Archytas shows that objects should be defined as combinations of Philolaus’ limiters with unlimiteds, whose arrangement can be determined mathematically. Not only the natural world but also political relationships and the moral action of individuals are explained in terms of number and proportion. Thus, the Pythagorean identifies rational calculation as the basis of both a flourishing state and a successful person. Archytas insists that reason is human beings’ sole faculty that can free them from the dominance of instinctual and emotional behavior.
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