No goalpost shifting. Procedures in classical mathematics require a series of decisions made based on absolute truths accessible by no process of reasoning. Ma

No goalpost shifting. Procedures in classical mathematics require a series of decisions made based on absolute truths accessible by no process of reasoning. Mathematics that includes entities created through such procedures avoid contradiction exactly because the truths are true, whether or not any reasoning exists that could show it. Computability limits itself to procedures involving decision processes that can themselves be reasoned about. Attempts to create computable analogs of classical decision procedures reveal a whole world of logical subtleties thanks to the unavoidable possibility of self-reference. The difference is this. In classical mathematics, diagonalization results in uncountable infinities. In computable mathematics, diagonalization results in undecidability. The reason why classical mathematics avoids undecidability is because decisions are made by appeals to absolute truth. Which represents a lack of process that therefore cannot be diagonalized.