Aristotle was no less impressed than Plato by the power of the axiomatization, but he did not believe Plato's optimistic claim that all knowledge could be founded upon a single set of axioms. For he was equally impressed by the apparent independence of the sciences. Mathematicians and doctors, biologists and physicists, work in different domains, discuss different objects, and follow different methods. Their disciplines rarely overlap. Nevertheless Aristotle felt the need for system: if human knowledge is not unitary, it is surely not a mere disconnected plurality either. 'The causes and principles of different things are different -- in one way; but in another way, if you speak universally and by analogy, they are all the same.' The axioms of geometry and the principles of biology are mutually independent, but they are the same by analogy: the conceptual apparatus and the formal structure of all the sciences are the same.
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