FOM: second-order logic is a sterile myth

[Pat Hayes]

>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.

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