In this paper a constructive empiricist account of scientific change is put forward. Based on da Costa's and French's partial structures approach, two notions of empirical adequacy are initially advanced (with particular emphasis on the introduction of degrees of empirical adequacy). Using these notions, it is shown how both the informativeness and the empirical adequacy requirements of an empiricist theory of scientific change can then be met. Finally, some philosophical consequences with regard to the role of structures in this context (...) are drawn.Now, we daily see what science is doing for us. This could not be unless it taught us something about reality; the aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations between things; outside those relations there is no reality knowable. (shrink)

Der Begriff ‘Modell’ leitet sich vom Lateinischen ‘modulus’ (das Maß) ab, im Italienischen existiert seit dem 16. Jh. ‘modello’ und R. Descartes verwendet im 17. Jh. ‘modèlle’. Während der Begriff in Architektur und Kunst schon seit der Renaissance gängig ist, wird er in den Naturwissenschaften erst im 19. Jh. verwendet.1 Dort greifen wissenschaftliche Modelle die für eine gegebene Problemstellung als wesentlich erachteten Charakteristika (Eigenschaften, Beziehungen, etc.) eines Untersuchungsgegenstandes heraus und machen diesen so einem Verständnis bzw. einer weiterführenden Untersuchung zugänglich. Es (...) ist üblich, zwischen Skalenmodellen, Analogmodellen und theoretischen Modellen zu unterscheiden. (shrink)

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of mathematics to informal reality is (...) not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed. (shrink)

The paper, as Part I of a two-part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage-setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, (...) which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided. (shrink)

When did the concept of model begin to be used in mathematics? This question appears at first somewhat surprising since “model” is such a standard term now in the discourse on mathematics and “modelling” such a standard activity that it seems to be well established since long. The paper shows that the term— in the intended epistemological meaning—emerged rather recently and tries to reveal in which mathematical contexts it became established. The paper discusses various layers of argumentations and reflections in (...) order to unravel and reach the pertinent kernel of the issue. The specific points of this paper are the difference in the epistemological concept to the usually discussed notions of model and the difference between conceptions implied in mathematical practices and their becoming conscious in proper reflections of mathematicians. (shrink)

This paper argues for a representational semantic conception of scientific theories, which respects the bare claim of any semantic view, namely that theories can be characterised as sets of models. RSC must be sharply distinguished from structural versions that assume a further identity of ‘models’ and ‘structures’, which we reject. The practice-turn in the recent philosophical literature suggests instead that modelling must be understood in a deflationary spirit, in terms of the diverse representational practices in the sciences. These insights are (...) applied to some mathematical models, thus showing that the mathematical sciences are not in principle counterexamples to RSC. (shrink)