Re: Mathematics Is Not a Science
From: John Edser (edser_at_tpg.com.au)
Date: 03/03/05
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Date: Thu, 3 Mar 2005 13:07:15 -0500 (EST)
Guy Hoelzer <hoelzer@unr.edu>
> >>>> 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:-
> >> The act of forming the hypothesis does not constitute a refutation
of
> >> anything.
> > JE:-
> > How am I supposed to respond to the above?
> > All you have done is repeat the
> > assertion which is under dispute.
> GH:0-
> That is correct. AFAIKS there is nothing in your response that
impinges
> on
> the validity of my statement. If my statement were false (even a
little
> bit) then we could do science merely by hypothesis formation.
JE:-
But I did NOT just _form_ a hypothesis.
I provided a theory and a hypothesis attached
to that theory and the tests that are required.
Your statement only refers to the act of hypothesis
formation so it had no valid context to this
discussion unless it inferred that was all I was
doing. Therefore I took it to mean this. However
such an inference is invalid. You must prove that
the theory and the hypothesis attached to it that
I provided were invalid before you can infer (via
any back door) that this was all I was doing.
>snip<
> >> GH:-
> >> 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:-
> > Do you agree or disagree that it is not acceptable
> > for population genetics to be based on non epistatic
> > gene fitnesses via Fisher's dictate when not one single
> > non epistatic gene fitness has ever been documented
> > within nature?
> GH:-
> It is acceptable to make simplifying assumptions like this when
modeling,
> and there are very many examples where these models make accurate
> predictions despite their simplifying assumptions. Population genetic
> models (single locus models) have also had great heuristic value,
IMHO.
JE:-
If "not one single non epistatic gene fitness
has ever been documented within nature" yet
Fisher required them if they are to be "heritable"
do you agree that Hamilton's model must also
require them for his model to be valid?
> GH:-
> On
> the other hand, the success of these models does not rely on, or even
> predict, that the fitness effects of alleles at a locus are additive.
JE:-
Fisher required additive (non epistatic)
gene fitnesses. Hamilton also required them
if his gene is not to be restricted to being
selected at just the one, same level of selection.
If Hamilton's gene produces organism
fitness altruism via selfish geneism
at just the one dependent level of selection and
not at any different independent level then
any gene that does so reduces that gene's
fitness via such an _irrational_ act.
> >>>>> 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:-
> >> I agree to a degree, but it is strange to talk about modeling
without
> >> regard to what is being modeled.
> > JE:-
> > It is much more than "strange" to talk
> > about modelling without regard
> > to exactly what is being modelled IMHO.
> GH:-
>snip<
> ...my comment was in response to
> your writing about "modeling without regard to what is being
modeled;"..
>snip<
JE:-
Do you agree or disagree that nobody here,
including yourself has never defined what these
models are simplified from until now?
> > JE:-
> > I have been requesting (for over 4 years) for
> > any professional Neo Darwinist that posts here
> > to provide what these models, e.g. Hamilton's
> > Rule, are simplified/oversimplified from. Nobody
> > will oblige. Do you agree that it is an act of
> > contempt for anybody to argue that a model
> > is a simplification/oversimplification but
> > fail to provide from what it was simplified/
> > oversimplified?
> GH:-
> I do not agree that it is "an act of contempt" because your question
> presupposes something irrelevant to most of us (if I might be so bold
as
> to
> speak for the others). Everybody realizes that it is simplified from
the
> complexity of nature, but it was not derived as a model of an
articulated
> theory that contested Darwinism.
JE:-
This represents the first response to this
question in over 4 years! I thank you for
your response. However, can't you see that
"the complexity of nature" is just
a dictate of something you believe in unless you
can provide a theory of what you are talking about?
I mean, for all I know you may be talking about
elves and hobgoblins as part of "the complexity
of nature".
Darwin provided a refutable theory of nature.
I have outlined an empirical experiment to test
his theory of evolution by natural selection to
refutation. You have always refused to comment
on it except in passing. If I recall correctly your
comments were "interesting" and something like
"there may be some sort of difficulties".
You never ever elaborated. Unless anybody here or
elsewhere can come up with an alternative refutable theory
of evolution then we are stuck with Darwin's as
the only empirically valid theory that we have.
This being the case, Hamilton's non refutable model
must have been simplified/oversimplified from Darwin's
theory of nature unless elves an goblins
are allowed as valid complexities of nature. I mean,
it is most certainly true that Darwinism cannot
explain any of _them_.
> GH:-
> It was derived from Darwinism itself, I
> suppose, in the sense that it extended the theory of natural selection
> beyond its historical bounds. Therefore, there was no pre-existing
> complex
> theory that was simplified in the creation of the kin selection idea.
JE:-
Your comment "It was derived from Darwinism itself" belies
belief. Are you suggesting that Darwin never supplied a
valid theory of evolution by natural selection?
> GH:-
> Your
> question just does not fit into the way science always works, or
worked in
> this case.
JE:-
Quite obviously, I disagree. My view is
that you are attempting to evade the only
possible way Hamilton can be said to be
joined to Darwin as an oversimplification
of Darwin. If Hamilton is not joined to
Darwin then Hamilton is just an irrelevant
heuristic.
> >> GH:-
> >> 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.
> > JE:-
> > Do you agree that it is invalid for any
> > simplified/oversimplified model to contest
> > the theory from which it was simplified/
> > oversimplified?
> GH:-
> If a model was designed to represent a particular theory in simplified
> form,
> then I would agree with you. This is just not what most modeling is
> about.
JE:_
What else can modelling be about? Science is about making
_empirical_ sense of the world via testable theories of
nature. Models can only help or hinder this process.
Obvious simplifications that mathematical models make
such as random mating, infinite populations or the
deletion of all epistasis including gene fitness
epistasis are only made to help concentrate logic on
a PART of a theory. No refutable theory of nature
that I know can or could assume these things.
If they did such a proposed theory of nature would be
thrown out as laughable. I put to you and sbe reader's
that the only valid use a model has is to help and
not hinder a fuller and easier understanding of a
testable theory of nature. If you divorce the model
form its parent theory and employ it as a stand alone
mechanism to interpret nature, then such an event is
absurd.
> >>>> 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.
> >> GH:-
> >> How is that different from saying that science is worse off when
> >> empiricism is done badly?
> > JE:-
> > These models remain irrefutable so
> > that Empiricism within the sciences has
> > "not been done badly" it has become emasculated.
> > All that can be empirically done with
> > models per se is verification or non verification.
> > Hamilton's Rule which is just a 100% relative
> > proposition cannot even measure what it claims
> > to be able to measure i.e. cannot provide
> > a verification let alone a refutation.
> GH:-
> Hamilton's Rule does not claim to be able to measure anything, so your
> comments here just don't make any sense.
JE:-
Yes, it cannot measure ANYTHING
Do you agree that the rule was misused to
measure when organism fitness altruism can
evolve within nature after group selection failed
to be able to do so over 50 years ago?
> GH:-
> I agree with you, however, that models are not very useful for
refutation.
> Surprisingly, a model is a kind of hypothesis, yet you argued above
that
> hypothesis formation (e.g., model building) CAN itself result in
> refutation.
> You seem to have contradicted yourself.
JE:-
You misunderstood me. I argued that a hypothesis
represents a refutable part of theory where a
refutation of the hypothesis does _not_ refute
the theory, just that part of it. Testing my
shoe size does not refute that I exist. e.g
I refuted that my shoe size was a size 11
only because size 7 actually fits.
Any hypothesis and therefore any model
(if it is to be regarded as a hypothesis)
must be attached to a refutable theory.
It is pointless arguing that the elves
at the bottom of my garden take
a size 6 shoe if no elves exist. In
the same way a model must be attached
to its parent theory and provide empirical
results in its own right.
> >>> JE:-
> >>> Then the assumption that I am a living form
> >>> is not a valid theory?
> >> GH:-
> >> 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.
> > JE:-
> > Then the division between living and non living is
> > only arbitrary?
> That could be an interesting question for discussion, but it has
nothing
> whatsoever to do with the issue at hand. No matter the answer, " the
> assumption that [you are] a living form is not a ... theory."
JE:-
You remain in serious error. Life is a refutable
theory because of death. The problem is life
cannot be separated from non living (things
that were never alive in the first place)
by simple verification. What is arbitrary
is not that life exists just the difference
between living and never alive in the first
place.
> >>>> 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:-
> Maybe it provides this to you implicitly, but it certainly does not do
so
> explicitly. You shouldn't assume that it does so for others.
JE:-
I see. No formal science of biology actually exists.
> >> GH:-
> >> The words "a living form" explains nothing to me. It certainly
does
> >> not provide me with a framework for understanding living forms.
> > JE:-
> > Would putting a loaded shotgun at your head help :-)
> GH:-
> This suggests that you were indeed relying on some sort of shared
> framework
> for understanding life forms that would have been implicitly evoked by
> your
> phrase "a living form," which would have filled in all the richness
> required
> by a theory. That is not sufficient or scientific.
JE:-
Then I suggest you make a simple empirical
experiment to settle the issue and pull
the trigger ;-)
> >>>>>> 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?
> >> GH:-
> >> Because your "simple example" was not
> >> a valid one due to the absence of a
> >> theory of anything.
> > JE:-
> > Untrue.
> > The refutable theory was: I am a living
> > thing.
> GH:-
> This was not refutable because you failed to provide the logical
> underpinnings of your claim.
JE:-
The entire science of biology exists just to
provide "the logical underpinnings" of
my claim. While I agree that life as
a verification remains arbitrary, life as
a refutation is NOT. I know of know
refutable theory of life that argues
that life continues after death.
>snip<
> > The refutable hypothesis was: my
> > foot size remains the same after
> > I have become an adult where the
> > shoe must be made to fit the foot and
> > not vice versa.
> GH:-
> The first part of this is a perfectly good and refutable hypothesis,
> although the claim that "the shoe must be made to fit the foot and not
> vice
> versa" is IMHO a poor excuse for a hypothesis and would not be
refutable.
JE:-
If _either_ cause can be applied, i.e. either the shoe
causes the foot size OR the foot size cause the shoe size
then the view would indeed be irrefutable because now the foot
can validly be chopped or stretched to _make_ it fit any shoe.
No rational test could be made that refutes the claim while
at the same time performing these "tests" may fatally damage
the hapless person being tested. I refer you to
similar tests of witches actually applied in the middle
ages to over 100,000 people. You must
choose if the hypothesis being tested is the foot causes
the shoe to fit or vice versa otherwise the hypothesis
remains irrefutable.
> > Proofs:
> > Life is a refutable theory via death.
> GH:-
> I can't make sense of this. You seem to be saying that if death
occurs it
> constitutes a proof that life does not exist.
JE:-
I am suggesting that life cannot be verified
but it can be refuted. I have suggested an
empirical proof that you may like to attempt ;-)
> > My foot size is a refutable hypothesis
> > because it only fits one shoe size.
> GH:-
> Your foot size makes no claims about anything, so it does not
constitute a
> hypothesis. It can be measured, but not refuted.
JE:-
My foot size is NOT making the claim,
only the hypothesis I have provided, is.
Are you arguing that I cannot make
such a hypothetical claim?
> > JE:-
> > If my foot fit every known
> > shoe size my hypothesis would be verifiable
> > but not refutable.
> GH:-
> If your foot fits every size, then
> it cannot be meaningfully measured.
JE:-
Not necessarily. If my foot was like
an amoebas then it could expand or
contract. In this situation any
hypothesis of foot size would
become irrefutable, i.e. meaningless
unless limits were defined. This must
mean that my foot cannot fit EVERY
size shoe.
> > JE:-
> > The refutation of the
> > hypothesis of my foot size does not refute
> > I am a living thing but it can refute
> > a part of the assertion of what I am as
> > one living thing allowing life forms to
> > have refutable differences.
> GH:-
> This is all gibberish to me. If there is any sense in your paradigm,
you
> would have to communicate it to me in a very different way.
JE:-
Is it clear that I remain alive even if
the hypothesis that I take a size 11
shoe is refuted when only size 10 fits
(as long as you cannot chop my
foot via invalid reverse causation)?
It is just a common observation of nature
that people have different sized feet. If
they didn't then evolving feet may become
a problem.
> >>>> GH:-
> >>>> Refutation is ultimate
> >>>> proof that it is false.
> >>>> Once refuted, a hypothesis can never be validly
> >>>> resurrected in the same form.
\
> >
> > JE:-
> > I have discussed in detail the refutation of Newtonian
> > Mechanics and its evolution into Special Relativity.
> > Darwinian Total fitness represents my detailed
> > empirical example of a refutable theory for the biological
> > sciences. Hamilton's Rule represents my example of a misused
> > irrefutable model. My consistent criticism of
> > the rule inflames some reader's for the same reason
> > a lot of people did not like the claim that a perpetual
> > motion machine cannot be built. Science is not about
> > political sensibilities.
> GH:-
> Well, we agree on this point.
JE:-
Yes. It is just a pity this happens
to be the case in the real world.
> > JE:-
> > Almost anything we propose we claim we
> > can ACTUALLY do provides a refutation.
> > Refutation is just commonsense. Popper
> > elaborated on this common sense notion.
> GH:-
> IMHO you don't get Popper or the cartoonish
> nature of his take on science..
JE:-
If Popper is "cartoonish" then
I am happy to be a part of the
cartoon called: reality. Happy
witch hunting :-)
My Regards,
John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia
edser@tpg.com.au
'
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