FOM: Russell01 meeting abstract

[Harvey Friedman]

>I am going to be at the same conference on Russell in Munich
>shortly, but I thought I'd raise a question for discussion
>that arises from Harvey Friedman's abstract.
>I'm inclined to agree with his conclusions, but nevertheless
>there is something that still bothers me.  Harvey writes:
>
> We Conjecture that all intellectually sensible consistent formal systems
> are formally interpretable in current set theory (with large cardinals). It
> should follow that all intellectually sensible consistent formal systems
> are synonymous with a fragment of current set theory (with large
> cardinals).
>
>Now, isn't it true that we tend to define "intellectually sensible"
>as "interpretable in current set theory"?  If so, there seems
>to be a circularity in the argument.

I mean this in a very broad sense. Something like "based on some readily
communicable idea, whatever its ultimate value or quality or coherence".

E.g., NF is easily ntellectually sensible in this sense.

The talk is like my usual stuff. It is not meant to be philosophy, but
rather philosophically relevant productive foundations of mathematics.
Philosophically unclear concepts like "intellectually sensible" become
somewhat clarified by the ensuing conjectures and theorems.

I will post on this after the meeting.