[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
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
(Add 1 and get 0)
http://www.eipye.com
More information about the FOM
mailing list