There is a great deal one can learn about logic and objectivity from mathematics. It is a very important subject to study. In Elementary Mathematical Analysis, Colin Clark says:
Suppose we wish to prove: “1 is the largest positive integer.”
Let x denote the largest positive integer. Then x>= 1, so that x^2 >= x. But x^2 is also a positive integer. Therefore x^2 = x. Dividing by x, we obtain x = 1.
What is the error in this “proof”? The moral of this example is that if we refer to nonexistent objects as if they existed, we may be led into foolish errors. Mathematicians seem to have learned this moral; politicians probably never will.
p. 107, Elementary Mathematical Analysis by Colin Clark, Wadsworth Publishers of Canada, Ltd., (c) 1982. ISBN 0-534-98018-X.
As Parmenides said: ‘What is not, neither is nor can be thought.’ A is A; A is Not Non-A.