FOM: second-order logic is a sterile myth

Pat Hayes phayes at
Wed Mar 24 12:03:41 EST 1999

>John Mayberry 23 Mar 1999 16:00:50 writes:
> > Steve Simpson really ought to cease his incessant repetition of the
> > mantra "Second order logic isn't logic because it lacks rules of
> > inference".
>Oh, but it's a wonderful mantra.  I like it a lot.  I plan to repeat
>it at every opportunity.  I recommend that other people help me by
>doing the same.

As the above suggests, and as is amply confirmed by a quick perusal of the
philosophical content available at his web-site, Steve Simpson sees his
work in political/religious terms as much as mathematical. He has an
agenda: to defend the integrity of mathematics against the dark forces of
postmoderism, especially those infidels who misuse Gödel's name.

I sympathise with this concern to preserve intellectual values against this
evil tide, but he is on the mainland. After years spent trying to defend
the intellectual integrity of AI, I find Steve's worries rather amusing. To
find out what the storms are really like, try living on a small volcanic
island which has only recently emerged from the ocean. The foundations of
mathematics may not reach to the Hilbertian bedrock of the universe, but
they are a damn sight stronger than almost anyone else's. Steve should
relax a little and not get so strident: he needn't feel so threatened. A
discussion about what 'first-order expressible' means could be conducted in
a civilized way, without thinking that giving up a single inch will risk
the dissolution of his monastery.

Pat Hayes

PS. For the record, I entirely agree with Randall Holmes posting of 23 Mar 99.

IHMC, University of West Florida		(850)434 8903   home
11000 University Parkway			(850)474 2091   office
Pensacola,  FL 32514			(850)474 3023   fax
phayes at

More information about the FOM mailing list