🚀 go-pugleaf

Apologies for my mistake about ZF vs ZF- , and the extra noise level it
intoduced into the discussion.  Incidentally, though a quick check shows that
ZF *does* include foundation as a usual convention, it is *not* quite universal,
(though I doubt this would help moderate the bullying tone of some who insisted
on universality).     An exception is 
 
"Introduction to Set Theory", Hrbacek & Jech; 1st edition  11.1; 2nd edn  12.1;
in both of which they give the standard axioms *without* foundation, stating it
to be ZF.  In fact they do not seem to mention foundation in the whole book.


Thanks to those who contributed to the discussion; especially...

Randall Holmes - for a simple and excellent account of the failure of 
             extensionality of my sets A & B (I liked the expression "hypnotized
by notation"; and ditto for the hierarchy induced by AFA.  I learnt a lot
from these posts; thanks indeed.

Torkel Franzen - for typically down-to-earth remarks about the silliness of
        taking various postures of principle about these matters, a sensible
view (though perhaps a little too formalist for some tastes).

Vaughn Pratt - for a sprightly and provocative series of posts that kept the
     ball rolling nicely (if randomly), I liked "inflammatory heresy". Also
for frank apologies and admissions of error where appropriate. (It's a pity
this admissory tendency isn't more widespread on the net.)

David Gudeman - for continuing to attempt clarification of his intuitive ideas
      in the face of a barrage of opposition.

Thanks all; it was a lot of fun.
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              Bill Taylor              wft@math.canterbury.ac.nz
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 Galaxies - results of chaotic amplification of quantum events in the big bang.
 Free will- the result of chaotic amplification of quantum events in the brain.
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