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 .)
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
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*...