The aim of this paper is to characterize the various structuralist reduction concepts as structure-preserving maps in a succinct and unifying way. To begin with, some important intuitive adequacy conditions are discussed that a good (structuralist) reduction concept should satisfy. Having reconstructed these intuitive conditions in the structuralist framework, it turns out that they divide into two mutually incompatible sets of requirements. Accordingly there exist (at least) two essentially different types of structuralist reduction concepts: the first type stresses the existence (...) of a deductive or inferential link between the reducing and the reduced theory; the second type emphasizes the greater explanatory power the reducing theory should have in comparison with the reduced theory. The problem of the incompatibility of equally plausible reduction concepts is treated in the last section and a proposal is made for its solution consisting in the definition of a multiple synthetizing reduction relation. (shrink)

In the last two sections of Structure, Thomas Kuhn first develops his famous threefold conception of the incommensurability of scientific paradigms and, subsequently, a conception of scientific progress as growth of empirical strength. The latter conception seems to be at odds with the former in that semantic incommensurability appears to imply the existence of situations where scientific progress in Kuhns sense can no longer exist. In contrast to this seeming inconsistency of Kuhns conception, we will try to show in this (...) study that the semantic incommensurability of scientific terms appears to be fully compatible with scientific progress. Our argumentation is based on an improved version of the formalization of Kuhns conception as developed in the 1970s by Joseph Sneed and Wolfgang Stegmüller: In order to be comparable, incommensurable theories need the specification of relations that refer to the concrete ontologies of these theories and involve certain truth claims. The original structuralist account of reduction fails to provide such relations, because (1) it is too structural and (2) it is too wide. Moreover, the original structuralist account also fails to cover important cases of incommensurable theories in being too restrictive for them. In this paper, we develop an improved notion of “reduction” that allows us to avoid these shortcomings by means of a more flexible device for the formalization of (partially reductive) relations between theories. For that purpose, we use a framework of rigid logic, i.e., logic that is based on a fixed collection of objects. (shrink)

Recently some philosophers have urged that connectionist artificial intelligence is (potentially) eliminative for the propositional attitudes of folk psychology. At the same time, however, these philosophers have also insisted that since philosophy of science has failed to provide criteria distinguishing ontologically retentive from eliminative theory changes, the resulting eliminativism is not principled. Application of some resources developed within the semantic view of scientific theories, particularly recent formal work on the theory reduction relation, reveals these philosophers to be wrong in this (...) second contention, yet by and large correct in the first. (shrink)

Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...) are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce. (shrink)