Question

While refining the formulation of the cosmological proof, you relied on rejecting the validity of an infinite regress, and when you explained why this rejection was made, you wrote that an infinite regress is acceptable, but only in inductive cases or in cases where there is a closed formula. From this it follows that you assume such a regress is acceptable precisely when it is constructive. There are intuitive arguments that allow the validity of claims that are not necessarily constructive (for example, the axiom of choice: from any collection of sets one can choose, for each set in the collection, an element that belongs to it, even without a formula). Why do we reject everything that cannot be directly constructed?