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" "There was a time when philosophy might have been defined as the science of human activity, so all-comprehensive was it. The ambitious Greek who would attach his name to a philosophical system must include in his scheme all that could be known, done, and speculated about God, the world, and man. In the course of time and the specialization of the sciences this view of philosophy fell away, and was replaced by the more exact and narrower conception of modern times.
Nicholas Murray Butler (April 2, 1862 – December 7, 1947) was an American philosopher, diplomat, and educator. Butler was president of Columbia University, president of the Carnegie Endowment for International Peace, and a recipient of the Nobel Peace Prize.
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Both anti-Semitism and the Ku Klux Klan are an insult to democracy and a contradiction of it. But faith honest, sincere, hopeful, opens a door to moving forward in this new and very difficult world in which our children must live. It opens the door into that world in a spirit inspired by something more than the merely human, the gain-seeking and the temporary. It brings us, our children and our grandchildren, in touch with the eternal verities which are the only possible foundation for a civilization and a life that are worthy of human ambition and human endeavor.
1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.