You can’t prove a negative.

If you check the colloquial definition of you can’t prove a negative, you will find the following distinction:

Two sides. One Coin.

evidence of absence, or absence of evidence. That, of course, is an understanding based on the ability to discover or measure something, scientifically. The implication is there is something to be discovered, directly. There is, however, another way established by The Buddha in Chapter 22: On Pure Actions in the Mahāyāna Mahāparinirvāṇa Sūtra. This alternative way is called “fathoming.”

Here is the distinction expressed in that chapter: “If Dharma is eternal, one cannot gain it. It is like space. Who can gain it? In worldly life, what originally was not, but is now, is called the non-Eternal. The same with the Way. If the Way can be gained, this is nothing but the non-Eternal. If Dharma is the Eternal, there can be no gaining of anything, no arising, as in the case of the Buddha-Nature, which knows no gaining and no arising.”… “There are two kinds of Way. One is eternal, and the other the non-eternal. Enlightenment, too, is of two kinds. One is eternal, and the other non-eternal.”

Later in the same chapter comes “fathoming.” “There are two kinds of seeing. One is seeing by outer signs, and the other by fathoming…It is like seeing fire from afar, when one sees smoke. Actually, one does not see the fire. Though one does not see it, nothing is false here…Seeing the actions of the body and mouth, we say that we see the mind. The mind is not seen, but this is not false. This is seeing by outer signs…What is seeing by fathoming? We see the flower and the leaf, and we say we see the root. Though we do not see the root, this is not false.”

The actions of mind and body, by necessity, presumes (e.g., requires) the existence of the unseen Mind. Can we prove the existence of “up?” Up cannot be proven directly, but it can indirectly with the existence of “down.” These two are opposite sides of the same coin. Remove one side, and the other side will disappear.

In the same way, proving a negative, by necessity requires a positive. Remove one, and the other disappears. When a positive comes into being, a negative must likewise be present. So can a negative be proven? We may not be able to prove a negative directly, but without a negative, a positive could not exist.