Cory, (01)
Edsger Dijkstra, one of the pioneers of computer science
(or as he preferred to say "computing science"), once made
a very important point: When asked what characteristic
is most important for being a good programmer, his answer
was "being able to express oneself clearly in one's own
native language." (02)
> My concern - one I would be most happy to be proved wrong
> about, is that we have a need to define concepts that are
> "hard" in FOL and that we may get tied up trying to invent
> a new logic or logic of logics. (03)
Whenever anybody suggests inventing a new logic to express
anything, I always tell them to start by expressing their
ideas as clearly as possible in their native language.
If they can't do that, they're not going to be able to
do anything useful in any formal language of any kind. (04)
> Is there sufficient foundation that we could start building
> a lattice of upper theories? (05)
There's a lot that can be done with just FOL (or CL which is
an extended version of the usual FOL). If you want a language
that can talk about language, then use FOL as a metalanguage
to talk about the object language, the concept of truth in that
language, and relate it to the model theory of that language.
That was Tarski's idea. If one metalanguage is not enough,
Tarski also introduced an infinite hierarchy of metalanguages. (06)
For a brief intro to Tarski's hierarchy and some applications
of the idea, see Section 4 of the following paper: (07)
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts (08)
John (09)
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