From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Newsgroups: sci.physics
Subject: Re: Axiom of Physics
Date: 2 Sep 92 21:18:15 GMT
Organization: University of Virginia

In article <1224@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>In article <1992Aug29.165242.20599@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>>In article <1217@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>>>Whether you can have non-falsifiable statements in science is a function of
>>>which philosophy of science you subscribe to. If every scientifically
>>>meaningful statement is supposed to be falsifiable, then there are no axioms.
>>
>>     Why?  I don't see how an axiomatic basis prevents falsifiability.
>How, for example does one possibly falsify the following (from Glimm and
>Jaffe):
>
>The pure states of a quantum mechanical system are rays in a Hilbert space H
>(i.e. unit vectors with an arbitrary phase).

    Agreed.  However, the use of such mechanisms usually implies 
    consequences.  These are then falsifiable.

    Also, a specific axiom that is not falsifiable in isolation certainly
    does not preclude the existence of other axioms that are falsifiable in
    isolation (e.g. the oft used lightspeed constancy across all inertial
    frames is certainly falsifiable in isolation).

    Of course if one defines an axiom as a statement that is not 
    falsifiable, then I suppose you are right.  However, my conception of
    a set of axioms are the not necessarily unique (probably not necessarily
    finite as well) assumptions that may be made to define a given theory.  
    Note that by this definition we may often have an assumed equation
    as an axiom of a system, for instance.

>>     Also, presumably the theory derivable (not necessarily actually derived)
>>     from an axiomatic basis (physically-based or not) is falsifiable.
>
>But the hard core instrumentalist will not let you use any such axioms. Most
>scientists are tolerant enough to include some non-falsifiable stuff, such as
>the above postulate.


     Hard core instrumentalists will have a very difficult time 
     talking about reality if they assume nothing.  After all, there
     is absolutely no reason to think a priori that there is any 
     order whatsoever in the universe and that one reading on the dial
     (if we assume that there is a dial, and not just nothing) is
     related in any special manner to any other reading on that dial or
     any other dial.  There are a bunch of assumptions
     (that I conceive as axioms) involved in just taking readings
     and searching for order in the readings.

     It also seems to me that from an epistemological point of view, it
     matters little whether the hard core experimentalists care for 
     my foundation on axioms or not, as long as the consequences of 
     such musings are falsifiable.

     It also seems to me that science must contain some non-falsifiable
     stuff (if only on the common linguistic level) in order to be
     able to communicate.

                               dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926