The hierarchies of knowledge and the mathematics of discovery

Rather than attempting to characterize a relation of confirmation between evidence and theory, epistemology might better consider which methods of forming conjectures from evidence, or of altering beliefs in the light of evidence, are most reliable for getting to the truth. A logical framework for such a study was constructed in the early 1960s by E. Mark Gold and Hilary Putnam. This essay describes some of the results that have been obtained in that framework and their significance for philosophy of science, artificial intelligence, and for normative epistemology when truth is relative.I am indebted to Kevin Kelly for several years of happy conversation from which the perspective and views of this paper grew, for comments on a draft of the paper, and for constructing some of the illustrations. A fellowship from the John Simon Guggenheim Memorial Foundation provided the liberty to write this paper. It was first presented in the Turing Colloquium, 1990.