Uncomputability: the Problem of Induction Internalized

I argue that uncomputable formal problems are intuitively, mathematically, and methodologically analogous to empirical problems in which Hume’s problem of induction arises. In particular, 11 I show that a version of Ockham’s razor (a preference for simple answers) is advantageous in both domains when infallible inference is infeasible. A familiar response to the empirical problem of induction is to conceive of empirical inquiry as an unending process that converges to the truth without halting or announcing for sure when the truth has been reached. On the strength of the analogies developed, I recommend the adoption of a similar perspective on uncomputable formal problems. One obtains, thereby, a well-defined notion of “hyper-computability” based entirely on classical computational models and on standards of success that have long been regarded as natural in the empirical domain.