Online research in philosophy

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.

Trenton Merricks argues that on any reasonable account, warrant must entailtruth. I demonstrate three theses about the properties ofwarrant: (1) Warrant is not unique;there are many properties that satisfy the definition of warrant. (2) Warrant need not entail truth; there are some warrant properties that entailtruthand others that do not. (3) Warrant need not be closed under entailment, even if knowledge is. If knowledge satisfies closure, then some warrant properties satisfy closure while others do not;if knowledge violates closure, then allwarrant properties violate closure.

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.

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.

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.

Offers a diagnosis of the easy knowledge problem, according to which easy knowledge is unjustified belief because the inferences that deliver easy knowledge feign evidential support that is not actually there. This diagnosis leads to a rejection of Closure. But, I argue, this rejection of Closure is more plausible than the traditional one endorsed by tracking theorists. I also argue that my diagnosis suggests a general plausibility argument against Closure, since a number of epistemic goods traditionally associated with knowledge do not transfer across known entailments. Finally, I defend Anti-Closure against two recent objections.

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.

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.

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.