Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of (...) physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction. (shrink)

This essay is an attempt to consider dynamic aspects of scientific theorising from a formal perspective. Our emphasis will be on the aims and methods for constructing formal models of theory dynamics which will be conceived from a general or 'theoretical' rather than 'applied' standpoint.

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide one.

Measures of theory-Distance are defined for theories formalizable within first-Order predicate logic by using distributive normal forms. The account is applied to give measures of verisimilitude.

A successor relation between theories T und T₁ express that T₁, the successor of T, has justifiably superseded T. In physics, for instance, Newton's theory of gravitation has superseded Kepler's laws and, in turn, Einstein's theory has become the successor of Newton's. By now there is no agreement on how a general concept of successor relation would have to be construed. In the present paper attention is drawn to two types of such relations, one deductive the other confirmatory. It seems (...) that what most people are looking for is the deductive type of relation. However, a deductive successor relation has to be justified by showing that if it holds then another, confirmatory relation holds, saying roughly that the actual empirical success of the deducing theory is at least as good as the corresponding success of the deduced theory. Under certain restrictions such a justification is given in the paper. (shrink)

In this paper we give the gist of our reconstructed notion of (limiting case) correspondence. Our notion is very general, so that it should be applicable to all the cases in which a correspondence has been said to exist in actual science.