 As Frege’s remarks suggest, one way to underpin an argument against the use of enumerative induction in mathematics is via some sort of non-uniformity principle: in the absence of proof, we should not expect numbers (in general) to share any interesting properties. Hence establishing that a property holds for some particular number gives no reason to think that a second, arbitrarily chosen number will also have that  property.[8]  Rather than the Uniformity Principle which Hume suggests is the only way to ground induction, we have almost precisely the opposite principle! It would seem to follow from this principle that enumerative induction is unjustified, since we should not expect (finite) samples from the totality of natural numbers to be indicative of universal properties.