For Plantinga, the nature of a thing is a conjunctive property the conjuncts of which are those properties the thing exemplifies in every possible world in which it exists.
In applying D3 to states of affairs like (e) and (f) it should be observed that a conjunct of a conjunctive state of affairs is a part of such a complex state of affairs.[4] As intended, D3 does not require an omnipotent agent to have the power to bring about either impossible or necessary states of affairs, or states of affairs such as (a - f).
ground* is grounded in a similar way there is an essential truth of the appropriate sort call it 'essence*' such that the conjunctive fact consisting of conjunction and essence* call this fact 'conjunction*' grounds ground*.
Fourth, while (e) is unrestrictedly repeatable, it is a complex state of affairs, namely, a conjunctive state of affairs whose second conjunct is not repeatable.
Note that since the second conjunct of (e) is not unrestrictedly repeatable, this is consistent with Hoffman and Rosenkrantz's account of omnipotence; their account does not require an omnipotent agent to be able to bring about a conjunctive state of affairs one of whose conjuncts is not unrestrictedly repeatable.
The general idea is to be able to express a problem's formulation as a set of clauses or, equivalently, as a formula in conjunctive normal form (CNF), that is, as a conjunction of clauses.
Complex universals accordingly come in two varieties: conjunctive — the constituents of which are simply its conjuncts — and structural.
Conjunctions are non-simple assertibles put together by the conjunctive connective 'both … and …'.
The former tell us that the truth of a disjunctive formula is determined by the truth of one or other of its disjuncts, whilst the truth of a conjunctive formula is determined by the truth of both its conjuncts.
Since all possible worlds would have the same necessary propositions, they are differentiated by their Big Conjunctive Contingent Fact (BCCF), which would contain different contingent propositions.
Here an arc with a number represents a conjunctive effect with a certain probability.
