[FOM] Arithmetical soundness of ZFC

[Harvey Friedman]

I am casually following the thread on arithmetical soundness of ZFC,  
but feel that it has yet to move into productive channels.

Let me suggest the following question for discussion:

WE ALL KNOW WHAT A PROOF OF THE INCONSISTENCY OF ZFC WOULD LOOK LIKE:  
A PROOF IN ZFC OF 1 = 0.

(As a student, I had a number of these 'proofs', sometimes convincing  
enough to write down, and in one case, enough to give the family  
lawyer a copy in order to be notarized and preserved).

BUT WHAT WOULD A PROOF OF THE NON ARITHMETICAL SOUNDNESS OF ZFC LOOK  
LIKE?

More vaguely,

WHAT WOULD EVIDENCE OF THE NON ARITHMETICAL SOUNDNESS OF ZFC LOOK LIKE?

We might get somewhere if we ponder this question.

Harvey Friedman