FOM: Re: Seismology

Michael Thayer mthayer at
Thu Nov 20 12:27:22 EST 1997

Joe Shipman asks:

>Has there EVER been an example of a principle of
>mathematical reasoning used widely for many decades being refuted?

Probably not, but if you say "discarded" rather than "refuted" 19th century
analysis might be said to have done that with much of the "reasonings" used
from the time of Newton/Leibnitz on....

On the point of inconsistency of ZF, I would agree with Lou that if there is
a culprit it would be powerset, not replacement: In the original Zermelo
formulation, replacement says that SOME subsets of a previously constructed
set exist, while powerset says one of two things: either ALL the subsets
exist (and are members of the powerset) or some of the members of powerset
DONT exist.

I suspect that one concept which belongs on Steve's list of "basic concepts"
is existence.

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