The fact that a group of axioms use the word 'true' does not guarantee that that group of axioms yields a theory of truth. For Davidson the derivability of certain biconditionals from the axioms is what guarantees this. We argue that the test does not work. In particular, we argue that if the object language has truth-valuegaps, the result of applying Davidson''s definition of a theory of truth is that no correct theory of truth for the language (...) is possible. (shrink)
An account of the logic of bivalent languages with truth-valuegaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. What (...) recommends this approach is (1) its relative simplicity, and (2) the fact that it leaves the fundamental features of classical logic intact. (shrink)
Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth values when (...) considered within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving (un)translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion. (shrink)
Among other good things, supervaluation is supposed to allow vague sentences to go without truth values. But Jerry Fodor and Ernest Lepore have recently argued that it cannot allow this - not if it also respects certain conceptual truths. The main point I wish to make here is that they are mistaken. Supervaluation can leave truth-valuegaps while respecting the conceptual truths they have in mind.
Central to any form of Deflationism concerning truth (hereafter ‘DT’) is the claim that truth has no substantial theoretical role to play. For this reason, DT faces the following immediate challenge: if truth can play no substantial theoretical role then how can we model various prevalent kinds of indeterminacy—such as the indeterminacy exhibited by vague predicates, future contingents, liar sentences, truth-teller sentences, incomplete stipulations, cases of presupposition failure, and such-like? It is too hasty to assume that these phenomena are all (...) to be modelled via some epistemic conception of indeterminacy whereby indeterminacy is just some special species of ignorance which arises because of our limited powers of discrimination. Some non-epistemic model is called for—at least for certain species of indeterminacy. On what is perhaps the most enduring and popular non-epistemic model, indeterminacy gives rise to truth-valuegaps. But is DT compatible with the possibility of truth-valuegaps? Compatibilism says Yes; Incompatibilism says No. The broad goal of this paper is to defend a form of Incompatibilism. If DT is to make sense of various kinds of indeterminacy then truth-valuegaps cannot be invoked to do so. The particular goals of this paper are: (i) To set forth a new form of Compatibilism which can address an argument against truth-valuegaps given by Williamson (1994, pp. 187-192). (ii) To offer a new argument against truth-valuegaps using principles entailed by DT, thereby undermining Compatibilism. (shrink)
It is argued that if there are truth-valuegaps then the disquotational theory of truth is false. Secondly, it is argued that the same conclusion can be reached even without the assumption that there are truth-valuegaps.
The question is asked whether one can consistently both be a minimalist about truth, and hold that some meaningful assertoric sentences fail to be either true or false. It is shown that one can, but the issues are delicate, and the price is high: one must either refrain from saying that the sentences lack truth values, or else one must invoke a novel non-contraposing three-valued conditional. Finally it is shown that this does not help in reconciling minimalism with emotivism, where (...) this latter is understood as involving the view that ethical sentences are neither true nor false. (shrink)
The paper asks: are all tautologies true in a language with truth-valuegaps? It answers that they are not. No tautology is false, of course, but not all are true. It also contends that not all contradictions are false in a language with truth-valuegaps, though none are true.
∗Thanks to J. C. Beall, Alex Byrne, Jason Decker, Tyler Doggett, Paul Elbourne, Adam Elga, Warren Goldfarb, Delia Graﬀ, Richard Heck, Charles Parsons, Mark Richard, Susanna Siegel, Jason Stanley, Judith Thomson, Carol Voeller, Brian Weatherson, Ralph Wedgwood, Steve Yablo, Cheryl Zoll, and an anonymous referee for valuable comments and discussions. Versions of this material were presented in my seminar at MIT in the Fall of 2000, and at the University of Maryland, Baltimore County. Parts of this paper also derive from (...) my comments on a paper of Scott Soames at the ‘Liars and Heaps’ conference at the University of Connecticut in the Fall of 2002. I am grateful for the help of these audiences, and especially to Prof. Soames. (shrink)
John McDowell (1982). Truth-ValueGaps. In L. J. Cohen (ed.), Logic, Methodology and Philosophy of Science VI: Proceedings of the Sixth International Congress of Logic, Methodology, and Philosophy of Science. North Holland Publishing Co.score: 90.0
Since the famous debate between Russell (Mind 14: 479–493, 1905, Mind 66: 385–389, 1957) and Strawson (Mind 59: 320–344, 1950; Introduction to logical theory, 1952; Theoria, 30: 96–118, 1964) linguistic intuitions about truth values have been considered notoriously unreliable as a guide to the semantics of definite descriptions. As a result, most existing semantic analyses of definites leave a large number of intuitions unexplained. In this paper, I explore the nature of the relationship between truth value intuitions and non-referring definites. (...) Inspired by comments in Strawson (Introduction to logical theory, 1964), I argue that given certain systematic considerations, one can provide a structured explanation of conflicting intuitions. I show that the intuitions of falsity, which proponents of a Russellian analysis often appeal to, result from evaluating sentences in relation to specific questions in context. This is shown by developing a method for predicting when sentences containing non-referring definites elicit intuitions of falsity. My proposed analysis draws importantly on Roberts (in: Yoon & Kathol (eds.) OSU working papers in Linguistics: vol. 49: Papers in Semantics 1998; in: Horn & Ward (eds.) Handbook of pragmatics, 2004) and recent research in the semantics and pragmatics of focus. (shrink)
In the notoriously obscure “Gray’s Elegy Argument” (GEA) of “On Denoting”, Russell argues against the theory of denoting concepts which he had set out in his earlier work The Principles of Mathematics (PoM). Nathan Salmon has argued that the GEA is intended to demonstrate the falsity of the thesis that definite descriptions are singular terms, a view which he attributes to the Russell of PoM. In a similar vein, Peter Hylton has argued that we can make sense of the GEA (...) by attributing to the early Russell the principle of truth-value dependence. In this paper I argue that Russell was committed to neither of these positions. If Salmon and Hylton mischaracterise Russell’s position in PoM, then they also, I suggest, mischaracterise the GEA. I close, therefore, by suggesting how my account of the relation between the theory of denoting concepts and Russell’s position in “On Denoting” can guide our approach to the GEA. (shrink)
Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...) and the set-theoretic paradoxes. (shrink)
There are least two different things we might mean when we say that truth is a value: that it is a norm of belief, and that it is an end of inquiry. This paper considers to what extent we might be irrealist about the former claim -- that truth is a norm of belief.
This paper is a reply to Michael Lynch's "Truth, Value and Epistemic Expressivism" in Philosophy and Phenomenological Research for 2009. It argues that Lynch's argument against expressivism fails because of an ambiguity in the employed notion of an 'epistemically disengaged standpoint'.
Philosophers disagree about whether vagueness requires us to admit truth-valuegaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate—a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is (...) some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is deﬁnitely true and those of which it is deﬁnitely false. Taking as primitive the operator ‘it is deﬁnitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is deﬁnitely true (or deﬁnitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (DΦ(x) ∧ D¬Φ(y)) → ¬R(x, y). Here ‘Φ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate—such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the deﬁnitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)
Frege held that the result of applying a predicate to names lacks reference if any of the names lack reference. We defend the principle against a number of plausible objections. We put forth an account of consequence for a first-order language with identity in which the principle holds.
This paper is an attempt to clarify the notion of semantic presupposition and to refute Böer and Lycan's critique of that notion. The author presents a feasible and coherent formal definition of semantic presupposition after examining several popular definitions of the notion. In terms of this definition, two central arguments against semantic presupposition presented by Böer and Lycan are analyzed and responded to with care. It is concluded that the notion of semantic presupposition is not empty but rather is philosophically (...) interesting and fruitful. (shrink)
Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to (...) refer to an entity whose existence or non-existence is a factual matter, e.g. ‘the king of France’: the failure of the presupposition that there is a unique French king makes some sentences with the term ‘the king of France’, in particular “The king of France is bald”, gappy. In this paper I will show that the sentence “The king of France is bald” must be false, and not gappy, according to Yablo’s own criteria and that, furthermore, the presupposition that the term ‘the king of France’ refers presents a fail-safe mechanism in the same way Yablo thinks abstract presuppositions do—this undermines his argument for metaontological antirealism. (shrink)
It is shown how frege's problematic connection between truth-Value and "bedeutung" (of a sentence) becomes more plausible when set against the background of german language and philosophy, Especially by comparing frege's position with the value-Theoretical school of neo-Kantianism (w windelband).
Antirealism about the past is apparently in conflict with our acceptance of a set of systematic linkages between the truth-values of differently tensed sentences made at different times. Arguments based on acceptance of these so-called truth-value links seem to show that fully accounting for our use of the past and future tenses will involve use of a notion of truth which is not epistemically constrained and is thus antirealistically unacceptable. I elaborate these difficulties through an examination of work by (...) Dummett and Wright. I agree with Wright's rejection of Dummett's proposal but go on to argue that Wright's account fares no better. Building on what I take to be the failure of Wright's account, I offer a solution for the antirealist which diagnoses the problem as stemming from an equivocation in the meanings assigned to the tensed truth predicates. I close by raising a different problem for antirealist accounts of the past, one which is, however, related to more general difficulties for antirealist theories of meaning. (shrink)
In the first half of the 17th century the Aristotelian view that the same statement or belief may be true at one time and false at another and, on the other hand, the conception of a mental proposition as a fully explicit thought that lends a definite meaning to a declarative sentence originated a lively debate concerning the question whether a mental proposition can change its truth-value.In this article it is shown that the defenders of a negative answer and (...) the advocates of a positive answer argued on the basis of different notions of what a mental proposition is:one side taking it as more or less equivalent to a specific utterance?meaning and the other side as more or less equivalent to a generic sentence-meaning. (shrink)
Can mystics intuit something of what modern physicists calculate? And if so, how? The question of the relation between the classical mysticisms and modern science is approached in Part I in terms of the multiple forms and definitions of 'truth value'. Intuition/epiphany, pragmatism, coherence, and correspondence are considered as forms of truth that have also been proposed for unitive mystical experience. Since 'correspondence' or 'representation' has been the definition at the core of modern science, it in particular is approached by (...) combining Lakoff and Johnson on the roots of all abstract knowledge in physical metaphor and Gibson on the ecological array of perception as the template from which such metaphors must be drawn. A series of similarities between the maximally inclusive metaphors underlying unitive mystical experience and cosmological physics, as abstracted from an ecological array already resonant with multiple levels of physical reality, suggests a basis for the correspondence between these otherwise distinct cognitive domains. Part II extends this approach to widely posited cross cultural values of spiritual or mystical realization, in terms of gratitude, compassion, faith, and inner freedom. When fully embodied as forms of personal conduct, these are also ultimately derivable from the openness and flow patternings of the ecological array itself. The possibility that the more abstract spiritual values of the major world mysticisms exemplify not only revelatory and pragmatic forms of truth, but are also broadly correspondent with both the principles of immediate concrete perception and modern physics, may eventually allow a contemporary re- formulation of the microcosm-macrocosm unities basic to traditional cultures. (shrink)
After summarizing approaches taken previously to the problem of the determination of truth-Value of statements constituting literary works (ryle, Russell, Quine, Strawson, Davidson, Et. Al.) the author argues for a treatment of the problem based upon the linguistic status of such statements as translocutions and their relation to the context in which they occur.
The purpose of the paper is to refute the fregean assumption that declarative sentences refer to truth-Values. A consequence of the assumption is that the truth-Value of a declarative sentence containing another as part remains unchanged when the part is replaced by another sentence having the same truth-Value, Provided that the part as part has only customary reference and expresses a complete thought. The refutation proceeds by demonstrating this consequence to be false.
The rift between science and religion needs to be assessed not merely on pragmatic grounds, on the basis of the effect of scientific versus religious beliefs on people's behavior, as John Caiazza's essay does, but also and above all in regard to the cogency of the respective beliefs in reference to what we can reasonably assume is the true face of reality. About such truth value, the conflict is not irremediable; there are elements of belief regarding the nature of reality (...) that are strikingly similar regardless of whether one arrived at them on the basis of faith in revealed knowledge or on the basis of knowledge acquired by reasoning from or in reference to experience. Two such items are selected here by way of example: belief that in certain states of mind and consciousness individuals can experience union with something larger or deeper than themselves, and belief that the universe we inhabit is the result of an original creative act. (shrink)
In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard (...) first courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)
The author recently claimed that Pr(P, Q), where Pr is a probability function and P and Q are two sentences of a formalized language L, qualifies as an estimate--made in the light of Q--of the truth-value of P in L. To substantiate his claim, the author establishes here that the two strategies lying at the opposite extremes of the spectrum of truth-value estimating strategies meet the first five of the six requirements (R1-R6) currently placed upon probability functions and (...) fail to meet the sixth one. He concludes from those two results that the value for P and Q of any function satisfying R1-R5 must rate "minimally satisfactory" and the value for P and Q of any function satisfying R1-R6 must rate "satisfactory" as an estimate--made in the light of Q--of the truth-value of P in L. (shrink)
This paper examines the concept of ‘areti’ as encountered in the Aristotelian ethical system in order to establish its relationship to the modern concept of virtue as well as to that of moral truth, that is, to identify its truth-value. I intend to show that the Aristotelian ‘areti’ as a developed state of character and as an advanced stage of ethical understanding entails moral truth. ‘Areti’ as a good-in-itself possesses an intrinsic value which reflects moral truth, and as a (...) means for the accomplishment of ‘eudaimonia’ (ultimate happiness) it possesses an instrumental value. I also wish to argue that this position calls for a realist as well as an objectivist (or nonrelativist) approach in Aristotle. To that effect, I examine the elements of ‘areti’ that relate it to truth, and then I use reference to some of theAristotelian virtues, such as ‘andreia’ (courage), ‘philia’ (friendship), ‘dikaiosyne’ (justice), and ‘megalopsychia’ (magnanimity), in order to examine the way moral truth functions. This examination will also try to show that Aristotle’s aretaic approach does not suffer from the ills of virtue ethics theories. (shrink)
Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate truth-value (...) so as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic. (shrink)
I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.
This chapter focuses on the question of whether true belief can have final value because it answers our ‘intellectual interest’ or ‘natural curiosity’. The idea is that sometimes we are interested in the truth on some issue not for any ulterior purpose, but simply because we are curious about that issue. It is argued that this approach fails to provide an adequate explanation of the final value of true belief, since there is an unbridgeable gap between our valuing the truth (...) on some issue for its own sake, and that truth's being valuable for its own sake. (shrink)
Relativism offers a nifty way of accommodating most of our intuitions about epistemic modals, predicates of personal taste, color expressions, future contingents, and conditionals. But in spite of its manifest merits relativism is squarely at odds with epistemic value monism: the view that truth is the highest epistemic goal. I will call the argument from relativism to epistemic value pluralism the trivial argument for epistemic value pluralism. After formulating the argument, I will look at three possible ways to refute it. (...) I will then argue that two of these are unsuccessful, and defend the third, which involves denying that there are any genuinely relative truths. (shrink)
Needs, Values, Truth brings together of some of the most important and influential writings by a leading contemporary philosopher, drawn from twenty-five years of his work in the broad area of the philosophy of value. The author ranges between problems of ethics, meta-ethics, philosophy of mind, and philosophy of logic and language, looking at questions relating to meaning, truth and objectivity in judgements of value. For this third edition he has added a new essay on incommensurability, in addition to making (...) minor revisions to the existing text. The volume will stand as a definitive summation of his work in this area. (shrink)
In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets (...) of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox. (shrink)
To what extent is possession of truth considered a good thing in the Republic ? Certain passages of the dialogue appear to regard truth as a universal good, but others are more circumspect about its value, recommending that truth be withheld on occasion and falsehood disseminated. I seek to resolve this tension by distinguishing two kinds of truths, which I label 'philosophical' and 'non-philosophical'. Philosophical truths, I argue, are considered unqualifiedly good to possess, whereas non-philosophical truths are regarded as (...) worth possessing only to the extent that possession conduces to good behaviour in those who possess them. In the non-philosophical arena it is an open question, to be determined on a case-by-case basis, whether falsehood is more efficacious in furthering this practical aim than truth. (shrink)
Truth is a value in that sense that a belief is good (or successful, or correct) just in case it is true. But it does not follow that truth is a good-making property, nor does it follow that the nature of truth explains its value. Instead, this paper argues that the nature of belief explains its value.
Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures.
The thought that truth is valuable for its own sake is obvious, yet difficult to explicate in a precise and vindicating way. The paper tries to explicate and vindicate this thought with an argument for the conclusion that truth is an epistemic value. Truth is an epistemic value in the sense that a commitment to the value of truth plays a role in the justification and explanation of a fundamental aspect of our epistemic practice, namely, critical reflection. The paper also (...) argues that this feature of truth is inconsistent with deflationary accounts of truth. The ideas are set against the backdrop of criticism of some recent work by Paul Horwich. (shrink)