Comment by fmoralesc

If one thinks that certain mathematical are mere constructions, one might also reject certain mathematical methods. Take intuitionism as a case: Brouwer thought that mathematics was the product of the human mind, and restricted maths to whatever is constructible in a very strict sense. Finitism adds even further constraints, disallowing infinitary methods altogether. In these cases, the position seems to be that we cannot hold on to the usual commitment to mathematical entities.