Incoherentism about Vagueness

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 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)

This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...) It is based on the intuition that a predicate is vague only if it is imprecise. The author considers some different definitions of linguistic imprecision, proposing that a predicate is imprecise if and only if there is no sharp boundary between objects to which its application yields some particular truth-value and objects to which its application does not yield that truth-value. The volume critically reviews the current theories of vagueness and proposes a new one, the Theory of Vagueness as Arbitrariness, which defines a vague predicate as an arbitrary predicate that must be precisified in order to contribute to a sentence that has truth-conditions. The main advantages of this theory over the current alternatives are that it satisfies all three criteria and systematizes the relevant intuitions. (shrink)

Rampant non-factualism is the view that all non-fundamental matters are non-factual, in a sense inspired by Kit Fine (2001). The first half of this paper argues that if we take non-factualism seriously for any matters, such as morality, then we should take rampant non-factualism seriously. The second half of the paper argues that rampant non-factualism makes possible an attractive theory of vagueness. We can give non-factualist accounts of non-fundamental matters that nicely characterize the vagueness they manifest (if any). I suggest (...) that such non-factualist theories dissolve philosophical puzzlement about vagueness. In particular, the approach implies that philosophers should not try to say which of the sorites-paradox-forming claims are true; we should not try to solve the sorites paradox in that sense. (shrink)

In this paper I will argue that to accept the principle of tolerance does not provide us with a good explanation of the phenomena of vagueness. I will be mainly concerned with the incoherentist strategy, which accepts tolerance and the consequent incoherence of vague predicates. In fact, incoherentism seems to be the most plausible way of accepting tolerance. Because of this, the rejection of incoherentism might be seen as a way to rescue the alternative theories from the objection that they (...) do not respect the principle of tolerance as a literal truth about vagueness. Despite this, I will conclude that neither incoherentism nor the main alternatives satisfy the criteria for an ideal theory of vagueness. (shrink)

The philosophical account of vagueness I call "transvaluationism" makes three fundamental claims. First, vagueness is logically incoherent in a certain way: it essentially involves mutually unsatisfiable requirements that govern vague language, vague thought-content, and putative vague objects and properties. Second, vagueness in language and thought (i.e., semantic vagueness) is a genuine phenomenon despite possessing this form of incoherence—and is viable, legitimate, and indeed indispensable. Third, vagueness as a feature of objects, properties, or relations (i.e., ontological vagueness) is impossible, because of (...) the mutually unsatisfiable conditions that such putative items would have to meet. In this paper I set forth the core claims of transvaluationism in a way that acknowledges and explicitly addresses a challenging critique by Timothy Williamson of my prior attempts to articulate and defend this approach to vagueness. I sketch my favored approach to truth and ontological commitment, and I explain how it accommodates the impossibility of ontological vagueness. I argue that any approach to the logic and semantics of vagueness that both (i) eschews epistemicism and (ii) thoroughly avoids positing any arbitrary sharp boundaries (either first-order or higher-order) will have to be not an alternative to transvaluationism but an implementation of it. I sketch my reasons for repudiating epistemicism. I briefly describe my current thinking about how to accommodate intentional mental properties with vague content within an ontology that eschews ontological vagueness. And I revisit the idea, which played a key role in my earlier articulations of transvaluationism, that moral conflicts provide an illuminating model for understanding vagueness. (shrink)

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)

I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its facticity (...) isn't comfortable with every sentence being true and false). Restoring the utility of the knowledge idiom motivates regimentation - the consistentist reinterpretation of natural language inferences (as they occur in real time). It's then sketched how to give the semantics of a natural language despite its inconsistency: Necessary and sufficient truth conditions are dropped in favor of necessary truth conditions and sufficient truth conditions. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

. According to Horgans transvaluationist approach, the robustness that characterizes vague terms is inherently incoherent. He analyzes that robustness into two conceptual poles, individualistic and collectivistic, and ascribes the incoherence to the former. However, he claims vague terms remain useful nonetheless, because the collectivistic pole can be realized with a suitable non-classical logic and can quarantine the incoherence arising out of the individualistic pole. I argue, on the contrary, that the nonclassical logic fails to resolve the difficulty and that the (...) incoherence afflicts Horgans collectivistic pole as well, consequently invalidating the entire transvaluationist approach. An alternative, coherent conception of robustness is suggested. (shrink)

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

The paper is a critique of Terry Horgan's transvaluationist theory of vagueness. It argues that Horgan's formulations equivocate between a semantic 'ought' and a semantic 'is'. On one reading, transvaluationism is trivially inconsistent. On another reading, it is consistent, but also consistent with an epistemic account of vagueness. In addition, the paper criticizes Horgan's attempt to recruit supervaluationism as a form of transvaluationism and his argument against vagueness in the world.

Supervaluationism, traditionally conceived, is the conjunction of three theses: Vagueness in a language gives rise to there being a multitude of acceptable assignments of semantic values to some expressions of the language, These assignments correspond to possible completions of the meanings of vague expressions, Truth is truth under all acceptable assignments, and falsity is falsity under all acceptable assignments. Supervaluationism has three chief virtues. It preserves classical logic. It provides an account of what vagueness is. And it extends nicely to (...) the vagueness of singular terms. I argue, however, that the existence of vagueifiers ‐ expressions like‘roughly’– pose problems for thesis of Supervaluationism, and that the supervaluationist can get around these problems only at a serious cost. Toward the end of the paper, I present an alternative analysis of vagueness, which preserves the main virtues of Supervaluationism, but which identifies vagueness as semantic Overdetermination, rather than as semantic underdetermination. (shrink)

The ancient sorites paradox has important implications for metaphysics, for logic, and for semantics. Metaphysically, the paradox can be harnessed to produce a powerful argument for the claim that there cannot be vague objects or vague properties. With respect to logic, the paradox forces a choice between the highly counterintuitive ‘epistemic’ account of vagueness and the rejection of classical two-valued logic. Regarding semantics, nonclassical approaches to the logic of vagueness lead naturally to the idea that truth, for vague discourse, is (...) not direct language-world correspondence grounded in referential connections linking a statement’s basic subsentential constituents (names, predicates, the apparatus of quantification) to real objects and real properties; rather, truth is a matter of indirect correspondence between vague language and nonvague reality. (shrink)

Transvaluationism makes two fundamental claims concerning vagueness. First, vagueness is logically incoherent in a certain way: vague discourse is governed by semantic standards that are mutually unsatisfiable. But second, vagueness is viable and legitimate nonetheless; its logical incoherence is benign.

I distinguish two broad approaches to vagueness that I call "robust" and "wimpy". Wimpy construals explain vagueness as robust (i.e., does not manifest arbitrary precision); that standard approaches to vagueness, like supervaluationism or appeals to degrees of truth, wrongly treat vagueness as wimpy; that vagueness harbors an underlying logical incoherence; that vagueness in the world is therefore impossible; and that the kind of logical incoherence nascent in vague terms and concepts is benign rather than malignant. I describe some implications for (...) logic, semantics, and metaphysics. (shrink)

Linda burns in her article 'vagueness and coherence' ("synthese" 68) claims to solve the sorites paradox. Her strategy consists in part in arguing that vague terms involve loose rather than strict tolerance principles. Only strict principles give rise to the sorites paradox. I argue that vague terms do indeed involve paradox-Generating strict tolerance principles, Although different ones from those burns considers. The sorites paradox remains unsolved.

I elaborate and defend the inconsistency view on vagueness I have earlier argued for in my (2002) and (forthcoming). In rough outline, the view is that the sorites paradox arises because tolerance principles, despite their inconsistency, are meaning-constitutive for vague expressions. Toward the end of the paper I discuss other inconsistency views on vagueness that have been proposed, and compare them to the view I favor.