Logic and Aggregation

Paraconsistent logic is an area of philosophical logic that has yet to find acceptance from a wider audience. The area remains, in a word, disreputable. In this essay, we try to reassure potential consumers that it is not necessary to become a radical in order to use paraconsistent logic. According to the radicals, the problem is the absurd classical account of contradiction: Classically inconsistent sets explode only because bourgeois classical semantics holds, in the face of overwhelming evidence to the contrary, that both A and A cannot simultaneously be true! We suggest (more modestly) that there is, at least sometimes, something else worth preserving, even in an inconsistent, unsatisfiable premise set. In this paper we present, in a new guise, a very general version of this preservationist approach to paraconsistency.     

Complex Systems from the Perspective of Category Theory: II. Covering Systems and Sheaves

Using the concept of adjunction, for the comprehension of the structure of a complex system, developed in Part I, we introduce the notion of covering systems consisting of partially or locally defined adequately understood objects. This notion incorporates the necessary and sufficient conditions for a sheaf theoretical representation of the informational content included in the structure of a complex system in terms of localization systems. Furthermore, it accommodates a formulation of an invariance property of information communication concerning the analysis of a complex system.     

Apocalyptic relevance

In their book, Relevance, Sperber and Wilson make an important contribution towards constructing a credible theory of this unforthcoming notion. All is not clear sailing, however. If it is accepted as a condition on the adequacy of any account of relevance that it not be derivable either that nothing is relevant to anything or that everything is relevant to everything, it can be shown that Sperber and Wilson come close to violating the condition.