This paper argues that evaluation of the truth and rationality of past scientific theories is both possible and profitable. The motivation for this enterprise is traced to recent discussions by I. Lakatos, L. Laudan and others on the import of history for the philosophy of science; several objections to it are considered and T. S. Kuhn is found to advance the most substantive. An argument for establishing judgements of rationality and truth in the face of scientific revolutions is presented; finally (...) evidence is offered for the value of such assessments to historiography and to debates on scientific progress. (shrink)

Intuitionistic meta-methodologies, which abound in recent philosophy of science, take the criterion of success for theories of scientific rationality to be whether those theories adequately explicate our intuitive judgments of rationality in exemplary cases. Garber's (1985) critique of Laudan's (1977) intuitionistic meta-methodology, correct as far as it goes, does not go far enough. Indeed, Garber himself advocates a form of intuitionistic meta-methodology; he merely denies any special role for historical (as opposed to contemporary or imaginary) test cases. What all such (...) positions lack is a base from which to inform, criticize, or restructure our core methodological intuitions. To acquiesce in this is to deny that exemplary cases can serve the sort of warranting role required for intuitionism. This point is reinforced by a series of reasons for denying the warranting role of pre-analytic judgments of rationality. These reasons point the way toward an improved approach to meta-methodology. (shrink)

In recent years philosophers of science have turned away from positivist programs for explicating scientific rationality through detailed accounts of scientific procedure and turned toward large-scale accounts of scientific change. One important motivation for this was better fit with the history of science. Paying particular attention to the large-scale theories of Lakatos and Laudan I argue that the history of science is no better accommodated by the new large-scale theories than it was by the earlier positivist philosophies of science; both (...) are, in their different ways, parochial to our conception of rationality. I further argue that the goal of scientific methodology is not explaining the past but promoting good scientific practice, and on this the large-scale methodologies have no obvious a priori advantages over the positivist methodologies they have tried to replace. (shrink)

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...) a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified. (shrink)