David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
|Through your library||Configure|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. Philosophia Mathematica 19 (3):227-254.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Carlos Pedro dos Santos Gonçalves & Maria Odete Madeira, A Systems Theoretical Formal Logic for Category Theory.
Colin McLarty (1990). The Uses and Abuses of the History of Topos Theory. British Journal for the Philosophy of Science 41 (3):351-375.
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
Makmiller Pedroso (2009). On Three Arguments Against Categorical Structuralism. Synthese 170 (1):21 - 31.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
Added to index2009-04-06
Total downloads13 ( #100,585 of 1,088,810 )
Recent downloads (6 months)0
How can I increase my downloads?