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Single Idea 9146

[catalogued under 18. Thought / E. Abstraction / 8. Abstractionism Critique]

Full Idea

In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}!

Gist of Idea

After abstraction all numbers seem identical, so only 0 and 1 will exist!

Source

Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1)

Book Reference

-: 'Journal of Philosophy' [-], p.4


A Reaction

Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets.