An alternative equivalent way of explaining the notion of strict implication is by saying that p strictly implies q if and only if it is necessary that p materially implies q. "John's tie is scarlet," for example, strictly implies "John's tie is red," because it is impossible for John's tie to be scarlet without being red (or it is necessarily true that, if John's tie is scarlet, it is red).
If it is logically impossible for a certain proposition, p, to be true without a certain proposition, q, being also true (i.e., if the conjunction of p and not-q is logically impossible), then it is said that p strictly implies q.
Within Lewis' systems S2 S5, a necessarily true proposition is strictly implied by any proposition whatsoever, and a necessarily false proposition strictly implies any proposition whatsoever.
If p is true and it strictly implies q, then q is true.
If p is a belief of mine, and p strictly implies q, it does not follow that q is a belief of mine.
That much divine help is all that the image of magnet and rings strictly implies, and it is no threat to a profession's understanding of itself.
If the burden of argument belonged wholly to the Academy, and the Academics were restricted to premises that were strictly implied by Stoic theory, AS seems to have been the case with Arcesilaus, the Academic case was not proved.
Consequently, longitudinal invariance of the factor variances strictly implies that the ratio between the latent factor variances of men and women stays the same for each cycle and longitudinal invariance of the factor means strictly implies that the difference between the latent factor means of men and women stays the same (in standardized units) for the three cycles.
Even if we suppose that all actual individuals are distinguished from one another by such 'distinctive' essential properties, this still does not, strictly speaking, imply that they have individual essences.
