The Epistemic Landscape: a Computability Perspective

Abstract: By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and properties associated with the fact that language technology is enumerable. G\"odel's numbering technique is universal for enumerable structures and shows strong limits of the language technology. Computability theory is a particular example: programs can be numbered and all sorts of limits can be studied from there. Computability is also at the heart of science since any experimental validation of a theory supposes that theoretical results have been computed, then checked against concrete experiments. It implies that limitations on what is computable ultimately are also limits of what we understand as "scientific theory", and more generally to all the transmissible knowledge. We argue that it is fruitful to look a epistemology from a computability perspective. We show that it allows to precisely define different kinds of knowledge acquisition techniques, and helps the study of how they are related to one another.