Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Carrie Jenkins and Michael Potter

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2 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

10712	If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
	Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets.
	From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8)

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

17730	Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
	Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness.
	From: Carrie Jenkins (Grounding Concepts [2008], 5.3)
	A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it.