Wednesday, December 23, 2009
Platonism and Oneness
Plato seems on occasion to regard the Form of the Good as the most important Form. Even if so, the essential Form is, plainly, the Form of Oneness, since the essence of Form is Unity. Further, since the Forms are self-subsistent entities, so too is The One. Thus, for Platonism, since the One is also a Cardinal Number, all Cardinal Numbers are self-subsistent entities, and Mathematics is a purely analytical science. But, in Formaterialism, the One is a derivative notion, an abstraction from both the Formal Principle, Many-becoming-One, and the Material Principle, One-becoming-Many. Counting entails both, so, likewise, do the Ordinal Numbers. For one neo-Platonist, Plotinus, The One is explicitly the master Form, and, furthermore, is the source of an Emanation that generates all Reality. In Formaterial terms, Emanation is, hence, actually a Material Principle, and if other Platonists had considered the Mathematical implications of Plotinus' Theory of The One, Platonism might have arrived, at minimum, at the position that Ordinal Numbers are not inessential derivatives of the Cardinals.
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