Some Philosophical Comments

The place of this paper in this book, which is devoted to the philosophy of science, calls for a few philosophical comments.

Its motivation could not be else than philosophical.

Its main feature is simplicity. Not a technical one, as I may say from the diffi­culty of putting order into its glimpses, but a philosophical simplicity. Reality

appears just like many physicists have perceived it since more than half a century: An objective classical datum, set upon an objective science of a quantum world (space-time being another matter). Only a keystone, which would have insured a mutual equilibrium of their representations, was missing. These comments assume that a part of the answer could look like the one, which is proposed in this paper.

As it appears here, the uniqueness of macroscopic Reality would emerge from a quantum sea. Can one then say that there is a veil on this reality, to borrow d’Espagnat’s striking expression? Yes, there would be a veil, but one, which would cover the two faces of reality, when seen with the eyes of philosophy.

I see personally no other basic veil than the one of mathematics. Quantum reality and macroscopic reality are joined together, as our science can see, by a mathe­matical unity and a mutual consistency of their laws. I believe that the greatest problem in the philosophy of science holds in a unique question: What is Mathe­matics? (Wigner 1967; Omnes 2004). To which one may add: What is the status of mathematics in a science, which aims at unity of its vision?

I do not propose an answer, but I may recall a remark, often heard and drawn from the history of mathematics: During more than two millenaries, mathematics looked as if inspired by (macroscopic) reality. Since about two centuries, it became its own field, much as if mathematics were discovering itself, more than finding its source in empirical reality or schematizing it. The irreplaceable place (or action?) of mathematics in the foundations of physical science, where it appears not only as a mode but also as a mold of thought, opens a view on an inner harmony of Being, in itself by itself, as Plato or Spinoza saw it.