Sentence examples for cannot both be true from inspiring English sources

Contraries may both be false but cannot both be true.

He saw clearly that, as the first kind of proposition is governed by the principle of contradiction (a proposition and its negation cannot both be true), the second is governed by the principle of sufficient reason (nothing exists or is the case without a sufficient reason).

They cannot both be true.

Contrary sentences are such that they cannot both be true.

Obviously the instrumental and definitional interpretations cannot both be true.

In all matter, contraries cannot both be true.

It presents a careful logical argument that leads him to a dilemma: thermodynamics with its Second Law on the one hand and gas theory (in the form as Zermelo understood it) on the other cannot both be literally true.

These cannot be both be true of the completed (or at least completable) sequence of divisions which would result from taking matter or substance as a thing-in-itself.[26] Now since the truth of both assertions has been shown to follow from that assumption, it must be false, that is, matter and extended substance are appearances only.

For example, if two responses cannot logically both be true, it is unclear which of the two is true.

As the contradictories of the two contraries, the subcontraries (e.g., Some pleasure is good, Some pleasure is not good) can both be true, but cannot both be false.

Could both be true?