Paul Rusnock

This paper is devoted to an examination of Bolzano’s notion of necessary existence, which has so far received relatively little attention in the literature. We situate Bolzano’s ideas in their historical context and show how he proposed to correct various flaws of his predecessors’ definitions. Further, we relate Bolzano’s conception to his metaphysical and theological assumptions, arguing that some consequences of his definition which have been deemed counterintuitive by some of his interpreters turn out to be more reasonable given the broadly Leibnizian background of his metaphysics. Finally, we consider some difficulties that arise from Bolzano’s evolving views on freedom, which, at least in his early thought, was intimately linked with contingency. In an appendix, we discuss a recent debate on Bolzano’s notion of necessary truth between Textor and Rusnock that has some bearing on our overall line of interpretation of Bolzano’s notion of necessary existence.

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.