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This is this, this ain't something else, this is this -Robert De Niro, Deerhunter his book may to some extent be viewed as the continuation of my T Doctoral thesis Epistemology, Methodology and Reliability. The dissertation was, first of all, a methodological study of the reliable performance of the AGM-axioms (Alchourr6n, Gardenfors and Makin- son) of belief revision. Second of all the dissertation included the first steps toward an epistemology for the limiting convergence of knowledge for scientific inquiry methods of both discovery and assessment. The idea of methodological reliability as a desirable property of a scientific method was introduced to me while I was a visiting Ph. D. -student at the Department of Philosophy, Carnegie Mellon University in Pitts- burgh, Pennsylvania, USA in 1995-96. Here I became acquainted with formal learning theory. Learning theory provides a variety of formal tools for investigating a number of important issues within epistemology, methodology and the philosophy of science. Especially with respect to the problem of induc- tion, but not exclusively. The Convergence of Scientific Knowledge-a view from the limit utilizes a few concepts from formal learning theory to study problems in modal logic and epistemology. It should be duely noted that this book has virtually nothing to do with formal learning theory or inductive learning problems.