This post is a little on the odd side, pertaining as it does to the philosophical underpinnings of physics. Science can answer a question, but only philosophy tells you what question to ask.
Human beings are binary creatures. That is, we are roughly symetrical. We have a right and left eye, right and left hand, and so on. Because of this, we tend to see the universe in a binary fashion: two options only. Some examples are below:
Do you get the idea? Our basic structure determines our outlook on the universe. Since we have a distinct right side and a distinct left side, every event can be boiled down to two possible choices. In other words, we view the universe as binary.
In computing, binary is the assembling of data using a series of ones and zeros is a particular sequence. Now, the difference between 1 and 0 is possibly the most fundamental mankind has yet discovered. 1 and 0 are infinitely distict from one another; there is no way to reconcile the two. In fact, it is impossible to prove that they are different, but all of mathematics only works because they are. Thus, the distinction between 1 and 0 is something that cannot be proved, it can only be known. Call it a fundamental truth if you want.
Seeing as we view the universe through our own binary eyes, to human beings the universe is essentially a collection of ones and zeros. To put it another way, either things exist, or they don't. There is no middle ground between existence and nonexistance.
Of course, a trinary universe would make things easier to explain. If something could simultaneously exist and not exist, then it would be subject to only some of the laws of nature. The universe could in essence violate all of its own laws if it were trinary in structure, instead of binary. This allows for things like a Big Bang happening out of nothing, and other similar absurdities.
Of course, finding a number that is equidistant from 1 and 0 without sharing any properties with either is the challenge. A human mind is simply incapable of concieving of such a number. Thus, if the universe really were trinary in nature (existence, nonexistence, something between the two) then its ultimate secrets will probably remain forever closed to us.