Paul Rusnock

Many contemporary philosophers favor coherence theories of knowledge (Bender 1989, BonJour 1985, Davidson 1986, Harman 1986, Lehrer 1990). But the nature of coherence is usually left vague, with no method provided for determining whether a belief should be accepted or rejected on the basis of its coherence or incoherence with other beliefs. Haack's (1993) explication of coherence relies largely on an analogy between epistemic justification and crossword puzzles. We show in this paper how epistemic coherence can be understood in terms of maximization of constraint satisfaction, in keeping with computational models that have had a substantial impact in cognitive science. A coherence problem can be defined in terms of a set of elements and sets of positive and negative constraints between pairs of those elements. Algorithms are available for computing coherence by determining how to accept and reject elements in a way that satisfies the most constraints. Knowledge involves at least five different kinds of coherence - explanatory, analogical, deductive, perceptual, and conceptual - each requiring different sorts of elements and constraints.

The history of speculation on a notion or notions called analyticity, now usually characterized as truth in virtue of meanings and independently of fact, is often viewed from the perspective of the Quine-Carnap dispute. Previous characterizations, due to Kant, Frege and others, are then seen as being of a piece with Carnap’s various definitions of analyticity, and thus open to Quine’s objections. Seen from this point of view, Bolzano’s claims about analyticity appear downright bizarre: for on his conception, analyticity is not only non-linguistic, but also independent of both apriority and necessity. In this paper, it is argued that the problem lies not with Bolzano, but rather with the received historical account, especially its interpretation of Kant.

Russell, in his History of Western Philosophy, wrote that modern analytical philosophy had its origins in the construction of modern functional analysis by Weierstrass and others. As it turns out, Bolzano, in the first four decades of the nineteenth century, had already made important contributions'to the creation of "Weierstrassian" analysis, some of which were well known to Weierstrass and his circle. In addition, his mathematical research was guided by a methodology which articulated many of the central principles of modern philosophical analysis. That Russell was able to discover philosophical content within mathematical analysis was thus not surprising, for it had been carefully put there in the first place. Bolzano can and should, accordingly, be viewed as a founder of modern analytical philosophy, and not necessarily as an uninfluential one. This paper considers his work in mathematical and philosophical analysis against some of the relevant historical background.