🚀 go-pugleaf

In <1992Aug27.173243.4672@klaava.Helsinki.FI> amnell@klaava.Helsinki.FI (Marko Amnell) writes:

>To me, your "naive and obvious" question "which reasonings are valid,
>and which not, when applied to the (one) Universe..." is not naive or
>obvious at all.  In fact, what you've done is to encapsulate most of
>epistemology! [...]
>I don't know how close I came to addressing your actual question.
>Marko Amnell

Not very close; but it's not your fault. My message was garbled, in
more than one way. (I didn't even manage to get my own telephone number
right. :-( ) I was probably conflating several different foundational
problems.

The point I meant to make was that whatever appearance of objectivity
there is in set theory results from there being a gentlemen's agreement
to treat the theory of sets in much the same way as Hilbert treated the 
Euclidean theory of points, lines, and planes (or tables, chairs, and
beer mugs); which politely ignores the fact that any definition of a
class of structured sets obviously depends upon having a concept of
"set". About the naive concept of set there is no agreement: not even
on what axiom system to use (e.g. ZFC is found irksome for formalizing
category theory), let alone on what sets really are. So metaphysical
argument is unavoidable (unless silence on a disputed point counts as
profound metaphysical wisdom :-) ).

It doesn't follow from this that set theory cannot help to clarify
metaphysical problems (so long as some help is allowed to go in the
other direction).

Incidentally, has Patrick Suppes worked out anything along these
lines? (I've been unable to track down his "A Set-Theoretical 
Philosophy of Science" - an exact reference would be appreciated, if
anyone can provide it.)
--
Angus H. Rodgers  (PhD student), | arodgers@dcs.qmw.ac.uk  
Dept. of Computer Science, Queen | [ +44 | 0 ] 71 975 5241   
Mary & Westfield College,  Mile  | This space has not been left blank,
End Rd., London E1 4NS, England  | intentionally or otherwise.