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.”