Contextual Epistemic Logic

One of the highlights of recent informal epistemology is its growing theoretical emphasis upon various notions of context. The present paper addresses the connections between knowledge and context within a formal approach. To this end, a "contextual epistemic logic", CEL, is proposed, which consists of an extension of standard S5 epistemic modal logic with appropriate reduction axioms to deal with an extra contextual operator. We describe the axiomatics and supply both a Kripkean and a dialogical semantics for CEL. An illustration of how it may fruitfully be applied to informal epistemological matters is provided

Reassessing truth-evaluability in the Minimalism-Contextualism debate

The debate between Semantic Minimalism and Radical Contextualism is standardly characterized as concerning truth-evaluability – specifically, whether or not sentences require rich contextualization in order to express complete, truth-evaluable contents. In this paper, I examine the notion of truth-evaluability, considering which kinds of mappings it might require from worldly states of affairs to truth-values. At one end of the spectrum, an exhaustive notion would require truth-evaluable contents to map all possible states of affairs to truth-values. At the other end, a liberal notion would require only that truth-evaluable contents map at least one possible state of affairs to at least one truth-value. I show that both Minimalists and Radical Contextualists rely on some intermediate, moderately strict notion of truth-evaluability, falling between these two poles. I consider four ways in which such a notion could be defined. However, I argue that each of these is ultimately implausible, giving us no reason to favour a moderately strict notion of truth-evaluability over the liberal alternative. This suggests that the debate must shift to more moderate ground; rather than concerning the in principle possibility of truth-evaluable contents, it fundamentally hinges on their explanatory value. More generally, paying close attention to the notion of truth-evaluability allows us to tease apart distinct strands in the Minimalism-Contextualism debate, and gain a better appreciation of what is at stake

Interpretation of quantal manifolds

In quantum gravity, one looks for alternative structures to spacetime physics than ordinary real manifolds. Here, we propose an alternative universal construction containing the latter as an equilibrium state under the action of the universal diffeomorphism group. Our theory contains many other previous proposals in the literature as special cases. However, the crucial point we make is that those have to be appreciated in the universal context developed here.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1101.511

Efficient holographic proofs

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 57-63).by Alexander Craig Russell.Ph.D

Epistemology as Engineering?

According to a common objection to epistemological naturalism, no empirical, scientific theory of knowledge can be normative in the way epistemological theories need to be. In response, such naturalists as W.V. Quine have claimed naturalized epistemology can be normative by emulating engineering disciplines and addressing the relations of causal efficacy between our cognitive means and ends. This paper evaluates that "engineering reply" and finds it a mixed success. Based on consideration of what it might mean to call a theory "normative," seven versions of the normativity objection to epistemological naturalism are formulated. The engineering reply alone is sufficient to answer only the four least sophisticated versions. To answer the others, naturalists must draw on more resources than their engineering reply alone provides

Ellipsis, economy, and the (non)uniformity of traces

A number of works have attempted to account for the interaction between movement and ellipsis in terms of an economy condition Max- Elide. We show that the elimination of MaxElide leads to an empirically superior account of these interactions. We show that a number of the core effects attributed to MaxElide can be accounted for with a parallelism condition on ellipsis. The remaining cases are then treated with a generalized economy condition that favors shorter derivations over longer ones. The resulting analysis has no need for the ellipsisspecific economy constraint MaxElide