It seems to me then that the difference which he begins by laying down between mathematics and physical science is considerably obscured in the sequel. And indeed how could Torricelli have seriously thought that the foundation of mathematics was a "fiction," when among his lectures one heard the title "in Praise of Mathematics"? In this lecture he says, quite in the Galilean style: "That to read the great Book of the Universe, the book on whose pages may be found the true philosophy written by God, mathematics are indispensable, will be seen by any one who with noble thoughts aspires to the science of the integral parts and greatest members of this huge body we call the World. The one alphabet, the only characters with which we can read the great manuscript of the divine philosophy in the book of the Universe are those poor figures you see in the text-books of geometry."[55] The most we can see in these statements is a vague and hazy presentment of the profound difference between physical truths and the so-called truths of mathematics.
In conclusion, until for the third of my three points we can discover much more obvious "sources" than those suggested up till now, I shall see no cause to modify my verdict upon the originality of Vico's conception of mathematics. This originality is further proved by the important consequences drawn by Vico from his theory of mathematics for his philosophical method; for every one knows that a thought taken over bodily from another remains inert and sterile, while an original idea is always active and fruitful.
_Note._--I have selected, of the various criticisms directed against my book on Vico, that concerning his "originality," because this gave me opportunities for researches and explanations of some value. But my book has been subjected to two general criticisms which do not lend themselves to the same treatment.
It has been said that in my exposition of Vico's philosophy I have followed my personal philosophical convictions: and sermons and epistles have been showered upon me preaching the duty of casting off prejudices, etc., and narrating the history of philosophy in an objective manner, etc. But I should like my critics to believe that my "convictions" cannot have, to my mind, the character of prejudices, but precisely that of liberation from prejudice, which is what they demand: that detachment and purity of understanding which is necessary for the comprehension of historical facts, and is not, as some fancy, a primeval innocence, but the fruit of laborious cultivation. To grasp Vico historically in his strict reality I have been compelled to undergo a _catharsis_ of prejudices, consisting in my case of the philosophy to which my own efforts had led me. My ideas may be untrue, but that is another question; and that means that if their falsity is proved I am bound to clear and purify my mind by means of less false ideas; but these in their turn must always be ideas and become convictions. In point of abstract method, no objection at all can be made to any one who looks at Vico through the spectacles of scholasticism if he thinks they make his sight more distinct and penetrating; the most we can do is to try and persuade him that there are better spectacles on the market. But we certainly have the right to smile if this same scholastic goes on to warn us that "in studying a philosopher, in investigating and reconstructing his thought, it is absolutely necessary to bring to the task a mind free from preconceptions and hostile to prejudices"; while all the time he is trying to pass off his scholastic opinions and religious beliefs under the banner of objectivity, sincerity and freedom from prejudice. "Philosophers"--I have seen this assertion too--"are unfitted for writing the history of philosophy, because they have ideas of their own." And who is fitted for it? People who are not philosophers? Does not Vico teach us precisely this, that where he who makes the facts (as the philosopher makes philosophy) himself narrates them, there history reaches its highest certainty?