Is it a contradiction, if
- mathematical objects are for me "mental constructions" -- like in intuitionism
- I accept classical mathematics and the Law oft excluded middle
It depends on what you mean by "mental construction":
If you mean mental construction, i.e. just in mind, then there is no contradiction.
If you mean mental construction, i.e. constructible step by step by a finite algorithm, then it is a contradiction.
1) mental construction: Mathematical objects are ideas, they do not exist as physical objects. Sophisticated concepts like Hilbert space or Riemann manifold have been created by man and fixed by definitions. Hence they are mental constructions. This opinion is not shared by all philosophers of mathematics. Instead, some keep alive the discussion whether mathematical objects have been invented or have been detected.
2) mental construction: Mathematicians from the school of intuitionism reject the existence of mathematical objects like the set of all natural numbers. They accept "potential" infinity like constructing one number after the other - without an end. But they reject "actual" infinity, which equals the cardinalty of the set of natural numbers taken as a whole. Instead, they request that any object must be constructible. Therefore they do not accept the method of indirect proof. It builds on the law of the excluded middle.