Logic and Computation in Philosophy Series – serie
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Those inquiring into the nature of mind have long been interested in the foundations of mathematics and vice versa. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. This volume's contributors have taken the link between conceptions of mind and mathematics as their topic, exploring and probing it from different perspectives.
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Solomon Feferman is one of the leading figures in the philosophy of mathematics. This volume brings together a selection of his most important recent writings, covering the relation between logic and mathematics, proof theory, objectivity and intentionality in mathematics, and key issues in the work of Gödel, Hilbert, and Turing. A number of the papers appeared originally in obscure places and are not well-known, and others are published here for the first time. All of the material has been revised and annotated to bring it up to date.
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This book considers the question of the reliability of scientific methods. One method of inquiry can be said to be more reliable than another if it eventually arrives at the truth in more possible circumstances than the other method can. Kelly begins with a discussion of the philosophical significance of reliability, examines the reliability of computable methods, provides a general, topological perspective on reliable inference by "ideal" agents, and investigates the possibility of reliable enquiry in the face of theory-laden evidence and incommensurability. The text is extensively and amusingly illustrated and assumes only introductory knowledge of basic logic and computability theory.