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Ad Infinitum... The Ghost in Turing's Machine
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This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical interpretation of whole numbers held by mathematicians, and replaces it with a radical alternative. The author bases his analysis on the development of a semiotic model that characterizes mathematics as a form of discourse organized around certain kinds of waking dreams or thought experiments. The model allows him to articulate the role of the sign-using mathematical subject and of that subject's imagined self which plays a crucial part in achieving mathematical persuasion. Ad Infinitum is a significant contribution to postmodern epistemology and the philosophy of science.
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