🚀 go-pugleaf

Just some quick responses to an otherwise very long posting ...

In article <1992Nov5.171453.22237@CSD-NewsHost.Stanford.EDU>, pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

> Now what I claimed in (B) was that hypotheses can be falsified in
> math.  Here Liebniz' hypothesis of the mathematical existence of
> infinitesimals, later endorsed by Cauchy, was eventually *falsified* by
> Dedekind.  (You can *prove* via reals as cuts that no real can be an
> infinitesimal, the only reals greater than 0 are too large to be
> infinitesimals.)  And my evidence for (C), the impermanence of
> falsification, is Robinson's restoration of infinitesimals to
> mathematically rigorous existence.

There is at least a real confusion here about *what* was "falsified".
It appears, at least from this story, that one *semantics* for 
a theory of infinitesimals was "falsified", while another semantics
(perhaps even for an at least slightly *different* theory) was not.

This story has a bit of the flavor of the claim that the existence
of phlogiston (the "active ingredient" in combustion) was falsified,
but that this (phlogistion) later really turned out to be oxygen!

> 
> The parallels with the corresponding story for particles and waves
> involve both (B) and (C) with physics in place of mathematics.  These
> intimate parallels makes it *very* hard to tease apart the processes of
> mathematics and physics in any useful way.

It remains not hard at all.  You may choose to attempt to minimize the
issue of direct empirical content as well as the significant methodological
differences, but these differences are nonetheless quite obvious.

You can take a mathematician and lock him in his little office with just
some writing materials and he will (a) be pretty happy, and (b) be able
and willing to do anything of a mathematical nature.  Even a committed
*theoretical* physicist will be very distressed under such circumstances
since he has not way to determining whether his theories (however abstract)
are *good* ones.

> The divergence between Natural Philosophy and Philosophy grew as the value 
> of knowing how many people a bridge could hold became economically more 
> important than knowing the number of angels that could fit on a pin ;-)
> 

I take this as an expression of some kind of ideology.  Certainly it is
not historically accurate.  The divergence has much more to do with the
development of *quantitative* methods and measurements, and (to use
a phrase beloved by some in the history of ideas and history of
philosophy) "the mechanization of the world picture".
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
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