We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffus...

The purpose of this paper is to question some commonly accepted patterns of reasoning involving nonmonotonic logics that generate multiple extensions. In particular, I argue that the phenomenon of floating conclusions indicates a problem with the view that the skeptical consequences of such theories should be identified with the statements that are supported by each of their various extensions....

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Sartre (1956) describes ways in which one may present oneself to others as being a certain sort of person. In one of his examples, a waiter presents himself as a waiter by as it were acting the part of a waiter. More generally, Sartre argues that, wanting to be, or at least to appear to others to be, a person of a certain sort or character, one often acts the part of a person of that sort of ch...

Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons (CR): S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn’t have ...

In this paper, I try to make sense of the idea that true knowledge attributions characterize something that is more valuable than true belief and that survives even if, as Contextualism implies, contextual changes make it no longer identifiable by a knowledge attribution. I begin by sketching a familiar, pragmatic picture of assertion that helps us to understand and predict how the words “S kno...

Has Tom spoken truly? Surely, Jones’s epistemic position seems good enough for satisfying the predicate ‘knows that the animals in the pen are zebras’ (henceforth ‘knows Z’): Jones has visual experiences of a black and white striped horse-like animal, she can discriminate reliably between zebras and antelopes, she has read the sign on the pen that reads ‘Zebra Pen’, etc. Thus, Tom’s utterance o...

the cause is the basis of the existence and non-existence of a thing and its consideration is prior to consideration of the thing. in accordance with subjective theory, the will is the substance of the contract and the other elements of a contract are conditions of will’s efficiency. in contrast, according to objective theory, object of the contract is the substance of it and the other elements...