Logics and Their Galaxies

Abstract

This chapter introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated with each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic. We explore some consequences of these developments.

Conjunctive and Disjunctive Limits: Abstract Logics and Modal Operators

“…We have argued (with Hilan Bensusan) in [1] that logical possibility and logical necessity are never absolute in the precise sense that what is logically possible in a given logic could be logically impossible in a different logic and vice-versa. The same applies, then, for logical necessity and, in more general terms, for all logical truths.…”

“…In this article, we use the concept of limit of a given sequence to redefine the notions of conjunctive limit and disjunctive limit in the universe of abstract logic. 1 By means of this strategy, we can formulate specific standards of logical possibility as well logical necessity pointing out that the same procedure could be extended to a great variety of sequences of objects (with very different natures, indeed).…”

Implications and Limits of Sequences

“…To point out that     , is a member of  the notation    is used, and we say that  is a consequence of  in     , . We proceed as in [1]. So, we do not need to specify any kind of property that  should satisfy.…”