentence which diagonalizes out of the basic theory. (shrink)

This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while (...) on a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in “Understanding the Liar” and other papers. (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)

The aim of this dissertation is to present a systematic account of F. H. Bradley's philosophy in so far as it is relevant to an understanding of his conception of the nature and criterion of truth. I argue that, for Bradley, the nature of truth is the identity of thought with reality given in immediate experience. There is no absolute separation between thought and its object. Bradley therefore rejects both the correspondence theory and epistemological realism. Thought is (...) not just a mirror which reflects an independently existing reality. ;Concerning the criterion of truth, I argue that his criterion for our ordinary and scientific beliefs is practice, and the criterion for philosophical positions is a kind of coherence based on the doctrine of relative truth. For Bradley, some positions are truer than others, and the best philosophy is a comprehensive system which contains the truth of all different positions. ;Bradley does not accept the coherence theory of justification as it is understood today, since it is based on the standard account of negation and the doctrine of absolute truth. Bradley has a different approach to negation and inconsistency, according to which there are no absolutely inconsistent beliefs. Further, he insists that truth is not absolute but "relative," a matter of degree. All philosophical positions contain some truth, and none is completely false. The truth in philosophy is a position which accounts for the whole of reality and includes all apparently inconsistent positions within it. ;I explain Bradley's place in the history of philosophy and show his connections with the British empiricist tradition. I believe one of Bradley's central concerns is to explain the nature and criterion of truth in philosophy within the constraints of empiricism. I also contrast Bradley's positions on important issues with those of philosophers in the Anglo-American analytic tradition, such as Russell, Moore, Ayer, Tarski, Quine, Churchland, Lehrer and Campbell. I argue that most recent commentators on Bradley overlook the importance of understanding his philosophy as a system constructed according to the doctrine of relative truth. (shrink)

In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.

In his essay “Afterwords”, Kuhn describes his “double goal” as To justify that science achieves knowledge of nature, and at the same time, To show that science neither achieves, nor should aim towards achieving, truth. I hold that Kuhn’s denial of truth helps to bring out a tension between the two goals of his enterprise: Kuhn cannot both maintain that science achieves knowledge of nature and dismiss the notion of truth altogether from his philosophy of science. The (...) same arguments that attack truth will ultimately damage the quest for knowledge. In this chapter, I intend explore this problem—which I will call the problem of inconsistency—and ultimately provide a defense on behalf of Kuhn. I argue that Kuhn can achieve both of his goals, and so remain consistent, by reevaluating the notion of truth in his philosophy of science. Here, I introduce an alternative correspondence theory of truth, which I call the phenomenal-world correspondence theory of truth. I will argue that Kuhn’s philosophy of science will remain consistent with this alternative view of correspondence. I believe that this notion of truth not only succeeds in defending Kuhn’s enterprise from the problem of inconsistency, but is also a kind of truth that Kuhn can accept into his philosophical enterprise despite his rejection of the traditional correspondence theory. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual (...) semantic connection of sentences, above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

The paper discusses the Inconsistency Theory of Truth (IT), the view that “true” is inconsistent in the sense that its meaning-constitutive principles include all instances of the truth-schema (T). It argues that (IT) entails that anyone using “true” in its ordinary sense is committed to all the (T)-instances and that any theory in which “true” is used in that sense entails the (T)-instances (which, given classical logic, entail contradictions). More specifically, I argue that theorists are (...) committed to the meaning-constitutive principles of logical constants, relative to the interpretation they intend thereof (e.g., classical), and that theories containing logical constants entail those principles. Further, I argue, since there is no relevant difference from the case of “true”, inconsistency theorists’ uses of “true” commit them to the (T)-instances. Adherents of (IT) are recommended, as a consequence, to eschew the truth-predicate. I also criticise Matti Eklund’s account of how the semantic value of “true” is determined, which can be taken as an attempt to show how “true” can be consistently used, despite being inconsistent. (shrink)

In this essay, I argue that the deflationary view of truth is inconsistent with Davidson's theory of meaning. I take deflationism to consist of two basic theses: the linguistic thesis that truth talk is always expressive and never explanatory, and the metaphysical thesis that truth is not a property. Since Davidson construes meaning in terms of truth-conditions, it appears that Davidson regards truth talk as explanatory, and truth as a property. Michael Williams argues (...) otherwise, suggesting that Davidson's theory of meaning can be understood in terms of his theory of radical interpretation, and that radical interpretation does not require a notion of truth richer than the deflationist allows. I argue that at the level of the T-sentences Davidson's theory of meaning entails (T-sentences yielded through the practice of radical interpretation), a non-deflationary notion of truth is indeed required. This is because, first, for Davidson, to grasp the meaning of a sentence is to grasp the T-sentence associated with it, and the T-sentence predicates the property truth of that sentencesecond, because it does so, in T-sentences "true" is explanatory, not merely expressive. I then consider the objection that T-sentences can be understood in terms of a norm of assertion, rather in terms of "true" as predicating a property of sentences, and I respond that the objection confuses pragmatic issues with semantic issues. (shrink)

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one (...) of philosophy's thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

In this essay, I present a new argument for the impossibility of defining truth by specifying the underlying structural property all and only true propositions have in common The set of considerations I use to support this claim take as that inspiration Alston's recent argument that it is impossible to define truth epistemically—in terms of justification or warrant According to what Alston calls the “intensional argument”, epistemic definitions are inconsistent with the T schema or the principle that it (...) is true that p if, and only if, p. Since the T-schema has great intuitive appeal, this is a powerful indictment of epistemic theories. But the basic argument that Alston employs, and the constellation of considerations which prosecute that argument, work against a much broader range of views than he considers While this implies that a traditional conceptual analysts of truth may be impossible, it opens the door to a pluralist approach to truth. (shrink)

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how (...) the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. (shrink)

In this essay, I present a new argument for the impossibility of defining truth by specifying the underlying structural property all and only true propositions have in common The set of considerations I use to support this claim take as that inspiration Alston's recent argument that it is impossible to define truth epistemically—in terms of justification or warrant According to what Alston calls the “intensional argument”, epistemic definitions are inconsistent with the T schema or the principle that it (...) is true that p if, and only if, p. Since the T-schema has great intuitive appeal, this is a powerful indictment of epistemic theories. But the basic argument that Alston employs, and the constellation of considerations which prosecute that argument, work against a much broader range of views than he considers While this implies that a traditional conceptual analysts of truth may be impossible, it opens the door to a pluralist approach to truth. (shrink)

A strong case can be made that Peirce’s formal rhetoric is primarily a theory of inquiry. Peirce’s convergence theory of truth requires a community of inquiry enduring indefinitely over time. Such a community, then, must promote “solidarity” in Peirce’s terms, a consistent practice of cooperation among inquirers over generations. One of the tasks of his formal rhetoric, then, is to analyze the conditions for solidarity. Using Peirce’s framework of a belief-desire model for practical action, solidarity can be (...) promoted if there are commonly desired ends and a consensus of beliefs about the best means to attain those ends in inquiry. Peirce recognizes, however, that the community of inquiry is constituted with different types of inquirers who have different purposes for inquiry. He divides them among the “pure” theoretical scientists, applied scientists and practical inquirers – the general public – who are interested in the practical applications that can bring betterment to their lives. It is argued here that Peirce’s apparent inconsistencies concerning the role and purpose of science can be attributed to cautions addressed to each of these different audiences. The remainder of the paper explores the problematics of solidarity in a community of inquirers who have different ends for inquiry, and how Peirce attempts to address the puzzles and paradoxes that result. (shrink)

A popular and enduring approach to the liar paradox takes the concept of truth to be inconsistent. Very roughly, truth is an inconsistent concept if the central principles of this concept (taken together) entail a contradiction, where one of these central principles is Tarski's T-schema for truth: a sentence S is true if and only if p, (where S says that p). This article targets a version of Inconsistentism which: retains classical logic and bivalence; takes the (...) class='Hi'>truth-predicate “is true” to pick out a property (and determine a non-empty extension relative to a given world); and holds that liar sentences exhibit a certain kind of indeterminacy in truth-value. Call such a view Modest Inconsistentism since it is somewhat more conservative in its outlook than various other forms of Inconsistentism. Such a modest view has its attractions: we retain the thesis that the liar sentence is meaningful; we get to respect the claims that there are truths and that there is a property of truth; we get to keep classical logic and bivalence; and, prima facie, no strengthened liar paradox is in the offing. The main aim in this paper is to show that Modest Inconsistentism, despite its initial attractions, is in deep trouble—because it does, after all, give rise to a strengthened liar paradox. We shall also see that there are related kinds of theory which are also subject to the same worry. (shrink)

The ambiguity theory of “knows” is the view that knows and its cognates have more than one propositional sense—i.e., more than one sense that can properly be used in “knows that” etc. constructions. The ambiguity theory of “know” has received relatively little attention as an account of the truth-conditions for knowledge ascriptions and denials—especially compared to views like classical, moderate invariantism and epistemic contextualism. In this paper, it is argued that the ambiguity theory of knows has (...) an advantage over both classical, moderate invariantism and epistemic contextualism. This advantage is that it is the only one of these views that can account for “diverging knowledge responses without inconsistency” —i.e., cases in which, for the same subject S and proposition p, one and the same speaker says truly “S knows p” but instead could have truly said “S does not know p” and vice versa. This paper argues both for the existence of DRWI scenarios and the ability of the ambiguity theory of knows to best explain their existence. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the (...) class='Hi'>inconsistency mentioned above is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

Weakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper compares (...) the proof-theoretic strength of an axiomatization of Kripke’s construction based on the paraconsistent evaluation scheme of $\textsf{LP}$, formulated in classical logic with that of an axiomatization directly formulated in $\textsf{LP}$, extended with a consistency operator. The ultimate goal is to find out whether paraconsistent solutions to the paradoxes that employ consistency operators fare better in this respect than paracomplete ones. (shrink)

We sketch an account according to which the semantic concepts themselves are not pathological and the pathologies that attend the semantic predicates arise because of the intention to impose on them a role they cannot fulfill, that of expressing semantic concepts for a language that includes them. We provide a simplified model of the account and argue in its light that (i) a consequence is that our meaning intentions are unsuccessful, and such semantic predicates fail to express any concept, and (...) that (ii) in light of this it is incorrect to characterize the pathology simply as semantic inconsistency; a more nuanced view of the problem is needed. We also show that the defects of the semantic predicates need not undercut the use of a truth theory in a compositional semantics for a language containing them because the meaning theory per se need not involve commitment to the axioms of the truth theory it exploits. (shrink)

There are often said to be five main 'theories of truth': correspondence, coherence, pragmatic, redundancy, and semantic theories. The coherence theory of truth equates the truth of a judgment with its coherence with other beliefs. Different versions of the theory give different accounts of coherence, but in all its forms the point is to exhibit truth as an internal relation between beliefs. The pragmatic theory of truth is akin to a coherence (...) class='Hi'>theory of this Kantian kind. No coherence theorist need deny the uncontentious claim that for a judgment to be true is for it to stand in a certain relationship, which can be called correspondence, with some state of affairs in the world. The conflict with the redundancy theory may be more apparent than real. For the redundancy theory is not a theory of what truth consists in, but a theory about the meaning of the words 'is true'. (shrink)

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

Aristotle's views on the fundamental nature of reality are usually taken to be inconsistent. The two main sources for these views are the Categories and the central books of the Metaphysics, particularly book Zeta. In the early theory of the Categories the basic entities of the world are concrete objects such as Socrates: Aristotle calls them 'primary substances'. But the later theory awards this title to the forms of concrete objects. Michael Wedin proposes a compatibilist solution to this (...) long-standing puzzle, arguing that Aristotle is engaged in quite different projects in the two works. The theory of Metaphysics Zeta is meant to explain central features of the standing doctrine of the Categories, and so presupposes the essential truth of the early theory. The Categories offers a theory of underlying ontological configurations, while book Zeta gives form the status of primary substance because it is primarily the form of a concrete object that explains its nature, and this form is the substance of the object. So when the late theory identifies primary substance with form, it appeals to an explanatory primacy that is quite distinct from the ontological primacy that dominates the Categories. Wedin's new interpretation thus allows us to see the two treatises as complementing each other: they are parts of a unified history of substance. (shrink)

Scott Aiken and Thomas Dabay contend that a satisfactory account of truth is both infallibilist and antiskeptical. Externalist correspondence theories, they say, preserve the infallibility of the truth-relation yet invite skeptical qualms. In tying truth to experience, pragmatist theories resist skeptical challenges, but embrace a fallibilism that renders their account of truth inconsistent and even incoherent. While agreeing with Aiken and Dabay that externalist accounts are vulnerable to skepticism, I dispute each of the four arguments they (...) offer against pragmatist fallibilism. Though partially successful against Peirce’s more popular view that truth is the final belief of a community of inquirers, their arguments are wholly ineffective against Dewey’s account of truth as warranted assertability. (shrink)

Aristotle's views on the fundamental nature of reality are usually taken to be inconsistent. The two main sources for these views are the Categories and the central books of the Metaphysics, particularly book Zeta. In the early theory of the Categories the basic entities of the world are concrete objects such as Socrates: Aristotle calls them 'primary substances'. But the later theory awards this title to the forms of concrete objects. Michael Wedin proposes a compatibilist solution to this (...) long-standing puzzle, arguing that Aristotle is engaged in quite different projects in the two works. The theory of Metaphysics Zeta is meant to explain central features of the standing doctrine of the Categories, and so presupposes the essential truth of the early theory. The Categories offers a theory of underlying ontological configurations, while book Zeta gives form the status of primary substance because it is primarily the form of a concrete object that explains its nature, and this form is the substance of the object. So when the late theory identifies primary substance with form, it appeals to an explanatory primacy that is quite distinct from the ontological primacy that dominates the Categories. Wedin's new interpretation thus allows us to see the two treatises as complementing each other: they are parts of a unified history of substance. (shrink)

This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to (...) the more-detailed cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)

In this paper, I first present an overview of Asay’s _A Theory of Truthmaking_, highlighting what I take to be some of its most attractive features, especially his re-invigoration of the ontological understanding of truthmaking and his defence of ontology-first truthmaking over explanation-first truthmaking. Then, I articulate what I take to be a puzzling potential inconsistency: (a) he appeals to considerations to do with aboutness in criticising how well ontological views account for truth while (b) ruling out (...) aboutness from the right account of truthmaking. He argues, instead, that necessitation is both necessary and sufficient for truthmaking (§3.3). I suggest that adding aboutness to one’s account in the right way is not just compatible with but important for ontology-first truthmaking. I do all this to invite Asay to clarify his position on these matters. Overall, Asay’s worldview displays the fruitfulness of an ontologically serious approach to metaphysics that puts truthmaking centre-stage. (shrink)

This book examines different views on the concept of truth in early Chinese philosophy, and considers a variety of theories of truth in Chinese and comparative thought.

It is argued that a certain form of the view that the semantic paradoxes show that natural languages are "inconsistent" provides the best response to the semantic paradoxes. After extended discussions of the views of Kirk Ludwig and Matti Eklund, it is argued that in its strongest formulation the view maintains that understanding a natural language is sharing cognition of an inconsistent semantic theory for that language with other speakers. A number of aspects of this approach are discussed and (...) a few objections are entertained. (shrink)

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

Douglas Patterson argues that the best way to respond to the semantic paradoxes that arise in natural language is to take natural language semantics to be (explosively) inconsistent. According to Patterson, to understand a natural language is to share with others cognition of a false semantic theory. Patterson’s main argument runs as follows. English is expressively rich. So, the first sentence occurring in this review could be.