axioms
Tom Givon
tgivon at uoregon.edu
Sat Jan 3 18:37:47 UTC 2009
RE: Bischoff:
Maybe it would be useful to point out that "axioms" is not really a
useful notion in empirical science, but rather belongs to the domain of
logic. It is of course true that formal linguists may have left some
with the impression that "axioms" can be imported into linguistics, but
this simply points out to a profound misunderstanding about what is or
isn't "empirical". The closest one comes in science to "axioms" are
facts that have been around for such a long time that, by general
agreement, we take them for granted, i.e. presuppose them at the start
of any new investigation. But their logical status is still not that of
"axioms", since initially they had to be discovered and defended on
empirical grounds. Axiomatic systems tend to be, by definition, closed
and and internally consistent. According to both Russell ('theory of
types') and Goedel, they are thus incomplete. Science, on the other
hand, is never closed, but rather an open-ended system that keeps
changing with new facts & new insights. Happy New Year, TG
More information about the Funknet
mailing list