"Philosophy" in fifth–fourth century Athens meant simply "higher education," that is, whatever disciplines, beyond elementary education in gymnastics and "grammar" and "music" (including poetry), might be needed for someone who wishes to live well and to rule his city (or even his own household) well. For different teachers, this would cover different disciplines. For Isocrates, "philosophy" meant rhetoric. For Plato, to judge from the ideal curriculum of
Republic VII, it meant mathematics (arithmetic, plane and solid geometry, astronomy, and "harmonics" or music theory) and dialectic (an art of regimented discussion, in which a respondent defends some thesis, typically a definition, and a questioner tries to refute it by yes-no questions leading to a contradiction); these are the means that will lead to knowledge of what really and eternally
is, and ultimately of divine things (the Forms and the Good).
Plato conspicuously leaves out rhetoric, which deals with mere opinions rather than with how things really are. He also leaves out pre-Socratic–style "physics" or "natural history," which he thinks is approximate and probable rather than precise and certain, and which explains things by placing them in a grand cosmogonic narrative of how things come to be, rather than (like mathematics and dialectic) by defining and demonstrating what things eternally are.
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