[FOM] Paradoxes and Platonism

[Martin Davis]

It is alleged that the Russell paradox of the set 
of all sets not belonging to themselves is a 
problem for Platonists. The most famous Platonist 
of them all, Gödel, pointed out that the sets 
that occur in mathematics are those built up from 
the empty set by iterating the power set 
operation indefinitely (so-called iterative 
notion of set - going back to Zermelo's 1930 
paper).  Since none of these sets are members of 
themselves, what the paradox tells us is that there is no universal set.



                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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                        http://www.eipye.com