364 THE POPULAR SCIENCE MONTHLY 



Nay, Descartes, the greatest mathematician of his age, and in spite of his 

 mathematics, also its greatest philosopher, was convinced from his own con- 

 sciousness, 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 mathe- 

 matics, 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 trifies (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, " Eegula 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. ' ' ^^ 



"The study of mathematics" (says Descartes, and he frequently repeats 

 the observation) "principally exercises the imagination in the consideration of 

 figures and motions. ' ' "" 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. ' ' ^^ 



These are Hamilton's references to Descartes which contain quota- 

 tions 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 mathe- 

 matics, nor ready to admit that mathematical training alone consti- 

 tuted adequate preparation for the study of philosophy. In quoting 

 from Descartes's " Eule 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 pre- 

 cedes 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 philo- 

 sophical inquiry. He says that he wishes to apply his method not 

 merely to the ancient " arithmetic and geometry," but to other sciences 



""La Vie de Descartes," P. I., pp. Ill, 112, 225; P. IL, p. 481. 

 '"'"Lettres," P. I., let. xxx. 

 " Loc. cit., p. 426. 



