Re: Mathematics Is Not a Science
From: John Edser (edser_at_tpg.com.au)
Date: 02/26/05
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Date: Sat, 26 Feb 2005 14:44:14 -0500 (EST)
> >>> 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.
> GH:-
> 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.
JE:-
Yes a theory can remain 100% implicit.
I think we call it "intuition". What scientists
seem to spend much of their life doing is
explicitly understanding what they already
know intuitively. Truth in science is like
justice, it has to be seen to be done.
The only way truth can be seen to be
done is via a testable theory of nature.
Nothing else will do. The fact that not
many of these exist means the few that
do exist should be all the more rigorously
guarded against corruption. One of them
is Darwin's theory. My argument is Neo
Darwinism has corrupted it removing its
refutable status.
> > JE:-
> > 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.
> 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.
> GH:-
> However, we probably agree
> that testing these hypotheses does not constitute testing of the
general
> proposition that evolution occurred.
JE:-
Yes. Non evolutionists make this
mistake almost all of the time.
> >> 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.
> GH:-
> I didn't actually say that it was required. I agree that on rare
occasion
> science is accomplished without the involvement of math.
JE:-
Then you agree that mathematics
is not a science because
the proposition that they are the
same stands refuted when just one
instance that empirically
demonstrates they can remain
separate is provided?
> 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?
> > 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.
> 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.
> >>> 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?
> 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.
> >> 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?
> >>> 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?
> GH:-
> 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.
JE:-
Not quite. I do not call your view
"blind" I call it a bonanza for
non refutable Neo Darwinism
with eyes wide open....
Regards,
John Edser
Independent Researcher
Po Box 266
Church Pt
NSW 2105
Australia
edser@tpg.com.au
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