Church's Thesis and Hume's Problem

Abstract

We argue that uncomputability and classical scepticism are both reflections of inductive underdetermination, so that Church's thesis and Hume's problem ought to receive equal emphasis in a balanced approach to the philosophy of induction. As an illustration of such an approach, we investigate how uncomputable the predictions of a hypothesis can be if the hypothesis is to be reliably investigated by a computable scientific method

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Is the Humean defeated by induction?Benjamin T. H. Smart - 2013 - Philosophical Studies 162 (2):319-332.
Empiricism, Probability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Journal of Applied Logic 12 (3):319–348.

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