FOM: Re: "Relativistic" mathematics?

[Charles Silver]

On Fri, 16 Oct 1998, Vladimir Sazonov wrote:


> > > Anyway, in each historical
> > > period (except the time of a scientific revolution) we usually
> > > *know* what is the ideal of mathematical rigour to which we
> > > try to approach in each concrete proof.

C.Silver:
> >Is the above an
> > application of Kuhnian philosophy?  Are you interpreting formal rules as
> > examples of his "paradigms"?

V. Sazonov:
> Unfortunately, I do not know about this. Could you give, please, any
> comments? 

	Sorry it has taken me so long to respond.  In the book _The
Structure of Scientific Revolutions_, Thomas Kuhn says that there are long
periods of time between scientific revolutions when scientists work within
a puzzle-solving paradigm.  During these periods the rules of the game are
well-known and workers in the field spend their time solving problems
within the prevailing framework.  Eventually, though, problems build up
that don't seem solvable within this paradigm.  This can lead to a
scientific revolution that brings with it a "paradigm shift."  Suddenly
there's a new framework and new ways to attack problems.  Some of the same
terms are used in the new framework that were used in the old, but their
*meanings* are now different....  

	Anyway, Kuhn's book came out in 1962 and has been tremendously
influential, especially in the social sciences.  The concepts of a
"paradigm shift" and "the incommensurability of theories"  have been used
to explain all sorts of things. Kuhn has not approved of some of the
applications of his principles and has written several essays afterwards
to try to clarify his views, especially about "paradigms" and "paradigm
shifts."  Recently, I think three or four months ago, the physicist Steven
Weinberg wrote a long piece in the New York Review of Books ostensibly
disagreeing with Kuhn's view of scientific change.  At any rate, I thought
you might have been alluding to Kuhn's views.

Charlie Silver