Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Keith Hossack and Georges Rey

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

10680	The theory of the transfinite needs the ordinal numbers [Hossack]
	Full Idea: The theory of the transfinite needs the ordinal numbers.
	From: Keith Hossack (Plurals and Complexes [2000], 8)

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10684	I take the real numbers to be just lengths [Hossack]
	Full Idea: I take the real numbers to be just lengths.
	From: Keith Hossack (Plurals and Complexes [2000], 9)
	A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity

23626	Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
	Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1)
	A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm.