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answer ascending scale aspects belong called common comprehend concept contradictions cosmic countless course deal denoted denumerable infinitude denumerable type Dignity of omniscience doctrine dogma domain elements emotions endlessly ensemble of points equally essen essential eternal example fact familiar feel finite fractions geometricians geometry golden point golden sphere higher Hyperspace hypothesis ideas imagination infinite manifolds Infinite of theology infinite region infinity integers kind light limits line-world logical logical implication matching mathematicians mathematics matter mean merable multitude nature number of points number of rays ology omnipresence once overworld pair plane postulates precisely present projective geometry proposition question rank rational theology reader realm reason regarded relation respect of dignity rience rigorously seen sense sheaf silver sphere space speak spirit subject-matter superrational suppose term-sum theological Infinite theology’s theory things thinkable thought tions totality transcending true type of infinitude understanding unendliche universe vision wealth whole number YALE UNIVERSITY
Page 98 - Wie alles sich zum Ganzen webt, Eins in dem andern wirkt und lebt! Wie Himmelskräfte auf und nieder steigen Und sich die goldnen Eimer reichen! Mit segenduftenden Schwingen Vom Himmel durch die Erde dringen, Harmonisch all
Page 88 - E, 0, and F are all infinite manifolds. "What is important is now obvious," says Keyser. "It is that we have here three infinite manifolds, E, 0, F, no two of which have so much as a single element in common, and yet the three together constitute one manifold M exactly equal in wealth of elements to each of its infinite components.
Page 105 - The general law of the land is in favor of the wager of battle, and it is our duty to pronounce the law as it is, and not as we may wish it to be. Whatever prejudices, therefore, may justly exist against this mode of trial, still, as it is the law of the land, the court must pronounce judgment for it.
Page 88 - This statement appears to be the mathematical version of the old theological doctrine that man is "made in the image of God." The heart of the book is contained on pages 90 and 91, as follows: "An infinite /of even the lowest type always contains not merely two or three or a million components each equal to it in plenitude of elements, but an infinity of such components. The like is equally true of the infinites of whatever type in the endless scale of types. Must we suppose the truth to fail in...
Page 3 - ... matters independent of opinion, passion, accident, and will; it is thus peculiarly hers to release human faculties from the dominion of sense by winning allegiance to things that abide; her meditations transcend the accidents of time and place; it is their idiosyncrasy to have for subject proper, not the fickle and transitory elements in the stream of a flowing world, but those aspects of being that present themselves under the forms of the infinite and eternal.
Page 47 - ... THE OLD THEOLOGY. By Cassius J. Keyser, Adrain Professor of Mathematics in Columbia University. New Haven : Yale University Press. 1915. Pp. v, 117. In spite of the title and the name of the author, this exceedingly suggestive and ingenious little work was not "made in Germany." The author contends that "we are in a world where it is easy to encounter a whole having a part whose elements are precisely as numerous as are the elements of the whole. Every whole of that kind is said to be infinite.
Page 3 - ... characterizes the highest art, — that of ancient Hellenism, for instance, which was equally careful to reproduce only the ideal in thought and only the beautiful in form. I have concluded that nothing could more certainly accomplish the desired end than a practical recognition of the relationship of art both to religion on the one hand and to science on the other, together with a recognition of the natural limitations to art which such a double relationship necessarily involves. — The Representative...
Page 97 - ... and so within the tiny sphere — indeed in every room however small — the whole dynamics of the universe is depicted completely and coenacted by motion of points and transformation of point configurations. There in miniature proceed at once the countless play and interplay of every kind of motion, small and large, simple and complex, the quivering dance of the molecule, the wave and swing of universal aether.