This is basically a repost of this blog post by John Carlos Baez: link. I wanted to share it with you since I find the result unexpectedly interesting.

The Law of Excluded Middle states that for any statement P we have that *either P or not P* is true. Almost all of us work under this assumption, but of course one can also work in a logic system, where this is not necessarily assumed.

Now assume that you do not assume the law of excluded middle, and pick at random any statement. What is the probability that the law of excluded middle is true for it? The answer is that it is at most 2/3, or otherwise the law of excluded middle actually holds in your used logic system!

You can find the concrete statement and a nice introductory example with *maybe abelian* groups in this blog post of Benjamin Bumpus: link.