This chapter begins with a quotation taken from the introductory essay to the mathematical summa edited by Aleksandrov, Kolmogorov, and Lavrent'ev. The opposition between the continuous and the discrete described by Aleksandrov has been the principal theme of this book, and has given the book its title. Aristotle maintains this opposition in a sharp, rigid way. Meanwhile, ancient quantum theorists undermined the opposition in the most radical way by eliminating the continuous in favour of the discrete. On the other hand, Stoic physical thought emphasizes continuity in the physical world at the expense of discreteness. At a mathematical level, means for overcoming this opposition were not available until the latter part of the nineteenth century.
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