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From: tjt@kobold.UUCP
Newsgroups: net.religion
Subject: Re: Truth in Philosophy of Science
Message-ID: <251@kobold.UUCP>
Date: Wed, 11-Jan-84 22:35:54 EST
Article-I.D.: kobold.251
Posted: Wed Jan 11 22:35:54 1984
Date-Received: Fri, 13-Jan-84 05:27:21 EST
References: mit-eddi.1137 <214@wxlvax.UUCP> <1161@mit-eddie.UUCP>
Organization: Masscomp, Westford, MA
Lines: 59

Greg Skinner (mit-eddie!gds) says:

    However, a statement such as 2 + 2 = 4 is not true by virtue of the
    symbology itself, but by the physical equivalents of the symbols.
    The statement 1 + 1 = 3 would not be false if one could logically
    construct a world in which a whole theory of numbers followed from this,
    but in our world such a statement has no physical equivalent.

This closely echos Alan Wexelblat (wxlvax!awex):

    One interesting note is that geometry is the only thing that is 
    *a posterioir analytically* true, in that it is ture by virtue of the
    way that the world if, but we can still construct proofs about it.  This
    is the case for both Euclidean and non-Euclidean geometries; the only
    difference is what you assume the universe to be like. 

I would take a third approach and claim that in the context of a
*mathematical theory*, making 2 + 2 = 4 or 1 + 1 = 3 are equally valid,
as are both Euclidean and non-Euclidean geometries.  However, theories
where 2 + 2 = 4 are more interesting than those where 1 + 1 = 3 because
they appear to more closely model our own world.  The *theory* is is
always "a priori analytically* true while a *model* is always *a
posteriori synthetically* true.  A theory is a game that can do
whatever you want it to, but a model maps concepts of the theory onto
objects and actions in the real world, and must agree with experimental
evidence.

Therefore, when a theory fails to model new experimental evidence, the
theory has to be revised.  Note that any *new* theory is constrained to
model the old evidence as well as the new evidence.

Occasionally, a new theory and a new model will change the
interpretation of old evidence.  This is acceptable because of some
uncertainty in any evidence.  For example, the negative resistance of a
tunnel diode was apparent in some earlier devices, but was ignored as
noise since the negative resistance was not very pronounced *and* the
existing theory did not predict that behavior.  Later on, the negative
resistance was recognized since the theory was extended to include
negative resistance (I'm sure to have made some blunders here -- I'm a
computer scientist, not a solid state physicist).

Going back to Greg's earlier article:

    Ancient man had evidence that the sun rose and shined every day, until
    the first eclipse came, then the evidence was false.

In this case, the *theory* is that the sun rose and shined every day.
The *evidence* for this is (presumably) that it always had in the past,
or more precisely: it came up yesterday, and the day before, and the
day before that and ...  If you number the days this becomes: the sun
rose and shined on day 1 and on day 2, day 3, ...  After the eclipse on
day N, the preceding evidence is still true: the sun rose and shined on
days 1 to N-1, but not on day N (or at least, something peculiar
happened on day N).  This requires a more complicated theory to model
the existing evidence, but hardly invalidates that evidence, and (in
this case) only partially invalidates the theory.
-- 
	Tom Teixeira,  Massachusetts Computer Corporation.  Westford MA
	...!{ihnp4,harpo,decvax}!masscomp!tjt   (617) 692-6200 x275