We are inclined to treat ancient argument at face value, except where we do not understand the significance of the argument. Then engagement with the material is difficult to maintain, because what we need to know isn't present. The argument is dependent on an esoteric interpretation long lost to us. Or at least that the consensus view.
Both Plato and Aristotle's writings contain arguments which either don't make clear logical sense within themselves, or in the context of the rest of the work. One translator of Plato's Philebus (Robin Waterfield) confessed in his preface that even after translating the work, he didn't know what it was about.
Sometimes the clues to the meaning of arguments are present elsewhere in the canons of both writers, even for the ones which clearly involve an esoteric level of understanding. The whole body of their outputs need to be taken on board in order to grasp the meaning of individual works. This is usually not done with the works of Aristotle. His Historia Animalium is read by biologists and specialists in animal taxonomies, but usually they read little else of his work. As if one work is unconnected to the others.
Sometimes arguments are unsatisfactory at a logical level. It would be easy to write these examples off as sloppy instances of argument. But we may be too quick to do this. Both Plato and Aristotle taught students, and we need to explore something of their approaches to the education of their students.
We can begin by considering Aristotle's laws of thought, which are the ancestor of most later systems of non-paradoxical logical modalities. They aren't as sound as they would seem to be, and his approach to the education of his students may have something to do with this.
Aristotle’s laws of thought are as follows:
A thing is itself and not something else. Which is known as the law of identity.
There is also the law of non-contradiction – a thing cannot be a thing other than itself, at least at the same time. Aristotle gives three definitions in his Metaphysics: Ontological: "It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect." (1005b19-20). Psychological: "No one can believe that the same thing can (at the same time) be and not be." (1005b23-24). Logical: "The most certain of all basic principles is that contradictory propositions are not true simultaneously." (1011b13-14)
The third is the law of the excluded middle. Meaning that a thing is either itself, or something else, not something in between. He states it as a principle in the Metaphysics book 3, saying that it is necessary in every case to affirm or deny, and that it is impossible that there should be anything between the two parts of a contradiction.
This is not part of Aristotle’s manual of logical procedure, known as the Organon. The Organon codifies how the human understanding should deal with identifying and differentiating aspects of reality, reasoning, deduction, detecting false or misleading conclusions and specious modes of argument (the text on Sophistical Refutations is part of the Organon). This work is based on the ancient practice of collection and division, of identifying the same, and what is different. We normally think of dialectic as what the Greeks did in the course of philosophical argument, but its original scope was much wider than that. They were engaged in the practice of collection and division in Babylonia and elsewhere in the second millennium B.C.E. Which is why the Babylonians and the Assyrians created lexical lists of objects which had something in common, such the property of whiteness (the purpose of which scholars initially found puzzling, and most still do).
The law of non-contradiction, as stated by Aristotle, isn’t actually provable, though he tried to demonstrate it. Many later philosophers have tinkered with the law, but its main use is as a guide to thinking, and it is useful to know, even if it is possible to give instances where it does not hold.
I've said elsewhere that Aristotle practised sophistry. I do not mean that he was a liar or that he was trying to make 'the worse cause appear better' (Plato’s accusation against the sophists). But he did create fictions. I used the conclusion of his Nicomachean Ethics as an example, in which he states that the gods cannot move or interact with the world, and that their function is restricted to contemplation. Which must have seemed like a denial of the role of the divine in the world, current at the end of the fourth century B.C.E.
I studied the Nicomachean Ethics in some depth as a student, and noticed that a part of his argument is repeated, in slightly different words (in Book 8 I think). It has been observed before that the cramped and compacted wording of Aristotle’s treatises is reminiscent of lecture notes taken down in the classroom. And that’s what we have here - someone has collated notes from at least two different hands, and added two passages which repeat the same section of one of Aristotle’s classes (there are three ethical treatises which are attributed to Aristotle, so this may have been a popular series of classes, perhaps repeated on different occasions, and in slightly different forms).
My point is that Aristotle was a teacher, and was creating lectures which weren’t simply to be absorbed whole as the final word on the subject by a great teacher. He was expecting his students to think. Some of the students would ask questions, query points, or perhaps argue against the main pillar of the argument, though most wouldn’t.
Both Plato and Aristotle had the concept of an inner and outer knowledge. Plato referred to these grades of knowledge as ta eso and ta exo. We know that students at Aristotle’s Lyceum attended two different sets of classes, one in the morning, and the second set in the afternoon. Exoteric knowledge was taught in the morning, and the esoteric understanding of things was reserved for those who attended in the afternoon.
Esoteric knowledge is by definition obscure in nature, and/or difficult to understand. Which is what the story of the prisoners in the cave in Plato’s Republic is all about. They see the shadows of reality on the wall before them, but not the reality itself. When they are released with suddenness, their reason is deranged by the experience. Instead they should have been released gradually, being shown details of reality first, without the whole of the shocking truth of reality being given to them all at once.
So both Plato and Aristotle were dealing in what they understood to be esoteric knowledge. In Mesopotamia there was a similar division of the types of knowledge. We are told by the Assyrian king Esarhaddon (Seventh century B.C.E.) that the common run of men are ‘deaf and blind throughout their lives’. Exoteric knowledge of divine things would consist of the names of the gods, their epithets, and stories told of the gods. This superficial knowledge could be imparted by fathers to sons, and could be taught in the schoolroom, as sometimes is said in tablet colophons. The esoteric knowledge was kept secret by the initiates and the priesthood, and tablets relating to the mysteries of the gods would state that they were not to be read by the uninitiated.
Aristotle’s Lyceum can therefore be thought of as a combination of school and college, with the classes in the morning providing a steady flow of students who had shown sufficient intelligence and independence of mind to be suitable for the classes which imparted esoteric knowledge in the afternoon. They could show this intelligence by challenging the sophistical arguments embedded in Aristotle’s lectures (as I’ve said, he attempted to prove some of his arguments, but didn’t always succeed. The students were supposed to spot when what he said was not soundly based).
"First then this at least is obviously true, that the word 'be' or 'not be' has a definite meaning, so that not everything will be 'so and not so'. Again, if 'man' has one meaning, let this be 'two-footed animal'; by having one meaning I understand this:-if 'man' means 'X', then if A is a man 'X' will be what 'being a man' means for him. It makes no difference even if one were to say a word has several meanings, if only they are limited in number; for to each definition there might be assigned a different word. For instance, we might say that 'man' has not one meaning but several, one of which would have one definition, viz. 'two-footed animal', while there might be also several other definitions if only they were limited in number; for a peculiar name might be assigned to each of the definitions. If, however, they were not limited but one were to say that the word has an infinite
number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning our reasoning with one another, and indeed with ourselves, has been annihilated; for it is impossible to think of anything if we do not think of one thing; but if this is possible, one name might be assigned to this thing."
— Aristotle, Metaphysics, Book IV, Part 4
He cannot mean this. All poetry, literature and art collapses at this point, where Aristotle claims that, in order to eliminate ambiguity in thought, there should be a one to one correspondence between words and definitions. This would have made no sense to the Babylonians and to the Assyrians, whose literature is woven all through with wordplay - homonyms, synonyms, ideograms, logograms, phonograms, metaphor, metonomy, and a litany of interchangeable signs and signifiers.
This is a good place to pass on to a discussion of the kind of logic invoked by Plato to understand the nature of reality. There are intimations in his canon that he understood pretty well the laws of thought that we find in Aristotle, but there is another logic present and discussed at length, which entirely cuts across the three laws, and enables a quite different picture of reality. Whereas Aristotle’s laws of thought provide guidance for understanding what exists in the world of physical existence, what Plato tells us about is an esoteric doctrine, which explains what is hidden and obscure, and relates to the gods, and what is divine. As one might expect, the rules for the gods are different.