It has also been recently asserted that the Vician philosophy of mathematics reappears bodily in Galileo and his school;[49] an astounding fact when baldly stated, since even though Vico opposes and prefers the great Pisan to Descartes for the moderate use he makes of mathematics in physical science, it is certain that for Galileo as for Leonardo da Vinci mathematics had an objective validity, and the book of nature is written in mathematical characters and geometrical figures. In any case, the passage of Galileo which has been quoted in this reference, on the intensive identity of human with divine knowledge, has nothing to do with the present question, and another passage which asserts that the explanations of terms are free, and it is in the power of every workman to circumscribe and define in his own way the things he is dealing with, without ever being led by this into error or falsehood, and that for instance one may call the bow the stern and the stern the bow, says nothing but a platitude hardly worth saying except by way of adorning a page of controversial rhetoric.[50] In controversy one is often obliged to insist upon platitudes, and the controversy upon which I am now engaged itself presents too many examples. A passage from the _Lezioni accademiche_ of Galileo's pupil Evangelista Torricelli in which he speaks of the difference between physical and mathematical definitions seems at first sight more convincing. But the critic who has called attention to this passage[51] says too much when he asserts that "it is beyond doubt that Vico had read it," since it is unquestionable that Vico had _not_ read it. The _Lezioni accademiche_ were published first posthumously in 1715[52] and Vico's theory of mathematics is expounded in the _De ratione_ in 1708 and the _De antiquissima,_ 1710. This, it is true, is of secondary importance, for Vico may have known Torricelli's doctrine through indirect channels, through other books or even orally through some Neapolitan friend or pupil of Torricelli; in any case, if the latter's theory though unknown to Vico was really identical with his own, the similarity of ideas between the two would be of the greatest interest. Unfortunately the critic has been too hasty, as it seems to me, even in his study and interpretation of the pages of Torricelli.