Timothy Williamson’s potentially most important contribution to epistemicism about vagueness lies in his arguments for the basic epistemicist claim that the alleged cut-off points of vague predicates are not knowable. His arguments for this are based on so-called ‘margin for error principles’. This paper argues that these principles fail to provide a good argument for the basic claim. Williamson has offered at least two kinds of margin for error principles applicable to vague predicates. A certain fallacy of equivocation seems to (...) underlie his justification for both kinds of principles. Besides, the margin for error principles of the first kind can be used in the derivation of unacceptable consequences, while the margin for error principles of the second kind can be shown to be compatible with the falsity of epistemicism, under a number of assumptions acceptable to the epistemicist. (shrink)

Artificial Intelligence (AI) pervades humanity in 2022, and it is notoriously difficult to understand how certain aspects of it work. There is a movement—_Explainable_ Artificial Intelligence (XAI)—to develop new methods for explaining the behaviours of AI systems. We aim to highlight one important philosophical significance of XAI—it has a role to play in the elimination of vagueness. To show this, consider that the use of AI in what has been labeled _surveillance capitalism_ has resulted in humans quickly gaining the capability (...) to identify and classify most of the occasions in which languages are used. We show that the knowability of this information is incompatible with what a certain theory of vagueness—_epistemicism_—says about vagueness. We argue that one way the epistemicist could respond to this threat is to claim that this process brought about the end of vagueness. However, we suggest an alternative interpretation, namely that epistemicism is false, but there is a weaker doctrine we dub _technological epistemicism_, which is the view that vagueness is due to ignorance of linguistic usage, but the ignorance can be overcome. The idea is that knowing more of the relevant data and how to process it enables us to know the semantic values of our words and sentences with higher confidence and precision. Finally, we argue that humans are probably not going to believe what future AI algorithms tell us about the sharp boundaries of our vague words unless the AI involved can be explained in terms understandable by humans. That is, if people are going to accept that AI can tell them about the sharp boundaries of the meanings of their words, then it is going to have to be XAI. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

I wish to present a proof that vagueness is impossible. Of course, vagueness is possible; and so there must be something wrong with the proof. But it is far from clear where the error lies and, indeed, all of the assumptions upon which the proof depends are ones that have commonly been accepted. This suggests that we may have to radically alter our current conception of vagueness if we are to make proper sense of what it is.

In chapter 5 of Knowledge and its Limits, T. Williamson formulates an argument against the principle (KK) of epistemic transparency, or luminosity of knowledge, namely “that if one knows something, then one knows that one knows it”. Williamson’s argument proceeds by reductio: from the description of a situation of approximate knowledge, he shows that a contradiction can be derived on the basis of principle (KK) and additional epistemic principles that he claims are better grounded. One of them is a reflective (...) form of the margin for error principle defended by Williamson in his account of knowledge. We argue that Williamson’s reductio rests on the inappropriate identification of distinct forms of knowledge. More specifically, an important distinction between perceptual knowledge and non-perceptual knowledge is wanting in his statement and analysis of the puzzle. We present an alternative account of this puzzle, based on a modular conception of knowledge: the (KK) principle and the margin for error principle can coexist, provided their domain of application is referred to the right sort of knowledge. (shrink)

The paper discusses some ways in which the phenomenon of borderline cases may be thought to bear on the traditional philosophical idea that certain domains of facts are fully open to our view. The discussion focusses on a very influential argument (due to Tim Williamson) to the effect that, roughly, no such domains of luminous facts exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an (...) illicit role in the argument. The paper investigates this issue by centring around the idea that vagueness brings with itself borderline cases, and that these in turn generate absence of a fact of the matter and hence epistemically benign lack of knowledge. It is argued that, given the possibility of absence of a fact of the matter, the idea of luminosity should be reformulated using the notion of determinacy, and that the resulting reformulation is not immediately subject to the original anti-luminosity argument. However, it is shown that the specific understanding of determinacy required by this strategy validates a new argument against the reformulated version of luminosity. Moreover, reflection on the connection between mistake and absence of a fact of the matter offers another argument against such version, with the surprising upshot that, granting the soundness of the original anti-luminosity argument, not even the determinacy of a certain fact would guarantee its knowability. (shrink)

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These (...) explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox. (shrink)

Every philosopher should wish for commentators as thoughtful and rigorous as Mario Gómez-Torrente and Delia Graff. Their papers contribute significantly to our understanding of the fine structure of vagueness, but not by undermining its epistemicist interpretation.

Forthcoming in D.H. Pritchard & V. Hendricks, New Waves in Epistemology,.