A Digital Theory of Knowledge

Abstract: The goal with this paper is to formally define knowledge from the assumption that our universe is computable. Based on this assumption, we will formulate a minimalist ontology that will be the theoretical basis for our formal definition of knowledge. We will use the classical definitions of knowledge like "reliabilism" (RTB) and "justified true belief" (JTB) as our starting point and formally translate them to our digital framework. To do this we will investigate what it means for a process to be as reliable as possible, in a theoretical sense, by presenting Ray Solomonoff's induction as a solution to the shortcomings with Baysian inference. We will then criticize JTB and RTB and in the spirit of Rudolf Carnap's idea of explications stipulate two, mutually inclusive and complementary definitions of knowledge that we will call "generative knowledge" and "absolute knowledge".