Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'The Philosophy of Logic' and 'Plurals and Complexes'

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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 / i. Cardinal infinity

18200	Very large sets should be studied in an 'if-then' spirit [Putnam]
	Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Quine says the large sets should be regarded as 'uninterpreted'.