Kuhn vs Popper, and why it's Important

Gödel, Kuhn, Popper, and Feyerabend*
Jonathan P. Seldin
Department of Mathematics and Computer Science
University of Lethbridge
docs.thinkfree.com/tools/download.php?mode=down&dsn=422308

Abstract
Thomas Kuhn (Kuhn, 1962) has presented a view of
the history of science as a succession of ‘paradigms’
which are not completely comparable with each other.
Karl Popper (Popper, 1970) has attacked this view as
being relativistic and denying that there is objective
scientific truth. Popper seems to be saying that in order
for science to be objectively true, every two scientific
theories must be completely comparable. In taking this
position, Popper is making a claim for a kind of
completeness that is ruled out for theories strong enough
to be ‘interesting’ by Gödel’s Incompleteness Theorem
and related results.

In this paper, Gödel’s
Incompleteness Theorem and related results will be used
to draw conclusions about this conflict between Kuhn
and Popper. In particular, it will be argued that if Popper
had taken Gödel’s Incompleteness Theorem into account,
he would have wound up with a position consistent with
that of Kuhn. Gödel’s Incompleteness Theorem will also
be used to argue that Feyerabend (Feyerabend, 1975)
does not really have an argument that there is no
objective scientific method. The paper will close with
some remarks on what might really count as objective
scientific truth.

more from the paper....

Thomas Kuhn (Kuhn, 1962) has presented a view of the history of science that
differs from the previously commonly held view of science as a gradual
accumulation of knowledge. He presents the history of science as a succession
of periods of ‘normal science,’ each of which is determined by a ‘paradigm.’
When for some reason the paradigm is no longer adequate for normal science
to proceed in the usual way, there is a ‘scientific revolution,’ and normal
science only resumes when a new paradigm is accepted by the scientific
community involved. Usually, this is a group of specialists, but sometimes it
may be a larger group than that.