"John Edser"  wrote in message
news:br6bvc$1bcs$1{at}darwin.ediacara.org...
>
>
> Kevin Aylward wrote:-
>
> >>> I don't believe Goedel has anything to do with
anything
> >>> outside of formal math.             ...tonyC
>
> >> But most rational models of the world *are* based on
math. if we cant
> >> put numbers to something its difficult to say anything
about it
> >> Irrespective of whether one can apply Goedel to a
particular real
> >> world problem, what it presents is the very *idea* that
there can
> >> exist true statements but be unprovable. This means
that in it may
> >> well be impossible to derive everything about the world
from exiting
> >> knowledge. Before Goedel there was no reason to hold
that this might
> >> be the case.
> >> Goedel really doesn't have anything to do with physical
practicalities
>
> KA:-
> Yep. It does.
>
> JE:-
> Godel was only concerned with propositions of
> pure mathematics. What he discovered was such
> propositions were always insufficient, i.e. always,
> within mathematics, propositions that were _not_
> of mathematics had to be imported just to make
> the mathematics work.
>
> I would like to point readers to the thread:
>
> "Intersecting Sets Of Fitness"
>
> for an example of propositions outside of mathematics
> being required within mathematics for any valid
> use of mathematics by the science evolutionary theory.
>
> Godel was only working with the principles of pure
> mathematics. These principles can be most easily
> understood by using Venn diagrams within set theory.
> Set theory, just using Venn circles, is simple enough
> to be taught within most High School mathematics courses.
> Here, sets either intersect or they join up (set union).
> Sets cannot do both, simultaneously, so these events are
> logically self exclusive. However, what can or cannot
intersect/
> join is determined by simple definition, where such
definitions
> are always propositions _outside_ of mathematics. WHY sets
can
> intersect or join is NOT determined by mathematics it is
always
> determined by definitions totally outside of mathematics.
However,
> HOW set intersect or join remains a proposition of
mathematics.
>
>
____________________________________________________________
_______
> Mathematics most basic inductive WHY propositions always
remain
> _outside_ of mathematics where explicit_ WHY propositions
are
> essential  for any valid scientific application of
mathematics,
> e.g. applying mathematics within Neo Darwinistic models of
the
> _science_ of biology.
>
____________________________________________________________
_______
>
> >snip<
>
> KA:-
> >snip<
> There is simply no way to know whether or not one has to
introduce new
> axioms into a theory to make it complete. For example,
there are some
> basic initial axioms to quantum mechanics. However, the
Pauli exclusion
> principle is an additional required assumption, not
contained in the
> basic axioms. Do we need more? What about quarks? These
were added. Do
> wo need some more axioms to account for quarks? What about
strings?
>
> This list is truly endless. Goedel tells us that instead
of trying to
> search for a new relation to connect existing relations,
we should just
> accept a new one as given and go down the pub instead.
>
> JE:-
> This is the difference between science and mathematics.
> Only science is involved with producing testable theories
> of cause an affect, i.e. valid WHY propositions of nature;
> mathematics isn't. What science does is produce
_refutable_
> absolute _assumptions_. Mathematics can only show how such
> assumptions play out, i.e. provide a HOW proposition.
> Mathematics cannot tell you if your absolute assumptions
> about the world are true or false but can show them to be
> valid or invalid. Refutability is not the same as
invalidity.
> When using just an invalid logic what you just said does
not
> follow from what you said previously. Thus a valid view is
> just a logically self consistent view where any logical
> self consistent view totally relies on definitions which
may be
> propositions outside of mathematics. Not all logically
self
> consistent views are true about nature. Science provides a
way
> to test for such natural truths. Of course, before science
> can even proceed, any theory of cause and affect it comes
> up with must firstly be logically valid otherwise the
absurdity
> remains that just an invalid view produces a verification.
> This does not matter that much because logical invalidity
will
> never allow the production of any valid points of
refutation,
> thus chaos always reigns when refutability is thrown out.
> This remains the intention of Post Modern Epistemology.
> The only things it can produce are blank epistemological
> cheques for anybody to say anything they like within the
sciences.
> This is why Sir Karl Popper stressed the _absolute_
necessity
> of refutation within all valid propositions of science.
>
> Best Wishes,

Yes, indeed--I agree completely. The OP and disciples seem
to not have heard that "the  map is not the territory"; and
likewise, traditional math is not reality--it just plays
same in teaching. The real foundations of reality (seen via
science) lie in the axioms chosen in math and assumptions in
correlating the math to the real world--these correlations
may be true or false, or degrees in-between, but we never
really "know" reality through math, we just model it. Many
math applications meant to describe the real world have
ultimately failed or found to be approximations in more
complex theories (Newton's thy of gravity vs Einstein's GR
for example.) There is no general math reality, only
different
simulations of reality.  Plato's shadows on the cave wall
was a pretty good metaphor for our limited view of reality,
regardless of how much math is utilized. :)        ...tonyC

> John Edser
> Independent Researcher
>
> PO Box 266
> Church Pt
> NSW 2105
> Australia
>
> edser{at}ozemail.com.au
>
>
>
>
>
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