Cartesianism and Physicalism
Descartes is remembered mostly for his method of doubt -- trying to doubt everything until what remained as indubitable could serve as the foundation for "first philosophy"
Most who come to Descartes' Meditations for the first time read the first two meditations, in which he gives an exposition of methodical doubt -- and this is probably what is of lasting value in Descartes. After Descartes' initial excursion into radical doubt, however, what follows reminds me of a passage from Kierkegaard:
What is madness? When a privatdocent, every time his scholastic gown reminds him that he ought to say something, says de omnibus dubitandum est, and at the same time writes away at a system which offers abundant internal evidence in every other sentence that the man has never doubted anything at all: he is not regarded as mad.
The Cartesian madness was to systematically set out to doubt all of traditional philosophy, and then to painstakingly reconstruct scholasticism. One of Descartes' favorite authors was Aquinas, and in the later portions of the Cartesian system there is more of Aquinas than there is of methodical doubt.
After doubting almost everything at the beginning of his philosophical effort, Descartes returns to a philosophical effort not unlike scholasticism, and patiently reconstructs not only the world simpliciter but also the philosophical world of his predecessors.
There is a sense in which this more comprehensive view of Cartesianism (i.e., understanding that once Descartes doubted the world away, he then reconstructed it in a fairly conventional manner for this time) resembles the theoretical position of physicalism.
Physicalism was formulated as a contemporary analog to materialism, though recognizing aspects of the world recognized in physical theory that did not figure in classical materialism. Contemporary physics requires a battery of entities that cannot be encountered in ordinary experience: "not just matter but energy, space, time, physical forces, structure, physical processes, information, state, etc." (as Wikipedia puts it).
Contemporary physics not only entails unobservable entities and theoretical entities, among the theoretical entities it requires are those required by mathematics. The mathematization of physics has made the two -- i.e., mathematics and physics -- inextricable.
Moreover, we know from indispensability arguments in contemporary philosophy (sometimes called Quine-Putnam Indispensability arguments) that contemporary physical science requires mathematics, and quite a bit of "higher" mathematics, so that the reliability of physical science entails the reliability of mathematics. Mathematics quantifies over abstract entities, therefore physicalism requires quantification over abstract entities. Exactly how much mathematics is necessary to physics is a matter of continuing controversy, but no one doubts that a good deal of classical mathematics is implicated in physics.
I would argue that there is very little mathematics that can be excluded in good conscience on physicalistic grounds, up to and including large cardinal axioms for the farther reaches of transfinite set theory. If we can quantify over "lower" abstract entities and manipulate "smaller" infinite sets, at what point do we draw the line for "higher" abstract entities and "larger" infinite sets? And how can we even confront this question without seeing that we face a sorites paradox here?
I would further argue that quasi-Kantian transcendental arguments can furnish a bridge from the higher mathematics indispensable to physics to other abstract objects and non-observable entities not specifically mathematical. Once again, a sorites paradox would force us a draw a line that would, in practice, be arbitrary. To paraphrase F. H. Bradley, short of Platonism mathematics cannot stop, and, having reached that goal, mathematics is lost, and strict physicalism with it.
And so it is that, like Descartes, beginning with radical doubt and ending with a nearly conventional scholasticism, physicalism begins with an apparent radical rejection of all non-physical phenomena but is compelled to let back in -- by the back door, as it were -- all (or almost all) of the conventional non-physical apparatus of ontology, and in so doing rendering physicalism meaningless because indistinguishable from theories that do not deny the non-physical dimenstion of the world.
