Set-Theoretic Redundancy Eliminated

“A possible world is a maximal conjunction of compossible abstract propositions (a BCF in our abbreviational terminology), with repetitions and other logical redundancies eliminated so as to avoid to set-theoretic paradoxes. Each world is individuated by its Big Conjunctive Contingent Fact (BCCF), which is the conjunction of all of the  contingent conjuncts in its BCCF.”

~Alexander R. Pruss and Richard M. Gale, A Response to Almeida and Judisch.

That makes a lot of sense to me. So then, we can talk about a logically possible world as a set of maximally compossible propositions none of which are redundant. Perhaps there is some analogy here with my idea of a simple predicate outlined in a previous post? So that logically possible worlds are maximally compossible/consistent sets of simple predicates. Maybe this is short sighted, because it seems as though prepositional truths (truths about relations) are not clearly included, but we can just say that with any such prepositional truth the relation is a property of ‘at least one‘ of the relata (or at least, I can’t see why we wouldn’t be able to say that).


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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