[FOM] Naturality of Con(ZFC)

Vaughan Pratt pratt at cs.stanford.edu
Thu Jan 17 23:43:01 EST 2013

(6) Somewhere there has to be a non sequitur in the following.

On 1/15/2013 10:07 AM, MartDowd at aol.com wrote:
> This posting is in response to Vaughn Pratt's comment:
>  > Meanwhile I will continue to ponder the possibility you raise that
>  > consistency of ZFC is unnatural.

Martin then advances evidence (5) for the naturality of Con(ZFC).

My comment above, which I'll number (4), was in response to Harvey's (3) 
"Con(ZFC) is not a natural principle when thinking about rainbows, 
horizons, and beauty."  This in turn was Harvey's response to my (2) 
"I'm not sure I understand your conjecture, Harvey.  Which of its 
conditions are not met by the principle Con(ZFC)?"   Harvey's conjecture 
was (1) "In ANY informal conceptual environment, we can formulate 
principles that are natural and sensitive and plausible in that 
environment, which are mutually interpretable with ZFC, and weak 
andstrong variants of ZFC."

Since my (2) was based on my long-held *unconditional* acceptance of the 
naturality of Con(ZFC), which (5) would appear to greatly strengthen, my 
naive analysis is that the non sequitur happened at (3).  But perhaps 
something deeper is going on here that I've overlooked, maybe a biblical 
reference (aleph), or an in-joke (omega), or something else.

Vaughan Pratt

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