Steve Landsburg writes about the ontological status of numbers. Am I the only one who senses a tension between his arguments?(*)
Paul Volcker writes about what should be done, but is there really "a core of common understanding that should provide a base for constructive negotiation"?
Assume that this anomaly due to leveraged ETFs really exists; Do you find it interesting that one way to trade it would be to buy/sell leveraged ETFs?
Finally, assuming that this anomaly is also real, would the most plausible explanation invoke the space aliens?
(*) He writes "a 'number' is that which all sets equinumerous to a given set have in common" but later "suggests that numbers are a more natural starting point than sets are".
6 comments:
I don't see much hope of improving on his Platonic notion that numbers "are just out there," though I'm not sure that implies some sort of existence beyond our minds.
Eventually we always confront the central dilemma of the great philosopher WBC, who noted:
"that it depends on what the meaning of "is" is."
WBC = WJC ?
>> I don't see much hope of improving on his Platonic notion
I think Brouwer's introduction of natural numbers ultimately makes the most sense. Math is basically an effort to describe our conscious experience and mathematical 'objects' themselves are elements of our experience.
But this is not my problem with S.L.
I just noticed that first he introduces numbers as properties of sets (btw sets of what?) and later emphasizes that numbers are actually more fundamental than sets.
People who understand that we really only know enough about the mind-body problem to recognize that it exists, somehow still think it's meaningful to pontificate about the ontology of numbers. To me, the ontology of numbers is a subset of the mind-body problem.
Lee - I don't think publishing one's struggles to understand necessarily counts as pontificating.
WBC = WJC ?
Doh!
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