Christoph Jäger (2004) argues that Dretske’s information theory of knowledge raises a serious problem for his denial of closure of knowledge under known entailment: Information is closed under known entailment (even under entailment simpliciter); given that Dretske explains the concept of knowledge in terms of “information”, it is hard to stick with his denial of closure for knowledge. Thus, one of the two basic claims of Dretske would have to go. Since giving up the denial of closure would commit Dretske (...) to skepticism, it would most probably be better to rather give up the information-theoretic account of knowledge. But that means that one of the best externalist views of knowledge has to be given up. I argue here that Jäger is mistaken and that there is no problem for Dretske. There is a rather easy way out of Jäger’s problem. (shrink)

The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are shorthand for ‘ordinary (...) proposition’ and ‘sceptical hypothesis’ respectively. (SKC), however, fails for familiar reasons: since knowledge entails belief (KB), we can derive the falsity (F) from (SKC) by hypothetical syllogism, and thus reduce (SKC) to absurdity: (KB) Kxt[p] → Bxt[p]. (F) (Kxt[p] ∧ (p → q)) → Bxt[q]. (shrink)

JUSTIFICATION and knowledge are thought to be closed under known implication..1 This widely shared assumption is embodied in the following principles of epistemic closure.

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

Peter Baumann and Nicholas Shackel defend me against a serious criticism by Christoph Jäger. They argue that my account of information is consistent with my denial of closure for knowledge. Information isn’t closed under known entailment either. I think that, technically speaking, they are right. But the way they are right doesn’t help me much in my effort to answer the skeptic. I describe a way in which information, like knowledge, fails to be closed in a way that makes an (...) information-based account of knowledge an effective tool in answering the skeptic. (shrink)

Kripke’s puzzle has puts pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g., if S is rational and knows that P and that P entails Q, then (...) if she considers these two beliefs and Q, then she is in a position to know that.. (shrink)

According to Fred Dretskes externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretskes epistemology is his denial that knowledge is closed under known logical entailment. I argue that, given Dretskes construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. This has far-reaching consequences. (...) For if it is true that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. The latter alternative would seem to be preferable. But taking this route would deprive one of the most powerfully developed externalist epistemologies of its foundation. (shrink)

This paper argues for a solution to a problem that contrastivism faces. The problem is that contrastivism cannot preserve closure, in spite of claims to the contrary by its defenders. The problem is explained and a response developed.

Epistemic closure, the idea that knowledge is closed under known implication, plays a central role in current discussions of skepticism and the semantics of knowledge reports. Contextualists in particular rely heavily on the truth of epistemic closure in staking out their distinctive response to the so-called "skeptical paradox." I argue that contextualists should re-think their commitment to closure. Closure principles strong enough to force the skeptical paradox on us are too strong, and closure principles weak enough to express unobjectionable epistemic (...) principles are too weak to generate the skeptical paradox. I briefly consider how the contextualist might live without (strong) closure. (shrink)

In early essays and in more recent work, Fred Dretske argues against the closure of perception, perceptual knowledge, and knowledge itself. In this essay I review his case and suggest that, in a useful sense, perception is closed, and that, while perceptual knowledge is not closed under entailment, perceptually based knowledge is closed, and so is knowledge itself. On my approach, which emphasizes the safe indication account of knowledge, we can both perceive, and know, that sceptical scenarios (such as being (...) a brain in a vat) do not hold. (shrink)

How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.

Comments on Sherri Rousch’s Tracking Truth for the 2006 Philosophy of Science Association conference.

I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our application of (...) DC is unrestricted. This restriction on the application of DC allows contextualists to meet an argument of Hawthorne’s that contextualism must lead either to absurd knowledge attributions or to constant shifting of the standards for knowledge. Even if the standard of knowledge remains constant, the absurd knowledge attribution is the conclusion of a sorites argument and should be rejected. (shrink)