Mathematics
Mathematics, rather unexpectedly, is the object of the first chapter of Spengler's book, which suggest its importance there. Conceptions of space, as expressed by an "Ursymbol" are central for each culture and, along with time and number, they form a specific "mathemetical style". Against the universal validity of mathematical results, Spengler asserts that mathemathics is not a single science but a plurality of sciences.
He notes that in Greek classical mathematics that there are only integers and no real concepts of limits or infinity. Therefore, without a concept of the infinite, all events of the distant past were viewed as equally distant, thus Alexander the Great had no problem declaring himself a descendant of a god. On the other hand, the western world—which has concepts of the zero, the infinite, and the limit—has a historical world-view which places a high amount of importance on exact dates.
Read more about this topic: The Decline Of The West
Famous quotes containing the word mathematics:
“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
—Amelia E. Barr (1831–1919)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)