 The slide towards this sort of formalist attitude to axioms can also be traced through Frege’s logicism. The logicist program sought to show that mathematics is reducible to logic, in other words that mathematical proofs can be shown to consist of logical deductions from logically true premises. For Frege, these logically true premises are definitions of the terms which occur in them. But this again raises the issue of what distinguishes acceptable from unacceptable definitions. The worry here is not just whether our axioms are true but whether they are even consistent (a pitfall which famously befell Frege’s own system). And this is a problem once self-evidence is abandoned as the ‘gold standard’ for axioms, whether we move from here to a formalist view or a logicist view. In both cases, some other bounds on the acceptability of candidate axioms must be provided.