[FOM] f.o.m. literature wanted

Dean Buckner Dean.Buckner at btopenworld.com
Mon May 19 14:49:22 EDT 2003

>>There appears to be a minority of philosophers of mathematics and
>>philosophical logicians who properly understand the issues and
>>nonissues regarding first order/second order axiomatizations for
>I'm with the majority.

>I'm sorry but I don't have the time to help you with this issue
>unless I see some very clear explicit way to do so. I didn't see any
>such clear opportunity for doing this by reading your posting.

Well, what is the one most important issue that you feel philosophers (if
they are the culprits) have misunderstood?  I don't actually have a problem
with quantifying over properties.  I have a problem, as I said before, with
carving "Socrates is bald" into two bits ("Socrates", "is bald") plus a
relation between the referents of the two parts.

>There is no difficulty, as there is a huge literature on various
>logics" in between first and second order "logic". If you are
>familiar with this literature, then the efficiency of communication
>would greatly increase.

If you or any other competent FOM member could suggest some sample
literature, I'll read it.  Preferably something available over the internet,
or via online journal, or in collection that is in print, or in book that is
in print.

Or in book/collection/offprint owned by FOM member who is prepared to sell
to me.  I will pay good prices (within reason).

>By thinking through what an interpretation is, you will clearly see
>the great power of f.o.m. in clarifying and addressing a huge range
>of issues including the ones that you raise. Do you agree with this?

Perhaps when I understand what an interpretation is!  I read some papers by
Feferman on his site, they suggest the notion is more difficult than your
previous summaries.

I read your VIGRE Foundations lecture, but the idea appears to be introduced
on p.10 without ceremony, where you write

"A relational structure consists of a non-empty set D called the domain,
together with interpretations of all constant, function, and relation

Grateful for any help.



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