Online research in philosophy

Epistemicists say there is a last positive instance in a sorites sequence-we just cannot know which is the last. Timothy Williamson explains that knowledge requires a margin for error and this ensures that the last heap will not be knowable as a heap. However, there is a class of disjunctive predicates for which knowledge at the thresholds is possible. They generate sorites paradoxes that cannot be diagnosed with the margin for error principle.

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.

In their paper “Vagueness, Ignorance, and Margins for Error” Kenton Machina and Harry Deutsch criticize the epistemic theory of vagueness. This paper answers their objections. The main issues discussed are: the relation between meaning and use; the principle of bivalence; the ontology of vaguely specified classes; the proper form of margin for error principles; iterations of epistemic operators and semantic compositionality; the relation or lack of it between quantum mechanics and theories of vagueness.

Timothy Williamson claims that margin for error principles govern all cases of inexact knowledge. I show that this claim is unfounded: there are cases of inexact knowledge where Williamson’s argument for margin for error principles does not go through. The problematic cases are those where the value of the relevant parameter is fixed across close cases. I explore and reject two responses to my objection, before concluding that Williamson’s account of inexact knowledge is not compelling.

This paper reveals and corrects a flaw in Nozick’s account of knowledge via inference. First, two counterexamples are provided by considering cases which would not typically be regarded as instances of knowledge although they are counted as such by Nozick’s theory. Then the general form of these counterexamples is given. From this it is apparent that the counterexamples show that Nozick’s theory fails to take account of cases in which the subject infers q from p, but in counterfactual situations some proposition other than p would entail q. In view of this, the theory is then revised to eliminate the counterexamples.

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 chapter 5 of Knowledge and its Limits, T. Williamson formulates an argument against the principle (KK) of epistemic transparency, or luminosity of knowledge, namely “that if one knows something, then one knows that one knows it”. Williamson’s argument proceeds by reductio: from the description of a situation of approximate knowledge, he shows that a contradiction can be derived on the basis of principle (KK) and additional epistemic principles that he claims are better grounded. One of them is a reflective form of the margin for error principle defended by Williamson in his account of knowledge. We argue that Williamson’s reductio rests on the inappropriate identification of distinct forms of knowledge. More specifically, an important distinction between perceptual knowledge and non-perceptual knowledge is wanting in his statement and analysis of the puzzle. We present an alternative account of this puzzle, based on a modular conception of knowledge: the (KK) principle and the margin for error principle can coexist, provided their domain of application is referred to the right sort of knowledge.

From the mid-1980‘s to the early 2000‘s the wide-ranging resources of the concept we now call sensitivity , which Robert Nozick used to give an analysis of the concepts of knowledge and evidence , went largely unappreciated in epistemology. This was in part because these resources were upstaged by a glamorous implication the condition has for skepticism, and in part because of loss of faith in the project of giving a theory of knowledge at all, due to the failure time and again to construct a theory without counterexamples. The sensitivity condition, or as Nozick called it the variation condition, which requires that were p to be false you wouldn‘t believe it, had its own apparent counterexamples. And while the implication of this condition for skepticism was elegant and principled – it is possible to know that there is a table in front of you without knowing you are not a brain in a vat – it had the price of denying closure of knowledge under known implication, that is, denying that knowing q and knowing that q implies p are together sufficient to make the belief in p that you have on that basis knowledge.

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 it is argued that sensitivity theory suffers from a fatal defect. Sensitivity theory is often glossed as: (1) S knows that p only if S would not believe that p if p were false. As Nozick showed in his pioneering work on sensitivity theory, this formulation needs to be supplemented by a further counterfactual condition: (2) S knows that p only if S would believe p if p were true. Nozick further showed that the theory needs a qualification on the method used to form the belief. However, when these complications are spelled out in detail, it becomes clear that the two counterfactuals are in irresolvable tension. To jibe with the externalist intuitions that motivate sensitivity theory in the first place, (1) needs a fine-grained grouping of belief-formation methods, but (2) needs coarse-grained grouping. It is therefore suggested that sensitivity theory is in dire straits: either its proponents need to provide a workable principle of method individuation or they must retrench and give up their claims to providing sufficient conditions for knowledge.