At 07:58 18/11/03 -0800, Norman Samish wrote:
>Gentlemen,
>Thanks for the opinions. You have convinced me that at least the empty
>set MUST exist, and "The whole of mathematics can, in principle, be
>derived from the properties of the empty set,
>Ø." (From
><http://www.hedweb.com/nihilism/nihilf01.htm>http://www.hedweb.com/nihilism/nihilf01.htm
>.)
I don't see why the empty set MUST exist. It seems there is a confusion
here between "no things", and "nothing", or if you prefer between
and
{}
Besides, I don't see how the whole of math can be generated from
the empty set. You need the empty set + a mathematician (or a least
a formal machinery, or a theory).
BTW, in "infinity and the mind" Rudy Rucker gives the best (imo) popular
account of the "schema of reflexion", a powerful axiom (or theorem
according to the chosen formal set theory) for generating almost
everything from almost nothing ... (it was an important axiom in my older
"machine psychology", but I succeed to bypass it since I use the Solovay
logic G and G*...
Bruno
Received on Wed Nov 19 2003 - 10:21:46 PST