دانلود کتاب Mathematics as sign : writing, imagining, counting

"Two features of mathematics stand out: its menagerie of seemingly eternal objects (numbers, spaces, patterns, functions, categories, morphisms, graphs, and on), and the hieroglyphics of special notations, signs, symbols, and diagrams associated with them. The author challenges the widespread belief in the extra-human origins of these objects and the understanding of mathematics as either a purely mental activity about them or a formal game of manipulating symbols. Instead, he argues that mathematics is a vast and unique man-made imagination machine controlled by writing."."Mathematics as Sign addresses both aspects - mental and linguistic - of this machine. Essays explore the status of these signs and the nature of mathematical objects, how mathematical ideograms and diagrams differ from each other and from written words, the probable fate of the real number continuum and calculus in the digital era, the manner in which Platonic and Aristotelean metaphysics are enshrined in the contemporary mathematical infinitude of endless counting, and the possibility of creating a new conception of the sequence of whole numbers based on what the author calls non-Euclidean counting."--BOOK JACKET.  Read more... Preface: Writing, Imagining, Counting --Toward a Semiotics of Mathematics --Making Marks on Paper --How Ideal Are the Reals? --God Tricks; or, Numbers from the Bottom Up? --Counting on Non-Euclidean Fingers.