Luminosity

The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I (...) provide a new theory of rational learning for the externalist. I defend this theory by arguing that its advice will be followed by anyone whose learning dispositions maximize expected accuracy. I then explore some of this theory’s consequences for the rationality of epistemic akrasia, peer disagreement, undercutting defeat, and uncertain evidence. (shrink)

The present paper argues that there is a knowledge norm for conversational implicature: one may conversationally implicate p only if one knows p. Linguistic data about the cancellation behavior of implicatures and the ways they are challenged and criticized by speakers is presented to support the thesis. The knowledge norm for implicature is then used to present a new consideration in favor of the KK thesis. It is argued that if implicature and assertion have knowledge norms, then assertion requires not (...) only knowledge but iterated knowledge: knowing that you know that you know that . . . you know. Such a condition on permissible assertion is argued to be plausible only if the KK thesis is true. (shrink)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or-to-if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail that (...) it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one’s actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non-factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

According to the probabilistic relevance account of confirmation, E confirms H relative to background knowledge K just in case P(H/K&E) > P(H/K). This requires an inequality between the rational degree of belief in H determined relative to two bodies of total knowledge which are such that one (K&E) includes the other (K) as a proper part. In this paper, I argue that it is quite plausible that there are no two possible bodies of total knowledge for ideally rational agents meeting (...) this requirement. Hence, the positive relevance account may have to be rejected. (shrink)

A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson’s Knowledge and Its Limits, a wave of recent work has explored whether there are any non-trivial luminous mental states. A version of Williamson’s anti-luminosity appeals to a safety- theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence (...) in p. However, the relevant notion of confidence is relatively underexplored. This paper develops a precise theory of confidence: an agent’s degree of confidence in p is the objective chance they will rely on p in practical reasoning. This theory of confidence is then used to critically evaluate the anti-luminosity argument, leading to the surprising conclusion that although there are strong reasons for thinking that luminosity does not obtain, they are quite different from those the existing literature has considered. In particular, we show that once the notion of confidence is properly understood, the failure of luminosity follows from the assumption that knowledge requires high confidence, and does not require any kind of safety principle as a premise. (shrink)

Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not provable (...) in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification. (shrink)

Many of our sources of knowledge only afford us knowledge that is inexact. When trying to see how tall something is, or to hear how far away something is, or to remember how long something lasted, we may come to know some facts about the approximate size, distance or duration of the thing in question but we don’t come to know exactly what its size, distance or duration is. In some such situations we also have some pointed knowledge of how (...) inexact our knowledge is. That is, we can knowledgeably pinpoint some exact claims that we do not know. We show that standard models of inexact knowledge leave little or no room for such pointed knowledge. We devise alternative models that are not afflicted by this shortcoming. (shrink)

I argue that no successful version of Williamson's anti‐luminosity‐argument has yet been presented, even if Srinivasan's further elaboration and defence is taken into account. There is a version invoking a coarse‐grained safety condition and one invoking a fine‐grained safety condition. A crucial step in the former version implicitly relies on the false premise that sufficient similarity is transitive. I show that some natural attempts to resolve this issue fail. Similar problems arise for the fine‐grained version. Moreover, I argue that Srinivasan's (...) defence of the more contentious fine‐grained safety condition is also unsuccessful, again for similar reasons. (shrink)

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

The early literature on epistemic logic in philosophy focused on reasoning about the knowledge or belief of a single agent, especially on controversies about "introspection axioms" such as the 4 and 5 axioms. By contrast, the later literature on epistemic logic in computer science and game theory has focused on multi-agent epistemic reasoning, with the single-agent 4 and 5 axioms largely taken for granted. In the relevant multi-agent scenarios, it is often important to reason about what agent A believes about (...) what agent B believes about what agent A believes; but it is rarely important to reason just about what agent A believes about what agent A believes. This raises the question of the extent to which single-agent introspection axioms actually matter for multi-agent epistemic reasoning. In this paper, we formalize and answer this question. To formalize the question, we first define a set of multi-agent formulas that we call agent-alternating formulas, including formulas like Box_a Box_b Box_a p but not formulas like Box_a Box_a p. We then prove, for the case of belief, that if one starts with multi-agent K or KD, then adding both the 4 and 5 axioms (or adding the B axiom) does not allow the derivation of any new agent-alternating formulas—in this sense, introspection axioms do not matter. By contrast, we show that such conservativity results fail for knowledge and multi-agent KT, though they hold with respect to a smaller class of agent-nonrepeating formulas. (shrink)

Williamson’s “anti-luminosity” argument aims to establish that there are no significant luminous conditions. “Far from forming a cognitive home”, luminous conditions are mere “curiosities”. Even supposing Williamson’s argument succeeds in showing that there are no significant luminous states his conclusion has not thereby been established. When it comes to determining what is luminous, mental events and processes are among the best candidates. It is events and processes, after all, which constitute the stream of consciousness. Judgment, for instance, is plausibly self-conscious. (...) If I am judging then plausibly I must know that I am. Similarly, deliberation is plausibly self-conscious. To be deliberating about some matter I plausibly must know that I am. That one is judging and that one is deliberating are thus plausibly luminous conditions. Furthermore, I argue, Williamson’s anti-luminosity argument fails to speak against this suggestion. This reveals that Williamson’s argument is more limited in scope than has been thought—something likely missed due to a misplaced focus on mental states in the luminosity debate as well as in epistemology and the philosophy of mind more generally. For all Williamson shows, there may be luminous events and processes of a sort apt to constitute a cognitive home. I conclude by considering how the anti-luminosity argument might be reinstated in the judgment case and argue that the natural way to do so fails. (shrink)

Suppose you’d like to believe that p, whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry : you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is (...) to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is part of our evidence, then that p is part of our evidence is itself part of our evidence. (shrink)

This article aims to show that Williamson's anti-luminosity argument does not succeed if we presuppose a constitutive connection between the phenomenal and the doxastic. In contrast to other luminists, however, my strategy is not to critically focus on the refined safety condition in terms of degrees of confidence that anti-luminists typically use in this context. Instead, I will argue that, given a certain conception of what Chalmers calls ‘direct phenomenal concepts,’ luminosity is guaranteed even if the refined safety condition in (...) terms of degrees of confidence is taken for granted. (shrink)

Since its appearance over a decade ago, Timothy Williamson's anti-luminosity argument has come under sustained attack. Defenders of the luminous overwhelmingly object to the argument's use of a certain margin-for-error premise. Williamson himself claims that the premise follows easily from a safety condition on knowledge together with his description of the thought experiment. But luminists argue that this is not so: the margin-for-error premise either requires an implausible interpretation of the safety requirement on knowledge, or it requires other equally implausible (...) assumptions. In this paper I bolster the margin-for-error premise against these attacks by recasting Williamson's own two-part defence, the first part intended to work on the assumption that there is no constitutive connection between the phenomenal and the doxastic, and the second intended to work without this assumption. Pace various luminists, I argue that the appeals to safety needed for Williamson's two-part defence are plausible. I also argue that all that is needed to generate the margin-for-error premise from these safety conditions is an empirical assumption about the kinds of creatures we are: that is, creatures whose beliefs are structured by certain dispositions. By recasting the anti-luminosity argument in this way, we can understand what is really at stake in the debate about luminosity: that is, whether we are luminous. (shrink)

The Gettier Problem and Moore’s Paradox are related in a way that is unappreciated by philosophers. If one is in a Gettier situation, then one is also in a Moorean situation. The fact that S is in a Gettier situation (the fact that S is “Gettiered”), like the fact that S is in a Moorean situation (the fact that S is “Moored”), cannot (in the logical sense of “cannot”) be known by S while S is in that situation. The paper (...) starts the job of mapping what can be said about this feature of Gettier situations. The goal is to stimulate further exploration into this yet uncharted territory. (shrink)

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

Among the key factors that play a crucial role in the acquisition of knowledge, Buddhist philosophers list (i) the testimony of sense experience, (ii) introspective awareness (iii) inferences drawn from these directs modes of acquaintance, and (iv) some version of coherentism, so as guarantee that truth claims remains consistent across a diverse philosophical corpus. This paper argues that when Buddhists employ reason, they do so primarily in order to advance a range of empirical and introspective claims. As a result, reasoning, (...) in particular inductive reasoning on the testimony of perception, is based on a theory of causation. (shrink)

A joint modelling of objective worlds and subjective perceptions within two-dimensional semantics eliminates the margin for error principle and solves the epistemic sorites paradox. Two objective knowledge modalities can be defined in two-dimensional frames accounting for subjective perceptions: “necessary knowledge” (NK) and “possible knowledge” (PK), the latter being better suited to the interpretation of knowledge utterances. Two-dimensional semantics can in some cases be reduced to one-dimensional ones, by defining accessibility relations between objective worlds that reflect subjective perceptions: NK and PK (...) are respectively equivalent to ${\square \square }$ and ${\lozenge \square }$ in some one-dimensional frame, and to ${\square }$ and another modality in some other. (shrink)

Recently, Timothy Williamson has argued that considerations about margins of errors can generate a new class of cases where agents have justified true beliefs without knowledge. I think this is a great argument, and it has a number of interesting philosophical conclusions. In this note I’m going to go over the assumptions of Williamson’s argument. I’m going to argue that the assumptions which generate the justification without knowledge are true. I’m then going to go over some of the recent arguments (...) in epistemology that are refuted by Williamson’s work. And I’m going to end with an admittedly inconclusive discussion of what we can know when using an imperfect measuring device. (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)

In this paper I show that a variety of Cartesian Conceptions of the mental are unworkable. In particular, I offer a much weaker conception of limited discrimination than the one advanced by Williamson (2000) and show that this weaker conception, together with some plausible background assumptions, is not only able to undermine the claim that our core mental states are luminous (roughly: if one is in such a state then one is in a position to know that one is) but (...) also the claim that introspection is infallible with respect to our core mental states (where a belief that C obtains is infallible just in case if one believes that C obtains then C obtains). The upshot is a broader and much more powerful case against the Cartesian conception of the mental than has been advanced hitherto. (shrink)

Questions about the transparency of evidence are central to debates between factive and non-factive versions of mentalism about evidence. If all evidence is transparent, then factive mentalism is false, since no factive mental states are transparent. However, Timothy Williamson has argued that transparency is a myth and that no conditions are transparent except trivial ones. This paper responds by drawing a distinction between doxastic and epistemic notions of transparency. Williamson's argument may show that no conditions are doxastically transparent, but it (...) fails to show that no conditions are epistemically transparent. Moreover, this reinstates the argument from the transparency of evidence against factive mentalism. (shrink)

The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains 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 such argument. The paper centres around the idea that vagueness brings with itself the prima facie plausibility of soritical principles. Using the diagnostics of sharpenings, it is first pointed out that, despite certain considerations to the contrary, the margin‐for‐error principle required by the anti‐luminosity argument may well derive all of its plausibility from an underlying soritical principle. The notion of confidence that is relevant to the argument is then isolated and sharply distinguished from the notion of subjective probability. Against this background, it is argued that the reasoning about confidence involved in the argument in favour of the problematic margin‐for‐error principle is fallacious in the same way in which sorites reasoning is. This reveals the possibility of having reliable knowledge even at the penumbral limit with falsity, a possibility for which a concrete formal model is constructed. The model in turn permits a deeper appreciation of the role played in the dialectic by the distinction between confidence and subjective probability as well as by confidence requirements on knowledge. It is concluded that careful heeding of vagueness and its phenomena, far from forcing new and surprising limits on our knowledge, actually removes one of the main barriers – unreliability – often thought to stand in its way. (shrink)

Timothy Williamson’s anti luminosity argument has received considerable attention. Escaping unnoticed, though, is a strikingly similar argument from David Hume. This paper highlights some of the arresting parallels between Williamson’s reasoning and Hume’s that will allow us to appreciate more deeply the plausibility of Williamson’s reasoning and to understand how, following Hume, we can extend this reasoning to undermine the “luminosity” of simple necessary truths. More broadly the parallels help us to identify a common skeptical predicament underlying both arguments, which (...) we shall call “the quarantine problem”. The quarantine problem expresses a deep skepticism about achieving any exalted epistemic state. Further, the perspective gained by the quarantine problem allows us to easily categorize existing responses to Williamson’s anti luminosity argument and to observe the deficiencies of those responses. In sum, the quarantine problem reveals the deeply fallibilistic nature of whatever knowledge we may possess. (shrink)

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

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)

In this paper I argue that there is no viable alternative to construing our knowledge and justified belief as resting on a foundation restricted to truths about our internal states. Against Williamson and others I defend the claim that the internal life of a cognizer really does constitute a special sort of cognitive home that is importantly different from the rest of what we think we know and justifiably believe.

Eighteen leading philosophers offer critical assessments of Timothy Williamson's ground-breaking work on knowledge and its impact on philosophy today. They discuss epistemological issues concerning evidence, defeasibility, scepticism, testimony, assertion, and perception, and debate Williamson's central claim that knowledge is a mental state.

In Knowledge and Its Limits Timothy Williamson argues against the luminosity of phenomenal states in general by way of arguing against the luminosity of feeling cold, that is, against the view that if one feels cold, one is at least in a position to know that one does. In this paper I consider four strategies that emerge from his discussion, and argue that none succeeds.

Hawthorne and Magidor's criticisms of the model of presupposition and assertion that I have used and defended are all based on a rejection of some transparency or introspection of assumptions about speaker presupposition. This response to those criticisms aims first to clarify, and then to defend, the required transparency assumptions. It is argued, first, that if the assumptions are properly understood, some prima facie problems for them do not apply, second, that rejecting the assumptions has intuitively implausible consequences, and third, (...) that the 'margin of error' argument against the principle of positive introspection has a false premiss. The paper concludes with a response to a criticism of what Hawthorne and Magidor call 'the uniformity principle' that is used in the model to explain some pragmatic phenomena. (shrink)

The linchpin of Williamson (2000)'s radically externalist epistemological program is an argument for the claim that no non-trivial condition is luminous—that no non-trivial condition is such that whenever it obtains, one is in a position to know that it obtains. I argue that Williamson's anti-luminosity argument succeeds only if one assumes that, even in the limit of ideal reflection, the obtaining of the condition in question and one's beliefs about that condition can be radically disjoint from one another. However, no (...) self-respecting defender of the luminosity of the mental would ever make such an assumption. Thus Williamson can only secure his controversial claims in epistemology by taking for granted certain equally controversial claims in the philosophy of mind. What emerges is that the best bet for defending an internalist epistemology against Williamson's attack is to take there to be a tight, intimate connection between (to take one example) our experiences and our beliefs upon reflection about the obtaining of those experiences, or between (to take another example) the rationality of our beliefs and our beliefs upon reflection about the rationality of those beliefs. (shrink)

ABSTRACT: Many of the results of Timothy Williamson's Knowledge and Its Limits depend upon his argument that many, if not all, of our mental states fail to be luminous in the sense that if we are in them, then we are in a position to know that we are in them. The purpose of this article is to show that his argument is unsound. I conclude by distinguishing between partial and total luminosity, and by arguing that even if mental states (...) are not totally luminous, they are at least partially so.RÉSUMÉ: Plusieurs des résultats du livre de Timothy Williamson, Knowledge and Its Limits dépendent de son argument à l'effet que la plupart, sinon tous nos états mentaux ne sont pas lumineux au sens où tout en se trouvant dans un tel état, nous sommes en position, de savoir que tel est notre état. Cet article a pour objectif de démontrer que ce raisonnement ne tient pas. Nous concluons par une distinction entre luminosité partielle ou complète et soutenons que, même si les états mentaux ne sont pas entièrernent clairvoyants, ils le sont en partie. (shrink)

Timothy Williamson has famously argued that the principle should be rejected. We analyze Williamson's argument and show that its key premise is ambiguous, and that when it is properly stated this premise no longer supports the argument against. After canvassing possible objections to our argument, we reflect upon some conclusions that suggest significant epistemological ramifications pertaining to the acquisition of knowledge from prior knowledge by deduction.

The Modern Philosophical Revolution breaks new ground by demonstrating the continuity of European philosophy from Kant to Derrida. Much of the literature on European philosophy has emphasised the breaks that have occurred in the course of two centuries of thinking. But as David Walsh argues, such a reading overlooks the extent to which Kant, Hegel, and Schelling were already engaged in the turn toward existence as the only viable mode of philosophising. Where many similar studies summarise individual thinkers, this book (...) provides a framework for understanding the relationships between them. Walsh thus dispels much of the confusion that assails readers when they are only exposed to the bewildering range of positions taken by the philosophers he examines. His book serves as an indispensable guide to a philosophical tradition that continues to have resonance in the post-modern world. (shrink)

Abstract: Williamson argues that when one feels cold, one may not be in a position to know that one feels cold. He thinks this argument can be generalized to show that no mental states are such that when we are in them we are in a position to know that we are in them. I argue that his argument is a sorites argument in disguise because it relies on the implicit premise that warming up is gradual. Williamson claims that his (...) argument is not a sorites argument; I explain why he has not given us any reason to accept the claim. (shrink)

Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...) that underlies the new require- ment provides a better account of inexact knowledge and higher-order knowledge than both Williamson’s and Halpern’s. (shrink)

Epistemicists say there is a last positive instance in a sorites sequence-we just cannot know which is the last. Timothy Williamson explains that knowledge requires a margin for error and this ensures that the last heap will not be knowable as a heap. However, there is a class of disjunctive predicates for which knowledge at the thresholds is possible. They generate sorites paradoxes that cannot be diagnosed with the margin for error principle.

Roy Sorensen's criticism of my use of margin for error principles to explain ignorance in borderline cases fails because it misidentifies the relevant margin for error principles. His alternative explanation in terms of truth-maker gaps is briefly criticized.

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