On Aug 29, 1:10 pm, Brent Meeker <meeke....domain.name.hidden> wrote:
>
> So are mathematics human creations (c.f. William S. Cooper, "The Evolution of Logic"). There is no sharp distinction between what is expressed in words and what is expressed in mathematical symbols. Darwins theory of evolution is no more accurately expressed in mathematical notation.
Any scientific theory (including Darwin's) *is* more accurate when
expressed in mathematical notation. You *can* draw a clear
distinction between the language used to express mathematical concepts
and the concept itself. Pure math concepts themselves consist of:
Formal Systems, Relations and Differential Equations. They are
abstract concepts which are precisely defined and it is provable
matter to determine the equivalence (or not) of different symbolic
representations of them.
>
> So Deutsch has an overly generous criterion for "exist". Does he consider epicycles real because they were indispensable to Ptolemy's theory of the cosmos. I'd go with Dr. Johnson - it exists if I kick it and it kicks back.
Deutsch uses exactly the example you just gave! Dr Johnson's
critera ;). Read his book.
>
> >Grammer doesn't match the criteria. Math does. It's
> > easy to cut out English concepts say, and replace them with other
> > modes of descriptions. I don't see scientists labriously trying
> > refactor all their mathematical explanations to refer only to material
> > observables.
>
> Actually a theory that dispenses with unobservables is usually considered preferable, by application of Occam's razor.
No, occam's razor says pick the theory with the most explanatory power
and the one that simplifies explanations the most. The quantity of
observations versus unobservables is quite irrelevent.
>For example in Newtonian mechanics force was an important concept, but later it was dropped. So what is it's status now? It's still a mathematical concept - but according to Deutsch it's not part of reality.
The concept hasn't been dropped just re-defined.
> Your argument, even if I agreed with it, would only justify counting as objectively real those mathematical concepts that appear in a true theory of reality - and unfortunately we never know which one that is.
>
> Brent Meeker
We don't have to know to certainty, just base judgements on available
evidence. At this point in the debate I guess we can just maintain
our entrenched positions. It all boils down to realist verus non-
realist philosophy. But I repeat my observation that as a purely
pragmatic matter, non-realist positions are not helpful for the
progress of science.
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Received on Wed Aug 29 2007 - 06:48:32 PDT