By Reuben Hersh
Number of the main attention-grabbing contemporary writings at the philosophy of arithmetic written through hugely revered researchers from philosophy, arithmetic, physics, and chemistry Interdisciplinary ebook that might be precious in different fields—with a cross-disciplinary topic region, and contributions from researchers of varied disciplines
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HIPPOCRATES Of course, it is true. SOCRATES Well, how about geometry? Can it not be applied in building houses, in making pots or in computing the amount of grain a ship can hold? HIPPOCRATES Of course, it can be applied, though it seems to me that for these practical purposes of the craftsman not too much mathematics is needed. The simple rules known already by the clerks of the pharaohs in Egypt are sufficient for most such purposes, and the new discoveries about which Theaitetos spoke to me with such overflowing fervor are neither used nor needed in practice.
Therefore”, although reflection on the philosophy of the past will remain one of the elements of future philosophy, “an adequate formal logic will be a second element of future philosophy”30. Kreisel claims that the approach to philosophical problems of the philosophical tradition is viable only “at an early stage, when we know too little about the phenomenon involved and about our knowledge of it in order to ask sensible specific questions”31. Such an approach must be replaced by one based on mathematical logic, which is “a tool in the philosophy of mathematics; just as other mathematics, for example the theory of partial differential equations, is a tool in what used to be called natural philosophy”32.
I saw the trilogy of Aeschylus at the theatre last year. SOCRATES Then tell me the story in a few words. HIPPOCRATES While Agamemnon, the king of Mycenae, fought under the walls of Troy, his wife, Clytemnestra, committed adultery with Aegisthus, the cousin of her husband. After the fall of Troy, when Agamemnon returned home, his wife and her lover murdered him. SOCRATES guilty? Tell, me Hippocrates, is it quite sure that Clytemnestra was 8 Alfréd Rényi HIPPOCRATES I do not understand why you ask me such questions.
18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh