 One version of this view was proposed by Curry (Curry 1958). On this view, mathematics consists of a collection of formal systems which have no interpretation or subject matter. (Curry here makes an exception for metamathematics.) Relative to a formal system, one can say that a statement is true if and only if it is derivable in the system. But on a fundamental level, all mathematical systems are on a par. There can be at most pragmatical reasons for preferring one system over another. Inconsistent systems can prove all statements and therefore are pretty useless. So when a system is found to be inconsistent, it must be modified. It is simply a lesson from Gödel’s incompleteness theorems that a sufficiently strong consistent system cannot prove its own consistency.