Alcibiades tells us, in Plato’s Symposium, that the “bite of philosophical reasoning is more acute for a young and gifted mind than that inflicted by a tooth of a serpent. Once you have suffered that bite, you never know what you will do or say... As I look around this room, all of you have participated in the same madness: the Bacchic frenzy that possesses the lover of wisdom.” Today I see in your eyes some faint spark of that fiery madness and crystalline wisdom that might have once enriched Plato’s Academy. I ask that you open your thoughts and direct your minds to search with me for this poisonous promise of philosophic wisdom.
Why should the “icy laws of outer fact” and science bend its knee to philosophy’s “private dream”? (William James, The Will to Believe, 1896) Plato answers that scientific knowledge today - no less than yesterday - requires that we, not only explain the necessary conditions for any consequence, but, moreover, apprehend these Ideas with a most erotic passion; and that it is better to “suffer anything” than live unreflectively through the fatuous misery of false opinions. (Rep. 516d)
Modern natural science follows Plato’s example in searching for the essential conditions that cause all natural phenomena. For every anomaly, science hypothesizes some new law, force, or element from which it may necessarily deduce the possibility of what has been observed. This 'hypothetical-deductive' scientific method, which Karl Popper called the “logic of scientific discovery” (1934), was founded in Plato's logic of Ideas. Hermann Cohen writes: Plato is the founder of the system of philosophy because he founded logic... by establishing logic's connection to science, and thus grounding logic... in the concept of the Ideas. (1902 446-7)
Plato's logic of Ideas is the earliest common ancestor of Aristotelian syllogistic logic, Hegelian dialectical logic, and modern symbolic logic: for Plato provided the ontological infrastructure for Aristotle's formalization of logic into an array of valid syllogisms; the unity, division, and mixture of concepts that motivates Hegel's self-oppositing dialectic; and the universal Ideas of predicates and functions for Frege and Russell 's symbolic quantified logic. Even in the ancient world, Plato’s dialogues were mined for the roots of classical logic, (Alcinous) and even today he has provided fresh inspiration for recent alternatives to classical logic. (Priest 2012)
Yet Plato’s most abiding and decisive contribution has been in the realm of theology. Within living memory of his teacher, Xenocrates had identified Plato's supreme Idea with Zeus, the king of the gods, and the lesser Ideas as his divine thoughts, sprung like Athena from his hallowed head. Numenius described Plato as 'Moses speaking Greek'. Philo and Origin of Alexandria later adapted Hellenistic Platonism to formulate the classical definition of God, as the one, transcendent, and perfect being. (Hartsthorne 2000 76) William Inge reflected that “Platonism is part of the vital structure of Christian theology... There is an utter impossibility of excising Platonism from Christianity without tearing Christianity to pieces.” (Gifford Lectures 1917)
The philosophy of Plato has, without exaggeration, been “the inspiration of innumerable poets and prophets who have called upon men to rise above ephemeral interests to the contemplation of all time and all being.” (More 1917 270) With this lecture on the logic and ontology of Plato, I hope, in some small measure to turn your thoughts to become, in the words of Ezra Pound, “suddenly conscious of the reality of the nous, of mind, apart from any man's individual mind, of the sea crystalline and enduring, of the bright as it wore molten glass that envelops us, full of light."
Socratic dialectic, or elenchus, is the art of questioning to expose the contradictions that emerge through the discursive elaboration of conflicting assumptions: for any thesis, Socrates advances a counter-thesis that, once agreed upon, results in a contradiction that may only be resolved by rejecting one of the contraries. (Vlastos 1983) Since contradictions are silent as to which of the contraries should be rejected, some further assumptions are invariably required to resolve the truth and falsity of the contraries. Yet if these further assumptions are also contradictory, then Socratic questioning must begin anew until all the contradictions among the conflicting assumptions have been completely resolved. Socratic dialectic thus proceeds from the contradictions between conflicting assumptions, to their tentative resolution in some further assumptions; and then, from any further contradictions, toward the resolution of all contradictions into knowledge of all truth and being.
This dialectic of conflicting assumptions can also be observed to operate in the history of Greek philosophy. Eduard Zeller writes that the “history of philosophy too has its own system of laws… One problem rather grows out of another by an inner necessity... Thus the history of the philosophy of a people mirrors the development of its thought.” (1889/1955 28) Parmenides had identified speech and thought with Being itself, but could not explain the contrary opposition between Non-Being inscribed in every determination of Being. Heraclitus purported to explain this opposition as the coincidence of contrary opposite properties in all beings, but could not explain the possibility of non-contradictory knowledge of beings. Socrates answered that, by exposing and rejecting false definitions, we might come to know the definitions of all beings; and Plato individuated Parmenides’ Being into a plentitude of universal Ideas, each of which perfectly unites the thought and being of some predicate-property.
Plato’s logic of Ideas may re-construct Aristotle’s syllogistic logic on the basis of universal Ideas of subject and predicate terms, which flow from universal Ideas to particular instances according to the higher-order Ideas of the laws of logic. This logic of Ideas is grounded, unlike Aristotle’s formal logic, in Plato’s ‘unwritten’ ontology: the original opposition of the One and the Dyad is mixed in the Triad to generate the numerical dyad, the Idea-numbers, and all complex mathematical and geometrical forms which comprise the World-Soul. This original opposition of the Dyad motivates the division of genera into many species, as well as the exclusion, opposition, and contradiction between the various assumptions of Socratic dialectic; even as the One unites these differences into ever richer triadic mixtures. In the waning years of the ancient world the promise of Plato’s ontology was unwittingly transmogrified - beyond all comprehension - by the external reflection of thinking into the poisonous thought of being beyond being that froze thinking in an icy mystery. Yet through the incarnation of God as Christ within the World-Soul, Christianity reanimated this thought to think itself as God is humanized, humanity is divinized, and God and man are reconciled.
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