(Math, science, ?)

Axiomathes 19 (3):61-86 (2009)
In science as in mathematics, it is popular to know little and resent much about category theory. Less well known is how common it is to know little and like much about set theory. The set theory of almost all scientists, and even the average mathematician, is fundamentally different from the formal set theory that is contrasted against category theory. The latter two are often opposed by saying one emphasizes Substance, the other Form. However, in all known systems of mathematics throughout history, mathematicians have moved fluidly between ideas conceived of as thing-like, property-like, and process-like. On the other hand one way to advance science is to better distinguish between thing, property, and process. All this constitutes a distracting background for those interested in, or distressed by, the possible application of category theory to science, and to mathematics as well.
Keywords Category theory  Elements  Evolution  Foundations  Neuropsychology  Number  Numerosity  Process  Property  Set theory
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DOI 10.1023/A:1013738831686
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References found in this work BETA
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
M. Bunge (1979). The Furniture of the World. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 10 (2):405-407.
Jean-Pierre Marquis (2006). Categories, Sets and the Nature of Mathematical Entities. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer 181--192.

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