Re: Mathematics Is Not a Science

From: Guy Hoelzer (hoelzer_at_unr.edu)
Date: 03/02/05 

Date: Tue, 1 Mar 2005 22:25:38 -0500 (EST)

[snip]

>> GH:-
>> Hypothesis formation never refutes anything.
>
> JE:-
> This can easily be shown to be untrue
> using the hypothesis of shoe size.
> A hypothesis (like a theory) must have
> a thesis and an anti thesis where the
> anti thesis reverses cause and effect
> within the thesis and constitutes
> a refutation of that thesis. The
> proposition to be tested is the foot
> causes the shoe size (the shoe size does
> not cause the foot). Thus the antithesis
> of the hypothesis that I take a size 7 shoe
> is any other size shoe that actually fits.
> The reason is simple: two different
> sizes cannot fit the same sized
> foot unless the foot has to fit the
> shoe (the anti thesis). When you reverse
> cause an effect you simply chop the foot to
> make the shoe fit. Mathematics does not
> care one way or the other.

The act of forming the hypothesis does not constitute a refutation of
anything.
 
[snip]

>> GH:-
>> 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.
>
> JE:-
> The proposition on the table was: mathematics
> is not a science. Just one empirical separation
> of them while both remain valid provides a
> refutation of the antithesis: mathematics is
> a science. Do you agree?

I agree that mathematics is not A science, although I find this a strange
turn of phrase. I perceive science in general as a coherent process.
Scientific disciplines come and go as science proceeds. The scientific
disciplines we recognize at any point in time ought to each involve both
theory and empiricism. Interestingly, population genetics had a very weak
empirical component until the late 1960's, when the advent of electrophorsis
began to yield plenty of relevant data. More than three decades of
empirically unconstrained modeling probably contributed to the problems of
scientific imbalance that you call abuse, much of which persisted as a
matter of scientific culture within population genetics for more decades
(even to this day, IMHO).

>>> JE:-
>>> Science has formalised this process and
>>> usefully employed mathematics within it.
>
>> GH:-
>> 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.
>
> JE:-
> No, I am arguing that mathematics is not a science.
> This does not exclude science employing mathematics
> but it does exclude mathematical models as science
> in their own right.

I agree to a degree, but it is strange to talk about modeling without regard
to what is being modeled. Once you include context as part of the modeling
exercise it is tied to empiricism and natural phenomena. Then is becomes a
scientific exercise IMHO.

>> GH:-
>> 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:-
> Science can be done without any mathematics but I agree that
> it _can_ be done better employing mathematics but I strongly suggest
> that science will be worse off when mathematics is misused.
> My example is Hamilton's Rule.

How is that different from saying that science is worse off when empiricism
is done badly?
 
>>>>> 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.
>
>> GH:-
>> I see nothing in your statement that could pass as a scientific
> theory,
>> which required IMHO the inclusion of internal justification.
>
> JE:-
> Then the assumption that I am a living form
> is not a valid theory?

Not even close. A theory might be assumed to be correct, but not all
assumptions have the rich constitution of theories. Your assumption is not
a theory.
 
>> GH:-
>> A theory must
>> also provide a framework for understanding some aspect of nature. A
>> simple assertion cannot be a theory.
>
> JE:-
> That is what the theory, "a living form"
> provided.

The words "a living form" explains nothing to me. It certainly does not
provide me with a framework for understanding living forms.
 
>>>> 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:-
> Why no explanation?

Because your "simple example" was not a valid one due to the absence of a
theory of anything.
 
>>>>> 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.
>
>> GH:-
>> What you mean by "non verification", which is not a term I have ever
>> seen used before, is failure to support a hypothesis.
>
> JE:-
> The term "non verification" is self
> explanatory and quicker than writing
> "failure to support a hypothesis".
>
>
>> GH:-
>> Refutation is ultimate
>> proof that it is false.
>> Once refuted, a hypothesis can never be validly
>> resurrected in the same form.
>
> JE:-
> Most people here are having great difficulty
> distinguishing between refutation and
> "failure to support a hypothesis".
> Could you please provide an example?

I don't have time to do your teaching for you. Why don't you provide
examples that don't related to anything Hamilton every wrote about? That
might help get the idea across without inflaming your readers.
 
Guy

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