Logical Modality in Classical Athens

The following is a sketch of a paper on an alternative reading of the understanding of logical modality in ancient Greece. It isn't yet properly annotated and referenced, and is subject to significant revision in the near future. Treat it as a working paper. It discusses an issue which surfaced in SHB, but which was explored differently there. It may also be of interest to those who have read my book on Frazer, since what follows below discusses how Plato was understood before Frazer argued that he was guilty of  'intellectual error'. 

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We are accustomed to the idea that Aristotle was the first person to codify the laws of thought which have come down to us as the basis of what is now formal logic. For the most part these laws are formulations and refinements of what is essentially common sense, so we are not forced to imagine that no-one had any clue about logical thinking before Aristotle.  Plato for example, is not deficient in the logic of his thought processes because he came before Aristotle’s codification.

However there is much in ancient writing, earlier and later, and also in the pages of Plato, which is not easily intelligible as being based on the laws of thought, or even based on plain common sense. In fact the laws of thought appear to be contradicted, and often. Are these just deficiencies in clarity of thought? Or is there another logical modality present in these writings, not codified by Aristotle or anybody else, but which was understood in classical Athens?

First, it is important to be clear about what is the essence of logical thinking, as codified by Aristotle. Aristotle’s laws of thought are as follows:

The first is that a thing is itself and not something else. Which is known as the law of identity.

The second, the law of non-contradiction, states that a thing cannot be a thing other than itself, at least at the same time. Aristotle gives three definitions of the law of non-contradiction in his Metaphysics:

At the ontological level, he says that: "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]. Looked at from the psychological level, he says: "No one can believe that the same thing can (at the same time) be and not be" [1005b23-24).  Finally, in terms of logic, Aristotle claims that: "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 [996b 26–30], 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).

The Metaphysics is a text which employs the ancient practice of collection and division; of identifying the same, and what is different. We normally think of dialectic (which is the Greek term for this critical technique, perhaps most clearly illustrated in Plato’s Sophist) as what the Greeks did in the course of philosophical argument, but its original scope was much wider than that. The practice of collection and division was also used 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 (scholars initially found the purpose of these lexical lists puzzling, and most still do). Marc van de Mieroop has recently published an intriguing study of the legal, divinatory, and literary texts, and word lists from Babylonia, which shows a strong adherence by the scholars to a logical understanding of what is the same, and what is different. Though he does not compare instances of the same and the different found in Babylonian literary texts and the word lists,  with discussion of the same and the different found in the pages of Aristotle. [‘Philosophy Before the Greeks’, Stanford, 2015].

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.

Plato had the concept of an inner and outer knowledge, which probably reflects something of a priestly understanding of both teaching and of reality. He referred to these grades of knowledge as ta eso and ta exo In the Theatetus. Which means that teaching operated at two levels – the exoteric and public level, and another which was esoteric in nature.

Esoteric knowledge is by definition obscure, 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 Plato was engaged with both exoteric and esoteric understandings of 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.

Did Plato understand a different kind of logic invoked by him 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 I think there is another pattern of 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.

In the Timaeus Plato refers to a principle of wholes, or totalities. It is later mentioned by the Neoplatonist Porphyry as a Pythagorean doctrine, and Pythagoras is supposed to have learned of it in a lecture in Babylon, after the fall of the city to the Persians in 539 B.C.E. Since this principle of totalities or wholes is ascribed to Pythagoras, if this ascription is correct, then the latest date of the principle is therefore the sixth century B.C.E.

It is of course, very much older. It can be detected in the Iliad, in Bk 18, where Hephaestus makes objects which, on account of their nature, can pass into the counsel of the gods, and return. The principle may have been brought back to the west by Pythagoras after his spell in Babylon and the Levant, or it may already have been part of a body of ideas already well established in Italy and in Greece. The principle might be simply put, as ‘things which are total participate in totality’, in the same way that Plato declared that ‘greatness is participation in the great.’ But it is so much more important than a statement that wholes conjoin with one another. It is the essence of the ascent from image to image to an apprehension of the Good which Plato refers to in the both the Timaeus and the Republic.

Each of these images must represent or embody an aspect of what Plato referred to as ‘the Good’. Each of the images must allow the supplicant to pass from one to the other via their essential identity (i.e., in that each image represents an image or embodiment of an aspect of the Good). What varies between them is the degree of their participation in the Good. Plato is very clear that the viewer of the images must be able to pass along the chain of images in either direction. The chain of images is not therefore purely about gaining an understanding of the Good (meaning the divine, or Being itself), either in reality or figuratively. Passage through the chain of images is about both the transcendence of images or forms, and about the descent of Being into the world of generation, as a generative power.

Each of these images is a symballō, a conjecture, based on certain agreed ideas among the sacerdotal class, and different across cultural groupings. The images are thrown or struck together in order to reduplicate and re-energise the power and presence of divine Being in the human world. For man, this might be seen as an act of worship or observance of what is holy, but it can also be understood also as a form of theurgy.

Given what we are given to understand about the differences between the patterns of the discussion of ideas in the near-east and in Greece, it may be surprising to hear that Pythagoras learned about the principles of wholes through lectures in Babylon. We know that ideas were discussed publicly in Mesopotamia, if usually in the form of a debate which explored the relative merits of one idea against another. It is possible that a lecture was the source of his knowledge of this doctrine, but it may be more likely, given the importance Pythagoras himself attached to the distinction between ‘hearers’ and ‘students,’ Pythagoras learned of the principle of wholes and totalities in some other way.

In the Timaeus  Tim 30a-b, Plato speaks through Timaeus, saying:

For God desired that, so far as possible, all things should be good and nothing evil; wherefore, when He took over all that was visible, seeing that it was not in a state of rest but in a state of discordant and disorderly motion, He brought it into order out of disorder, deeming that the former state is in all ways better than the latter. For Him who is most good it neither was nor is permissible to perform any action save what is most fair. As He reflected, therefore, He perceived that of such creature as are by nature visible, none that is irrational will be fairer, comparing wholes with wholes, than the rational….

Plato, in using the phrase ‘comparing wholes with wholes’, is referring to the principle of wholes and totalities mentioned in Porphyry’s account of Pythagoras.

It is interesting that Pythagoras is said to have associated with the ‘other Chaldeans,’ after Porphyry mentions his conferring with the king of Arabia. The current academic view is that the Chaldean dynasties were essentially Arab dynasties, and that they were in control of Babylon at this time.  This helps to confirm the reliability of some of the detail in this important passage, written so long after the lifetime of Pythagoras. 

So what did Pythagoras take from his long sojourn in Egypt, and the near-east? Is his doctrine like Plato’s? Porphyry’s account tells us that:

He cultivated philosophy, the scope of which is to free the mind implanted within us from the impediments and fetters within which it is confined; without whose freedom none can learn anything sound or true, or perceive the unsoundedness in the operation of sense. Pythagoras thought that mind alone sees and hears, while all the rest are blind and deaf. The purified mind should be applied to the discovery of beneficial things, which can be effected by, certain artificial ways, which by degrees induce it to the contemplation of eternal and incorporeal things, which never vary. This orderliness of perception should begin from consideration of the most minute things, lest by any change the mind should be jarred and withdraw itself, through the failure of continuousness in its subject-matter.

To summarise: the principle of wholes can be understood as a logical modality which connects the world of the mundane with transcendent reality. The definition of transcendent reality in Plato (articulated by Socrates) is that it is a place beyond shape, form, size, etc., and occupies no place on earth. It is however the place where knowledge has its reality (the ‘eternal and incorporeal things’ mentioned by Pythagoras). Connection with transcendent reality is possible by the likenesses to the transcendent which have existence on earth, such as things which are complete and whole, which therefore participate in the completeness and wholeness of the transcendent reality. Completeness and wholeness require (in the world of the mundane) delineation and limits, and so the limits and the extremes of things are also things which participate in transcendent reality.

The principle of ascent to the ‘eternal and incorporeal things’ is entirely a mental process, which does not involve any of the senses. It proceeds via chains of similitudes, both up and down, as a sequence of orderly perceptions. The goal is a form of communion with that which never varies, and which is always one and unchanging, as Plato tells us in the Sophist. The return from the communion with the Good delivers beneficial things, because the Good is the source of all knowledge.

Is this a logical modality? Yes it is. It is the inverse of what is implied in Aristotle’s three laws of thought, in that Aristotle is arguing that things are themselves and nothing else. And he suggests that similitude and likeness with other things is without meaning: no connection is opened to another level of reality. And that reason is only possible if the symbols we use in order to reason – words – have a one to one correspondence with the things we are talking about.

Aristotle knew his teacher’s work and views very well, and he spent many years in the Academy. So he would have been very conscious that he was contradicting Plato’s argument about ascending to knowledge via the Forms. Whether this was a serious assault on Plato, or just an argument which was intended to flush out the intelligent student, is a question which is very hard to answer.

[text correction October 1, 2017]