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

[Harvey Friedman]

I don't know. But my point is that you can't draw the line at
arithmetical because for any T you can consider "every arithmetical
sentence provable in T is true".

Harvey Friedman

On Fri, Dec 27, 2019 at 1:37 PM Joe Shipman <joeshipman at aol.com> wrote:
>
> Well, OK, but that implies Con(ZF) and thus gives new arithmetical facts as well. It sounds like you are asserting that we know Con(ZF). How high are you willing to go before you are uncomfortable stating that the corresponding consistency statement is a “known fact”?
>
> — JS
>
> Sent from my iPhone
>
> > On Dec 27, 2019, at 1:10 PM, Harvey Friedman <hmflogic at gmail.com> wrote:
> >
> > What about "every arithmetical sentence provable in ZF is true"?
> >
> > Harvey Friedman
> >
> >> On Fri, Dec 27, 2019 at 1:07 PM Timothy Y. Chow
> >> <tchow at math.princeton.edu> wrote:
> >>
> >> Joe Shipman wrote:
> >>> At the moment, there aren’t any propositions other than arithmetical
> >>> consequences of ZF that I would be willing to assert are “mathematical
> >>> facts”, but I’d be happy to have someone argue either that some such are
> >>> not facts, or that some non-arithmetical statements are matters of fact.
> >>
> >> I wonder if someone familiar with Feferman's account of a "definite
> >> mathematical question" can give an explicit example of a non-arithmetical
> >> statement that Feferman would have considered a "definite mathematical
> >> question"?
> >>
> >> Tim_______________________________________________
> >> FOM mailing list
> >> FOM at cs.nyu.edu
> >> https://cs.nyu.edu/mailman/listinfo/fom
>