Answer:
Literally the sentence means: affirmation of one [reality] is the exclusion of its alternative.
The word "alternative" comes from the Latin root of alter (nominative) alterius (genitive) which is the other of two. This expression must therefore refer to the fact that in arguing or discussing an issue with only two possible solutions, the evidence proving the one [solution] eliminates the veracity of its alternative or second possible solution. This is my guess. Frankly I never heard of this expression before, and I am an old man.