Tuesday, 5 November 2019

Around Black Athena (1990), Seminar Two (Tim Cornell)

This is an extract from my notes made at the second seminar in the series ('Representations of Carthage'), held on the 25th January 1990 in the Institute of Archaeology at UCL. There is a full set of notes for the entire seminar series, except for the first, which I missed because I didn't catch sight of the poster in time (no web in those days). The volume (Around Black Athena: the Origins of Graeco-Roman Culture) is under pressure from other work in progress, but it will eventually arrive. TY.


[Introductory preamble: Last week set up the central themes of this conference and on Martin Bernal’s book. Bernal has set the agenda. Now we explore different directions, and try to explain the pressures on our understanding, and on historiography].

Tim Cornell began by saying that he was not speaking as an expert on Carthage. After reading Bernal’s book he wondered if there was a hidden truth in it. Perhaps there was an unconscious and systematic attempt to overlook Carthaginian culture. It is definitely a neglected area. Within the format of the study of the ancient world, there are few general books on Carthage.

Cornell mentioned the names of a few authors (Warmington, Picard), who use a standard sort of treatment of their subject. Like books on the Etruscans, there is a standard menu – an outline of the format: date, colonizations and contacts, wars in Sicily with the Greeks. And then the Punic Wars, and the final destruction of Carthage in 146 BCE. This format indicates that Carthage is of interest insofar as the Carthaginians had dealings with the Graeco-Roman world. I.e., Carthaginian culture is somebody else’s problem. Carthage is an earlier foundation than the Greek colonies. Timaeus argued that Carthage and Rome were founded in the same year (i.e., the Dido story). Punic war seen as war against the Carthaginians.  Modern scholars identify with the Romans. A product of the sources being from outside, and hostile. Is there a hidden programme here? Archaeology, especially since the end of WW2, has done little to redress the balance. Especially concerning the Punic Wars. Stresses an impoverished culture. Often the evidence is interpreted in the light of literary sources.

The Carthage we have is a stereotype. Aristotle is an ancient exception – in his Politics he admired their constitution, but the account of this is lost. Polybius also regarded it well, though he was critical of it. We know that there were pro-Carthaginian accounts also written in antiquity. Now lost. Plautus wrote on the subject of Carthage, shortly after the Hannibalic War, but it presents the Carthaginians in a most unsympathetic way. In general they got a hostile press, and this is also true of modern works. Stereotypes in modern works include (1) racism and antisemitism, and (2) orientalism (as discussed by Said).

For (1) the ancient prejudices involve the stereotype of the Carthaginians as intelligent, but in a mean and self-serving way. Expressed in terms of cunning and trickery. They were notorious to the Romans for treachery. For ( 2), they were dependent on trade, and are shown as greedy and corrupt by Polybius, who contrasted the Romans and the Carthaginians, and attributes a leaning to bribery and corruption to the latter.

They were also depicted as capable of great courage in certain circumstances, but essentially unwarlike, which was seen as a weakness. They failed to press their advantage. (Diodorus). They were interested in commerce rather than war. Cicero said that this destroyed their will to fight. This was illustrated by their use of mercenaries. Note the contrast between Hannibal and the opposition and lack of support from the government at home. The Romans thought of him as a worthy enemy (this view is presented more by modern writers than in antiquity).

Some writers suggest that the Carthaginians were not actually Phoenician. This racism was not in the ancients for they treated subject peoples harshly (Spaniards). [Bk10.36]. Polybius says harsh on subject people in North Africa – they doubled city taxes, and took half the crop [Whitaker – Carthaginians land imperialism late 4th century]. No tribute from Sicily until quite late. 

Carthage was not interested in imperialism abroad in the 6th and 5th centuries, but they were interested in alliances (Etruria, and Rome). Protection for trade. Warfare in Sicily was perhaps originated by the Phoenicians and was prosecuted together (hence mercenaries). They did not use coinage till late. Not specifically Carthaginian. Hence perhaps a failure to follow up this advantage. Only in the third century did they carve out provinces, coinage, tax and mercenaries – the harshness of the Carthaginians noted in Polybius is to this period and circumstances, and is not seen as a racial characteristic.

They were servile to those who were stronger (college porter obsequiousness and arrogance). Plutarch said they were ”a hard and gloomy people”, etc. Cruelty was a frequent charge -  punishments included crucifixion (the torture of Regulus, etc). Their cruelty was demonstrated by their regular holocausts of children and the killing of prisoners in a sacrificial manner. There is a brutal account in Diodorus of indiscriminate killing – severed heads on javelins, etc.

The vices are seized on by modern detractors, who add others which are modern. There is some basis in the sources, but the tone of the passages is misleading – antisemitism and vulgar orientalism. The sources show no disgust at the physical appearance of the Carthaginians among the ancients.  Other modern notions arise from modern passages with no source warrants. It is a feature of orientalism that orientals are specifically given to religious fanaticism – Hindus, Etruscans, etc. It is taken as a sign of the eastern character {See Warmington). However there is no evidence in the sources for an especial religiosity among the Carthaginians (quantification of religiosity is meaningless anyway). There is a christianizing evaluation of oriental religiosity in some of the sources. Observers (Philo of Byblos, Tertullian) had their own axe to grind. Cult practice is prominent in surviving sources, but there may be a bias in the survivals.


Wednesday, 30 October 2019

The Esoteric Conception of Divinity in the Ancient World (full text)

This article was first published in the Newsletter of the Bibliotheca Philosophica Hermetica in December 2015. In October 2019 the website went down, and hasn't come back up. So I'm posting the full text of the article here in the meantime. It covers both the subject of The Sacred History of Being, and also something of how the book came to be written. In 2018 the article was published as a chapter in Man and the Divine.

TY, October 30, 2019.


 “Enki’s beloved Eridug, E-engura whose inside is full of abundance! Abzu, life of the Land, beloved of Enki! Temple built on the edge, befitting the artful divine powers!”
From: ‘Enki’s journey to Nibru.’  (Black, Cunningham, Robson, Zόlyomi, The Literature of Ancient Sumer, 2004, p. 330)

The Sacred History of Being (2015) is about philosophy and its origin in the context of ancient cultic life. As such it argues that philosophy as a discipline is very old, as Plato himself said in the Protagoras, and that it was not invented by the Greeks.

In my twenties, I was struck by the strong interest the ancients had in the idea of limit – in art, architecture, philosophy, and ritual. This interest did not much seem to engage modern scholarly attention, with a couple of notable exceptions. Initially I had no idea at all what the significance of the idea of limit might be, and no idea where pursuing it would take me. Or that it would lead to a book it would take me four years to write, and which would reshape my understanding of human intellectual history in the process.

There is a standard form of image from the earliest years of civilization, which consists of two opposed figures, standing on either side of an object. The object can be a tree, an altar, a table heaped with produce, lotus blossoms, animal foreparts, loaves, and so on. The opposed figures can be human, animal, god or genie. This kind of image can be found throughout the archaeological record of the Ancient Near East, and in Egypt.

Questions arise from the ubiquity of this image, which appears in the context of those who had great power in the world, and also in funerary contexts, particularly in Egypt. It appears prominently in royal contexts in Assyria and in Babylonia. The image can be traced back as least as far as the settlement at Çatal höyük, now in modern Turkey, dating to some eight or nine thousand years before the present.

What does this image mean? It is nowhere explained, but clearly had some kind of explanation at some time, even if its transmission in later centuries was enabled simply by its status as a traditional iconographic element. Why is it so prominently displayed, so persistent throughout time, and apparently not discussed in the cultures in which it appears?

Some details of esoteric lore were written down in the Ancient Near East – the colophons of the relevant tablets make it clear that the contents were for the initiated only. The ritual procedures for the installation of divine statues in Assyria and Babylonia survive, together with some incantations which were part of the ritual. These tell us about the ritual, and the elements involved in the ritual – the thigh of a ram, best beer, mashatu-meal, and sacralised reeds, plus information about which stellar constellations and planets a statue was to be pointed at as part of the installation; and about the selection of craftsman’s tools which were disposed of as part of the ritual (enclosed in the ram’s thigh, and deposited into the river), in order to remove their responsibility for making divine images (not a thing for mortals to undertake).

But we find no discussion of the rationale of the installation ritual. Or discussion of the rationale of any other ritual which they documented. This suggests that there were levels in the esoteric life of Assyria and Babylonia: that the ritual details were important to record to ensure consistency in the performance of the ritual, but the meaning of the details, and the underlying rationale for the ceremony were transmitted orally, and never committed to writing.

The image with the opposed figures standing around a ritual object is clearly an image whose meaning and function was too important to record in a temple or palace document. In which case it might appear that we can never know what it signified, and why it was so important.

But, it is not so. Assyriologists have explored this image as it appears in the Mesopotamian context, and have made some headway in understanding the scope of its significance. They have established that, in terms of the iconography, the Sacred Tree may stand in for the King. In other words, the two ideas were understood to represent the same thing. The contemporary understanding of the nature of the role of king in Assyria was that he was the Regent of the god Ashur on Earth, and therefore the king represented an emulation and image of the Divine on Earth.

But why a tree? The tree can stand in for the king, because of two further ideas which are connected in the definition of what the king is.

The contemporary scholarly definition of the Divine in Assyria, framed it as the source of all excellences and perfections, and all knowledge.*1 Hence the importance of excellences and perfections of the life of the king, as we find recorded in the Annals of Ashurbanipal in the late 7th century B.C.E. (found in the ruins of his palace at Nineveh at the end of the nineteenth century). As Ashur’s representative on Earth he excels in military skills, in throwing the javelin, in horse riding, in the use of weapons; in divining the will of the gods through divination by oil, and other arcane skills; also in scribal excellence and mathematics – he is able to read the ‘obscure and difficult to master’ texts written in Sumerian ‘from before the flood’. And so on.

The excellence and perfection of the king’s skills were understood to place him in proximity to the god Ashur. He is thus at the limit of what a mortal may do and be; as Ashur is at the limit or zenith of Reality itself. Ashur is Reality itself. That the Tree may stand in for the king suggests that it was understood also as an esoteric and symbolic representation of the idea of limit, taken to the nth degree, and also of Reality itself.

Much of the discussion found in Plato concerns the nature of what he calls ‘The Good’. The Good is in a sense the Crown of Creation, and it is the target of human attention because of that status. He refers to the Good rather than ‘God’ because he is talking about the ultimate abstraction, which has commerce with other abstractions – as he says, ‘things pass into one another’. The Good is perfect, complete, whole, and the ultimate source of justice, good order, beauty, wisdom, and all the other abstract concepts which have some form of existence in the temporal world. He is careful to say (through the words of Socrates) that this ultimate Reality, the Form of Forms, has ‘no shape, size or colour’. In its nature it wholly transcends physical reality.

Plato’s Republic tells of the craft of passing from the contemplation of one Form to another, entirely intellectually, and without distraction, with the intention of eventually arriving at the contemplation of The Good. The man returning from this journey comes back with knowledge beyond the scope of any wisdom to be found on the Earth.

The Platonic discussion of the Forms is treated by modern scholars as a species of literary fiction. Meaning it has no detectable connections with cultural activity in Greece, or in any other part of the civilised world in the two millennia before the Common Era. But Plato is very clear that it is important to look to the ‘One Thing’, the ur-Reality which underpins the world of the here and now. So he is talking of a conception of God, which gives rise to all other things which may be understood by the mortal mind, though the ultimate abstract conception of Reality may lie forever beyond human understanding.

How old is this conception of the Divine? If the Divine is understood to have its reality at the limit of physical and perceptible reality, and to be the most abstract of abstractions, historians of philosophy would say this notion was first discussed in Classical Greece. If on the other hand, the iconography of the two opposed figures, facing a ritually significant object between them, represents the most abstract conception of limit, beyond any physical instance, then this conception of the Divine is thousands of years older than the middle years of the 1st millennium B.C.E.

The Assyriologist Simo Parpola has shown that there is a connection between the Kabbalah and the Assyrian Sacred Tree. Each of the Mesopotamian gods was associated with a divine number, and sometimes they were referenced in documents by their number alone. He was able to reconstruct the Assyrian version of the Kabbalistic tree, populating the sefirotic nodes (understood in the Middle Ages as divine powers and qualities), with the key Mesopotamian divinities, their properties and numbers.

The Kabbalah enshrines a philosophical notion of transcendent divinity in the concept of the ‘en sof’. It has been assumed by modern scholars that this is an imported idea, perhaps borrowed from Gnosticism in the early centuries of the Common Era. If in fact the idea of the ‘en sof’ was in the Assyrian version of the Sacred Tree, then we understand something new and profound about Hebrew ideas of divinity from the middle of the 1st millennium B.C.E. onwards.  The relationship between the Assyrian and Jewish Sacred Trees which Parpola has been able to show, by itself pushes a philosophical conception of the Divine back to at least the 14th century B.C.E., which is when the representation of the Assyrian Tree first appears.

This philosophical equation of the idea of limit with what is transcendent is an important factor in ancient religious ritual. In Mesopotamia the ritual installation of divine statues took place in locations with clear boundaries, including riverbanks and quays, and a key part of the ritual involved a temple threshold, as the surviving texts tell us. These boundaries were understood to have proximity to the primal reality, the Abzu, house of Ea/Enki, in the sweet waters at the bottom of the sea. Reeds used in the ceremony were spoken of has having their roots in the Abzu. The association of limit with ritual performance tells us something about the logic of the installation: the rites serve to make the images one with the company of gods in Heaven. The statue becomes itself Divine by its exposure to repeated representations of Divinity in the course of what was described in Mesopotamia as the ‘most sacred and secret of rituals’.

A great age for a philosophically conceived notion of Divinity, coequal with Reality itself, makes it possible to make much sense of many otherwise obscure texts and inscriptions which have been excavated over the past two centuries.  The determination of classicists over two centuries (since the European Enlightenment) to downgrade and deny the connections between Greek civilization and other civilizations around the Mediterranean and the Near East, both in classical times, and in the 2nd millennium B.C.E., has made it very difficult to make sense of both Greek philosophy, and the intellectual life of the other cultures of the ancient world. The Greeks accorded the Egyptians the status of philosophers, and Plato represents Solon having conversations with Egyptian priests in the Timaeus, who had knowledge ‘hoary with age’.  But archaeological excavation in Mesopotamia and elsewhere, and the recovery of thousands of texts, made possible the idea of writing something like The Sacred History of Being.

The structure of the book is relatively simple. There are three main parts. The first begins with reflections on philosophy, both ancient and modern. This goes some way to explain how I came to pursue this project. The second half of the first part discusses the ontological argument, which has its origins in the early modern period, which has come to be the principal way in which the reality of Divinity is discussed. We have made it very difficult to understand ancient theological ideas by promoting the ontological argument to its current status.

The second part explores Plato’s writing, and the strikingly different way in which Divinity was discussed. It also explores wider Greek thought, and earlier instances of the kind of understanding of Reality found in Plato.

The third part examines ideas common to Greece, Israel and Mesopotamia, plus the significance of the Assyrian Sacred Tree for the scholars of the Assyrian royal court, and the significance of the Jewish Kabbalah, which descends from parallel Mesopotamian ideas. Two of the chapters in part three work through the Mis Pî tablets from Nineveh and Babylon, which describe the ritual for the installation of images of the gods, and discuss the significance of the ritual.

1 The Babylonian scholar Berossus, former priest of Bel, who wrote about Babylonian culture and religion after moving to Athens,  tells us of the encounter of the first legendary sages with an emissary of the Divine. The emissary granted them knowledge of the arts and crafts, of husbandry, and the apportioning of land.

Tuesday, 29 October 2019

An Appetite for Knowledge

I have argued elsewhere that ideas of Being, of the nature of reality, and the divine, were once approached  in terms of conjectures about the reality (or otherwise) of the one and the many. These conjectures follow on from the initial question, which is: why is there something rather than nothing? Plato’s argument, following on from propositions made by Parmenides, who declared that we should look only to the one, and that only the one truly is real, is the most sophisticated of all discussions in antiquity concerning why there should be something rather than nothing.

Plato argues that we should always look to the ‘one true thing’. This is different from saying only the one exists, or only the one is truly real.

The anthropologist and classicist J.G. Frazer was very dismissive of Greek questions concerning the one and the many, saying that they constituted ‘popular questions of the day’. The argument of Parmenides about the nature of Being  remained entirely undiscussed by Frazer.  But then he argued that questions concerning Being were entirely barren, since nothing could be predicated of Being.*1

This of course is a spectacular instance of intellectual blindness, by which the richness of the intellectual matrix of ancient Greek thought was spirited into nothingness. We like to see Plato’s articulate discussion of Being as the surfacing of a human capacity to grapple with abstract ideas, and the marker of our emancipation from irrational ideas about the world and the gods. For Frazer, Plato was as guilty of intellectual error as any of his contemporaries, as well as his predecessors.

In late Hellenistic times, there seems to have been a very poor grasp of the context of the development of philosophy around the Mediterranean. Nods were made toward the notion that the discipline of philosophy might not have been first developed in Greece, including (tellingly) at the beginning of Diogenes Laertius’ Lives of the Philosophers.  Plato after all argued against the idea that this was so in the Protagoras, saying that the practice of philosophy was of a great age – perhaps contemporary with the arrival of peoples from Egypt, who settled in the Peloponnese, and also in Crete. He also presented Solon in discussion with Egyptian priests in the pages of the Timaeus, who found the Greeks to be very young, and not conversant with knowledge ‘hoary with age’.  

Aristotle presented the common sense view that philosophy was first developed in a place where there was a leisured class, with the time and resources to think about philosophical questions. He may have had Egypt in mind, since Egypt had professionalised priesthoods. Later philosophers such as Porphyry suggested that key parts of Pythagorean doctrine came west to Greece from Babylon, in the late sixth century B.C.E.*2  Plato references details of this doctrine, without connecting it explicitly to Pythagoras.*3 Aspects of that doctrine can be found elsewhere in the pages of Herodotus (concerning Solon),*4  and also in Homer’s Iliad (Book 18), where a number of key details associated with the doctrine are run together in close order, without being explained. *5

The former Priest of Bel at Babylon, Berossus, moved to Athens, and wrote about Babylonian history and philosophy, describing their system of knowledge as based on the idea of an initial plenum (which is a philosophical concept) using the image of a sage emerging daily from beneath the sea (symbolising primal fulness and abundance), granting knowledge to man about the sciences, agriculture, and the practical arts. *6 He also gave information about the Babylonian New Year festival (Enuma Elish), the liturgy for which contained accounts of two creations: the first irrational, and the second one, rational, and which was given its rational character by the chief of the Babylonian gods.*7  Berossus' book was the Babyloniaka, unfortunately now lost. But the christian writer Eusebius had access to it as late as the early fourth century C.E, and quoted a number of passages from it which survive in his writings. Recovered Mesopotamian texts, including tablets containing the Enuma Elish liturgy, generally confirm the accuracy of Berossus. 

Not much of this was of use to the Enlightenment agenda, which preferred to look at the development of philosophy in Greece as the first beginnings of a rational understanding of the world. And so the information was deprecated and ignored. The phrase ‘I doubt that’ is a dangerous one in the classics community. It is a way of saying ‘this is not the consensus view of scholars and the profession’. Usually no discussion follows, since the opinion is usually an opinion of the worth (or otherwise) of evidence. Scholars weigh evidence, and they do so (they are convinced) with better tools than were available to ancient scholars. The judgement is fitted to modern requirements. So, as a result, it is clear that it is unlikely that Solon visited Egypt, and that Pythagoras visited Babylon. Tread carefully, or your credibility as a scholar may be in doubt.

Thus, the scholarly consensus is that philosophy is an autochthonous development. The culture of the modern west rests on this idea.Why in Greece? The idea of the ‘Greek genius’ won’t cut the mustard any more, at least by itself, but I have heard the phrase uttered by people who should know better. But during the high days of the enlightenment, and the beginnings of what became the fully-fledged discipline of Classics, that is what the scholars wanted. Something pure and out of the orbit of other cultures, which, by definition, had no philosophy or anything which would measure up to something like rational thought.

Sometimes history is built backwards. It isn’t just a matter of looking to the historical record and starting from that. History always has been in part about critical scrutiny of sources and judgements, even among the Greeks *8 But as Bernal pointed out in the first volume of his Black Athena, the critical revision begun in the enlightenment was wholesale, and created an alternative representation of the origins of European civilisation.

That was the agenda. To reinterpret the past, and in terms of a rational and enlightened understanding of the world. Hence, the philosophe Denis Diderot wrote not just about ideas and philosophy in his Encyclopédie, but also about the arts and crafts. The latter may have been wrapped up with myth, folklore, and superstition, but they were still essential to the rational life of man, so these were also added to the Encyclopédie. Everything from the past which served some purpose, or which could be made to serve some purpose within the rational enlightenment model of reality, was critically examined, and reworked to fit what was intended to become a new understanding of man and his place in a new world of reason. A new understanding of how man might live.

I wrote in the article ‘Logical Modality in Classical Athens’ that there are in fact two logical modalities present in the writings of Plato and Aristotle. Aristotle is mostly (though not always) concerned with the modality which has come down to us as the basis of formal logic. Plato is clearly aware of this modality, but, though no modern academic has dared to identify the other modality as logical, it is. It is simply that to us, it does not describe relationships which should be described as logical. Plato  talks about this other logical modality several times, in the Republic and in the Timaeus. It is connected with the doctrine of wholes and totalities, and is the basis of explaining how things may participate in other things, which is not a pattern of ideas which fits with Aristotle’s general understanding of logic.*9

Why is this important? Simply put, it matters because it is the basis of the Greek understanding of how transcendent reality relates to secular and physical existence, which was a matter of great significance up to the middle of the first millennium B.C.E, and beyond.  The doctrine underpins the understanding of the divine as something which can be both transcendent, and immanent, and thus be present in existence. *10 *11 It also points to a rather strange conclusion about the nature of the reality in which we live and think.*12

It might be imagined therefore that this doctrine would be the subject of a great deal of scholarship. In fact there is very little on the subject. The dialogues in which the doctrine appears have been written about endlessly over the last two centuries, but, though Plato’s discussion is noted, the fact that his discussion is based on an alternate logical modality is not acknowledged, and the conclusions which might follow from treating it as such, do not follow, and are therefore not discussed. It is treated as it is often presented by Plato – as mathematical and geometrical metaphors for how things might possess some form of congruence with each other.

I've argued elsewhere that there is, in general, very little appetite for attempting to understand Plato in his own terms.*13  When he talks about transcendent reality, this is treated as some sort of literary fiction, which has no necessary properties of its own. When Plato talks about the Forms, this also is treated as a species of literary fiction, which Plato records as being demolished in his Parmenides and in the Sophist. When Plato discusses the soul (in the Timaeus), it turns out that it is something which has the property of being connected with the Form of the Good, and so he argues that knowledge is acquired by the activation of that connection. We have forgotten what we knew (apparently) through the shock of physical birth, but it is possible for us to reacquire this knowledge by looking to the one true thing.*14 

Deriving all knowledge from the Form of the Good is also seen as a bafflingly impenetrable notion to the modern mind, since Plato talks about ascending purely in the mind from Form to Form, and then descending back to the world of physical reality, Form by Form, and says this is the only way to acquire genuine knowledge. How can real knowledge be acquired in this way? Why should Plato argue like this?  How can any of this make sense to us?

It makes very little sense to us, because we have lost the original doctrinal context of his discussions, and we are not that interested in attempting to recover what we can of that context, even for the purposes of a better scholarly understanding of what he is talking about. So the study of Plato languishes lifeless in the seminar room, taught and discussed from generation to generation by people who have no clear idea of what Plato meant. Books and papers are published, which clear up a minor detail here, discuss another one there, but do not leave us much the wiser.

We can understand the range of existing discussion about Plato in terms of what scholars do not or cannot understand about Plato, and their attempts to fit what they think they understand about his work into some kind of modern frame. It is their minds, and the categories of their own understanding which create the problem, not the obscurity of Plato’s ideas.

One of the principal reasons we cannot easily understand Plato is down to the loss of an understanding of that alternative logical modality. That understanding needs to be restored, along with a basic comprehension of why it is important. Not just for our understanding of Plato himself, but also for our understanding of his cultural context; the context in which philosophy was understood to be of inestimable value; and also for an understanding of some very strange things about the ancient world, which are all the stranger because (it seems) they made sense in antiquity (sacrifice, divination, idolatry, prophecy, omens, oracles, etc.).

One of the most valued books in my library is Religion and Magic: Approaches and Theories, which is a survey of modern anthropological thought. *15 The author is Graham Cunningham, a specialist in the ancient Near East and the relevant languages. Anthropology is a relatively young discipline, though crowded with many points of view. *16 Cunningham’s book covers the whole range of these, at least in terms of summarising the views of those who first suggested those theoretical approaches. He divides the approaches into several sections, which are:
1 German pioneers, 2 Early Intellectualist approaches, 3 Emotionalist approaches, 4 Phenomenological Approaches, 5 Structural Functional Approaches, 6 Symbolic Approaches, 7 Recent Intellectualist Approaches, 8 Structural approaches, 9 Cognitive Approaches, 10  Feminist Approaches.
All of these approaches were developed and used without any meaningful distinction being made between ancient cultural phenomena and cultural phenomena of modern times. I write carefully here, since there are unpleasant presumptions in the discipline of anthropology, which have not yet been rooted out. Anthropology as a formal subject was founded in the early nineteenth century, and the presumptions of the time are necessarily locked into the work of the pioneers. Many of these can be called into the light of day if you scratch the modern anthropologist in the course of discussion. The fact is that a dangerous equation was early made between the cultures of antiquity and the world of  'the primitive and the savage' in the modern world (which the Classicist D’Arcy Wentworth Thompson referred to as ‘running folklore to the death’).*17

So Cunningham’s book covers two centuries of thought about culture, civilization, religion, magic and ritual. All premised on the assumptions, understanding and categories of knowledge of those living and working in those two centuries. Nothing about those matters is covered from earlier centuries. It is as if the study of human culture, human thought, and the nature of man himself, began only in Hegel’s study, and nothing of worth came before Hegel. *18 

I could digress here, and lay out what came before in detail, but that is for another time. I will allow myself to say that Plato had something else to bring to the party, which is not covered in Cunningham’s survey; the Neoplatonists (who thought of themselves as Platonists, but we will not let them be what they are) would have brought the same thing to the party, as would some of the early Gnostic writers. The Platonists of the Italian and English Renaissances also understood what Plato was writing about, at least for the most part, and would be shocked that, not only do we not understand Plato, but that we have chosen to explain much of human culture in terms of a fundamental conceptual error about the way reality works, and with a complete disregard for the way the human mind was once understood to engage with that reality.

It is assumed by the moderns (in the west, at least) that philosophy is a cultural phenomenon which, in historical terms, follows on from religious thought, and does not precede it. We are sure of this because we are sure we know what religion is, and what philosophy is. We think that religion enshrines a form of knowledge about the world and the universe which is less than rational, and that the devotees of religion are often credulous. Religious thought is often transfixed by the numinous and the invisible, and its responses to these things are unfathomable to the rational mind. We also think religion, to a great extent, developed in response to the ideological needs of social groups, sometimes in conflict with other social groups, which can give very distinctive structures to the myths and rituals which become part of the bedrock of the public show of these religions.We believe this (admittedly oversimplified) picture to be a correct interpretation of what religion is. Modern religion differs from ancient religion only in details.

Whereas philosophy is about a critical and rational understanding of the world and how it presents itself to us. Religion is cast as an un-philosophical and irrational understanding of that reality. The development of philosophy represents progress.

These notions are subject to nuance of course, but this is the core of the enlightenment idea of what these things are.

We assume that religion, as it presents itself to us in the form of the relatively young Abrahamic religions, is not fundamentally different in nature to other religions, either elsewhere now, or in the distant past. We make such an assumption, because there is nothing in our understanding of other religions which suggests to us, at least not with any clarity, that any other process is active in the creation and operation of religion. The dynamics are the same, and the functions are the same.

Graham Cunningham’s postscript makes it clear that religion is generally understood by anthropologists to be a relic of an earlier time where rational thought was absent. Certainly in terms of what we would recognise. Somehow religion is still with us, because large parts of the human race believe in the importance and efficacy of belief in the divine: that belief in the reality of the divine is something which is essential to the religious life, and the religious understanding of reality. *19

Yet this is not what ancient writers tell us. They tell a different story, as I’ve suggested, and one which is not represented by any current anthropological approach. That different story is that religion in the ancient world was not about belief, but concerned both knowledge and conjecture about the nature of the divine; and about the nature of reality itself.*20

I prefer to write about ancient religion in terms of divine cult. I distinguish the two for clarity - religion is often understood in the modern world in terms of sociological and ideological functions. And indeed religion has these functions: it often provides social cohesion, ideology, and useful rules of social behaviour. But to attempt to explain the core of divine cult in such terms is presumptive. If the core of a divine cult involves rational conjecture about the nature of reality itself, we will not easily find this out, even if the evidence is screaming this at us. In antiquity the ritual practice of divine cult was often a private affair, rather than a public one, which implies an important division between the performative function of ritual, and the outward show. Ritual and observance were the important things. The public show might echo the thought behind the cult in some respects, and offer clues to its significance and nature, but it is not the cult itself. *21

The association of knowledge with the core divine cult (and, consequently, a confirmation of the  connection of the cult with the divine itself), gave the rituals of ancient religion (both private and public) their efficacy, and patterned their meaning. But this did not involve belief.  Belief is something which is not supported by credible argument, or is a step beyond the limits of an rational argument.  That is not what was involved in ancient discussion of questions concerning the divine. Can you have knowledge without rational modes of thought? And what did the ancient writers mean by knowledge of the divine, and by equating knowledge with the divine? Clearly, it is not possible to have actual knowledge of something without rational modes of thought. But what rational thought is, is another one of those things which we are quite clear about in modern times, even if the evidence points to a different conclusion, and exists in teeming quantities.


 1. Frazer wrote this in his prize essay of 1879 on the 'Growth and Development of Plato's Ideal Theory'. Published finally in 1930. I'd found this essay after noticing that there were odd features in the structure of The Golden Bough. I wrote about this in J. G. Frazer and the Platonic Theory of Being (2016), and also in the more compact essay 'Frazer and the Association of Ideas', published in Understanding Ancient Thought (2017).
2. In his 'Life of Pythagoras' Porphyry tells us that Pythagoras travelled extensively around the Near East and Egypt in the service of Cyrus. Discussed in 'Pythagoreanism, the Divine, and the Nature of Eternity'.
 3. In the Timaeus. Discussed in 'The Platonic Theory of Being' (full text with notes). Originally published in The Sacred History of Being (2015).
4. Discussed in 'Solon in the Court of Croesus' (extract). The full text is a chapter in The Sacred History of Being (2015).
5. Discussed in 'Working Wonders: Hephaestus and the Armour of Achilles'. A retitled chapter from The Sacred History of Being (2015), originally titled  'Being in Homer'.
 6. Discussed in 'Oannes and the Instruction of Mankind', which is one of the appendices to The Sacred History of Being (2015).
7 Discussed in 'The Babylonian Creation': an extract from the chapter 'Creation' in The Sacred History of Being (2015).
 8. Modern scholars are well aware of this. Ancient historians arranged information, but also questioned it. The Assyrians seemed to have a similar attitude to their materials - the chronicles associated with Ashurbanipal's reign exist in more than one version, with events recorded in a different order.
 9. Discussed in 'Logical Modality in Classical Athens' which is a chapter in Understanding Ancient Thought (2017).
10. Consequently this ought to be a matter of interest to Christian theologians, owing to the importance of the idea of the incarnation of the divine in the Gospels. For centuries the incarnation has been presented as a mystery (to both believers and theologians), without any kind of theoretical basis. But the theoretical basis is present in ancient literature, in various places. It even surfaces in a text in the Nag Hammadi documents.
 11. The logical basis of the incarnation is discussed in 'The Keys of the Kingdom: Binding and Loosing in Heaven and Earth', a chapter from Echoes of Eternity (2019).
12. Discussed in 'The Transcendental understanding of Reality', and in 'The Greek Ontological Model in the 1st Millennium B.C.E.'  from Echoes of Eternity (2019).
13.  'The Sweet Song of Swans'. The full text of this chapter, which concerns (among other things) the modern creation of the Greeks as the originators of philosophy, was published in the The Sacred History of Being (2015).
 14. In the chapter 'Plato's Theory of Vision', from The Sacred History of Being (2015). This extract concerns the discussion of the cosmos as “a perceptible God made in the image of the Intelligible.”
 15. Cunningham, Graham, Religion & Magic: Approaches & Theories, Edinburgh University Press, 1999.
 16. That there are so many conflicting views might suggest that perhaps few, or even none of the approaches are correct, but are simply the product of the failure to grasp the sophistication of ancient thought.
17. Discussed in 'Running Folklore to the Death', an extract from section 13 of J.G. Frazer and the Platonic Theory of Being (2016).
18. I've discussed Eriksen and Nielsens' A History of Anthropology (2001) in the chapter 'Before Anthropology', which book illustrates that modern anthropology is sometimes about how things ought to be, rather than a profound engagement with the evidence. They do however give a useful account of what came before Hegel. Published in Man and the Divine (2018).
 19  We tend to inject our presumptions about the past onto the evidence, as if common sense is a servicable tool in understanding it. It takes more than that. Discussed in 'Beyond the Religious Impulse'. Published as a chapter in Understanding Ancient Thought (2017). See also 'Distinguishing Belief and Faith', in Man and the Divine (2018).
20 A close look at Assyrian divination reports makes it clear that there was nothing mystical or vague about Assyrian queries about the future. The queries to the Sungod (Shamash) were expected to provide accurate information in response. This is because the diviners and scholars formulating the questions understood the universe to be rooted in a plenum. In which case,  all things which might be, already exist in the plenum. The diviners were therefore asking the Sungod for information which was available to the god. Twenty divinatory queries are available on the page 'Who will Appear before the City?' The concept of the plenum and its connection with the Mesopotamian story of the creation is discussed in the chapter: 'The Idea of the Plenum in Babylon'; further discussion of  the concept can be found in  'Pleroma, Cosmos, and Physical Existence', both from Understanding Ancient Thought (2017).
21. Discussed in 'Shar Kishati and the Cult of Eternity', published in Understanding Ancient Thought (2017).

Draft version, October 29, 2019. Final version, All Hallows Eve, 2019. TY

Saturday, 28 September 2019

Pythagoreanism, the Divine, and the Nature of Eternity

[I compiled this paper in December 2017 to provide background detail for a speculative discussion of ancient patterns of thought outside Greece, and in particular in connection with thought in Britain before the arrival of the Roman legions. This question is worth looking at since we are told by a number of ancient writers that there were certain resemblances between the ideas and beliefs held by the priests in the British Isles, and those associated with the followers of Pythagoras.

That was a very specific reason for compiling this paper, but the compilation of the details of Pythagorean doctrine and its resemblances, and the discussion of the likely philosophical background to Pythagorean doctrine,  is useful in itself. So I've extracted that part of the paper, and re-edited it to stand alone, along with a little material that was not in the original]. 

Abstract: This paper explores the idea that there is a connection between some core Pythagorean mathematical and geometrical concerns, and ideas of divinity and Eternity.  On the basis of a close examination of Pythagorean ideas in the 1st millennium, for which we have extensive documentation, It is suggested that this connection is a logical one.

Key words: Pythagoras, Philosophy, Religion, Number, Mathematics

The Longevity of Ideas

We often underestimate the longevity of patterns of ideas. Sometimes when they are linked to a religious or theological structure, they can have a very long existence. Though much of modern knowledge about the physical world has been developed since the European Enlightenment, there are still ideas around which have persisted with very little change, since the first millennium B.C.E. Hinduism is still much as it was for example, as is Buddhism. Later religions such as Christianity, built as it was on the Old Testament, preserves many aspects of Hebrew ideas [Christ is made to paraphrase YHWH’s statement in the Old Testament that he is ‘first and last, and beside him there is no other god’, by characterising the divine as the ‘alpha and the omega’].

In short, there are still religious ideas and formulations around in the world, and contained in the human mind, which are more than two and a half millennia old. And in some cases, much older than that. Languages and peoples may change, but ideas are sometimes much slower to change, and may survive alteration of language, people, and material culture.

This paper explores a hypothesis: the hypothesis that some ideas which we habitually consider to be around two and a half millennia old, are in fact much older than that. In the west, these ideas find powerful expression in Pythagoreanism, written about by both Plato and the later Neoplatonists. Looked at in the Greek context alone, this body of ideas extends over nearly eleven hundred years (if a floruit of the mid sixth century BCE for Pythagoras is correct), until the closure of the philosophical schools in 529 CE.

So how old is philosophy? Classicists are ready to be very specific about the matter. Their view (which became orthodoxy during the European Enlightenment of the eighteenth century) is that the Greeks pioneered philosophy from the seventh and sixth centuries B.C.E. onwards, culminating in the intellectual enlightenment of the 5th and 4th centuries B.C.E.

Yet as late as the 2nd century of the Common Era, the Christian writer Clement of Alexandria said that:
Philosophy..., with all its blessed advantages to man, flourished long ages ago among the barbarians, diffusing its light among the gentiles, and eventually penetrated into Greece.
Note that Clement places the Greeks not at the beginnings of philosophical thought, but as the late inheritors of a practice which had flourished for long ages, and among those who did not speak Greek.

Clement goes on to be more specific, and says of philosophy that:
Its hierophants were the prophets among the Egyptians, the Chaldeans among the Assyrians, the Druids among the Galatians, the Sramanas of the Bactrians, and the philosophers of the Celts, the Magi among the Persians who announced beforehand the birth of the Saviour, being led by a star till they arrived in the land of Judaea, and among the Indians the Gymnosophists, and other philosophers of barbarous nations.

— Clement of AlexandriaStromata 1.15.71 (ed. Colon. 1688 p. 305, A, B).

So there is the possibility that there is another narrative which we can reconstruct. 

2 Pythagoreanism in 1st Millennium Britain

We have Greek and Roman sources for the supposed origins of Pythagorean modes of thought. These point in different directions. We have the story that Pythagoras was present at the fall of Babylon in 539 BCE, and he is also supposed to have spent some time in Egypt (around twenty years), learning from the priestly cults. On the other hand, we have information about the beliefs of the Gaulish priests from the mid-first century B.C.E., in the wake of Julius Caesar’s campaigns in north western Europe. Caesar described the Gauls in his Commentarii de Bello Gallico, [The Gallic War], book VI.

According to Caesar, the Gaulish priests were concerned with "divine worship, the due performance of sacrifices, private or public, and the interpretation of ritual questions." He also said that they played an important part in Gaulish society, being one of the two respected classes, the other being the equites (the Roman name for ‘’knights - members of a privileged class able to provide and equip horsemen). They also functioned as judges in disputes. Among other interesting details, Caesar also said that they met annually at a sacred place in the region occupied by the Carnute tribe in Gaul (possibly Chartres), and that Britain was the home of priestly study. Caesar also said that many young men were trained as priests, during which time they had to learn large amounts of lore by heart. 

Metempsychosis was the principal point of their doctrine: “the main object of all education is, in their opinion, to imbue their scholars with a firm belief in the indestructibility of the human soul, which, according to their belief, merely passes at death from one tenement to another; for by such doctrine alone, they say, which robs death of all its terrors, can the highest form of human courage be developed”.

He also tells us that they were concerned with "the stars and their movements, the size of the cosmos and the earth, the world of nature, and the powers of deities". So the components of their religious cult involved the study of astronomy, cosmology, natural philosophy, and theology.

Alexander Polyhistor, in a passage preserved by Eusebius, described the Gaulish priests as philosophers, and explicitly called them ‘Pythagorean’ on account of their understanding of reality. He wrote that "The Pythagorean doctrine prevails among the Gauls' teaching that the souls of men are immortal, and that after a fixed number of years they will enter into another body."

Diodorus Siculus, writing in 36 BCE, also said that the Gaulish priesthood followed "the Pythagorean doctrine", that souls "are immortal, and after a prescribed number of years they commence a new life in a new body."

There are other descriptive references to the Gauls and their religion from antiquity, but it is not necessary to review all of them here. These are the main evidential details we have for the presence of Pythagorean ideas in Gaul and in Britain in the last two centuries of the 1st Millennium BCE. It is likely that both Polyhistor’s account and the account of Diodorus Siculus drew on the source used by Caesar.

3.The Principal Sources for Pythagoreanism

The preceding descriptions are usually all that is mentioned when religion in Gaul and in Britain before the arrival of the Romans is discussed. This is because we do not have written records from Gaul or Britain from earlier times. And so this is where historical discussion usually stops. The rest of the story of these cultures becomes a matter for archaeological investigation.

However, we need not stop here, looking at nothing. Much of what we know about the other philosophical details of the Pythagoreans is quite extensive, if not always consistent across the range of sources.  There is a life of Pythagoras by Iamblichus, and another by his pupil Porphyry. A life of Pythagoras by Diogenes Laertius also contains useful information. Plato and the later Platonists wrote in detail about Pythagorean doctrine, if not always being explicit that they were referencing his ideas. 

Plato is the best place to start. He had the concept of an inner and outer knowledge, which reflects something of a priestly understanding of both teaching and of reality. He referred to these grades of knowledge as ta eso and ta exoWhich 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.  Plato was engaged with both exoteric and esoteric understandings of knowledge, but mostly what he 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.

The Core of Pythagorean Doctrine

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 BCE. The doctrine 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 might, as Porphyry suggests, have been brought back to the west by Pythagoras after his spell in the east, 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 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. 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. The images are constructed in the way they are 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, even if the technical term post-dates classical Athens by several centuries.

In the Timaeus [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.

Pythagoras is said by Porphyry to have associated with the ‘other Chaldeans,’ after he 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. 

What did Pythagoras take from his long sojourn in Egypt, and the near-east? Is his doctrine like Plato’s? The point of the doctrine of wholes and totalities, is to establish connection between the divine world and secular reality. 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’ in the doctrines of both Plato and Pythagoras, 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.

Diogenes Laertius on Pythagoreanism

Diogenes Laertius is generally not regarded as a great historian of the philosophy of the ancient world, but his Lives of the Philosophers is the only general account which survives from antiquity. We get snippets from elsewhere, but not the comprehensive sweep that he gives. He does not always have good materials, or understand them well. But with his writing on Pythagoras, we get something different. He is working with some very good materials indeed. His date (actually quite uncertain) may be contemporary with the Neoplatonists who also wrote about Pythagoras, and possibly he is using the same now long vanished materials, since he reproduces the same sort of inconsistencies of detail which appear in Iamblichus’s Life of Pythagoras. These inconsistencies, mainly concerning religious observances, may be explained by the fact that the core of Pythagoras’s doctrine isn’t about these things at all, but about an agrapha, or ‘unwritten doctrine’, revolving around deeper matters.

As already mentioned, it was a popular opinion in antiquity that Pythagoras did not write any books – “There are some who insist, absurdly enough, that Pythagoras left no writings whatever” [D.L., Book VIII, 6], however Diogenes says that ‘Heraclitus, the physicist, almost shouts in our ear, “Pythagoras, son of Mnesarchus, practised inquiry beyond all other men, and in this selection of his writings made himself a wisdom of his own, showing much learning, but poor workmanship”’. Heraclitus therefore seems to recognise the disparate origins of the material used by Pythagoras (in his book On Nature), and feels that it has not been worked properly. Diogenes tells us that Pythagoras wrote three books altogether, which were (since we no longer have them): On Education, On Statesmanship, and On Nature. Other works were also attributed to him [D.L., Bk VIII 7].

Diogenes appears to have had access to the three Pythagorean texts, or extracts from them, or perhaps from epitomes of them, since he talks about the contents [D.L., Bk VIII 9-10]. He says that Pythagoras was understood to be the first to speak of the idea of metempsychosis – he declared that “the soul, bound now in this creature, now in that, thus goes on a round ordained of necessity”. D. L. says that ‘so greatly was he admired that his disciples used to be called “prophets to declare the voice of God” [D.L., Bk VIII 14].

The books seem to have been kept secret, since Diogenes says that “Down to the time of Philolaus it was not possible to acquire knowledge of any Pythagorean doctrine” until Philolaus “brought out those three celebrated books.” Diogenes says that Plato sent a hundred minas in order to purchase these texts [D.L. Bk VIII 15]. He cites Aristoxenus in the tenth book of his Rules of Pedagogy “where we are …. told that one of the school, Xenophilus by name, asked by someone how he could best educate his son, replied, “By making him the citizen of a well-governed state.”’ This is of course the clearest anticipation of Plato’s interest in education.

Diogenes relates some details, not always in agreement with each other, of the religious nature of Pythagoras' philosophy: “He used to practise divination by sounds or voices, and by auguries, never by burnt offerings, beyond frankincense. The offerings he made were always inanimate; though some say that he would offer cocks, sucking goats and porkers, as they are called, but lambs never. However, Aristoxenus has it that he consented to the eating of all other animals, and only abstained from ploughing oxen and rams” [D.L., Bk VIII 20]. Diogenes relates later that ‘Apollodorus the calculator’ says “he offered a sacrifice of oxen on finding that in a right-angled triangle the square on the hypotenuse is equal to the squares on the sides containing the right angle”.

There was therefore some uncertainty in antiquity about exactly what the religious practice of Pythagoras was – it may not have been consistent in its nature, and it follows that it is possible that some of the practices attributed to Pythagoras, (vegetarianism, avoidance of killing animals, the avoidance of beans, etc.) are not in themselves of essential importance to Pythagorean doctrine, but only seemed so to compilers and commentators in late antiquity.

If we look at some further statements by Diogenies we can guess what the important things in Pythagorean doctrine are. Diogenes says that Pythagoras advised his disciples to say to themselves when entering their own doors: ‘Where did I trespass? What did I achieve? And unfulfilled what duties did I leave?’ [D.L., Bk VIII 22]. This indicates (among other things) the importance of the threshold or limit to Pythagoras.

Pythagoras also urged that the memory be trained. This was also extremely important to Plato, and he regarded the invention of letters to have been a disaster on the grounds that they impaired the training of the memory through making its importance less clear. There were in any case already people in Greece who held large parts of the Homeric poems in memory, since the poems were not committed to writing until the time of Peisistratus (some time after he first became tyrant of Athens in 560 BCE). Memory seems to have been cultivated in Egypt, and was certainly practised (and discussed) in late antiquity in various parts of the Roman Empire (Cicero mentions it, and it surfaces in the work of St. Augustine).

Pythagoras also said that men should sing to the lyre and by hymns to show due gratitude to gods and to good men. He bade men “to honour gods before demi-gods, heroes before men, and first among men their parents”. The principal image here is the gods, who are more important than the demi-gods, in terms of their claim on our worship and honour. Heroes stand in the same relation before men, and our parents stand in the same relation to us. He amplifies the importance of this metaphorical perspective, by saying that men should ‘honour their elders, on the principle that precedence in time gives a greater title to respect; for as in the world sunrise comes before sunset, so in human life the beginning before the end, and in all organic life birth precedes death’ [D. L., Bk VIII 22-4].

At one level this kind of metaphor-making looks trivial, which is one of the reasons why little has been made of these passages. However. Pythagoras is setting up oppositions between extremes within defined classes (Gods and demi-gods, who are immortal, Heroes and men, who are mortal, etc.), and making a comparison between them. He is also establishing a line of connection between them. He isn’t just comparing one image with another, he has created chains of images, with one end of the chain representing the extreme of reality (the Gods), and we stand at the other extreme.

The image of ourselves and our parents might be taken to suggest a parallel with the relation between Gods and demigods. In terms of the relationships implied in the image, the familial image can be understood as a copy of sorts, more or less imperfect, of the relationships between Gods and demigods. We are of course familiar with the Greek Gods and their shocking personal relations with each other, which often suggest an earthly and dysfunctional extended family.

Like Plato, Pythagoras had an agrapha, since some Pythagoreans “used to say that not all his doctrines were for all men to hear” – which is perhaps why it was so difficult to acquire knowledge of Pythagorean doctrine until the indiscretion of Philolaus [D.L., VIII 15-6]. Diogenes authority for this is the tenth book of Aristoxenus’ Rules of Pedagogy. Diogenes draws details of the Pythagorean philosophy from another lost author – Alexander, author of Successions of Philosophers, who claimed to find the following in the Pythagorean memoirs:
The principle of all things is the monad or unit; arising from this monad the undefined dyad or two serve as material substratum to the monad, which is cause... [D.L., VIII 25].
This is very like the conception of the Neoplatonists, who argued that in order that the good should remain untainted with generation and change, a copy came into being, which did participate in creation:

from the monad and the undefined dyad [the ‘undefined dyad’ may also be translated as ‘unlimited dyad’, or ‘unbounded dyad’ (the Greek term is ‘aoriston’) spring numbers; from numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four, fire, water, earth and air. These elements interchange and turn into one another completely, and combine to produce a universe animate, intelligent, spherical, with the earth at its centre… [D.L., VIII 25].

Once again we have a chain of images: the monad and the undefined dyad, numbers, points, lines, plane figures, solid figures, sensible bodies, the four elements. Note that we don’t have the monad included in his sequence – the first image in the sequence is the monad and the undefined dyad, which “serves as material substratum to the monad, which is cause…”

Each of these conceptions is an imaging of the properties of the monad, one leading to the other, increasing in definition, attributes and properties until we reach the sensible bodies with the properties of fire, water, earth and air, all of which can interchange into one another completely. This chain represents an order of generation, rather than an order of perception.

That each of the sensible bodies can interchange into one another completely is a corollary of the fact that they arise from the undefined dyad. They are differentiations of the undefined dyad, and their fundamental identity resides there. Thus, fire may stand metaphorically for water, earth for air, and so on. The interchange occurs with reference to the monad and undefined dyad, since the combination of the monad and undefined dyad is the fount of all cause, generation and change.

The monad itself is an image, but can have no definition beyond the ‘One’. The numbers did not arise from the monad itself: for that to happen, something else was necessary. That he does not say that numbers arise from the monad is an important clue towards understanding that not only is Pythagoras speaking in terms of images, but that these images are related to an account of another level of reality, referred to, but not articulated. This level of reality is entirely without rational form, and which has an esoteric nature. Such an account of reality also informs Hesiod’s version of the creation, in which there is an ultimate reality which does not conform to the categories of our understanding (i.e., ‘chaos’).

In addition, there is a strong ethical element to Pythagoras’ life and philosophy, and it is clearly associated with the properties of the threshold, where one thing conjoins with, or turns into another. It would not be unreasonable to describe Pythagoras’ philosophy as theurgic in nature, since he is concerned that man should control his own destiny, and not trust to the gods alone. He also laid down precepts for religious practice and religious discipline, meaning that there was understood to be an efficacious ritual element in the transformation of the human soul.

For example, Pythagoras urged that victims ought not to be brought for sacrifice to the gods, and that worship should be conducted “only at the altar unstained with blood”. In addition, he stipulated that the gods should not be called to witness, “man’s duty being rather to strive to make his own word carry conviction”. He also said that men should avoid excess of flesh, and that they should respect all divination. Abstention from beans was recommended “because they are flatulent and partake most of the breath of life; and besides, it is better for the stomach if they are not taken, and this again will make our dreams in sleep smooth and untroubled” [D.L., Bk VIII 23-4].

That they ‘partake most of the breath of life’ is an objection to beans seems a little odd, unless by this Pythagoras is indicating that the target of the transformation of the individual through discipline, ritual and understanding is a condition which does not partake of the breath of life. We recall that Socrates in his final moments asked that a cock be sacrificed to Asclepius, which was to mark a return to health – in this case a healing from the trials and tribulations of life.

Pythagoras seems to have shared this view of earthly life. In vol 2, Bk. VII on Zeno (333-261 BCE, of Citium in Cyprus, a city which ‘had received Phoenician settlers’), we are told by Diogenes that the author Hecato, and also Apollonius of Tyre, in his first book on Zeno, that Zeno consulted the oracle (presumably Delphi) ‘to know what he should do to attain the best life’. The response of the god was that ‘he should take on the complexion of the dead’. Diogenes Laertius takes from his sources that Zeno’s interpretation of this is that ‘he should study ancient authors’. We can see that the true meaning of the oracle was both much more straightforward and much more profound than that.

6 Pythagorean Thought in Italy

Pythagoras was creating an eclectic doctrine, by syncretising elements from different sources. This is what Heraclitus means by saying that the collections of information in the three books are ‘poorly worked’. Not much interest has been shown in what Pythagoras, a long-time resident in Italy, might have drawn from Italian sources. In fact, it would seem that much of what was later passed off as Pythagorean in origin, actually has its origin among the Latins.

For example, the Romans also had a tradition of veneration of the boundaries and limits of things. Oskar Seyffert says of the god Janus that “even the ancients were by no means clear as to his special significance; he was, however, regarded as one of the oldest, holiest, and most exalted of gods”.

Of course, if the special significance of Janus was close to the heart of Roman religion, an absence of discussion might, rather than signifying a lack of clarity about his special significance, mean quite the opposite, and that the written tradition is quite misleading as to the Roman understanding of Janus, at least within the priestly community. 

“In Rome the king, and in later times the rex sacrōrum, sacrificed to him. At every sacrifice he was remembered first; in every prayer he was the first invoked, being mentioned even before Jupiter”. Which is indication of high status. If we recall the remarks of Pythagoras on what comes first and why, we can see that the significance of Janus is extremely important indeed. This is further emphasised by the fact that “in the songs of the Salii (‘jumpers’ or dancers) he was called the good creator, and the god of gods; he is elsewhere named the oldest of the gods and the beginning of all things.” The Salii were an old Italian college of priests of Mars, said to have been originally introduced at Rome by Numa Pompilius, the legendary 2nd king of Rome. He was said to be a native of Cures in the Sabine country, and was elected king a year after the death of Romulus.

William Smith says that Numa Pompilius “was renowned for his wisdom and piety; and it was generally believed that he derived his knowledge from Pythagoras”. Given that the foundation of Rome is traditionally 753 BCE, this is impossible, since Numa and Pythagoras would have been two centuries apart. However, the fact that later the institutions of Numa were associated with Pythagorean influence suggests that there was a perception of a relationship between the doctrines of Pythagoras and the foundation of Roman religion. Smith continues: “…he devoted his chief care to the establishment of religion among his rude subjects”, and to giving them appropriate forms of worship. He was instructed by the Camena Egeria (Aegeria), one of the twelve nymphs in Roman mythology. Numa later dedicated the grove in which he had his interviews with the goddess, in which a well gushed forth from a dark recess, to the Camenae.

Seyffert continues regarding Janus: “It would appear that originally he was a god of the light and of the sun, who opened the gates of heaven on going forth in the morning and closed them on returning at evening”. Rather, Janus, being the divinity associated with boundaries, is associated with gates, crossings, risings and settings, beginnings and endings, and the daily movement of the sun is the most important visible instance of beginnings and endings. In course of time (Seyffert suggests) “he became the god of all going out and coming in, to whom all places of entrance and passage, all doors and gates were holy” [my italics]. He continues:
In Rome all doors and covered passages were suggestive of his name. The former were called ianuae; over the latter, the arches which spanned the streets were called iani.
Many of these were expressly dedicated to him, especially those “which were situated in markets and frequented streets, or at crossroads”. In the case of crossroads, Seyffert tells us that “they were adorned with his image, and the double arch became a temple with two doors, or the two double arches a temple with four”. The way Janus was generally represented was “as a porter with a staff and a key in his hands, and with two bearded faces placed back to back and looking in opposite directions.”

Further, he is also the god of entrance into a new division of time, and was therefore saluted every morning as the god of the breaking day (pater matutinus); the beginnings of all the months (the calends) were sacred to him, as well as to Juno; and, among the months, the first of the natural year, which derived from him, Ianuarius. For sacrifices on the calends twelve altars were dedicated to him; his chief festival, however, was the 1st of January, especially as in B.C. 153 this was made the official beginning of the new year. On this day he was invoked as the god of good beginnings, and was honoured with cakes of meal called ianuae; every disturbance, every quarrel, was carefully avoided, and no more work was done than necessary to make a lucky beginning of the daily business of the year; mutual good wishes were exchanged, and people made presents of sweets to one another as a good omen that the new year might bring nothing but that which was sweet and pleasant in its train.

For the Romans, this juncture of the year, like every other juncture over which Janus presided, was a region in which change was more possible, more likely, than at any other time. Therefore, any immoderate behaviour, any departure from the normal daily pattern of life, whether through a quarrel or some other unpleasantness, might easily have taken root, and they might have found their whole lives dislocated as a result.

Seyffert continues that:
the origin of all organic life, and especially all human life, was referred to him; he was therefore called consivius (‘sower’). From him sprang all wells, rivers, and streams; in this relation he was called the spouse of Juturna, the goddess of springs, and father of Fontus, the god of fountains.

7 The existence of Irrational numbers

It is generally supposed that the Pythagoreans understood the world to be rational in nature, and it had long been argued that rational numbers were the product of ratios of other numbers. Their belief in rational whole numbers seems to have been a principal concern, possibly because whole numbers are often commensurable. The ancient assumption that the world was a rational creation, was maintained at least at the level of open public discussion.

There is however a famous story about the discovery of irrational numbers by the Pythagoreans, and their utter horror at the discovery. The discoverer of irrational numbers was supposedly drowned at sea, perhaps in consequence of this discovery. In fact, the story is likely to have a quite different meaning at an esoteric level, which I will discuss at the close of this paper.

So how was the Pythagorean proof of the existence of irrational numbers achieved? We should remember that The Eleatic school (home to Parmenides and Zeno, the former of which argued for the One and unmoving reality transcending the world of appearances) attacked Pythagorean doctrine by assuming their opponents' tenets, using the reductio ad absurdum technique to examine their credibility. The effect of such arguments was to reinforce the importance of the incommensurate in the world of number.

The Greeks attempted to extricate themselves from these difficulties by distinguishing between things which they would have preferred to have been commensurable (numbers and magnitudes), thereby rendering them incomparable. So the diagonal of a square could be regarded as a magnitude rather than as a length equal to the ratio of two numbers. By this means, irrational numbers could be largely ignored (a similar convenient fiction to one devised by Aristotle in connection with infinity, in which he subverted the difficulty of the infinite by dividing it into two: a potential infinite, and the actual infinite, which could be ignored).

From Thomas Heath:
We mentioned... the dictum of Proclus... that Pythagoras discovered the theory or study of irrationals. This subject was regarded by the Greeks as belonging to geometry rather than arithmetic. The irrationals in Euclid, Book X, are straight lines or areas, and Proclus mentions as special topics in geometry matters relating (1) to positions (for numbers have no position) (2) to contacts (for tangency is between continuous things), and (3) to irrational straight lines (for where there is division ad infinitum, there also is the irrational).
...it is certain that the incommensurability of the diagonal of a square with its side, that is, the irrationality of root 2, was discovered in the school of Pythagoras... the traditional proof of the fact depends on the elementary theory of numbers, and... the Pythagoreans invented a method of obtaining an infinite series of arithmetical ratios approaching more and more closely to the value of root 2.
Thomas Heath was writing at a time (1921) when classicists had very little knowledge of what was coming out of the ground in Mesopotamia and elsewhere, so his certainty that the school of Pythagoras ‘discovered’ the incommensurability of root 2 is a product of that time. He writes:
The actual method by which the Pythagoreans proved the fact that root 2 is incommensurable with 1 was doubtless that indicated by Aristotle, a reductio ad absurdum showing that, if the diagonal of a square is commensurable with its side, it will follow that the same number is both odd and even. This is evidently the proof interpolated in the texts of Euclid as X. 117... [Heath, T. (1921) Vol. 1 pp. 90-91].

It is a proof based on the law of non-contradiction. However, it is the consequence of the properties of Pythagorean triangles as they are represented to our understanding. The point of this demonstration is that: how things are represented to us is not the same as how they actually are. Or how they are in what we might term ‘transcendent space’.

Heath continues:

We have first the passage of the Theaetetus recording that Theodoras proved the incommensurability of root 3, root 5…. Root 17, after which Theaetetus generalized the theory of such 'roots.'... The subject of incommensurables comes up again in the Laws, where Plato inveighs against the ignorance prevailing among the Greeks of his time of the fact that lengths, breadths, and depths may be incommensurable as well as commensurable with one another, and appears to imply that he himself had not learnt the fact till late, so that he was ashamed for himself as well as for his countrymen in general.

This is interpretation about what Plato is saying which isn’t warranted. Plato was quite plain elsewhere (in the Republic and the Timaeus) that all things may pass into one another, and hence are in some way commensurate. He says this in connection with the Forms. As a general statement, it implies that the same is true for both commensurable and incommensurable numbers. We find ourselves in a strange place where the incommensurate may also be commensurate. Heath continues:
But the irrationals known to Plato included more than mere 'surds' or the sides of non-squares; in one place he says that, just as an even number may be the sum of either two odd or two even numbers, the sum of two irrationals may be either rational or irrational. An obvious illustration of the former case is afforded by a rational straight line divided 'in extreme and mean ratio' (Euclid XIII. 6) proves that each of the segments is a particular kind of irrational straight line called by him in Book X an apotome; and to suppose that the irrationality of the two segments was already known to Plato is natural enough if we are correct in supposing that 'the theorems which' (in the words of Proclus) 'Plato originated regarding the section' were theorems about what came to be called the 'golden section', namely the division of a straight line in extreme and mean ratio as in Euclid. II. 11, and VI. 30. The appearance of the latter problem in Book II, the content of which is probably all Pythagorean, suggests that the incommensurability of the segments with the whole line was discovered before Plato's time, if not as early as the irrationality of root 2. [Heath, T. (1921) Vol. 1 pp. 304-305].

8 Religious aspects of Pythagoreanism

Pythagorean thought is therefore a species of transcendentalism. It is a pattern of thought which understands reality itself (whatever that may be) as a principal concern, and as something which, as it is, transcends mundane earthly reality.

Within this pattern of thought however, earthly reality has properties and characteristics which have counterparts in the divine world. If 'God is Great’ for example, there are earthly examples of greatness, and so greatness is understood to be a property held in common between the worlds. What is held in common was understood by those of a transcendentalist persuasion to offer a connection between the worlds.

In essence the transcendentalist outlook among the Greeks holds that Being, or the ultimate reality, is both transcendent, and also present in the physical world. It is hard to imagine how such a view could arise except as the result of sophisticated logical discussion of the nature of reality. The idea defies common sense, and is counter intuitive.

This view of the world represents a paradoxical understanding of reality, in that the divine both transcends mundane reality, but is also at the same time present in every aspect of that reality. The connections between reality itself and earthly reality are not obvious, and often not easy to discover. The difficulty in discovering the connections is an index of the distance between the worlds. Yet it is possible to discover these connections. Reading the mind of the divine was of course a major concern in antiquity, since interpreting divine intention conferred knowledge and earthly power.

Working on or with the gods (theurgy) is often thought of these days as some obscure form of theological lunacy practised by the Neoplatonists and a few other groups in the dying days of the Roman empire. It is however a very old idea, based on the understanding that the sacred and profane worlds are connected with each other. It is also built into Plato’s account of the creation of the cosmos (in the Timaeus). The practice of theurgy is a corollary of the transcendentalist outlook, since if reality is transcendent, but we are also paradoxically part of it, then human will and intention are important to the way in which the world works. Physical reality does not represent a copy of transcendent reality, which Plato labelled as a likelihood only, but rather a subjective understanding of that reality *[note 1].

According to this way of thinking, there are processes which we can use to enhance what we have in common with divinity. Most often this was expressed in terms of gaining knowledge of the divine, since the supreme divinity was necessarily the fount of all knowledge (both Plato and the Mesopotamians concur on this point). If theurgy is an important component in early religious practice, it tells us something about how much knowledge was prized at the time, and also something of the scope of that knowledge in antiquity. Unlike homeopathic magic, which theurgy sometimes resembles, the practice of theurgy is entirely dependent on an understanding of Being for its effective use.

9 The Pattern of Eternity

That Socrates says at Phaedrus 247c that he dares to speak the truth concerning the nature of the region above heaven implies strongly that it is dangerous to do so - and after all, one of the charges against him was that he made theological innovations. Xenophon suggests that, though he was not formally charged with disbelief in the gods per se, Socrates was suspected of a form of atheism ["And how could he, who trusted the Gods, think that there were no Gods?" Memorabilia Bk 1 ch.1.5]. To hold the ultimate reality to be virtually indistinguishable at root from chaos, a place devoid of justice, beauty, order, etc., (and without location in time or space) except in potential, would be indistinguishable to the ordinary citizen from atheism. No wonder therefore that Plato writes the ironical words at Tim 40d:
Concerning the other divinities, to discover and declare their origin is too great a task for us, and we must trust to those who have declared it aforetime, they being, as they affirmed, descendants of gods and knowing well, no doubt, their own forefathers.
And at Tim 29a, concerning the model after which the universe was patterned, Timaeus asks:

Was it after that which is self-identical and uniform, or after that which had come into existence?

The latter implies change and disorder; therefore
if so be that this Cosmos is beautiful and its Constructor good, it is plain that he fixed his gaze on the Eternal, but if otherwise (which is an impious supposition), his gaze was on that which has come into existence.
Which is no more than an appeal to common sense. The nature of the arguments which might be adduced in antiquity to explain the world of appearance are, as the Sophist shows, much more complex.

Conditioned therefore both by the difficulty of the subject matter, and the social impracticability of the doctrine, we are forced to work out the doctrine for ourselves. That the method employed to convey the doctrine sometimes created unnecessary difficulties for the understanding, quite apart from its inherent difficulty is shown by the remark at 48c where some matters are not explained:

solely for this reason, that it is difficult for us to explain our views while keeping to our present method of exposition.

Nevertheless, the description of the Receptacle at Tim 50-51 is possibly the clearest exposition in Plato of the Real:
... it is right that the substance which is to receive within itself all the kinds should be void of all forms... that the substance which is to be fitted to receive frequently over its whole extent the copies of all things intelligible and eternal should itself, of its own nature, be void of all the forms... a Kind invisible and unshaped, all--receptive, and in some most perplexing and most baffling way partaking of the intelligible...
If then, Plato's unwritten doctrine (agrapha) placed chaos at the heart of Being, his conclusion would not be out of place among Greek speculations in general as to the nature of the arche: the difference is simply that he underpinned this conclusion with philosophical argument [Compare for example lines 116-128 of Hesiod's Theogony]. These we do not have for the earlier speculations, and therefore it is easy to conclude that they did not in fact exist; that the early speculations were not supported by cogent argument, and that the idea of chaos as the root or beginning of things never was any more than a concrete image of disorder. But Plato himself, putting the argument into mouth the of Timaeus at Tim 30a, uses such a concrete image, saying that God
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...
We have virtually the whole of the Platonic corpus: of the earlier philosophers we have fragments like the one above. We should be cautious in presuming the absence of clear reasoning behind images simply because we have no direct access to such reasoning: that we do read concrete conceptions into the concrete images of the Presocratics is partly due to the fact that this was often the practice among the ancients themselves, and partly because, building upon this fragmentary and distorted evidence, we can frame a satisfying scheme in which there is a beginning, middle and notional end to the history of ideas, starting with concrete images and working up to pure abstraction.

10 Pythagorean Syncretism

It is important to recognise that the syncretism of Pythagoras draws on mathematical and geometrical ideas, as well as religious ideas. We normally choose to keep these separate. We imagine that they are separate. However, it is clear from the discussion of Pythagorean mathematics, number and geometry, that they perceived the necessary impact of the various puzzles and paradoxes which investigation of mathematics and geometry had on their view of reality. These were not parlour games.

Pythagoras was putting together a new religion, rather than a secular philosophy. It is unlikely to have occurred to him that a secular philosophy was possible, or for him to imagine what that would mean. We think of Pythagoras as a philosopher, because of how we understand what came after Pythagoras and his school. It is possible for us to so distinguish religion and philosophy, because we have lost sight of some very important aspects of how the gods were understood in antiquity. Pythagoras was well aware of the importance of the mathematical and geometrical aspects of religion, which is why he included them with the materials that we more naturally understand as religious ideas.

We know that Pythagoras drew on many sources for what became known as Pythagoreanism. He is likely to have drawn on both Italian and Greek ideas, and, as already mentioned, he travelled in Egypt, talking with the priests of the various cults (though we are told that most of them were not much interested in answering his questions); and also in the Levant, Arabia, and Babylon. He borrowed from them too.

We are accustomed to thinking that the intellectual life of these disparate cultures must have been as distinct as their iconography, their mythologies, languages, and systems of writing. But it is not necessarily so. Much of what we think we understand of ancient religion is the product of a more or less modern view, which sees a continuity between the religion of the common era and antiquity. So, since ’rational belief’ concerning the divine, rather than actual knowledge of the divine was (and is) of great importance in the major religions of the common era, it is assumed that ancient religions drew their strength from the same source, and are qualitatively similar phenomena. Modern scholarship is able to hold this view because, since the Enlightenment, we see the phenomenon of religion as irrational. The behaviour which supported ancient cultic life (sacrifice, divination by entrails, the worship of statues, etc.) is clearly more irrational than medieval religious practice, so there is little about it which demands the application of modern critical thought.

If belief is what is important in ancient religion, then we have missed nothing. If however there is a technical substrate to ancient religious thought, a substructure which depends on a combination of logical analysis, number theory, mathematics and geometry, then we have missed almost everything. Such a substructure does exist, and Pythagoras was aware of it, which is why religious precepts, number theory, mathematics and geometry were all present in his work.

It is possible to make a list of things which are part of this technical substructure in the religions of the ancient world. These are:

Extremity, the Mean, Totality, Perfection, Completion, Invariance, Integral (whole) numbers, the Incorruptible, the Commensurate, Greatness, Rising, Setting, Beginning, Ending, Duration, Periodicity, Points of transformation. And so on.

This list illustrates some of the things have exemplars on both the earth, and in the sky. These characteristics would, within this conceptual model of Pythagoras, have been understood to provide points of contact, and a bridge to the divine.

Why would Pythagoras want to create a synthesis of key components of ancient religions? There are many possible reasons, but the most important may be the intention to restore the technical level of religious thought and practice, then experiencing a long slow decline, so that number, mathematics and geometry might serve again, to make sense of the transcendental understanding of reality.

11 Pythagoreanism and the Deep

Returning to the question of the Pythagorean disciple who drowned at sea, we are told that the drowning occurred because, either he had discovered irrational numbers, or because he had divulged the fact that they exist (the sources for the story are inconsistent, which is often a pointer to glossed interpretation). In the 1st and 2nd millennia B.C.E, 'Ocean' was an image which referenced the idea of Being. Like Being itself, ocean seems without limit, and to be without form, shape and colour. It was an idea which was common to the Greeks and to Near Eastern cultures.

In Mesopotamia, there was an important story which told how man was first educated in the sciences, agriculture, and land-measure, by an amphibious creature (the sage Oannes) who emerged from the sea in the daytime and conversed with men, before disappearing back into the deep in the evening. As a creature of the ocean, and a sage of Being itself, he had access to all knowledge.

The idea of this is reduplicated in the more famous Mesopotamian story of Gilgamesh, which opens with the protagonist diving down to the depths of the sea. This makes sense once it is understood that the poem was known to the Mesopotamians as: ‘He who saw the deep’, meaning that Gilgamesh had access to knowledge of divine things. Perhaps the real meaning of the story of the drowning of the Pythagorean disciple is that, in understanding the fact that there are such things as irrational numbers, and that both irrational and rational numbers can be commensurate with each other, he was in possession of an esoteric understanding of the divine, which lay at the heart of the unwritten doctrine of the Pythagoreans.


1. In William Sullivan’s The Secret of the Incas, it is argued that the Incas were attempting to turn back the precession of the equinoxes, in order to preserve a heavenly bridge that they imagined gave them access to the divine world. The subtitle of the book is: myth, astronomy and the war against time. They came to the view that they could turn back time because of a transcendentalist understanding of reality, and the place of the Incas within it. It is a completely counter-intuitive outlook.


Caesar, Julius, Commentarii de Bello Gallico, [The Gallic War], book VI.  Harvard, Loeb Classical Library, 1917.
Cory, Isaac P., Cory’s Ancient Fragments, [contains the account of Berossus concerning the encounter with the sage Oannes, and passages from Alexander Polyhistor and Diodorus Siculus], London, 1828.
Diodorus Siculus, Bibliotheca historica, Harvard, Loeb Classical Library, 1989.
Diogenes Laertius, Lives and Opinions of Eminent PhilosophersHarvard, Loeb Classical Library, 1925.
EuclidThe Elements: Books I–XIII. Translated by Sir Thomas Heath, Barnes & Noble, 2006.
George, A.R., The Babylonian Gilgamesh epic: introduction, critical edition and cuneiform texts. Vol.1. OUP, 2003.
Guthrie, K. G., The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Phanes Press, 1987.
Heath, Thomas L., A History of Greek Mathematics2 vols., OUP, 1921.
Hesiod, Theogony; Works and days. Harvard, Loeb Classical Library, 2006.
Homer, Iliad, Harvard, Loeb Classical Library Iliad. Books 1-24, 2nd ed. 1999.
Iamblichus, On the Mysteries and Life of Pythagoras. Works of Thomas Taylor, Vol. XVII. Prometheus Trust, 2004.
Plato, TimaeusRepublicTheaetetus, Phaedrus, etc. [twelve volumes]. Harvard, Loeb Classical Library, 1929.
Seyffert, Oskar, Dictionary of Classical Antiquities. Revised and Edited, with Additions by Nettleship and Sandys. Article: ‘Janus’. Swan Sonnenschein, Macmillan, 1906.
Smith, William, A Smaller Classical Dictionary. Article: ‘Janus’. John Murray, 1891.
Sullivan, William, The Secret of the Incas: myth, astronomy and the war against time. Three Rivers Press, 1996.
Xenophon, Memorabilia, Harvard, Loeb Classical Library, 2013.