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)

Inter-theoretical reduction has always been a major topic in the structuralist philosophy of science. This paper reviews criteria of adequacy which were put forward by Adams, Sneed, Stegmuller, Mayr, Pearce, Kamlah, and Mormann. The criteria are formalized in a simplified structuralist model, and the logical relations between them are investigated. It turns out that various parts of these criteria are incompatible.

We revive the idea that a deductive-nomological explanation of a scientific theory by its successor may be defensible, even in those common and troublesome cases where the theories concerned are mutually incompatible; and limiting, approximating and counterfactual assumptions may be required in order to define a logical relation between them. Our solution is based on a general characterization of limiting relations between physical theories using the method of nonstandard analysis.

In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.

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)

Review of David Faust's The Limits of Scientific Reasoning.

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally tractable. Such activities (...) are compared with reduction types established in philosophy of science. (shrink)

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and (too) high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally tractable. Such (...) activities are compared with reduction types (more) established in philosophy of science. (shrink)

According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. (...) I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction. (shrink)

We begin by highlighting some points related to Kuhn’s later thoughts on the incommensurability thesis and then show to what extent the standard version of the thesis given by the structuralist metatheory allows us to capture Kuhn’s ideas. Our main aim is to establish what constitutes the basis of comparability between incommensurable theories, even in cases of incommensurability with respect to theoretical and non-theoretical terms. We propose that comparability between incommensurable theories requires some connection between their respective ontologies that can (...) be captured by means of an ontological non-reductive relation. At this point, the structuralist notion of “echeloned partial substructure” may be of help. When the incommensurability is very drastic, the existence of ontological connections between the theories involved may only be evident by common terms of their non-characteristic vocabularies. So, this notion of non-characteristic vocabulary becomes relevant in our proposal. (shrink)

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the (...) key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4). (shrink)

Russell’s claim that only structural knowledge of the world is possible was influentially criticized by Newman as rendering scientific discoveries trivial. I show that a version of this criticism also applies to the “structural realism” more recently advocated by Worrall, which requires continuity of formal structure between predecessor and successor scientific theories. The problem is that structure, in its common set-theoretical construal, is radically underdetermined by the entities and relations over which it is defined, rendering intertheoretic continuity intolerably cheap. I (...) show that this problem may be overcome by supplementing the purely formal relation of intertheoretic isomorphism with the semiformal “Ontological Reductive Links” developed by Moulines and others of the German “structuralist” approach to the philosophy of science. (shrink)

Dogmatic, naive and sophisticated falsificationism are construed as being distinguished by different views on the revisability of scientific theories. Then Lakatos's methodology of scientific research programs (SRP) is reinterpreted: The structure of an SRP is a target theory equipped with a priority structure for hypothetical revisions that accommodate idealizing assumptions. Idealizations pointing "backwards" capture predecessor theories, thus showing both their virtues and limitations. The core of an SRP is assigned top priority; its positive heuristics consists in a strategy of how (...) to work off the idealizing assumptions. In the dynamics of SRP's, progressive intertheoretic relations within an SRP are characterized as generating continuity through revisions, while those that hold across SRP's only have excess empirical content. Finally, we contrast our account with a reconstruction of Lakatos's in the structuralist philosophy of science (W. Stegmüller). (shrink)