## The New Infinite and the Old Theology |

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answer aspects belong called collection 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 evident example fact familiar feel finite Freedom geometricians geometry golden point golden sphere higher Hyperspace hypothesis ideas infinite manifolds Infinite of theology infinite region infinity integers kind light limits line-world logical logical implication matching mathematicians mathematics Mathesis matter mean merable multitude nature number of points number of rays ology omnipresence once overworld pair plane possible postulates precisely present proposition question range from zero rank rational theology reader realm reason regarded relation respect of dignity rience rigorously seen 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

### Popular passages

Page 4 - ... New Infinite and the Old Theology") says, "Mathematics is indeed a humble servant— a drudge, if you please; an unsurpassed drudge — in the sense that nothing else does a larger share of humble and homely work. To imagine, however, that her place in the hierarchy of knowledges is thereby defined is hardly the beginning of wisdom in the matter. It is necessary to look much higher. Her rank in the ascending scale is not that of a useful drudge, immeasurable as is her service in that capacity;...

Page 90 - 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 107 - 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 4 - ... shipwreck. Mathematics is vastly more than a tool; it is a type of thought, and even high school students gain indispensable training in mental activities from it — such training as cannot be gained so well from any other study. Professor CJ Keyser ("The New Infinite and the Old Theology") says, "Mathematics is indeed a humble servant— a drudge, if you please; an unsurpassed drudge — in the sense that nothing else does a larger share of humble and homely work. To imagine, however, that...

Page 90 - 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 49 - ... 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 5 - ... 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 99 - ... 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.

Page 1 - ... qualified this science to shed new light upon some of the harder problems of rational theology. No demand will be made upon the reader's knowledge of mathematical technique; all that is required is a fair measure of mathematical spirit, which is simply the spirit of logical rectitude.

Page 103 - Nous sommes aujourd'hui tellement familiarises avec cetti notion que nous pouvons en parler, meme dans un cours d'universite, sans provoquer trop d'etonnement.