Arithmetic, enumerative induction and size bias

Abstract Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states even greater than 2 the sum of two primes. Enumerative inductive evidence for such usually consists small cases. In absence supporting reasons, mathematicians mistrust arithmetical generalisations, more so most other forms non-deductive evidence. Some philosophers have also expressed scepticism about value enumerative in arithmetic. But why? Perhaps best argument known instances an conjecture are almost always small: they appear at start sequence. Evidence this kind consequently suffers from size bias. My essay shows sort comes many different flavours, raises challenges them all, and explores their respective responses.