Re: Mathematics Is Not a Science

From: Guy Hoelzer (hoelzer_at_unr.edu)
Date: 02/26/05 

Date: Fri, 25 Feb 2005 23:57:07 -0500 (EST)

in article cvnrl6$1vei$1@darwin.ediacara.org, John Edser at edser@tpg.com.au
wrote on 2/25/05 10:43 AM:

> Guy Hoelzer <hoelzer@unr.edu>
>>> JE:-
>>> It is possible to test something to
>>> to verification or refutation without
>>> having to even count. A prohibited
>>> empirical observation that requires the
>>> senses does require a rational proposition
>>> but it may not require counting to
>>> test it. e.g. the theory that I take a
>>> size 10 shoe is not verified if it does
>>> not fit but it stands refuted when a size
>>> 11 fits.
>
>> GH:-
>
>> This cannot possibly be a theory. It is a hypothesis, or a
> prediction,
>> which might or might not be derived from a theory.
>
> JE:-
> Hi Guy,
> You cannot have a prediction without
> a theory/hypothesis because a
> prediction has to be derived from
> something.

I agree, but if the underlying theory remains vague or implicit (e.g., the
source of gut feelings), then it is effectively absent for scientific
purposes.
 
> A hypothesis is not different in kind
> to a theory. The difference is a hypothesis
> only remains a part of a theory that can be
> verified/ non verified or refuted in its own
> right without compromising the theory it is
> a part of. An example is the hypothesis that
> evolution occurs in large jumps or via gradual
> changes. Either way evolution remains non
> refuted.

Hypothesis formation never refutes anything. However, we probably agree
that testing these hypotheses does not constitute testing of the general
proposition that evolution occurred.
 
>> GH:-
>> As I argued in the
>> snipped portion of my previous post, math plays a very important role
>> in the
>> theory side of science. So your reply failed to respond in any
>> meaningful way to my argument.
>
> JE:-
> Absolutely not. Theory/hypothesis building
> and testing is commonplace within ordinary
> life without any mathematics being required.

I didn't actually say that it was required. I agree that on rare occasion
science is accomplished without the involvement of math. My argument is
that math is a key component of the process of theorizing, particularly in
modeling, which has become an increasingly important aspect of theorizing
over the past couple of centuries.

> Science has formalised this process and
> usefully employed mathematics within it.

Indeed. So it seems that you agree math has taken on a key role in science,
but you are arguing that other sorts of tools might be equally effective.
Can you suggest alternatives that might relieve science from its current
reliance on math? Can you suggest an alternative that you think is better
than math? Do you think that science might be better off without math?
 
>>> JE:-
>>> Mathematics was not required to
>>> make these tests
>
>> GH:-
>> These tests do not constitute science if they occurred in a
>> theoretical vacuum.
>
> JE:-
> No theory vacuum existed. The theory
> supposed was quite simple: I am a
> living form. The hypothesis was:
> I have feet that can wear shoes.

I see nothing in your statement that could pass as a scientific theory,
which required IMHO the inclusion of internal justification. A theory must
also provide a framework for understanding some aspect of nature. A simple
assertion cannot be a theory.
 
>> GH:-
>> You just hid the important role of math in your assertion that
>> your prediction was based on a theory.
>
> JE:-
> Please explain where any mathematics was
> required in my simple example and where
> I could have possibly hidden it.
>
>>> JE:-
>>> (Note: most confuse
>>> non verification with refutation.)
>
>> GH
>> Not me.
>
> JE:-
> I am surprised because you have
> rejected Popper and therefore
> any need to provide a refutation
> for a theory. However, please define
> the difference between a non verification
> and a refutation for the benefit of
> sbe readers.

What you mean by "non verification", which is not a term I have ever seen
used before, is failure to support a hypothesis. Refutation is ultimate
proof that it is false. Once refuted, a hypothesis can never be validly
resurrected in the same form. And you are correct, I don't think that
refutation plays much of a role in science as it is practiced, and I don't
see how it could. You call my view blind, and I see your view as naïve.

Guy Hoelzer

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