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- James L. White (1991). Knowledge and Deductive Closure. Synthese 86 (3):409 - 423.The question whether epistemological concepts are closed under deduction is an important one since many skeptical arguments depend on closure. Such skepticism can be avoided if closure is not true of knowledge (or justification). This response to skepticism is rejected by Peter Klein and others. Klein argues that closure is true, and that far from providing the skeptic with a powerful weapon for undermining our knowledge, it provides a tool for attacking the skeptic directly. This paper examines various arguments in favor of closure and Klein's attempted use of closure to refute skepticism. Such a refutation of skepticism is mistaken. But the closure principle is in any case false, so the skepticism that depends on it is undermined. The appeal of the closure principle derives from a failure to recognize an important feature of our epistemological concepts, namely, their context relativity.
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This paper compares two kinds of epistemic principles-an underdetermination principle and a deductive closure principle. It argues that each principle provides the basis for an independently motivated skeptical argument. It examines the logical relations between the premises of the two kinds of skeptical argument and concludes that the deductive closure argument cannot be refuted without refuting the underdetermination argument. The underdetermination argument, however, can be refuted without refuting the deductive closure argument. In this respect, the deductive closure argument is the stronger of the two.
This paper compares two kinds of epistemic principles-an underdetermination principle and a deductive closure principle. It argues that each principle provides the basis for an independently motivated skeptical argument. It examines the logical relations between the premises of the two kinds of skeptical argument and concludes that the deductive closure argument cannot be refuted without refuting the underdetermination argument. The underdetermination argument, however, can be refuted without refuting the deductive closure argument. In this respect, the deductive closure argument is the stronger of the two.
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.
It is widely thought that if knowledge requires sensitivity, knowledge is not closed because sensitivity is not closed. This paper argues that there is no valid argument from sensitivity failure to non-closure of knowledge. Sensitivity does not imply non-closure of knowledge. Closure considerations cannot be used to adjudicate between safety and sensitivity accounts of knowledge.
Cartesian skepticism about epistemic justification (‘skepticism’) is the view that many of our beliefs about the external world – e.g., my current belief that I have hands – aren’t justified. I examine the two most influential arguments for skepticism – the Closure Argument and the Underdetermination Argument – from an evidentialist perspective. For both arguments it is clear which premise the anti-skeptic must deny. The Closure Argument, I argue, is the better argument in that its key premise is weaker than the Underdetermination Argument’s key premise. However, it’s also likely that the motivation for accepting both key premises is exactly the same. So there may be a sense in which both arguments provide exactly the same motivation for skepticism. Then I argue that if I I’m right about what the motivation for accepting the arguments’ key premises is, then neither argument succeeds in providing a good reason to accept skepticism. I conclude by explaining why I think epistemologists are right to expend a lot of time and effort on refuting these arguments, even if neither argument provides any motivation for skepticism.
Closure is the principle that a person, who knows a proposition p and knows that p entails q, also knows q. Closure is usually regarded as expressing the commonplace assumption that persons can increase their
knowledge through inference from propositions they already know. In this
paper, I will not discuss whether closure as a general principle is true. The aim of this paper is to explore the various relations between closure and knowledge through inference. I will show that closure can hold for two
propositions p and q for numerous different reasons. The standard reason
that S knows q through inference from p, if S knows p and knows that p
entails q, is only one of them. Therefore, the relations between closure and inferential knowledge are more complex than one might suspect.
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.
Is there a plausible argument for external world skepticism? Robert Nozick’s well-known discussion focuses upon arguments which utilize the Sensitivity Requirement and the Closure Principle. Nozick claims, correctly, that no such argument succeeds. But he gets almost all the details wrong. The Sensitivity Requirement and the Closure Principle are compatible; the Sensitivity Requirement is incorrect; and even if true, the Closure Principle is structurally incapable of generating a plausible and valid global skeptical argument. It is therefore a mistake to take the Closure Principle as central in discussions of skepticism. The paper concludes by examining the prospects for a plausible skeptical argument.
Is there a plausible argument for external world skepticism? Robert Nozick’s well–known discussion focuses upon arguments which utilize the Sensitivity Requirement and the Closure Principle. Nozick claims, correctly, that no such argument succeeds. But he gets almost all the details wrong. The Sensitivity Requirement and the Closure Principle are compatible; the Sensitivity Requirement is incorrect; and even if true, the Closure Principle is structurally incapable of generating a plausible and valid global skeptical argument. It is therefore a mistake to take the Closure Principle as central in discussions of skepticism. The paper concludes by examining the prospects for a plausible skeptical argument.
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.
Discussion of James L. White, Knowledge and deductive closure
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