The purpose of this study is to gain a better understanding of the role of abstraction and idealization in Galileo’s scientific inquiries into the law of free falling motion, and their importance in the history of science. Because there is no consensus on the use of the terms “abstraction” and “idealization” in the literature, it is necessary to distinguish between them at the outset. This paper will argue for the importance of abstraction and idealization in physics and the theories and (...) laws of physics constructed with abduction from observations and that these theoretical laws of physics should be tested with deduction and induction thorough quasi-idealized entities rather than empirical results in the everyday world. Galileo’s work is linked to thought experiments in natural science. Galileo, using thought experiments based on idealization, persuaded others that what had been proven true for a ball on an inclined plane would be equally true for a ball falling through a vacuum. (shrink)

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested (...) in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. (shrink)

This paper surveys three controversial new directions in research about the nature of science and briefly summarizes both the intellectual and sociological impact of this work. A bibliographic introduction to the major literature is provided and some fruitful directions for future research are proposed. Philosophers of science are also exhorted to perform 'community service' by correcting misunderstandings of the methods of science fostered by these new approaches.

This paper introduces coupled clustering—a novel computational framework for detecting corresponding themes in unstructured data. Gaining its inspiration from the structure mapping theory, our framework utilizes unsupervised statistical learning tools for automatic construction of aligned representations reflecting the context of the particular mapping being made. The coupled clustering algorithm is demonstrated and evaluated through detecting conceptual correspondences in textual corpora. In its current phase, the method is primarily oriented towards context-dependent feature-based similarity. However, it is preliminary demonstrated how it could (...) be utilized for identification of relational commonalities, as well. (shrink)