July 14, 2007
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Against Reductionism:
A Note from the
Catholic University
of America
The August 2007 issue of Notices of the American Mathematical Society
contains tributes to the admirable personal qualities and mathematical
work of the late Harvard professor George Mackey. For my own
tributes, see Log24 on March 17, 2006, April 29, 2006, and March 10, 2007. For an entry critical of Mackey’s reductionism– a philosophical, not mathematical, error– see Log24 on May 23, 2007 (“Devil in the Details”).Here is another attack on reductionism, from a discussion of the work
of another first-rate mathematician, the late Gian-Carlo Rota of MIT:“Another theme developed by Rota is that of ‘Fundierung.’ He shows that
throughout our experience we encounter things that exist only as
founded upon other things: a checkmate is founded upon moving certain
pieces of chess, which in turn are founded upon certain pieces of wood
or plastic. An insult is founded upon certain words being spoken, an
act of generosity is founded upon something’s being handed over. In
perception, for example, the evidence that occurs to us goes beyond the
physical impact on our sensory organs even though it is founded upon
it; what we see is far more than meets the eye. Rota gives striking
examples to bring out this relationship of founding, which he takes as
a logical relationship, containing all the force of logical necessity.
His point is strongly antireductionist. Reductionism is the inclination
to see as ‘real’ only the foundation, the substrate of things (the
piece of wood in chess, the physical exchange in a social phenomenon,
and especially the brain as founding the mind) and to deny the true
existence of that which is founded. Rota’s arguments against
reductionism, along with his colorful examples, are a marvelous
philosophical therapy for the debilitating illness of reductionism that
so pervades our culture and our educational systems, leading us to deny
things we all know to be true, such as the reality of choice, of
intelligence, of emotive insight, and spiritual understanding. He shows
that ontological reductionism and the prejudice for axiomatic systems
are both escapes from reality, attempts to substitute something
automatic, manageable, and packaged, something coercive, in place of
the human situation, which we all acknowledge by the way we live, even
as we deny it in our theories.”– Robert Sokolowski, foreword to Rota’s Indiscrete Thoughts
Fr.
Robert Sokolowski, Ph.D., is Professor of Philosophy at The
Catholic University of America in Washington, D.C. Ordained
a Roman Catholic priest in 1962, he is internationally recognized
and honored for his work in philosophy, particularly phenomenology.
In 1994, Catholic University sponsored a conference on his
work and published several papers and other essays under the
title, The Truthful and the Good, Essays In Honor of Robert
Sokolowski.The tributes to Mackey are contained in the first of two feature articles in the August 2007 AMS Notices.
The second feature article is a review of a new book by Douglas
Hofstadter. For some remarks related to that article, see
Thursday’s Log24 entry “Not Mathematics but Theology.”
