The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains...

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. What has not always been clear, however, is that the circle continued to serve Kepler as a central element in his astronomy after the discovery of the elliptical orbit of Mars. Moreover, the circle also functioned for Kepler in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology (...) to select the basic aspects. His basic set of polygons consisted of those figures that could be constructed using only a compass and a rule; the set of fundamental harmonies consisted of the consonances of the just intonation; and the traditional set of astrological aspects were enlarged by Kepler to include three new aspects in order to make the astrological set consistent with geometry and music. And as the circle served to unify these three areas, so also did it serve to supply the fundamental answers to astronomical problems well after the discovery of his new astronomy—a topic to be discussed in Part II of this paper. (shrink)

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

In this article, I address the epistemological role that geometry plays in Kepler’s Harmonices Mundi Libri V and argue that the framework he develops there is meant to address concerns regarding the confirmation of astronomical hypotheses, which are supported by comments in earlier works regarding empirical underdetermination. The geometrical epistemology that he constructs to combat these concerns in the Harmonices Mundi is introduced in Book I and then is extended to his theory of harmonic proportion in Book III, finally providing (...) the foundation for his derivation of the planetary motions in Book V. To argue for these claims, I begin by discussing Kepler’s concern with underdetermination in earlier works. Then I turn to the Harmonices Mundi and argue that Kepler seeks to provide a geometrical system that directly links the theorist with the world. Finally, I show how he applies this system to his astronomy via his harmonic theory. This account not only helps us to understand Kepler’s scientific methodology better but also sheds light on Kepler’s enthusiasm for the results of the Harmonices Mundi by showing how they provide an example of the successful application of his geometrical epistemology. (shrink)