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Logic, Symbolic and mathematical.

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Mathematicians --- Logic, symbolic and mathematical. --- Gentzen, Gerhard.

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Algebra, Abstract --- Combinatorial analysis --- Logic, Symbolic and mathematical

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That the structure V = UaVa be the universe of all sets, that the set theoretical axioms be true assertions about V or that a question like the Continuum Hypothesis be still open (since it is undecided whether it holds or fails in V) are common assertions in set theory. How one is to understand them, tough, is not an obvious matter. The aim of this book is just to interpret the façon de parler that V is the universe of all sets in a way that is faithful to what is actually done in set theory.

Mathematics --- Set theory. --- Logic, Symbolic and mathematical. --- Philosophy.

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Kuhn and Feyerabend formulated the problem. Dilworth provides the solution. In this highly original and insightful book, Craig Dilworth answers all the questions raised by the incommensurability thesis. Logical empiricism cannot account for theory conflict. Popperianism cannot account for how one theory is a progression beyond another. Dilworth’s Perspectivist conception of science does both. While remaining within the bounds of classical philosophy of science, Dilworth does away with the logicism of his competitors. On the Perspectivist view theory conflict is not contradiction, and theory superiority does not consist in deductive subsumption or set-theoretic inclusion. Here the relation between theories is analogous to the application of individual concepts, and the question of theory superiority becomes one of relative applicability. In this way Dilworth succeeds in providing a conception of science in which scientific progress is based on both rational and empirical considerations. "[Dilworth] convincingly works out how from his point of view it is possible to explain the conflict between two theories as an incompatibility of perspectives, and at the same time avoid sliding into relativism by giving criteria for scientific progress." Dialectica.

Science --- Philosophy. --- Methodology. --- Scientific method --- Logic, Symbolic and mathematical --- Normal science --- Philosophy of science