Nay, Descartes, the greatest mathematician of his age, and in spite of his mathematics, also its greatest philosopher, was convinced from his own consciousness, that these sciences, however valuable as an instrument of external science, are absolutely pernicious as a mean of internal culture. "It was now a long time" (says Baillet, his biographer under the year 1623, the 28th of the philosopher) "since he had been convinced of the small utility of the mathematics, especially when studied on their own account, and not applied to other things. There was nothing, in fact, which appeared to him more futile than to occupy ourselves with simple numbers and imaginary figures, as if it were proper to confine ourselves to these trifles (bagatelles) without carrying our view beyond. There even seemed to him in this something worse than useless. His maxim was, that such application insensibly disaccustomed us to the use of our reason, and made us run the danger of losing the path which it traces." ("Cartesii Lib. de Directione Ingenii, "Regula 4, MS.) "In a letter to Mersenne, written 1630, M. DesCartes recalled to him that he had renounced the study of mathematics for many years; and that he was anxious not to lose any more of his time in the barren operations of geometry and arithmetic, studies which never lead to anything important." Speaking of the general character of the philosopher, Baillet adds, "In regard to the rest of mathematics [he had just spoken of astronomy, which Descartes thought, 'though he dreamt in it himself, only a loss of time'], those who know the rank which he held above all mathematicians, ancient and modern, will agree that he was the man in the world best qualified to judge them. We have observed that, after having studied them to the bottom, he had renounced those of no use for the conduct of life, and the solace of mankind."[1]
"The study of mathematics" (says Descartes, and he frequently repeats the observation) "principally exercises the imagination in the consideration of figures and motions."[2] Nay, on this very ground, he explains the incapacity of mathematicians for philosophy. "That part of the mind," says he, in a letter to Father Mersenne, "viz., the imagination, which is principally conducive to a skill in mathematics, is of greater detriment than service for metaphysical speculations."[3]
These are Hamilton's references to Descartes which contain quotations from Descartes or his biographer Baillet. Evidently Hamilton was guided more by what Baillet stated about Descartes than upon what Descartes himself actually said. The letters to Mersenne simply show that Descartes was not inclined to confine his activities to mathematics, nor ready to admit that mathematical training alone constituted adequate preparation for the study of philosophy. In quoting from Descartes's "Rule Four" for conducting philosophical inquiries, Bledsoe puts into italics the passage garbled by Hamilton and Baillet. It can thus be easily read in connection with what immediately precedes and follows, and one can readily see how Hamilton's extract, by itself, conveys an impression quite the opposite of that conveyed by the entire passage. Descartes gives an exposition of his method of philosophical inquiry. He says that he wishes to apply his method not merely to the ancient "arithmetic and geometry," but to other sciences
