Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

INTRODUCTION 3
the nature of the thing appraised. We are, therefore,
not surprised to find that researches concerning the essential nature of mathematics have been prosecuted, especially in recent times, far more resolutely and systematically than such as aim at a critical estimate of its significance and value. In Plato and in Aristotle, as you
know, research of both kinds produced results of great
importance. I shall not speak of the great Greek mathematicians for their interest centered, not in the philosophy
of their subject, but in the science of it. They were swimmers mainly-not non-aquatic students of swimming. It
seems incredible that, after Plato and Aristotle, no important contribution to the philosophy of mathematics was
made in the course of twenty hundred years. Yet that
is the fact. Even the brilliant and exquisite De L'Esprit
Géometrique of Pascal is thoroughly Aristotelian. The
great revival had to await the appearance of Leibniz
-of him who said, 'Ma métaphysique est toute mathematique." As students of philosophy, you know that
throughout his life this marvelous man was haunted by a
magnificent dream-the dream of "a universal mathematics." In his manifold endeavors to make the dream
come true is found the origin of that great critico-constructive movement which has done more than all previouis centuries to disclose the essential nature of rigorous
thought and which, after notable vicissitudes of fortune,
is known today, in all scientific countries of the world,
under the characteristic name of Symbolic Logic.
The leading names of its pioneers and contributors —
Leibniz, Lambert, De Morgan, Boole, Jevons, Schrôder,
Peirce (C. S.), MacCall, Frege, Peano, Russell, Whitehead, Hilbert, Huntington, Couturat, and others-sufficiently indicate it4 international interest and the variety