Francis Bacon (15611626) wrote that good scientists are not like ants (mindlessly gathering data) or spiders (spinning empty theories). Instead, they are like bees, transforming nature into a nourishing product. This essay examines Bacon's "middle way" by elucidating the means he proposes to turn experience and insight into understanding. The human intellect relies on "machines" to extend perceptual limits, check impulsive imaginations, and reveal nature's latent causal structure, or "forms." This constructivist interpretation is not intended to supplant inductivist or experimentalist (...) interpretations, but is designed to explicate Bacon's account of science as a collaborative project with several interdependent methodological goals. (shrink)

The instability inherent in the historical inventory of mathematical objects challenges philosophers. Naturalism suggests we can construct enduring answers to ontological questions through an investigation of the processes whereby mathematical objects come into existence. Patterns of historical development suggest that mathematical objects undergo an intelligible process of reification in tandem with notational innovation. Investigating changes in mathematical languages is a necessary first step towards a viable ontology. For this reason, scholars should not modernize historical texts without caution, as the use (...) of anachronistic notation tends to impede, rather than enhance, our ability to recognize the emergent nature of mathematical objects. (shrink)

When rare documents are collected and reprinted as Opere, Oeuvres, and Gesammelte Schriften, new diagrams are introduced. For the most part the new are faithful reproductions of the old. Sometimes, however, editors correct or simplify diagrams. Thus, before one writes, “so-and-so represents the area to be squared by seven parallelograms,” the more meticulous among us make a before-and-after comparison to insure that the “So-and-so” dividing the space is in fact the mathematician under scrutiny, and not some subsequent draftsman. This underlines (...) the importance of the facsimile edition. (shrink)