Let’s look at another step-by-step example of PEM at work to further emphasize just how intuitively basic it appears to us in common cases. This time around, let’s look at a proposition with the verb ‘to be’ in the past tense to illustrate that PEM holds in straightforward propositions about the past as well.
In the case of past events, as in the case of present ones, evaluating the truth of 1. is a matter of checking against the facts of the world to see if there is a correspondence between what was/is the case and the content of the proposition. It seems trivially true that either dinosaurs were large on average, or they weren’t – whatever the relevant state of affairs indicates will make one of the two disjuncts true; therefore, the entire expression, “Either dinosaurs were large on average, or they weren’t.” will be true by virtue of one of the contradictories in the pair being true. So far, so good. What PEM is saying further is that generally, for any pair of contradictories, this result holds.
The above example is a Universal Affirmative proposition. Clearly enough, it is false – there were small dinosaurs. By the square of opposition, the falsehood of example 2 implies the truth of its contradictory opposite, namely that “Some dinosaurs are not large.” This is obvious enough on the face of it, but we might reasonably ask a further question: why should we believe that the implication holds? Put otherwise, why should we think that the relation of contradictory opposition works in this way? The answer: PEM. The principle gives us reason to believe – it justifies – that contradictory opposition works exactly as we expect it to.