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Xenocrates recognized three grades of cognition, each appropriated to a region of its own: knowledge, sensation, and opinion.
He referred knowledge ( episteme ) to that essence which is the object of pure thought, and is not included in the phenomenal world ; sensation ( aisthesis ) to that which passes into the world of phenomena ; opinion ( doxa ) to that essence which is at once the object of sensuous perception, and, mathematically, of pure reason-the essence of heaven or the stars ; so that he conceived of doxa in a higher sense, and endeavoured, more definitely than Plato, to exhibit mathematics as mediating between knowledge and sensuous perception All three modes of apprehension partake of truth ; but in what manner scientific perception ( epistemonike aisthesis ) did so, we unfortunately do not learn.
Even here Xenocrates's preference for symbolic modes of sensualising or denoting appears: he connected the above three stages of knowledge with the three Fates: Atropos, Clotho, and Lachesis.
We know nothing further about the mode in which Xenocrates carried out his dialectic, as it is probable that what was peculiar to Aristotelian logic did not remain unnoticed in it, for it can hardly be doubted that the division of the existent into the absolutely existent, and the relatively existent, attributed to Xenocrates, was opposed to the Aristotelian table of categories.

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