[FOM] Fact and opinion in F.O.M.

[Hendrik Boom]

On Thu, Dec 26, 2019 at 04:58:36PM -0500, Timothy Y. Chow wrote:
> Joe Shipman wrote:
> 
> > (1) all the arithmetical consequences of all the axioms that have ever
> > been proposed appear to be compatible with each other.
> > (2) this is completely untrue for statements of higher type.
> 
> Okay, how about the following suggested definition of "fact"?
> 
>   (*) A mathematical statement X is a fact if no axiom that has ever
>       been seriously proposed (or ever will be seriously proposed)
>       implies not-X.

The constructive development of synthetic differential geometry is 
actually inconsistent with the principle of excluded middle.

Would this require we have to treat excluded middle as an opinion 
rather than a fact?

-- hendrik