 Propositions thus seem to have structure that bears on the validity of inferences, even ignoring premises/conclusions with propositional parts. In this sense, even atomic propositions have logical form. And as Aristotle noted, pairs of such propositions can be related in interesting ways. If every S is P, then some S is P. (For these purposes, assume there is at least one S.) If no S is P, then some S is not P. It is certain that either every S is P or some S is not P; and whichever of these propositions is true, the other is false. Similarly, the following propositions cannot both be true: every S is P; and no S is P. But it isn’t certain that either every S is P, or no S is P. Perhaps some S is P, and some S is not P. This network of logical relations strongly suggests that the propositions in question contain a quantificational element and two general elements—and in some cases, an element of negation; see  logic: classical.  This raises the question of whether other propositions have a similar structure.