Virgil
Posts:
8,833
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 23, 2013 6:29 PM


In article <a8a6b8ba562a40408d3fa2fae56aeec8@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> Numbers, contrary to material atoms, are ideas.
Most of what we think of as being atoms are only ideas about what we think atoms may act like.
>Ideas that nobody can have or > think are not ideas.
Ideas that WM is unable to think are quite often very good ideas.
> > > >> > We already Know that you reject the axioms of ZFC, > > > > > > > >> Not even that. I reject only the erroneous interpretation of the axiom of > >> infinity. For every set A there exists the set {A} is obviously true > > > > Since AoI is part of ZFC, you reject ZFC. > > > AoI is ok. Only the common erroneous interpretation of "set" as form of > actual existence is mistaken.
Sets exist only as ideas, and any idea that acquires the properties of a set is a setidea, at least to those capable of thinking all those lovely mathematical thoughts that WM is incapable of thinking. > > > > You claim the real numbers can't be wellordered because > of "real world" conditions. > > Do you believe Euclidean Geometry is true in the "real world"? > > That has not yet been finally decided for the universe as a whole. In small > parts of the world, like my office, it is true without doubt. It may be true in WM's office TO WITHIN EXPERIMENTAL ERROR, but to claim it absolutely true is to claim, as WM is in the habit of doing, what he cannot prove and therefore does not know for sure. 

