David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Michael Kary & Martin Mahner (2002). How Would You Know If You Synthesized a Thinking Thing? Minds and Machines 12 (1):61-86.
Elaine Landry & Jean-Pierre Marquis (2005). Categories in Context: Historical, Foundational, and Philosophical. Philosophia Mathematica 13 (1):1-43.
F. William Lawvere (2003). Foundations and Applications: Axiomatization and Education. Bulletin of Symbolic Logic 9 (2):213-224.
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