P1: Nothing positive which a false idea has is removed by the presence of the true insofar as it is true.

Dem.: Falsity consists only in the privation of knowledge which inadequate ideas involve (by IIP35), and they do not have anything positive on account of which they are called false (by IIP33). On the contrary, insofar as they are related to God/Nature, they are true (by IIP32).

So if what a false idea has that is positive were removed by the presence of the true insofar as it is true, then a true idea would be removed by itself, which (by IIIP4) is absurd.

Therefore, Nothing positive which a false idea has, etc., q.e.d.

Schol.: This proposition is understood more clearly from IIP16 C2. For an imagination is an idea which indicates the present constitution of the human Body more than the nature of an external body—not distinctly, of course, but confusedly. This is how it happens that the Mind is said to err.

For example, when we look at the sun, we imagine it to be about 200 feet away from us. In this we are deceived so long as we are ignorant of its true distance; but when its distance is known, the error is removed, not the imagination, i.e., the idea of the sun, which explains its nature only so far as the Body is affected by it. And so, although we come to know the true distance, we shall nevertheless imagine it as near us. For as we said in IIP35 S, we do not imagine the sun to be so near because we are ignorant of its true distance, but because the Mind conceives the sun’s size insofar as the Body is affected by the sun. Thus, when the rays of the sun, falling on the surface of the water, are reflected to our eyes, we imagine it as if it were in the water, even if we know its true place.

And so it is with the other imaginations by which the Mind is deceived, whether they indicate the natural constitution of the Body, or that its power of acting is increased or diminished: they are not contrary to the true, and do not disappear on its presence.

It happens, of course, when we wrongly fear some evil, that the fear disappears on our hearing news of the truth. But on the other hand, it also happens, when we fear an evil that is certain to come, that the fear vanishes on our hearing false news. So imaginations do not disappear through the presence of the true insofar as it is true, but because there occur others, stronger than them, which exclude the present existence of the things we imagine, as we showed in IIP17.