Combining Philosophers

Ideas for J Fodor / E Lepore, Nicholas of Autrecourt and Kit Fine

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

10573	Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
	Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1.
	From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
	A reaction: See Idea 10572.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

10575	Why should a Dedekind cut correspond to a number? [Fine,K]
	Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut?
	From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero

10574	Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
	Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say.
	From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)