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'.
***
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]