Entire volumes can and have been written about Socrates, Plato, and Aristotle individually. Even more, volumes can be written about the relationship among these, the greatest of Greek thinkers. What follows will be an attempt to summarize briefly the influence these men had not only on their contemporaries, but on modern philosophy, as well.
What logicians today call logic is not what the layperson today calls logic. And neither of these is what the Greeks called logic. The Pre-Socratics seem to have had a notion of logic or at least logical demonstration. The Pythagoreans probably best exemplify this in that they understood that the rigorous method of demonstration that accompanied geometric proofs constituted a formal, objective, and authoritative proposition about some geometric figure. It is unclear if the Pythagoreans influenced Socrates. He was definitely a practitioner of the dialectic method of investigation, however. We see this method employed in the Theaetetus, but the Pre-Socratics were also aware of the method and also utilized it. Zeno of Elea is probably the best-known example, as he regularly applied the reductio ad impossibile approach to proving his mentor�s (Parmenides) arguments against motion (Kneale & Kneale, 1962, pp. 6, 7). Plato advanced the dialectic approach even further, being more greatly influenced by the Pythagoreans. It is clear that the concept of geometric proofs and validity became important to Plato and has Socrates applying many rudimentary logical principles in the dialogues, especially the Theaetetus and Sophist. One problem with Plato�s logical system, however, is that he frequently confuses metaphysical propositions with logical principles. But this was common among the Greek prior to Aristotle, so it is difficult to fault Plato in particular for it, but that we should expect more from such a great mind. Plato�s Sophist also presents Socrates as arguing a �collection and division� dialectic that would later serve as the basis for the Tree of Porphyry, named for the Neoplatonist who posited it. When we come to Aristotle, we find logic differentiating itself finally from the many philosophical sub-disciplines. Before this could happen, truth had to first be wrenched from the grips of ethical philosophy and realized as a separate epistemological notion devoid of ethical considerations in that context. Aristotle was thus able to create a formal system of valid inference that has been magnificently influential throughout the years. Though Fregean predicate logic has largely ruled since the late 19th and early 20th centuries, new thinkers such as Fred Sommers are finding the new logic to be much too artificial and are synthesizing the old logic (Aristotelian) with modern propositional logic. The result is an elegant and coherent system that can actually be applied by the layperson.
What the layperson still yet does not understand is the philosophical notion of knowledge. Socrates, in fitting with his sophist heritage, was very much a skeptic. Part of the problem in identifying where Socrates stood on the idea of knowledge is that his dialectic method of examination in dialogue naturally prevents the establishment of much in the way of positive arguments. We see Socrates leveling many negative arguments, but precious few positive ones. His disciple Plato was much more lucid, though. Plato saw all knowledge as being a priori in the World of Ideas. All that is �truly� knowledge exists therein. In the Theaetetus, Plato claims knowledge is justified true belief (189E-190A). It is not enough that one have an opinion, for if two have contradictory opinion, they surely cannot both be true. And if something is false, how indeed can it be said to be an object of knowledge? Even more, if it be true and my belief, perhaps I have but guessed: perhaps my belief that it is raining in Japan (and the fact that it is) is unwarranted; do I thus know it? Plato and most people would say no. Thus, justification is the missing link. Even to this day, the overwhelming majority of the discussion regarding epistemology centers on the theory of justification. Plato was something of a skeptic, something of a rationalist, believing that our experience of material objects is not truly knowledge, for we do not know the thing in itself (Kant�s Ding an sich), but a fallible combination of Ideas. Only when one ascends to the World of Ideas and grasps the Thing in question can knowledge be truly attained. This view has come to be known as Platonic realist. Aristotle was also a realist, but not in a Platonic sense. He believed that we truly do know the thing we sense, which is comprised of two parts: matter and form. For most purposes, Aristotle�s matter is generally what we think of today, minus all the atomic theory that sometimes coheres in the common connotation of the word. Thus, by simple, controlled observation of the world before our senses, Aristotle believed we could obtain knowledge.
Plato�s Symposium poses a bit of a difficulty for us in trying to determine whether it is Plato that holds the view of love presented or whether the words expressed by the character Socrates are actually those of the ancient figure. Given the later date of the Symposium and the other elements introduced, especially the character of Diotima, who is generally believed to be the only named fictitious character in Plato�s dialogues (�Diotima,� 2006, � 3, 4), we are lead to believe that Plato expresses his own views. A particularly compelling argument for this conclusion is the distinctly Platonic answer given by Diotima in the conclusion of the dialogue:
He who under the influence of true love rising upward from these begins to see that beauty, is not far from the end. And the true order of going or being led by another to the things of love, is to use the beauties of earth as steps along which he mounts upwards for the sake of that other beauty, going from one to two, and from two to all fair forms, and from fair forms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the notion of absolute beauty, and at least knows what the essence of beauty is. (Plato, 2000, p. 37)
The overwhelmingly Platonic theme in this passage can only lead us to believe that Plato saw love as participation in the Idea Beauty. Unfortunately, it seems that, since Plato is our only source of information concerning Socrates, that if the latter spoke on the subject, such information is lost to us. Aristotle also seemed to be disinterested in the subject, and so we are left with Plato�s thoughts alone among the greatest of the Greeks.
We thus come to the final point of comparison: ontology. For some reason, modern philosophers think they have ontology quite figured out. The ancient Greeks had no such misconceptions. The Sophists plied their trade on the unsuspecting populace and “proved” such absurd conclusions as �non-being exists.� Now, such a silly proposition is clearly meaningless as it is self-contradictory, but then, the ancient Greeks did not enjoy the well-developed system of logic we have today. Plato�s theory of ontology is intimately tied to his metaphysics. There is the World of Ideas, which most certainly exists, and the Ideas are certainly particulars (upsetting modern logicians who denounce subalternation), and also certainly existence. But the world shaped by the Demiurge based on these Ideas is an imperfect mishmash. Thus, for Plato, what we see as a rock is really only a rock insofar as it participates in the Idea Rock. It is the Rock that exists, not the rock. The rock is simply an imperfect representative of Rock. Aristotle thought this all a very silly distinction. He retained Plato�s realism, but introduced an empirical epistemology. This shifted his ontological position to be that objects truly do exist as we sense them. The rock I hold in my hand is actually a rock: it is formed in the form of a rock and it is made of the matter that rocks are made of. These two essential qualities make this really a rock.
While the ancient Greeks are frequently studied and paid lip service as being heavily influential on modern philosophy, this is usually a disingenuous homage. But it is actually more the case that philosophy has probably advanced only moderately from the Greeks. More appropriately, it seems that we have simply made it more complex and more confused with the infusion of new terms and new revisions of old ideas. Any way one looks at it, clearly we owe a great deal to these three groundbreaking men.
Soli Deo Gloria
Jon
References
Bruder, K., & Moore, B. N. (2002). Philosophy: The power of ideas (6th ed.). Boston: McGraw-Hill Higher Education.
Diotima. (2006, March 23). Retrieved April 9, 2006, from http://en.wikipedia.org/wiki/Diotima.
Kneale, W. & Kneale, M. (1962). The development of logic. Oxford: Clarendon Press.
Plato. (2000). Symposium. In S. Rosen (Ed.), The philosopher�s handbook, (pp. 27-37). New York: Random House.