I argue that Copernicus accepted the reality of celestial spheres on the grounds that the equant problem is unintelligible except as a problem about real spheres. The same considerations point to a number of generally unnoticed liabilities of Copernican astronomy, especially gaps between the spheres, and the failure of some spheres to obey the principle that their natural motion is to rotate. These difficulties may be additional reasons for Copernicus's reluctance to publish, and also stand in the way of strict (...) realism as applied to De Revolutionibus, although a realistic astronomy may be envisioned as a goal for Copernicus's research program. (shrink)

Descartes' image of the tree of knowledge from the preface to the French edition of the Principles of Philosophy is usually taken to represent Descartes' break with the past and with the fragmentation of knowledge of the schools. But if Descartes' tree of knowledge is analyzed in its proper context, another interpretation emerges. A series of contrasts with other classifications of knowledge from the seventeenth and eighteenth centuries raises some puzzles: claims of originality and radical break from the past do (...) not seem warranted. Further contrasts with Descartes' unpublished writings and with school doctrines lead to the ironic conclusion that, in the famous passage, Descartes is attempting to appeal to conventional wisdom and trying to avoid sounding novel. (shrink)