axioms

[Steen, G.J.]

Dear funknetters,

Karl Popper would not agree with Tom Givon that axioms are not a useful notion in empirical science. In his The Logic of Scientific Discovery, he discusses how axioms can be used to construct and re-construct scientific theories that can be tested (1977: 71-75 and elsewhere). Popper thus makes an attempt to make the notion of axiom productive for empirical science in a way that has been rather influential in subsequent philosophy of science. You do not have to agree with him, but may learn a lot from his analysis.

Best,

Gerard Steen

Professor of Language Use and Cognition
Director, Language, Cognition, Communication program
Faculty of Arts, 11A-35
Department of Language and Communication
VU University Amsterdam
De Boelelaan 1105
1081 HV Amsterdam

T: ++31-20-5986433
F: ++31-20-5986500

http://www.let.vu.nl/staf/gj.steen/
________________________________________
From: funknet-bounces at mailman.rice.edu [funknet-bounces at mailman.rice.edu] On Behalf Of Tom Givon [tgivon at uoregon.edu]
Sent: 03 January 2009 19:37
To: funknet
Subject: [FUNKNET] axioms

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