Problems for contrastive closure: resolved and regained

The standard contextualist solution to the skeptical paradox is intended to provide a way to retain epistemic closure while avoiding the excessive modesty of radical skepticism and the immodesty of Moorean dogmatism. However, contextualism’s opponents charge that its solution suffers from epistemic immodesty comparable to Moorean dogmatism. According to the standard contextualist solution, all contexts where an agent knows some ordinary proposition to be true are contexts where she also knows that the skeptical hypotheses are false. It has been hoped that contrastivist theories of knowledge can mirror the contextualist solution while avoiding this epistemic immodesty. I review the main problems for contrastive closure and argue that none of the arguments currently in the literature pose an insurmountable problem for the contrastivist solution. However, I argue that contrastivist theories of knowledge, like their contextualist rivals, are indeed committed to epistemic immodesty.     

Operators in the paradox of the knower

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.I am deeply indebted to Robert F. Barnes and Evan W. Conyers, without whom these ideas might not have germinated and certainly would not have grown. Many of the results offered here evolved in the course of mutual discussion and correspondence. I am also grateful to an anonymous reviewer forSynthese for many very helpful suggestions.The current paper contains the technical results promised in Footnote 25 of Grim (1988) and Footnote 26, Chapter 3, of Grim (1991).     

When the Other-Mind Skepticism Encounters the Happy Fish

In this paper, we reconstruct the debate between Zhuangzi 莊子 and Hui Shi 惠施 that took place on the bridge over the Hao River 濠水 as a substantive debate concerning the epistemic other-mind skepticism according to which no one mind knows the mental states of the other. We demonstrate how this reconstruction leads to substantive conclusions of the viability of Hui Shi’s position in particular and of the other-mind skepticism in general. This demonstration is accomplished by means of the contemporary philosophical development regarding, for example, whether asserting a proposition implies that the asserter knows the proposition, whether the closure principle of epistemic logic should be held, and whether knowing something is a mental state. We hold that this debate’s resolution is substantively entangled with contemporary philosophical concerns.     

A representational account of mutual belief

Although the notion of common or mutual belief plays a crucial role in game theory, economics and social philosophy, no thoroughly representational account of it has yet been developed. In this paper, I propose two desiderata for such an account, namely, that it take into account the possibility of inconsistent data without portraying the human mind as logically and mathematically omniscient. I then propose a definition of mutual belief which meets these criteria. This account takes seriously the existence of computational limitations. Finally, I point out that the epistemic logic (or theory) needed to make the definition work is subject to the Kaplan/Montague Paradox of the Knower. I argue that this is not a defect of the account, and I discuss briefly the bearing of recent work on the paradox of the Liar upon this problem.Much of this work was carried out with the support of a grant from the National Science Foundation to the Center for Cognitive Science at the University of Texas at Austin (Grant No. IRI-8719064). Much thanks to Tyler Burge, Nicholas Asher, and Brian Skyrms for their criticisms and suggestions.     

On Pragmatic Encroachment in Epistemology

We argue, contrary to epistemological orthodoxy, that knowledge is not purely epistemic—that knowledge is not simply a matter of truth-related factors (evidence, reliability, etc.). We do this by arguing for a pragmatic condition on knowledge, KA: if a subject knows that p, then she is rational to act as if p. KA, together with fallibilism, entails that knowledge is not purely epistemic. We support KA by appealing to the role of knowledge-citations in defending and criticizing actions, and by giving a principled argument for KA, based on the inference rule KB: if a subject knows that A is the best thing she can do, she is rational to do A. In the second half of the paper, we consider and reject the two most promising objections to our case for KA, one based on the Gricean notion of conversational implicature and the other based on a contextualist maneuver.     

In Defense of Sensitivity

The sensitivity condition on knowledge says that one knows that P only if one would not believe that P if P were false. Difficulties for this condition are now well documented. Keith DeRose has recently suggested a revised sensitivity condition that is designed to avoid some of these difficulties. We argue, however, that there are decisive objections to DeRose’s revised condition. Yet rather than simply abandoning his proposed condition, we uncover a rationale for its adoption, a rationale which suggests a further revision that avoids our objections as well as others. The payoff is considerable: along the way to our revision, we learn lessons about the epistemic significance of certain explanatory relations, about how we ought to envisage epistemic closure principles, and about the epistemic significance of methods of belief formation.     

Epistemic closure,assumptions and topics of inquiry

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic closure is an intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemic closure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemic closure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources.     

A strategy for assessing closure

This paper looks at an argument strategy for assessing the epistemic closure principle. This is the principle that says knowledge is closed under known entailment; or (roughly) if S knows p and S knows that p entails q, then S knows that q. The strategy in question looks to the individual conditions on knowledge to see if they are closed. According to one conjecture, if all the individual conditions are closed, then so too is knowledge. I give a deductive argument for this conjecture. According to a second conjecture, if one (or more) condition is not closed, then neither is knowledge. I give an inductive argument for this conjecture. In sum, I defend the strategy by defending the claim that knowledge is closed if, and only if, all the conditions on knowledge are closed. After making my case, I look at what this means for the debate over whether knowledge is closed.     

Problems in Epistemic Space

When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what is epistemically possible for ordinary, non-ideally rational agents like you and me. I will argue that the prospects look dim for successfully constructing such a space. In turn, this will make a case for the claim that we cannot use the standard possible worlds framework to model what is epistemically possible for ordinary agents.     

Pragmatic encroachment in accounts of epistemic excellence

Recently a number of philosophers have argued for a kind of encroachment of the practical into the epistemic. Fantl and McGrath, for example, argue that if a subject knows that p, then she is rational to act as if p (Fantl and McGrath, Phil Phenomenol Res LXXV(3):558–589 , 2007). In this paper I make a preliminary case for what we might call encroachment in, not knowledge or justification, but epistemic excellence, recent accounts of which include those of Roberts and Wood (Intellectual virtues: an essay in regulative epistemology, 2007), Bishop and Trout (Epistemology and the psychology of human judgment, 2005), and Baehr (The inquiring mind, 2011). I believe that practical considerations bear on whether a disposition is an epistemic excellence, and I propose a practical condition on epistemic excellence that is roughly analogous to the practical condition on knowledge proposed by Fantl and McGrath. Since the view is also an epistemic analogue to a kind of moral rationalism in ethics, we might also call it a variety of ‘epistemic rationalism’.     

Defending Klein on Closure and Skepticism

In this paper, I consider some issues involving a certain closure principle for Structural Justification, a relation between a cognitive subject and a proposition that’s expressed by locutions like ‘S has a source of justification for p’ and ‘p is justifiable for S’. I begin by summarizing recent work by Peter Klein that advances the thesis that the indicated closure principle is plausible but lacks Skeptical utility. I then assess objections to Klein’s thesis based on work by Robert Audi and Anthony Brueckner. One finding is that the typical statement of the relevant closure principle can express a number of different closure principles, and that recognizing this helps to resolve certain disputes.     

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely‐held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single‐premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker‐than‐classical K₃ logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to—whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non‐classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.     

Have a Cake and Eat it Too: Identifying a Missing Link in the Skeptical Puzzle

The skeptical puzzle consists of three allegedly incompatible claims: S knows that O, S doesn’t know that ~U, and the claim that knowledge is closed under the known entailment. I consider several famous instances of the puzzle and conclude that in all of those cases the presupposition that O entails ~U is false. I also consider two possible ways for trying to make it true and argue that both strategies ultimate fail. I conclude that this result at least completely discredits any solution that denies the principle of epistemic closure. At most, denying that O entails ~U can itself be seen as a novel solution to the puzzle, preferred to any other solution: it accommodates both non-skeptical and skeptical intuitions but does not require us to give up the principle of closure, embrace contextualism or subject-sensitive invariantism, or deny any commonly accepted principle of epistemology or logic.

     

Epistemic contextualism defended

Epistemic contextualists think that the extension of the expression ‘knows’ (and its cognates) depends on and varies with the context of utterance. In the last 15 years or so this view has faced intense criticism. This paper focuses on two sorts of objections. The first are what I call the ‘linguistic objections’, which purport to show that the best available linguistic evidence suggests that ‘knows’ is not context-sensitive. The second is what I call the ‘disagreement problem’, which concerns the behaviour of ‘knows’ in disagreement reports. These may not be the only objections to epistemic contextualism, but they are probably the most influential. I argue that the best current epistemic contextualist response to the linguistic objection is incomplete, and I show how it can be supplemented to deal with the full range of linguistic objections. I also develop a new solution to the disagreement problem. The upshot is that neither sort of objection gives us any reason to reject epistemic contextualism. This conclusion is, in a sense, negative—no new arguments for epistemic contextualism are advanced—but it’s a vital step towards rehabilitating the view.     

Memory as a Generative Epistemic Source

It is widely assumed that memory has only the capacity to preserve epistemic features that have been generated by other sources. Specifically, if S knows (justifiedly believes/rationally believes) that p via memory at T2, then it is argued that (i) S must have known (justifiedly believed/rationally believed) that p when it was originally acquired at T1, and (ii) S must have acquired knowledge that p (justification with respect to p/rationality with respect to p) at T1 via a non-memorial source. Thus, according to this view, memory cannot make an unknown proposition known, an unjustified belief justified, or an irrational belief rational–it can only preserve what is already known, justified, or rational. In this paper, I argue that condition (i) is false and, a fortiori , that condition (ii) is false. Hence, I show that, contrary to received wisdom in contemporary epistemology, memory can function as a generative epistemic source.     

Horgan on Sleeping Beauty

With the notable exception of David Lewis, most of those writing on the Sleeping Beauty problem have argued that 1/3 is the correct answer. Terence Horgan has provided the clearest account of why, contrary to Lewis, Beauty has evidence against the proposition that the coin comes up heads when she awakens on Monday. In this paper, I argue that Horgan’s proposal fails because it neglects important facts about epistemic probability.     

On Two Versions of ‘the Surprise Examination Paradox’

In this paper, I consider a popular version of the clever student’s reasoning in the surprise examination case, and demonstrate that a valid argument can be constructed. The valid argument is a reductio ad absurdum with the proposition that the student knows on the morning of the first day that the teacher’s announcement is fulfilled as its reductio. But it would not give rise to any paradox. In the process, I criticize Saul Kripke’s solution and Timothy Williamson’s attack on a key step of the student’s reasoning. I then consider the condemned prisoner case in W. V. Quine’s paper ‘On a So-Called Paradox’. I argue that the prisoner’s reasoning as conceived by Quine is more relevant and reasonable than the student’s argument in the popular version of the surprise examination case. I also argue that Quine’s criticism of the prisoner’s reasoning is correct, and therefore that the condemned prisoner case, and the surprise examination case as well, would not generate any paradox.     

Knowledge despite falsehood

I examine the claim, made by some authors, that we sometimes acquire knowledge from falsehood. I focus on two representative cases in which a subject S infers a proposition q from a false proposition p. If S knows that q, I argue, S's false belief that p is not essential to S's cognition. S's knowledge is instead due to S's belief that p′, a proposition in the neighbourhood of p that S (dispositionally) believes (and knows). S thus knows despite her false belief. The widely accepted and plausible principle that inferential knowledge requires known premises is unscathed.     

Impurism,Practical Reasoning,and the Threshold Problem

I consider but reject one broad strategy for answering the threshold problem for fallibilist accounts of knowledge, namely what fixes the degree of probability required for one to know? According to the impurist strategy to be considered, the required degree of probability is fixed by one's practical reasoning situation. I distinguish two different ways to implement the suggested impurist strategy. According to the Relevance Approach, the threshold for a subject to know a proposition at a time is determined by the practical reasoning situations she is then in to which that particular proposition is relevant. According to the Unity Approach, the threshold for a subject to know any proposition whatsoever at a time is determined by a privileged practical reasoning situation she then faces, most plausibly the highest stakes practical reasoning situation she is then in. I argue that neither way of implementing the impurist strategy succeeds and so impurism does not offer a satisfactory response to the threshold problem.