[FOM] The Gold Standard

[Arnon Avron]

On Sun, Feb 19, 2006 at 05:47:26PM -0500, Harvey Friedman wrote:
> On 2/19/06 10:43 AM, "Arnon Avron" <aa at tau.ac.il> wrote:
> 
> > On Sat, Feb 18, 2006 at 02:01:50AM -0500, Harvey Friedman wrote:
> > 
> >> ZFC + large large cardinals. Justification:
> >> "inconsistencies should be easy
> >> and not take long to find, like Kunen's for ZFC + j:V into V, and this
> >> hasn't happened yet over a 'long' period of time", and "go for it!"
> > 
> > Great. So from now on I recommend to accept and use NF. 
>> Justification: "inconsistencies should be easy
> > and not take long to find, like Kunen's for ZFC + j:V into V, 
>> and this > > hasn't happened yet over a 'long' period of time", 
>> and "go for it!"
> > 
> Just yet another argument against just one of the natural stopping 
> places in  the natural hierarchy (the level which essentially 
> represents not stopping).

Sorry. I was not giving any argument against anything. I was only 
drawing the logical conclusions of what you have written. 
According to what I understand about logic, if someone brings
some argument as the justification  of A, and the same argument  
applied word by word to B, than the same person (if he is a logican)
necessarily sees A and B as equally justified. Note that *I* did not
say whether I find NF justified or not (after all, we dont know nearly
enough about FOM to tell!). What is clear is that
in your posting *you* found it necessary to add some arguments 
to distiguish between the cases of NF and ZFC + j:V into V.
This *logically* means that *you* don't
find your own  justification of ZFC + j:V into V
as sufficient. Do you have a better one? (I hope it is not going 
to be: the original justification augmented with the thesis that
there are no good reasons to reject ZFC + j:V into V, while
there are such reasons for any other system to which
the original justification applies, but you don't like them).


Arnon Avron