Online research in philosophy

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.

Penelope Maddy has defended a modified version of mathematical platonism that involves the perception of some sets. Frederick Suppe has developed a conclusive reasons account of empirical knowledge that, when applied to the sets of interest to Maddy, yields that we have knowledge of these sets. Thus, Benacerraf's challenge to the platonist to account for mathematical knowledge has been met, at least in part. Moreover, it is argued that the modalities involved in Suppe's conclusive reasons account of knowledge can be handled without recourse to either laws of nature or possible worlds, and that this approach is preferable.

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.

The paper consists of three parts. In the first part five kinds of defeasibility are distinguished that is ontological, conceptual, epistemic, justification and logical defeasibility. In the second part it is argued that from these, justification defeat is the phenomenon that plays a role in legal reasoning. In the third part, the view is defended that non-monotonic logics are not necessary to model justification defeat, but that they are so to speak the natural way to model this phenomenon.

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.

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.

This paper is an examination of modest foundationalism in relation to some important criteria of epistemic dependence. The paper distinguishes between causal and epistemic dependence and indicates how each might be related to reasons. Four kinds of reasons are also distinguished: reasons to believe, reasons one has for believing, reasons for which one believes, and reasons why one believes. In the light of all these distinctions, epistemic dependence is contrasted with defeasibility, and it is argued that modest foundationalism is not committed to criteria of epistemic dependence on which foundational beliefs are indefeasible. Modest foundationalism is contrasted with coherentism and is shown to be hospitable to a causal criterion of epistemic dependence, compatible with reliabilism, and neutral with respect to skepticism.

In, “Some Conclusive Reasons Against ‘Conclusive Reasons’”, Pappas and Swain have criticized Dretske’s theory that conclusive reasons are necessary for knowledge. In their view this condition is too strong. They attempt to show this by means of two purported counterexamples: the cup-hologram case and the generator case. This paper defends Dretske’s analysis against these challenges.

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.