Working wonders: Hephaestus and the Armour of Achilles

This is a retitled chapter from The Sacred History of Being (originally titled: 'Being in Homer'). It analyses Book XVIII of The Iliad. It is something of an eye-opener about the intellectual life of what became known as the Greek Heroic Age. Much of the intellectual and tropic detail in this book of The Iliad strongly resembles ideas and themes which can be found in Mesopotamian and Phoenician sources.

It is not much studied in modern times for an understanding of Greek life and thought, since it is full of fantastical elements, whose context we think we lost long ago. It may be studied for the language and the poetry, and also for the narrative of a small but crucial part of the conflict between the Achaeans and the city of Troy.

There is an exception however, which is discussed (among other things) in this chapter. It is a favourite subject of classicists and ancient historians, but they find it hard to agree about why the passage is present in the poem, and what it means. Looking at the entire book, which hangs together extremely well as an artistic enterprise, it is perfectly clear why the passage is present, and what its meaning is.

The text of the chapter is unchanged, and I've retained the footnotes (though they have been renumbered).


TY, February 19, 2018.

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A passage in Homer’s Iliad, often thought to be a later interpolation in the text, the famous ‘Shield of Achilles’ episode, features a collocation of images, struck together on an imaginary shield. The shield edge is bounded by Ocean, which among the ancient Greeks connotes border, the edge of the world. It is also the place of generation, which is associated with Being and the gods. There is a scene where a dispute is being resolved, which is an image of justice. This is an allusion (in the Greek context) to the sun God Apollo, who, like his Mesopotamian counterpart, Shamash, is a god of justice. This image, rather than being a later interpolation, can be shown to echo the themes in the same section of the Iliad.

If we follow the story from the beginning of the eighteenth book of the Iliad, where Thetis comforts her son Achilles who is grieving for the death of his friend and kinsman Patroclus, we shall see how the images point to an articulate idea of Being. The essence of the events in this book is that Thetis promises to procure her son Achilles new armour from Hephaestus. At the command of Hera, Achilles attacks and strikes terror into the enemy. The body of Patroclus is recovered, and prepared for funeral rites. The armour is prepared by Hephaestus for Achilles.

Achilles is expecting to die, recalling that his mother once informed him that, though he was the bravest of the Myrmidons, he would, though now still surviving, would leave the light of the sun ‘by the hands of the Trojans’. Twice in this passage, his contemplation of the fate of the Achaeans is described as a ‘revolving’ in his mind (and once in his soul), which is reminiscent of Plato’s description of rational thought in the Living Animal. He grieves for the fallen Patroclus, killed by Hector. He gives a dreadful moan, and we are told that ‘his venerable mother heard him, while she was sitting in the depths of the sea.’ This passage is a close parallel to the Mesopotamian image of Ea/Enki at home in the midst of the waters of the Apsu. We are told that Thetis was beside her aged father in the depths, and that she immediately lamented for her son’s grief.  [i]  We are also told that ‘all the goddesses were assembled around her, as many Nereids as were at the bottom of the sea’, so this is a place where a totality (of Nereids) is collected together. In the Mesopotamian story the location is a house, whereas Thetis resides in a cave.

We are given a list of many of their names, and these repay attention.

The list is Glauce, Thaleia, Cymodoce, Nesaea, Spio, Thoa, and ‘large-eyed’ Halia, Cymothoë, Actaea, and Limnorea, Melita, Iaera, Amphithoë, and Agave, Doto, Proto, Pherusa, and Dynamene, Dexamene, Amphinome, and Callianira, Foris, Panope, and distinguished Galatea, Nemertes, Apseudes, and Callianassa.  In addition are mentioned Clymene, Ianira and Ianassa, Maera, Orithya, and fair-haired Amathea. There were others, but they are not named by Homer. The cave is described as ‘resplendent’ and full of Nereids.

Some of these are particularly interesting. Glauce as an adjective might qualify thalassa as ‘gleaming sea,’ as it does at II, 34. Thaleia probably connotes ‘abundance’ (thallo, as in thalassa), Nesaea means ‘island’ or ‘islet, from nēsos.  Spio probably means ‘cavern, cave or grotto’, derived from ‘speos’ (in Homer appearing as speious).  Halia may mean ‘blowing seaward’ (Homer uses haliaēs to mean this in the Odyssey. In connection with the epithet ‘large-eyed’, Halia is an Ionian word meaning ‘assembly of the people’. Homer is punning), and Cymothoë ‘billowing waves’.  Actaea means coast, (Aktaia), Limnorea may connote a large pool of standing water, or directly indicate the sea, Melita may be honeyed mead, or perhaps 'sweet water', and Amphithoë suggests 'running quickly around,' as water does when it is loosed from its bounds.

And so on. The pattern is clear. These are mainly attributes of water or liquid in different states, and therefore a collection of terms which might be used to describe aspects of the sea, or of the primal ocean, which might be the focus of priestly contemplation. Other terms refer to things associated with the sea, such as caves, and shorelines, and so on. We have here a partial list of attributes and properties of images which reference the divine. It may be that the origin of this list is one or more temple documents, compiled for a cult centre, in order to standardise a set of images and descriptions which might be used to approach the reality beyond images.

Ten of the names of the Nereids appear to be similar, but in different forms. These are Amphithoë and Amphinome, Callianira and Callianassa, Cymodoce and Cymothoë, Dynamene and Dexamene, and Ianira and Ianassa. The pairing of names in divine genealogy is well known in Mesopotamia, and usually indicates a twin birth. If this is the pattern which is being followed, it suggests that the Nereids might have been part of a complete theology at one time, perhaps imported from the near East, or perhaps brought to Greece by an incoming population group. It is also possible that the Nereids are very old and local to Greece. Unfortunately we have very little other information about the Nereids from any source other than Homer.  [ii]  We do know that the Phoenician theology was also focused on the depths of the sea, paralleling part of the Mesopotamian theology, with the god Ea living in the abyss at the bottom of the ocean. And that the Greeks did extensive business in their emporia along the coast of Phoenicia.

Achilles grief stems in part from the fact that the armour of Patroclus has been removed by the Trojans. Achilles own armour was also taken by the Trojans. The decision of Thetis to supply her son with the finest possible set of armour represents an inversion of the desecratory action of Hector, which has a bearing on the design represented on the shield made by Hephaestus, since it shows good order opposed to bad order.

Thetis and all the Nereids leave the cave, weeping, ‘and the wave of the ocean was cleft around for them.’ This is an image which recalls the creation, in that the ocean may be understood as a god, and to part the waves is to cut the divine body in two, as described in both Plato's account of the creation, and the Mesopotamian  account.

The concept of fate in the Iliad is strikingly inexorable, like that found in Mesopotamian literature – Achilles says: ‘may I die then immediately, since it was not destined that I should aid my companion now slain.’ Nevertheless he asks that bad order be replaced with good, and so ‘therefore contention might be extinguished from gods and men; and anger, which is wont to impel even the very wisest to be harsh.’ This idea is represented in the design of the shield, with two communities, one of which is based on brigandage, the other a place where contention has been banished. Thetis (‘the silver footed’) had urged Achilles ‘not to enter the slaughter of Ares’ before he sees her return at dawn with the armour from king Hephaestus.

Thetis then turns away from her son, and addresses the Nereids, saying that they should now enter the ‘broad bosom of the deep’, about to behold the ‘marine old man, and the mansions of my sire, and tell him all things’. The Nereids return to Ocean here is not simply a retracing of steps, but entry into the world of the divine. It is a place which must know all things. Thetis travels alone to ‘lofty’ Olympus, to Hephaestus, ‘the skilful artist,’ to ask if he is willing to make the armour.

In the meantime, Achilles is visited by the goddess Iris (peace), sent by Hera, to remind him of the disgrace that would be the consequence of the body of Patroclus being abandoned to the Trojans. She isn't urging peace.  However Achilles tells her of his mother’s admonition not to join the battle until her return. Iris then urges that he go toward the ditch and show himself to the Trojans, so that in their terror they may desist from battle, at least for a while.

Achilles rose after the departure of Iris. The goddess Minerva threw around his strong shoulders her fringed aegis. ‘And the divine one of goddesses crowned his head around with a golden cloud, and from it she kindled a shining flame’, and the flame from his head reached to the sky. He stood, having advanced from the wall to the trench only, and did not mingle with the Greeks, mindful of the advice of his mother. Three times he shouted over the trench, and three times were the Trojans and their allies thrown into confusion, with the assistance of Pallas Minerva. By this means the body of Patroclus was recovered.

So Achilles did not fight, but recovered the body of Patroclus by the use of his intelligence, through the assistance of the goddess of wisdom. It is good order to succeed through throwing your enemies and their allies into confusion, rather than achieving your aim by violence and slaughter. This part of Homer's text reflects a time when social and political issues were often resolved through angry and divisive contention. Thetis had urged Achilles not to enter the slaughter of the god of warfare, Ares, until she returned: Ares, in a sense, is as responsible for bad order as the Trojans and their allies.

This is followed by another striking image involving Ocean. ‘Large-eyed, venerable Hera’ ‘sent the sun to return to the flowing of the ocean, against his inclination.’ The sun therefore set, and the Greeks and the Trojans stopped fighting. The Trojans assembled in their council before they even thought to eat, which suggests they were impelled by anger more than sense. They were addressed by ‘prudent’ Polydamus, the son of Panthus. The name Panthus (Panthoos) again references the ideas of the telos and of Being, where everything is embraced, including past and present. In fact, the son of Panthus is described as one who, alone among them, ‘saw both the future and the past’. Hector and Polydamus were both possessed of excellences and virtues. Born on the same day, Hector excelled in counsel, and the other ‘greatly in the spear.’ Polydamus advised to guard the towers and the city overnight, dressed in their armour. Hector effectively told him to shut up, and advised that they should fight by the Greeks ships in the morning, and that if Achilles has arisen at the ships, ‘it will be the worse for him’.

The irony here is that it is Polydamus, who excelled 'greatly in the spear' and is therefore excellent in warfare, who makes the prudent proposal. Hector, by contrast and against expectation, provided bad counsel. So the Trojans assented to Hector, and cheered him. But they were foolish, since Pallas Minerva ‘had taken their senses away from them.’ They assented to Hector’s advising of destructive things, and no one assented to the prudent counsel of Polydamus.

By this time (after sunset, when the sun is below the waves) Thetis had reached the home of Hephaestus on Olympus – incorruptible, starry, and remarkable among the brazen immortals. Hephaestus therefore is remarkable, but not divine, though he possesses attributes of the divine.  He makes statues of the gods, or in fact ‘makes gods’ as was the understanding of the early part of the 1^st millennium B.C.E.  He thus has very special attributes, like the Mesopotamian Nudimmud, and can make things in heaven as well as on earth.

Homer tells us that Thetis found him sweating, working at the bellows, making twenty tripods to stand around the wall of his ‘well-built palace’. These tripods had golden wheels placed under the base of each, so that ‘of their own accord they might enter the heavenly council, and again return home – a wonder to be seen.’

Here is another image which references the world of Being. It also associates the divine world with the idea of council: the two are associated through the idea of totality, since totality is an attribute of both council and Being. And in a sense, they are interchangeable through their common possession of totality. We are told of the perfection of the work which has produced these tripods, as we were told of the perfection of the body of the living animal in the Timaeus: “so much finish had they, but he had not yet added the well-made handles, which he was preparing; and he was forging the rivets.”

So we have three attributes of the divine referenced in this passage: totality, perfection and council, struck together. The tripods have golden and therefore incorruptible wheels. They are also circular, and complete. By virtue of these attributes alone, they can pass into the heavenly council, and also return, again by virtue of these attributes.

This is a clear anticipation of the theory of wholes or totalities attributed to Pythagoras, and repeated by Plato, in which completeness by itself allows participation in the divine, and indeed identity with the divine. This passage is virtually impossible to explain outside the context of a theory of this sort. In which case, the theory of wholes and totalities was known to Homer in the 9th or 8th century B.C.E.  [iii]

The tripods are able to move between the worlds, which makes sense, if the worlds are conceived of as being physically distinct - one way in which commerce with the divine can be framed. That these remarkable objects are tripods probably reflects two things - that the objects can have reality in this world, and the worlds above and below this one. The tripod is also a common ritual object in the early 1st millennium B.C.E, and not only in Greece. It might be used to hold a vessel for burning incense, or for collecting the blood of a sacrifice, and so on. The image carries these and other associations of commerce with the divine world.

Thetis is greeted by Hephaestus, and then his wife Charis. Hephaestus recalls that “an awful and revered goddess… saved me when distress came upon me, fallen down far by the contrivance of my shameless mother,  [iv]  who wished to conceal me, being lame.”  [v]  He then focuses on the importance of Ocean for him, saying: “Then should I have suffered sorrows in my mind, had not Eurynome and Thetis received me in their bosom; Eurynome, daughter of the refluent Ocean.”  [vi]  He tells us he was with them for nine years, during which time he made in brass “many ingenious works of art, buckles, twisted bracelets, and clasp-tubes, in the hollow cave,” while “round us flowed the immense stream of Ocean, murmuring with foam: nor did any other either of gods or mortal men know it; but Thetis and Eurynome, who preserved me, knew it.” He asks Charis now to set before Thetis “good hospitable fare”, and lays aside his tools. “He went out of the doors limping, and golden handmaids, like unto living handmaidens, moved briskly about the king.” Here we have the art of statuary associated with a former inhabitant of Ocean – and it is the art of creating living statues of which Hephaestus is a master craftsman.

We are told something of their attributes: “in their bosoms was prudence with understanding, and within them was voice and strength; and they are instructed in works by the immortal gods.” We have been told earlier that Hephaestus can make objects which can enter the heavenly council of their own accord, and return again, which was “a wonder to be seen”. So we know that setting up statues within Heaven is within his abilities. He can make living creatures which have within them the attributes of prudence and understanding. They are also instructed in works by the immortal gods, which means that these golden handmaids are expressions of the divine will and intention.

At this point Thetis makes her request to Hephaestus, that he make armour for her son Achilles. The armour of Achilles was lost when Patroclus was slain, since Achilles had given him his own. Thetis explains that “All day they fought round the Scaean gates, and certainly on that day had overturned Troy, had not Apollo slain, among the foremost warriors, the gallant son of Menoetius, after having done such mischief, and given glory to Hector.” Apollo is the god of justice as well as of the Sun, and so is the dispenser of victory and defeat to men in battle.  [vii]

It is particularly interesting to consider how it is that negative characteristics can have positive qualities, as we find in the Iliad and the Odyssey.  Odysseus has the epithet ‘Sacker of Cities’, and at the time Homer was writing, it is clear that being a ‘sacker of cities’ was not seen universally as reprehensible to the society of the time, but Homer himself objects to it.  [viii]  Hence the 'Shield of Achilles' passage, where the contrast is made between a prosperous city and a city under siege, open to destruction and the division of spoils. The idea is planted that the rapacious behaviour of former times, in a time before reason, may not have much to recommend it.

Underlying the idea that the ‘sacking of cities’ is something which may have honour and glory associated with it, is the abstract notion of greatness. The sacking of a city is greatly destructive, and so participates (within this simplistic model) in greatness. What we have here is an idea which fits within the mental model in which it is possible to connect with divinity through extreme action. There would have been many objections to this, on the grounds that such action did not promote the good, or good order. Hence it was a question which would have exercised the Greeks as being a pattern of behaviour which superficially made sense within a mental model of the world of the late Bronze Age.

[i] It is interesting and possibly significant that Homer never mentions Nereus by name, but is referred to as the 'aged father' of Thetis.

[ii] It is well known that Homer composed the Iliad and the Odyssey somewhere in Anatolia, and so the Nereids may have been part of the theology of an Anatolian cult, rather than a Greek one. It is unnecessary to explore here that even in ancient Greece it was accepted by some that a significant number of their gods had a foreign origin.

[iii] The alternative would be to argue that not only is the 'Shield of Achilles' passage a later interpolation, but that much of the eighteenth book of the Iliad comes from a much later date. I don't think that would be a credible suggestion. The very fact that so much in Homer has been difficult to explain for so long, argues that the text we have comes from an age with a different set of preconceptions about how things work.

[iv] In later accounts, Hephaestus is son of Hera, without the intervention of a father. Here he is son of Zeus and Hera, sister and wife.

[v] The lameness of Hephaestus reflects the awe in which workers in metal were once held: they seem to work magic, and yet they are here on earth. They seem to work with heavenly fire, but are not actually divine.

[vi] Eurynome is daughter of Okeanos, as he says. But her name means something like 'wide pasture'. The first part of her name translates literally as 'broad' or 'wide'.

[vii] His equivalent in Assyria is Shamash, who has similar qualities, and is sometimes represented in palace reliefs as hovering over the field of battle, represented by his symbol of the winged circle.

[viii] 'Destruction of cities' is included among the lists of Sumerian 'mes'.

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]