[FOM] Existence of omega sequence and Platonism and NYC

Martin Davis martin at eipye.com
Thu Feb 23 20:24:56 EST 2006

Nicholas Weaver is surprised that anyone would regard the assumption of the 
existence of an omega sequence as a form of Platonism. His marks on paper 
are so clear in his mind that it's hard for him to imagine any thoughtful 
person not sharing that vision. This is a problem with this kind of 
discussion. Participants are so convinced of the correctness of their own 
view that they can only regard reticence to accede as obstinacy or worse.

Subscribers have the luxury to stop reading when a point of diminishing 
returns has been clearly reached. I as the moderator must read it all if 
only to be sure that I don't need to ask for modifications in the direction 
of civility. I try to be even-handed, but I do have my own views. I 
personally regard the marks on paper as a very fragile reed indeed, but on 
the other hand have convinced myself that I have a very clear understanding 
of P(N). Weaver presents as a virtue of his outlook that omega sequences 
fail to be unique in the way the set theoretic hierarchy allegedly is. 
Curiously Benaceraf has famously taken the same point as arguing that the 
notion of natural number is somehow incoherent. In fact the set theoretic 
hierarchy is only unique if the empty set is.  And that (relative) 
uniqueness could be thought to be a virtue.

In any case I will be in New York next week, and will have much less time 
to devote to FOM. So it would be nice if the present frenetic pace of FOM 
postings slow down a bit.


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
                          (Add 1 and get 0)

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