Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Paul J. Cohen and David S. Oderberg

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

12238	The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg]
	Full Idea: The Aristotelian account of numbers is that their existence depends on the existence of things that are not numbers, ..since numbers are abstractions from the existence of things.
	From: David S. Oderberg (Real Essentialism [2007], 1.2)
	A reaction: This is the deeply unfashionable view to which I am attached. The problem is the status of transfinite, complex etc numbers. They look like fictions to me.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

14248	We could accept the integers as primitive, then use sets to construct the rest [Cohen]
	Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
	From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
	A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.