Proving a Universal Negative: Is It Possible?

"And in that day, seven women shall take hold of one man, sayingy: [...] let us be called by thy name to take away our reproach."
-2 Nephi 14:1 (Book of Mormon)

A universal negative is a statement of the form "There exists no object or entity 'X' which satisfies condition 'Y'." It seems like a fairly simple statement to make, but as it turns out statements of this form are extremely difficult, in some cases impossible, to prove (for those of you who have read my first two blog posts, this is why gnosticism comes with the burden of proof).

Take the following example, where object 'X' is a unicorn and condition 'Y' is existence in the universe. There is no possible way to search through the universe an prove the nonexistence of unicorns, but do you believe they exists? No, you most likely do not. This is where we get into "reasonable doubt." You have never seen a unicorn, and there have never been any reliable historical sightings recorded of a unicorn sighting, and since you have never been presented with evidence of its existence, you do not accept its existence to be a true claim. It is unlikely, however, that you ever have said, "Unicorns don't exist and I can prove it!" Rather, it is more likely for you to have said, "No, I do not believe in unicorns, but if you show me one, obviously I will be convinced!"

I can't claim to be able to disprove the existence of certain things, like unicorns, but other things can be proven to not exist. According to Aristotle's law of Non-Contradiction, a statement about an object cannot be both true and untrue at the same time. For example, I can 100% positively say that there is no such thing as an invisible pink unicorn. The definition of invisible is that it cannot be seen, and pink is a color which, by definition, requires visibility. It is not possible for such an entity to exist, as its own identity contradicts itself. Another example could be a spherical cube. Cubes have eight vertices by definition, and spheres have none. No matter how long you mess around with Play-Doh and no matter how far you look in the universe, I can positively say that this entity does not and cannot exist, because its properties are such that, were it to exist, its own attributes would contradict themselves, thereby proving this object could not possibly exist.

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