From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.physics
Subject: Re: Axiom of Physics
Date: 30 Aug 92 04:57:10 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Organization: SCRI, Florida State University

Ah, after killing off a few hundred threads after my return from a 
week in Colorado enjoying some hikes up in the Maroon Bells while 
the new students at FSU learn not to park in faculty spaces, another 
nice on appears.... 

In article <1992Aug26.174922.6115@pellns.alleg.edu> frisinv@alleg.edu writes:
>A friend and I have a small disagreement about the existance of an axiom  
>of physics. She claims that all assumptions in physics are made from  
>empirical evidence and therefore there are no axioms in physics. I  

This is, of course, the old induction/deduction debate started 
(popularized?) by Karl Popper.  Popper is, of course, wrong.  ;-) 

It is not the case that all assumptions in physics come from empirical 
origins, although most of the ones encountered in basic physics would 
appear to be of inductive origin.  What is the case is that our 
*acceptance* of such axioms is based on empirical evidence.  My 
distinction between mathmatics and physics is that both build up 
logical systems based on axioms and theorems, but then physics 
proceeds to ignore all of those that do not produce testable 
results in accord with experiment. 

(I like the point that the biggest axiom is that the process I just 
described, of a mathematical description of nature, is valid.  There 

Now the question of to-what-extent-were-my-axioms-guided-by-experience 
is a hard one and one discussed in the history and philosophy of science, 
and *is* significant.  For example, I think a lot of the trouble 
people have with wave-particle duality is because of the load of 
experiences brought in with those words, just as the distinction 
between weight and mass is troublesome for new students.  But this is 
not strictly germane to the question at hand. 

There is another important difference, and that is in the use of 
approximations and "model building".  Here one does not follow a 
strictly deductive proof to get from axioms to testable results, 
but the result is still an edifice that will be accepted or rejected 
based on experimental fact.  However, in this case the model, but 
not the axioms themselves, might be all that can be rejected. 

>maintain that the conservation of mass/energy is an axiom. Here is my  
>argument: an axiom must be based on evidence. Euclid didn't just say  
>parallel lines don't intersect, he saw evidence that they didn't and then  
>stated the postulate. 

Ah, but then he proceded to abstract the postulate and built up a 
system of knowledge completely decoupled from the real world.  After 
all, parallel lines on the earth do intersect, and triangles on the 
earth have angles that add up to more than 180 degrees.  The 
curvature of the earth was known to the Greeks, but fortunately 
Euclid ignored it and left it for later mathematicians. 

A better example than the one discussed in this thread, the conservation 
laws, might be the axioms of QCD.  Here one states that the interaction 
between quarks is governed by the generators of the mathematical "group" 
known as SU(3), with an empirical coupling constant, and procede to 
derive or compute the properties of protons etc etc and compare them 
to experiment.  This is a very abstract starting point.  It is related 
to the earlier inductive insight into use of the SU(3) group for 
the description of patterns in the masses of particles, but only in 
a mostly accidental way.  

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)