axioms

[Tom Givon]

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