4 found
Madeline M. Muntersbjorn [4]Madeline Mary Muntersbjorn [1]
  1. Representational innovation and mathematical ontology.Madeline M. Muntersbjorn - 2003 - Synthese 134 (1-2):159 - 180.
  2. Francis Bacon's philosophy of science: Machina intellectus and forma indita.Madeline M. Muntersbjorn - 2003 - Philosophy of Science 70 (5):1137-1148.
    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 (...)
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  3. Naturalism, notation, and the metaphysics of mathematics.Madeline M. Muntersbjorn - 1999 - Philosophia Mathematica 7 (2):178-199.
    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 (...)
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    The Quadrature of Parabolic Segments 1635–1658: A Response to Herbert Breger.Madeline M. Muntersbjorn - 2000 - In Emily Grosholz & Herbert Breger (eds.), The growth of mathematical knowledge. Boston: Kluwer Academic Publishers. pp. 231--256.
    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 (...)
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