Plato and the Transcendental Infinite

 

[This post is an extract from:'Evading the Infinite',   one of twenty-one essays in the book Man and the Divine, published in August 2018.  Information about Man and the Divine can be found here] Part of a critical commentary on Adrian Moore’s A History of the Infinite, broadcast in ten episodes by the BBC (on Radio 4) across two weeks in late September/early October 2016. The first episode was broadcast on the 19^th September. The book is available in ePub format from leading retailers of eBooks, such as Barnes & Noble, Blio, Kobo, Itunes, Inktera, Smashwords, etc.

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I have spent many years studying Greek philosophy, and as a result I found both Moore’s arguments and his narrative concerning the idea of the infinite to be oddly structured. There is a gaping hole at the start, since Plato is scarcely mentioned, and none of his arguments appear in the narrative (sometimes voiced in the dialogues by his master Socrates).  He does discuss the ideas of Pythagoras, but in such a way that it is hard to recognise him, and the many parallels which exist in Plato’s writing. As a result, this history of the infinite is not a complete history, tracing the discussion of the idea from the earliest period possible, but a history with a strong point of view, which begins at a point which is convenient for the arguments which follow (Moore’s book on the infinite has a much broader compass).

Part of my purpose here is to outline Plato’s engagement with the idea of the infinite, and to place it before Moore’s chosen point of departure. Understanding what Plato said concerning the unlimited and unbounded necessarily changes the interpretation of Aristotle’s views and arguments, with which Moore begins. Simply writing Plato out of the narrative not only creates something of a fictitious narrative, but also creates difficulties that otherwise would not exist.

Oddly for an account of man’s engagement with the infinite, the first of the series of programmes is titled ‘Horror of the Infinite’. Moore quotes the mathematician David Hilbert:

The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have; but also the infinite, more than other notion, is in need of clarification. 

Moore accepts Hilbert’s characterisation of the idea of the infinite. He begins by saying that

ever since people have been able to reflect, they’ve been captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all powerful god. People have been by turns attracted, fascinated, perplexed, and disturbed, by these various different forms of infinity. 

Indeed yes. But Moore’s account appears to start at ‘disturbed’, rather than ‘attracted’.

Is God the Infinite, and Reality itself? Moore does not much concern himself with this question in this sequence of programmes, at least not in the terms in which the Greeks understood the question. The following is an extract from The Sacred History of Being (2015):

 The Greeks did not contemplate the idea that the ‘existence’ of God, or the supremely perfect Being, was subject to proof. This would have been anathema to them, for the reason that they understood the very concept of the divine is inevitably beyond the capacity of the human mind to understand, or to frame. It is also beyond space and time. It is possible to say something about the divine, but that is all. Saying that the supreme perfect Being has a property ‘perfection’ is fine, but the meaning of this perfection is strictly limited in its human understandability. To attribute the property of secular ‘existence’ to this Being would have been regarded as absurd.

Yet it would be granted that one could argue that, without the property of existence, the perfection, or the completeness of God, was compromised. But for it to be in the world of change and corruption would also be understood as compromising the perfection of the supreme Being. At least in terms of public discussion. Thus the Greek view of reality and the Divine was that there was a paradox at the root of reality and the gods, and that it was not possible to define the nature of the Divine without exposing that definition to contradiction. The enlightened enquirer into the nature of the divine therefore is spared further pointless argument about the nature and the very existence of God. Both are conceivably true. But the true nature of the Divine, being a paradox, rises beyond our capacity to argue about that nature. It remains a matter of conjecture.

Our human experience tells us we live in a world in which change is possible, and inevitable. The definition of the Divine on the other hand, tells us, the divine reality beyond this world of appearances is a place of eternal invariance. It suggests that at the apex of reality, it is not possible for the divine to act in any way, or to participate in the world of change. Again there is a difficulty if we hold that the greatest and most perfect Being can do nothing without contravening its essential nature. A whole range of properties would clearly be missing from the divine nature.

It would seem that the Greek solution to this problem was to argue, as Plato and the neoplatonists did, that the world of reality was in fact invariable, as the theory requires. And it did not at any time change. But a copy was made. As a copy it was less than perfect, and this imperfection created the possibility of change, action, and corruption. This copy is eternally partnered by the original, which stands behind it, unchanging and unchanged by anything which happens in the copy of the original divine model. As a copy it is the same, but as a copy it is different.

This however, is a solution which Plato labelled as a likelihood. Which is code for: ‘this is not the answer to the problem’. 

One of the properties of the supremely perfect Being would be that he was one and not two. In the creation of a copy, the invariability of the divine has been breached, and the divine is now two, not one. Two, not one, would seem to be a fatal objection. Firstly the copy is a representation of the original, and not the original itself. Secondly, the copy is imperfect, and through the act of representation, it has become different. The original continues complete in its original nature, with its original properties and characteristics.  Plato hints at territory beyond this contradiction, but does not venture into it overtly.

This is the key mystery of ancient thought. To understand the full significance of this problem, and its implications for ancient models of reality, we need to look closely, as they would, at what a copy of Being actually means. There can be no copy, at least not in an objective sense. And if there is no objective copy, then the world which moves and which has existence, must be a subjective view of Being.

Apart from anything else, if the world is a wholly subjective experience, occurring (if we dare to use that word) within Being itself, then the change and motion which is apparent to us, and which contradistinguishes the world of existence from Being, which is itself and only itself, must be illusory. The illusion may be convincing, but ultimately it remains as an illusion, however persuasive it is to us, that there is an objective reality which is subject to change and movement.

This is the correct answer to the problem. Our experience in the world is of finite things, which are finite representations of things which are infinite. But this world is also infinite, and at the same time. It is therefore a matter of apprehension, understanding, and will, if man is to engage with infinity, and reality itself.

Hence Plato’s discussion of the ascent to The Good via the Forms, to that infinite place where all knowledge is to be had, and to descend again with divine knowledge, again entirely via the Forms, to the world of sensibles. What he is actually talking about is a formal process and discipline by which the finite human mind can engage with infinity.

Pythagoras was much closer to Plato in terms of doctrine than scholars normally allow. I can demonstrate this by quoting the Neoplatonist Porphyry who wrote about Pythagoras many centuries after his lifetime. 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.

That is exactly the doctrine of the ascent and descent via the Forms which is described by Plato. The definition of transcendent reality in Plato (articulated by Socrates) is that it is a place beyond shape, form, size, etc., and occupies no place on earth. It is however the place where knowledge has its reality (the ‘eternal and incorporeal things’ mentioned by Pythagoras). Connection with transcendent reality is possible by the likenesses to the transcendent which have existence on earth, such as things which are complete and whole, which therefore participate in the completeness and wholeness of the transcendent reality. Completeness and wholeness require (in the world of the mundane) delineation and limits, and so the limits and the extremes of things are also things which participate in transcendent reality.

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

What is transmitted to us via the writings of the Platonists, is something of the basis of both their understanding of what the Divine actually is (the Infinite, the Limitless, and Reality itself), and how man may have commerce with the Divine, through sacred rather than profane practices, in a world which has a double nature, and in which man has a choice.

Looked at in this way, rather than being a history of infinity, Moore’s argument is about the idea of the infinite from the point of view of finitude. This is the way Aristotle chose to deal with the infinite, by dividing the concept into the actual infinite, and a potential infinite, and dealing with the latter. Moore has said elsewhere that the way he treats the infinite is generally in terms of an Aristotelian Finitism.

We might pause here and consider what the implications might be of the identification of the Infinite and the Divine, which seems to be implicit in the views of a number of ancient philosophers. If they did so identify these concepts, then much of Greek religious thought and practice was based on a philosophical understanding of the infinite. In which case, Moore’s history is a history of what happens when the actual importance of the infinite in the life of man is forgotten, misunderstood, and eventually no longer noticed for what it is. Much of Moore’s argument is shaped by his Aristotelian Finitism.

In the first programme, Moore argues that the Pythagoreans thought finite things were good, and that infinite things were bad (this information comes to us via Aristotle), and that they thought they had evidence that the finite had some kind of control over what was infinite. And that the usefulness of rational numbers showed that this was the case. This is clearly a garbling of Pythagorean thought from a distant age, if Pythagoras thought that ascent to eternal and incorporeal things was important, as I’ve suggested. There is also discussion of musical ratios, and the Pythagorean discovery that different string lengths with simple ratios are more consonant to the ears than those which involve large values. Their ‘discovery’ of irrational numbers, which can be found using the theorem of Pythagoras, is said to have filled the Pythagoreans with horror, and the story of one of their number being drowned at sea after revealing their existence, is referenced. Rather than revealing their horror of irrational numbers, this is a story which points to their interest in whole numbers. The idea that they once had no idea about the existence of irrational numbers is absurd.  

The programme moves on to consider whether other ancient Greeks had the same resistance to the infinite. The views of Anaxagoras on infinite divisibility are discussed. Anaxagoras was relatively comfortable about these ideas. Zeno’s paradoxes in connection with infinite divisibility are also discussed, including his paradox of travelling by an infinite number of half distances, which seems to imply that movement is impossible. The similar paradox of Achilles and the Tortoise is also referenced. Observation and reflection thus seem to contradict each other. Zeno distrusted observation to the point that he believed that movement was impossible. Parmenides was Zeno’s teacher, and taught the universe to be a simple unity. So, only the appearance of motion is possible. Otherwise the universe would have to have infinite complexity. Moore winds up the episode by suggesting that because of these paradoxes, and the existence of irrational numbers, that there is some truth in the suggestion that the Greeks had a horror of the infinite.  

Looking at the content of this episode in the light of the added preamble about ideas of the infinite held by Plato and Pythagoras, we can see that something old and valuable is contained in the writings of some earlier philosophers, transformed into more or less secularised accounts of the arguments the Greeks used to illustrate the paradoxical nature of the infinite aspects of the world, as they manifest in the world of the finite. 

We  get many clues about the Greek understanding of the infinite and the unlimited from a number of Plato’s dialogues, including The Timaeus, The Sophist, The Republic, The Theaetetus, The Laws, and The Parmenides. In skipping Plato, the first reference to Parmenides and his notion of the universe as simply one and one alone, is as an introduction in the first episode to his pupil Zeno of Elea, and his response to paradox. There is no discussion of Plato’s demolition of Parmenides arguments, no discussion of the Platonic forms, no discussion of the relationship of the forms to the form of the Good, which is another way of talking about what is infinite, and no discussion of what amounts to a different logical modality in the pages of Plato (where he discusses things passing into one another by means of their similitude), which is a way of understanding the relationship of finite things to the infinite.  

Essentially Aristotle’s rapprochement, which Moore characterises as an attempt to make the concept of the infinite more palatable to the Greeks, involved dividing the idea of the infinite into two. As already mentioned, one of these was the potential infinite, and the second was the actual infinite. As outlined in the first episode, Zeno’s paradoxes depended on the idea of an infinite divisibility, which seemed to make the idea of any kind of movement impossible, since that would require a universe of infinite complexity. Zeno therefore regarded all forms of movement as illusion. Since in order to travel a certain distance, you would have to travel half the distance to your destination, and then half of the distance remaining, and then half of that, and half of what still remained, and so on. Which would result in an infinite number of steps. Which would be impossible. 

Aristotle’s response was that though the various stages of the journey could be understood in such a way, the stages were not marked, and did not have to be considered in making a journey. The idea of limit is however a crucial point. What Aristotle was saying is that there are two ways of looking at the idea of what a limit is.  Essentially there is limitation which is defined by what a thing is, and there is limitation which is not. In the first case the limit of a thing cannot be transcended without the nature of that thing turning into something else.

The essence of this argument is that there are forms of limit which can be ignored. One of which is the actual infinite: instead we should deal with the potential infinite. The actual infinite, by its nature, is always there. But we cannot deal with it. The potential infinite we can work with, since it is not always there, and spread infinitely through reality. So we can count numbers without ever arriving at infinity, or ever being in danger of arriving there. Moore mentioned that this conception of infinity more or less became an orthodoxy after Aristotle, though not everyone accepted that his argument against actual infinity was solid. Which is something of an understatement. Aristotle’s distinction between the potential infinite and the actual infinite is between what is, in practical terms, something we can treat as finite, and what is actually infinite. 

It might seem surprising that Moore’s first port of call in part three is the philosopher Plotinus, who was writing in the third century C.E., some five centuries after Aristotle. The reason that he has jumped to Plotinus is because he argues that Plotinus claimed not only that the divine was infinite, but that the divine was the infinite. Thus conflating the ideas of divinity and infinity in a way that – he says – no one had done before. Or, to be more precise, he declared the identity of the divine and the infinite in a way no-one had done before.  

Well no. As I’ve argued at the beginning of this essay, Plato’s principal interest was in a transcendent reality, which it would be hard to distinguish from the infinite, except in hair-splitting terms. He refers to the necessity of ‘looking to the one thing’, and that the ‘one thing’ is something which is found nowhere on earth. In one of his dialogues, he has Socrates describe that transcendent realm as something which possesses ‘no form, shape or colour.’ It is clearly without definition and limitation, with no finite properties and attributes, which means it is unlimited, and infinite. It is also the ultimate source of all knowledge. So it also seems to possess the properties and attributes which are associated with the divine. Plotinus’ supposed innovation is therefore no such thing. Anaximander’s understanding of the ‘apeiron’ (the unlimited) as the cause of all things is just such an equation of the divine with the infinite, which means the idea was around in the sixth century B.C.E. 

12th Annual Smashwords 2020 Summer/Winter Sale!

July 1, 2020 - July 31, 2020

This promotion has now closed. Thanks for your interest and participation. 

Four of my books sold through Smashwords will be  discounted during the month of July, so this is a chance to pick up a bargain! The catalog for the sale goes live at one minute past midnight on July 1 Pacific time, and expires 11:59pm on July 31. Clicking on the image of each book's cover below will take you through to the Smashwords page for it. Clicking on the title will taken you to a blog page giving further details.

During the sale period the price at Smashwords is the discounted price. Prices at Itunes, Barnes & Noble, Blio, Walmart, Inktera, etc. are not discounted. My new book, 'Echoes of Eternity' will be available for sale on June the 30th 2020 at the full list price, during and after the sale.

The bargains:

The Sacred History of Being (2015), is available during the sale period at 50% off the full Smashwords price.

Formerly argued by classical scholars to have been first discussed by the ancient Greeks in the middle of the first millennium B.C.E., the articulate concept of Being can now be traced as far back as the middle of the second millennium, and the state of Assyria. 

The Greeks themselves had several stories about the origins of philosophy, a discipline which essentially deals with abstractions, including that it originated elsewhere, but that is not the received narrative. The consequence of this, is that all historians of ideas, when constructing their accounts of the intellectual development of man before the arrival of Parmenides and Plato, have had to negotiate the Greek invention of philosophy, and the corollary, that articulate discussion of the abstract concept 'Being' didn’t happen before this.

This can now be shown to be a faulty understanding, resulting in many absurdities. The Old Testament has examples where God declares his identity with Being itself (‘I am that I am’, better translated into English as ‘I am that which is,’ and ‘I am the first, and I am the last; and beside me there is no God', for example), but these are not regarded by scholars as evidence of a sophisticated discourse around the idea of Being. Instead these statements indicate inchoate ‘notions’ about the nature of god, rather than anything more profound. The statement in Malachi, however, that 'I do not change', is an explicitly philosophical understanding of the nature of God.

Published by the Anshar Press.  

J.G. Frazer and the Platonic Theory of Being (2016) Is available during the sale period at a 25% discount from Smashwords.

When he was only twenty-four years old, James Frazer won a Cambridge fellowship with an essay on the development of Plato's theory of the Forms or Ideas (eidos). In this essay he argued that there was no overarching theory of Being in Plato's mind before he embarked on the writing of his dialogues, and that consequently differences in approach and discussion apparent in his work are the result of the development of his thought. He also argued that the very idea of Being is a barren notion, in that nothing can be predicated of Being. As a result Plato made a mistake, effectively conflating an epistemology with an ontology. 

Though the essay was written in 1879, it was not published until 1930, after much of his later work was done. Frazer became famous for his monumental study The Golden Bough, which explored a vast range of ancient and primitive myth and ritual. Here too he found intellectual processes founded in error. What was Frazer's intention in re-interpreting Plato against what Plato himself said, and his wholesale restructuring of ancient thought by reducing much of it to a pattern of error?

In sixteen sections, with prefaratory material and a conclusion. Over 23 thousand words, a preface, select bibliography, and extensive notes. Published Spring 2016 by the Anshar Press.  

A couple of related blog posts explore J.G. Frazer's discussion of Plato, and the implications for the writing of The Golden Bough. The two articles are synthesised together in a third article: Frazer and the Association of Ideas.

Understanding Ancient Thought (2017), is available during the sale period at 50% off the full Smashwords price.

Understanding Ancient Thought is the third in a series of books which examines how we assess evidence from antiquity, and frame models to make sense of that evidence.  

The book consists of eighteen essays, which cover a number of subject areas which are in thrall to what Foucault described as an ‘episteme’. In other words, the way the subject areas are understood within the academy is in terms of what our cultural models, language and assumptions will allow us to understand. The actual evidence may suggest an alternative view, but it is not possible to see it, or to think it. At least until the paradigmatic frame shifts to another ‘episteme’.  

The main thrust of the book is that two hundred years of modern scholarship concerning the past has, for the most part, assembled a fictive and tendentious version of the ancient world. 51 thousand words. Published by the Anshar Press, 

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Man and the Divine: New light on Man's Ancient Engagement with God and the History of Thought, is also discounted by 50% during the Smashwords Summer/Winter sale. Published by the Anshar Press. ISBN 9780463665473. It is now available at Smashwords https://www.smashwords.com/books/view/872542. Published in August 2018.

Many of the essays deal with the question of esoteric knowledge in antiquity, often from slightly different angles. The book contains the following essays:

The Enlightenment of David Hume;  Richard Dawkins and Deism; Mathematics and Geometry;  Evading the Infinite;  The Esoteric Conception of Divinity in the Ancient World. Unwritten Doctrine, Ancient Silence; What is Sacred, and what is Profane?;  Intentionality, Conjecture, and What is Holy; Excellence and the Knowledge of Divine Things; Cultural Continuity in the Ancient World, and Bernal’s Black Athena. 

Transcendental Reality in the Ancient World (Writing to Marie aux Bois)

Date: Thu, 19 Mar 2020 16:24:58 
To: Marie aux Bois
From Thomas Yaeger

Marie,

Re: the paper on the mathematics of the megalithic yard - there's been a lot of movement since I wrote it in the middle of February, and I will write several other articles on the back of it. One of the objections to the argument will be that arriving at Euler's number would have been impossibly complicated for them to do (quite apart from the general case I'm making as to the sense it made for them to want do this). But it isn't true that this is complicated to do, particularly if you work it out geometrically, and use the right kind of exponentiating series (i.e., ones which arrive at the limit of the series in the shortest number of steps). I've already drafted this one.

The argument of the article is fine I think, but at various points it trades on what I know, and what I've written about elsewhere. So I'm going to write another article which brings the relevant information together.

I can make a list of the most significant things in the article:

1. It brings together concepts which were present in Greek civilization and philosophy, as well as in Mesopotamia. So the same ideas are going on in their heads, even if on the face of things the cultures are quite different. For the neolithic case, they are writing in terms of number and geometry.

2 If this argument is sound, it pushes the development of sophisticated mathematical and geometric thought back to the middle to late 4th millennium (3500 -3200 BCE).

3. The argument shows that, on the basis of the mathematics and geometry in the stone circles, that the builders had the same general concept of the existence of a transcendent level of reality which we know for certain the Greeks had. Indeed, historians of ideas pick the Greeks as the originators of the idea of a transcendent level of reality, and behave as if all the other religions in the world did not, before this time.

4 This transcendent level of reality was in fact infinity itself. They came to this conclusion in the Neolithic on the same basis as the Greeks did much later. Which is that the version of reality we inhabit isn't reality at all, but a poor copy of it (I echo Plato's words here). This was established on purely logical grounds, and on the basis of puzzling things about the physical universe (why is there something rather than nothing? If reality itself is necessarily one, otherwise it breaches its nature, how is it possible that there is multiplicity?)

5. And how is it that there are irrational numbers? Again, historians of ideas argue that before the Greeks, and the Pythagoreans in particular, people had no knowledge or understanding of irrational numbers, and when the Pythagoreans discovered their existence, they tried to keep this secret. In fact *the entire basis of Pythagorean thought, both in Greece, and the protoPythagorean megalithic culture was based on the existence and significance of irrational numbers.* I've talked around this issue both in SHB, and in "Understanding Ancient Thought", firstly by discussion of how ancient people conceived that commerce between the Gods and Man was possible, and by discussion of the logical modality that Plato discusses in the "Timaeus", which is based on irrationals.

6. The esoteric core of ancient religion was often kept secret. We know this for sure about the Pythagoreans, the Spartans, the Athenians, and also the ancient Romans. Plus the Assyrians and Babylonians. Modern historians assume that a transcendentalism isn't involved, but rather a doctrine which serves societal and political functions. But what if the esoteric core is too difficult and too dangerous to  convey outside a tight circle of those who understand?

7. Plato discusses how the disagreements about the nature of reality in antiquity might be resolved, in more than one place in "The Sophist". The position  which must be accepted (he says) is that *Reality is both One and Many at the same time*. In other words, the esoteric core of religion, based on the consideration of natural puzzles and the reality of irrational numbers, is that transcendent reality is necessarily paradoxical in nature.

8. Hence the common representation of the transcendent reality as *the inversion of ours* (look up 'Seahenge'). It is the same as this one, but it has different properties. In that transcendent reality, all things are commensurate.

9. Finally, this argument offers the possibility of proving that  transcendental thought did exist at the close of the 4th millennium around a number of cultures. If transcendental thought about the nature of reality was expressed mathematically and geometrically, and  necessarily involved irrational numbers, we should be able to find such references to transcendentalism in many of the architectural and engineering achievements of the ancient world. These have been noticed already in a number of structures, long before I started pursuing this question, but (for example) the golden section, clearly present in a number of Egyptian structures, is written off as a coincidence, or as consequence of the way the structure was laid out in practical terms, and that the builders had no knowledge of  its presence, and did not think the proportion had any significance in itself.

We know the measures the Egyptians used. Scope I think for a nifty little computer programme to number crunch all of these, to look for the presence of Euler's number, and other irrationals.

Best, Thomas

The paper 'The Mathematical Origins of the Meglalithic Yard' is at: https://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html

The Roots of Philosophy: Six Books by Thomas Yaeger

The Sacred History of Being (2015)

The discipline of philosophy was not invented by the Greeks, but was in existence elsewhere, and as far back as the middle of the second millennium BCE. It has its origin in ancient divine cult. The detail of its presence can be traced in the civilizations around the ancient Near East, and particularly in Assyria and Babylonia. The Sacred History of Being collects the key evidence together, and examines the idea of the divine as a philosophical concept in Greece, Israel, and ancient Mesopotamia. Published as an eBook by the Anshar Press, November 2, 2015. 113k words. Available from Barnes & Noble, Itunes, Kobo, Blio, Inktera, Smashwords, etc. More information available at: https://shrineinthesea.blogspot.co.uk/p/the-sacred-history-of-being-as-its.html

J.G. Frazer and the Platonic Theory of Being (2016)

When he was only twenty-four years old, James Frazer won a Cambridge fellowship with an essay on the development of Plato's theory of the Forms or Ideas (eidos). In this essay he argued that there was no overarching theory of Being in Plato's mind before he embarked on the writing of his dialogues, and that consequently differences in approach and discussion apparent in his work are the result of the development of his thought. He also argued that the very idea of Being is a barren notion, in that nothing can be predicated of Being. As a result Plato made a mistake, effectively conflating an epistemology with an ontology. Though the essay was written in 1879, it was not published until 1930, after much of his later work was done. Frazer became famous for his monumental study The Golden Bough, which explored a vast range of ancient and primitive myth and ritual. Here too he found intellectual processes founded in error. What was Frazer's intention in re-interpreting Plato against what Plato himself said, and his wholesale restructuring of ancient thought by reducing much of it to a pattern of error? Over 23 thousand words, a preface, select bibliography, and extensive notes. Published by the Anshar Press, April 4, 2016. http://shrineinthesea.blogspot.co.uk/p/j.html

Understanding Ancient Thought (2017)

'Understanding Ancient Thought' is the third in a series of books which examines how we assess evidence from antiquity, and frame models to make sense of that evidence. The book consists of eighteen essays, which cover a number of subject areas which are in thrall to what Foucault described as an ‘episteme’. In other words, the way the subject areas are understood within the academy is in terms of what our cultural models, language and assumptions will allow us to understand. The actual evidence may suggest an alternative view, but it is not possible to see it, or to think it. At least until the paradigmatic frame shifts to another ‘episteme’.The main thrust of the book is that two hundred years of modern scholarship concerning the past has, for the most part, assembled a fictive and tendentious version of the ancient world. 51 thousand words. Published by the Anshar Press, August 20, 2017. Available via Smashwords, Itunes, Barnes and Noble, Blio, Kobo, etc. http://shrineinthesea.blogspot.com/p/first-look-at-my-new-book-which-should.html

Man and the Divine (2018)

A collection of essays on philosophy, ancient cultic thought, and the problems of addressing and interpreting ancient evidence. The book also examines the nature of esoteric thought in antiquity, and the transcendentalist nature of ancient religion.  21 chapters. 

The Enlightenment of David Hume. Though Hume's empirical approach was not wholly successful, some of his intuitions expanded our collective understanding of how we perceive reality – for example, his insight that we have no actual knowledge of the process of causation at all, and only a customary expectation of causal process, was a powerful one. We can describe causal processes, we can differentiate the nature of different causal processes, and we can formulate rules in connection with them, but we cannot know how causality itself operates, or even be sure that a perceived causal relation, often observed before, will obey the implicit rule the next time it is under scrutiny by us. However, it is no longer clear that Hume was exploring his mental processes and understanding entirely within the framework of western secular thought. This chapter is based on intriguing research by Alison Gopnik.

The Death of Socrates. It is a puzzle that, in the midst of a thoroughly polytheistic culture in Athens, with its plethora of gods, its many cults and priesthoods in the service of those gods, that both Socrates and Plato could speak of ‘god’ in the singular. Our difficulty here is the result of a modern understanding of the significance of polytheism, which sees the phenomenon as the inevitable precursor to monotheistic belief, which excludes other gods from consideration, or credibility. For modern scholars, polytheistic belief in ancient Greece was something which developed, higgeldy-piggeldy, out of a plethora of local and tribal deities, much embellished with myths about their lives and actions, which served important social functions, but which had no universal meaning, and were not rooted in a model of reality which embraced consideration of what the nature of reality itself might be.

The Irrationality of Atheism, Atheists do not deny the existence of the world, its laws and properties: they just argue that the concept of God is not required to accept the world, and to have an understanding of it. But this leaves them at a loss to explain how the world came to be, and why it should have come into existence.

Richard Dawkins and Deism. Modern atheism is actually dependent for its nature on the ontological argument, and the terms in which it is framed. Meaning that eight hundred years of argument about the nature and existence of God underpins the point of view of those who regard themselves as atheists. Dawkins makes a distinction in ‘The God Delusion’ between theism and deism. Theism is a pattern of belief which enshrines the idea that the Divine is responsive to man, and his rituals of worship and prayer. It is a pattern of belief dependent on the idea that God can act in the world. By contrast, deism contemplates the idea that a creator God has existence, and necessarily created the world, but that he is not active in the physical world beyond that. This essay argues that Dawkins is in fact a modern deist rather than an atheist.

Contra Plantinga. Alvin Plantinga was kind enough to accept a copy of The Sacred History of Being. I sent two supplementary emails which outlined the implications of its criticism of the traditional ontological argument, whose function is to support a rational basis for belief, which are reproduced here.

Distinguishing Belief and Faith. Modern scholarship has a track record of making easy assumptions about the continuity of religious ideas and patterns of practice, and the accompanying social compacts. At the time the Assyrian palaces, temples and cities were being dug from the sand and soil in northern Mesopotamia, it was assumed that the relationship between the royal and temple establishments could be understood in terms of a modern division between church and state. This notion turned out to hold very little water on close analysis. It is also the case that belief is not a conspicuous feature of ancient religions.

Logic, Sophistry, and the Esoteric in Ancient Education. Both Plato and Aristotle's writings contain arguments which either don't make clear logical sense within themselves, or in the context of the rest of the work. Sometimes the clues to the meaning of arguments are present elsewhere in the canons of both Plato and Aristotle, and some of them clearly involve an esoteric level of understanding. The whole body of their outputs need to be taken on board in order to grasp the meaning of individual works. This is usually not done with the works of Aristotle: his Historia Animalium is read by biologists and specialists in animal taxonomies, but usually they read little else of his work.

Beyond Mathematics and Geometry. The process of separating ourselves from an interpretation of the world in terms of simple apprehension is driven initially by the practical necessities of our existence. But this process does not need to stop there. Intelligence consists in being able to adjust the categories of our understanding so that we do not mistake one thing for another. It is a mental development which might have no end. This is essentially how Kant understood human intellectual development, which he framed (in his Prolegomena) in terms of a general theory of a priori concepts, not based on empirical sense data, or even a mathematical or geometric understanding of anything in the world.

Evading the Infinite: A Review of A.W. Moore’s ‘History of the Infinite’. This chapter is a critical response to Adrian W. Moore's radio series 'The History of the Infinite', broadcast in the autumn of 2016, and his book 'The Infinite', published in the early 90s. His treatment of the subject hardly references Plato at all. Adding Plato to the discussion changes the way in which the argument should be framed. The actual infinite is the principal source of ancient ideas concerning the divine, not Aristotle's potential infinite, so Moore's argument concerning our knowledge of God is forced to take refuge in the quasi-mystical Calvinistic idea of a 'sensus divinitatis'. His argument also makes it impossible to understand Kant's treatment of religion.

The Esoteric Conception of Divinity in the Ancient World. 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 reframe my understanding of human intellectual history in the process.

Unwritten Doctrine, Ancient Silence. It is often assumed by students of antiquity that there is no special importance to be attached to remarks that certain items of information are to be kept secret and not imparted to the unworthy, and to the ordinary mortal. This assumption is based on the presumption that there was, and is not, anything about which it is impossible to speak of, before those not used to dealing with information about religion and the divine. This is a curiosity of modern times, in that the ignorance of theology among the moderns makes it impossible for them to credit the importance of theology in antiquity - both to those who understood its subtleties and and those who didn’t.

Ancient Conjectures, and Fictive Intellectual History. Plato argues that we should always look to the ‘one true thing’. J.G. Frazer also argued that questions concerning Being (‘the one true thing’) were entirely barren, since nothing could be predicated of Being. 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. In antiquity, 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 philosophy was invented by the Greeks in the Protagoras, saying that it was of a great age – perhaps contemporary with the arrival of peoples from Egypt, who settled in the Peloponnese, and also in Crete.

What is Sacred, and what is Profane? Each of the divine names of Marduk, the head of the Mesopotamian pantheon, has a description, and each of the lesser gods can be understood as abstractions of aspects of the rational creation. They represent excellences in the world. Marduk represents the sum total of these. This is the clue to understanding much of the ancient understanding of what the divine is. Each described excellence resembles reality itself in terms of its properties. The excellence may serve social functions, as does a skill or specialism, but it should be performed for its own sake. The performance of these excellences recalls the perfection and completeness of the plenum, and reinforces the presence of the divine in the world. 

Intentionality, Conjecture, and What is Holy. Intentionality explains why the ancients created a multiplicity of gods. If the divine itself cannot by definition be completely defined and understood, at least certain properties and attributes can be understood. These can therefore be defined and named as ways of accessing the divine. This does not at all conflict with the idea that the reality of the divine is in question. Instead this view argues that there is in fact a subjective component in the reality of the divine, at least insofar as it is possible for us to have commerce with it.

Excellence and the Knowledge of Divine Things. Plutarch opens his life of Alexander with a cheerful complaint about the sheer extent of the materials available to him to write on Alexander. So the details which are in his essay are there because he regarded them as important in showing Alexander’s character, his disposition, and the content of his mind. On the basis of his sources he says that it is thought that Alexander was taught by Aristotle not only his doctrines of Morals and Politics, but also those more abstruse mysteries which are only communicated orally and are kept concealed from the vulgar: for after he had invaded Asia, hearing that Aristotle had published some treatises on these subjects, he wrote him a letter in which he defended the practice of keeping these speculations secret.

Egypt in the Shadows. Since the European enlightenment, the influence of Egypt on the development of abstract and philosophical thought has been deprecated. Yet, as Martin Bernal showed in the third volume of Black Athena, many Greek words have plausible etymologies from Egyptian. It is also the case that several of the concepts used by Aristotle in his philosophical writing were known to Egyptians nine hundred years before his time, such as the idea of completion (it is connected with the idea of birth in Akhenaten’s Hymn to the Aten, which dates to the fourteenth century BCE). There is also abundant evidence for the existence of philosophical thought among the Hebrews in the books of the Old Testament. Yahweh is described as ‘the first and last, and beside me there is no God’. His name (minus the vowels) is a variant of the verb ‘to be’, which suggests that his isolation is due to the fact that he was understood to be Being itself.

Polytheism, Monotheism, and the Cult of the Aten. The Aten is first mentioned (to our knowledge) in the Story of Sinuhe, which dates at least as far back as the twelfth dynasty, where the dead king is described as uniting with with the sun-disk in the heavens. Akhenaten’s iconography never shows the god in anthropomorphic form – instead the Aten is always shown as the sun disk with rays of light extending from it, with hands at the end of each ray. The Sun god was considered to be neither male nor female, but both simultaneously, an idea which was reflected in the depiction of Akhenaten in sculpture and reliefs. His full title however was ‘The Ra-Horus who rejoices in the horizon, in his/her Name of the Light which is seen in the sun disk’. We find this full rendering of the Aten’s name on the stelae placed around Akhetaten, which was Akhenaten’s newly founded capital. Sometimes the full name was shortened to Ra-Horus-Aten, or just ‘Aten’. Since two of the names of Akhenaten’s god refer to the sun (Ra being an older name for the sun god), it seems that some kind of intellectual synthesis of older ideas had taken place.

Cultural Continuity in the Ancient World, and Bernal’s Black Athena. Martin Bernal’s intention was to take ancient Greece out of its exalted orbit above all other civilizations, and root it in what he assumed to have been a cultural continuum around the Mediterranean sea from at least the mid-2nd millennium B.C.E up until the classical period of Greece in the 5th and 4th centuries B.C.E. Bernal pointed to the evidence within the texts of the 1st millennium which suggested cultural continuities with ancient Egypt – all dismissed by the classicists in favour of evidence in texts which could be interpreted as suggesting the opposite. Bernal’s attempts to establish cultural continuity with the civilizations around the Mediterranean were hampered by the fact that myths are not simply encodings of historical and political change, and that the exchange of words between linguistic groups is, by itself, weak evidence for cultural continuity. He was correct to guess at the existence of the cultural continuity, I think, but ill-equipped to establish such a thing. To do this requires moving things around – particularly re-anchoring the relationship of Greek philosophy to patterns of religious belief and cult practice; and the establishing of the relationship between Greek patterns of religious belief and cult practice to parallel ideas and behaviour in the Near East and in Egypt.

The Tangled Thread: Universals in History. The liturgies and the description of ancient rituals have been published and translated, and their signifcance and meaning have been discussed by scholars. But they make difficult reading for the reason that they involve a different set of preconceptions from those understood by Mesopotamian scholars. It is hard to break through to an understanding of what was understood to be going on. The Mesopotamians employed ideas which they considered to be universally valid, such as all wisdom being present in the Abzu, and that the acquisition of knowledge depended on some kind of ritual engagement with Ea and the Abzu. And that the good order of the world depended on man's relation to the world of the divine. Since the European Enlightenment however, we have adopted another set of universal notions, which do not depend at all on the reality of the divine and the gods. In fact it pushes such notions into the shadowlands of unreason. So there is little inclination among scholars who specialise in Mesopotamia to spend time trying to makes sense of things which they regard as intrinsically unreasonable.

The Age of the Lord Buddha. Scholars acquiesce in the convention that an articulate and technical understanding of the idea of Being was first broached by the Greeks in the middle of the 1st Millennium BCE. It follows therefore that all references to the divine in the ancient near east before that date are not articulate and technical references, but notional and inchoate. The consequence must be that we can learn nothing useful about ancient intellectual processes and concerns from these notions, since they are beliefs entirely unsupported by rational argument. This would come as a surprise to many ancient cultures, if they were still around. The date of the Buddha's floruit for western scholars is much closer to our own time than it is for scholars in the east. We place him around the 5th century BCE, since there is clearly an interest in universals in the texts. The Puranas provide a chronology of the Magadha rulers from the supposed time of the Mahabharata war, and Buddha is supposed to have become enlightened during the reign of Bimbisara, the 5th Shishunaga ruler, who, according to this chronology, ruled between 1852-1814 BCE. His birth date may have been 1887 BCE. Chinese scholarship has long maintained that Buddhism came to China from India around 1200-1100BCE.

Stone Circles, Phenomenology, and the Neolithic Mind. The evidence from the megaliths makes the importance of the sky very clear: in Britain and around the megalithic world, the sky was seen as a representation of divinity, of Being. As an image of the divine, it was an image of totality itself. The megalithic observatory, or temple, according to this hypothesis, was a device to embody aspects of divinity, of Being, actually in its structure, in the same way in which the gods in Mesopotamia might be invited to occupy their representations on earth.

Available from my distributor Smashwords, and various retailers, including Itunes, Barnes and Noble, Blio, Inktera, etc, and a number of library distributors.

56,320 words. Published by The Anshar Press, Aug. 12, 2018. https://shrineinthesea.blogspot.com/p/man-and-divine-2018.html

Echoes of Eternity (2020)

My new book, will be available in May 2020 (rescheduled). The final word count will be around 56 thousand words. Two of the chapters - 'The Greek Ontological Model in the 1st Millennium B.C.E', and 'Patterns of thought in Late Neolithic and Early Bronze Age Britain', are quite large pieces of work (6k and 10k words respectively).

Much of the cultural production of the ancient world, east and west, was based on the idea of reflecting aspects of the divine in human life and thought. Many social structures and institutions were based on this approach. The model for these things was was astronomy and the heavens, and the heavens were conceived of as a moving image of eternity, and eternity was understood to be coterminous with the Divine. Since it moved, it contained life and thought, and repaid the attention of man. We still live, work and think inside what is a scarcely changed neolithic temple, which is the sky.

The chapter list:

Introduction: The Interpretation of Ancient History

Part One

Camera Obscura: Marx, Aristotle & Ptolemy

Synoikismos and the Origins of the Polis

Kingship in Ancient Assyria

Proskynesis, and the Deification of Alexander

Part Two

The Greek Ontological Model in the 1st Millennium B.C.E.

Post-Enlightenment Plato, and That Which Cannot Move

Greece and the cultural Impact of the Assyrian Empire

The Threshold in Ancient Assyria

Symmetry and Asymmetry in the Iconography of the Ancient Near East

Part Three

The Keys of the Kingdom: Binding and Loosing in Heaven and Earth

Being and Eternity in the Neolithic

Patterns of thought in Late Neolithic and Early Bronze Age Britain
The Mathematical Origins of the Megalithic Yard

What We Have Lost, and How the Ancient Concept of the Cosmos Died

Marx and Historicism

Visit my profile page at Smashwords and scroll down for the books.

Updated May 28,  September 6, October 1, December 11, 2019, and May 2, 2020.

[The Death of Pan replaces 'The Origins of Transcendentalism in Ancient Religion', (forthcoming).]

This is a short book about a very large subject – the transcendentalism which is present in ancient religions, located to the west of India. 

Normally it is assumed that there is very little in the way of transcendentalist thought associated with these ancient religions, and that the evidence we are looking at is mainly built out of concrete imagery, fanciful myth, poetry, irrational associations, all of which are in the service of religion and the state. In other words, religion serves a series of social and ideological functions, and it is to those functions that we should look for the explanation of the cultural remains, rather than the minds of the ancients themselves.

Is this actually so? Or are we the victims of an enlightenment agenda which sought to remake the history of religion and religious thought in terms of a profound irrationality?

That is one of the arguments of this book – that we have been sold short by enlightenment presumptions and certainties, and that what we think we know and understand about ancient religion is so far from its real basis that, for the most part, it is nearly impossible for modern scholars to make intelligible sense of it.

This book is short, not because the questions it addresses are simple, and have easy answers. It is short because I have written five other books before this one, and, to a significant extent, it references argument and discussion which can be found in those books. It was not possible to write a short and credible introduction to an understanding of the transcendentalism which can be found in ancient religions, without first covering an enormous amount of ground.

Scholars must decide for themselves if the argument of this book is soundly based.  The problem for scholars  is that they live and work within what Michel Foucault called an ‘episteme’. This is a model of reality dependent on many presumptions. Not only does the episteme shape discussion, it controls what can actually be discussed, or even be seen by those within it.

Preface

An Appetite for Knowledge
The Death of Pan
On Ancient Religion
Parallels and Discontinuity between Contemporary and Ancient Religions
The definition of Transcendentalism in Religion

The Origin of the Transcendentalist Perspective 

The Nature of Reality 

Contradiction and Paradox 

Transcendence and Immanence 

Detecting the Presence of Transcendentalist Thought 

The Future of our Understanding of the Past

Appendices:

The Obsolescence of Oracles (Plutarch).
Who Will Appear Before the City?
Wearable Fictions, Phenomenology, and the Grammar of Human Thought 

Notes

*Update, May 22, 2020:

Sometimes a book changes during the process of research and writing. The writer of anything is in a dialogue with both his materials and his thoughts. That is what has happened with this book. It will contain the discussions outlined above, but it will be significantly different, since it will also discuss a famous essay from late antiquity (The Obsolescence of Oracles), which illuminates the underlying argument of the book, and shows that there was a consciousness present in the second century C.E., that ways of thinking about the Divine were changing, and that the older modes of thought were about to be largely lost.

The author of this essay understood that the patterns of thought of the ancient world would no longer be accessible to those who came afterwards. Rational discussion of these patterns of thought would disappear, and would be replaced by an entirely ersatz mode of discussion, and shape almost everything which could be thought or said afterwards. With almost none of it making any kind of sense.

The title of the book will be different, reflecting the changes to the book's contents. There will be a new page for this shortly. TY

Update: Jun 6, 2020

The book title is now 'The Death of Pan'. We commonly imagine that what we regard as modern rational thought emerged from an intellectual world that was not rational at all. But ancient civilizations regarded themselves as rational. What actually happened is that one form of rational thought experienced a long and slow collapse, and began to be replaced by another (also a slow process). We have imposed this notion of a progressive development of rational ways of thinking onto our intellectual history, despite the fact that the evidence we have available to us tells another story altogether.

Updated June 6, 2020

Symmetry and Asymmetry in the Iconography of the Ancient Near East

Symmetry and Asymmetry

I first noticed a regularity (and accompanying irregularities) in images from the ANE a long time ago, and mentioned the phenomenon in 'The Sacred History of Being'. I described a number of images in detail because at the time I had no money to have the images copied (in the early eighties).  This extra labour turned out to have consequences. In compiling these descriptions I noticed that, where images possessed a symmetry, the same images often (but not always) contained some kind of breakage of the symmetry. It is easy to write this sort of detail off as carelessness on the part of the maker, but that attitude to what we are seeing just excuses us from trying to figure out the significance.

This kind of imagery is a legacy from the Neolithic. I've seen the same sort of pattern in iconography from Catal Hoyuk. So it seems to reflect a way of thinking which has had a long history. This does not mean that it is a continuous history as something which was always understood. But that this kind of image keeps turning up, means we should try to fathom what is going on with symmetrical images broken by asymmetries. At least before we decide the details of the images are unimportant.

I studied the ANE in London (89-92), not just because I was interested in ancient civilizations. My principal interest is the history of ideas (as my twitter feed illustrates). By the time I got there I'd come to the conclusion that the idea that philosophical thought was a creation of the Greeks, was in fact a scholarly construct. Much of my work since has focussed on demolishing this construct. The construct serves the function of removing the need for close attention to the details of rational thought before the middle of the first millennium B.C.E., because we know it isn't there: the Greeks were the first.



The Plenum

The idea that there is nothing worth discussing is obviously a major problem. Another major problem is that, in the west at least, an important concept has dropped out of our ways of thinking. This idea is the plenum. It is important for us to understand it because it was important in antiquity. If we discuss civilizations in the ANE without the knowledge that this was so, we are just studying  representations of the civilisations, convenient to our own way of thinking, rather than what is there to be understood.

What is the plenum? It is the idea that the physical reality in which we live is not reality itself. Reality itself is a primal fulness, beyond physical existence. The world of physical existence is therefore a kind of selective representation of what is possible, beyond space and time. The primal fulness has no physical existence, but it gives rise - in some way we do not understand - to the existent world. It is the other place. It is eternity. And it was a key idea in Mesopotamian civilization.



The Plenum in Mesopotamia

This idea underpins Mesopotamian religion, and the role of the King. The idea that reality itself lies beneath the world in which we have our existence is the reason why there are two creations in the Enuma Elish - the first an irrational one, before Marduk imposed order. This is why the first created beings are an irrational jumble of possible forms. All of the forms are present (at least in potential) in the plenum, but not everything which is possible is either desirable, or rational. So there is a second and rational creation, in which Marduk establishes order. That rational order is also described in the Enuma Elish,  in the form of his fifty names, and the description of his attributes.

This same idea of the plenum is the root of the Mesopotamian idea that destinies can be fixed. All possible destinies already have a reality in the plenum. But the gods, and their representatives on earth, have the power to fix the destinies, because of their close contact with the entity which contains the possible destinies. The plenum is most often referenced in terms of the Abzu. It is at the bottom of the sea, because the sea (as discussed in The Sacred History of Being) is an image of the primal fulness of the plenum - it appears limitless, it has no form, no shape, no colour.

The Abzu is also the place where all knowledge is to be had, and Ea/Enki is the lord of the Abzu. The earthly king strives to embody the attributes of Ea/Enki, and to be as wise as he is.

The plenum in Mesopotamia is also sometimes referenced as totality. That is what it is. Not the totality of the physical world, which is merely an earthly representation of it, but the totality of everything that is real. Hence Shamshi Adad I using the epithet 'King of Totality' (Shar Kishati) as part of the description of himself. According to Neoplatonist sources (more than one) a doctrine of totalities was taught in Babylon, and was supposedly brought back to Europe by Pythagoras. The doctrine is referenced (indirectly) by Plato.

Why do kings and genies hold a basket or pail, particularly in the vicinity of the Assyrian Sacred Tree? The banduddu is another symbol of the plenum - of all that is possible. One of the representations of the banduddu in the British Museum shows doves at each side. They are there because that primal reality, beyond space and time, requires to be laid out in a rational order, if life is to be possible. The doves symbolise the laying out of the fabric of the world and its dimensions, stretched out of the transcendent reality in which there is no space and time.

So the banduddu represents the all of reality itself, out of which the physical world is created. The other object is the mysterious pine cone. It represents (I think) an opposite to the banduddu, which is multiplicity. There is no multiplicity in the plenum. It is what it is. It does not move and it does not think. But the rationally created world is full of multiplicity and difference. The primal fulness is held in one hand, and the multiplicity of creation is held in the other. The king (or other divine power) is between the two extremes - between reality itself, and its physical representation. He has the power to shape the created world - to fix the destinies, and to create good order on earth. 

The king (or another divine power) is represented twice around the tree. The image is symmetrical. But the symmetry of the image is superficial, since it is broken by simple details. One being is shown bringing the pine cone close to the tree; on the other side of the tree, the opposing being is making contact with the tree. What is being represented here is the power of decision which both the king and divine beings possess. Which is the power of rational creation, and the establishment of good order in the physical world.

What is being represented is two separate states. The first represents the potency of the king, where it is the king being represented; the second represents the actualisation of the power which he has. So the image represents both the power of kingship, and the function of the king. Which is why there was such a representation behind the throne in Ashurbanipal's palace.

This implies that the king has a connection with reality itself. The tree is another image of that reality (reduplication of themes is a major part of ancient iconography). We can tell a lot about what it means on the basis of the way it is used in other contexts. Elements of the tree (alternating lotus buds, open and closed, etc.) can be used in pavements and porches, or used to mark the boundary between wall reliefs. So it represents a form of limit. The king accesses that limit, and because he has access to it, he has divine power. The limit is the plenum, because it is at the edge of physical reality. What is at the edge of physical reality is coterminous with divine reality.

"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, Z lyomi, The Literature of Ancient Sumer, 2004, p330

This is why sacrifices used to take place mainly at sunrise and sunset, because at that moment representations of the divine crossed from one reality to another (crossing the horizon between earth and heaven). It was the most propitious time for connecting the earth with the world of the divine.

The installation of divine images in Babylon and Assyria involved limits also - part of the ritual took place in a garden next to a river bank, where the long reeds were conceived to reach all the way down to the Abzu itself. And the rivers were themselves divine (DINGIR.ID), because water was an image of the divine reality.

The first sage,  Oannes, emerges from the sea to impart knowledge to mankind, for the same reason.


Transcendentalism in Mesopotamia

All of this makes sense only if Mesopotamian religion (or more accurately, Mesopotamian divine cult), was transcendentalist in nature. Meaning that the Mesopotamians (or at least some among the scholars, the 'priestly' class, and certain privileged members of the artisan class) understood there to be at least two levels of reality, one of them transcendent of physical reality, which gave rise to the world of physical existence. And that is what is described in their rituals and liturgies. Once the idea is grasped of the initial plenum, which forever lies behind the physical world, much of the rest of Mesopotamian literature makes sense, or at least offers clues to what is going on. Without a grasp of that idea, we have no clue.

A classicist would be likely to object to the above on the grounds that a transcendentalist nature to Mesopotamian religion would imply a contemporary grasp of philosophical concepts, and the ability to frame complex arguments about abstract questions and the nature of reality. But the Greeks invented all of that in the middle of the 1^st millennium B.C.E., so it is obviously wrong. They would follow up by saying that transcendentalist thought around the world does not predate the Greeks either. A history of transcendentalist thought has to start with the Greeks.

So we are back with the fiction. Transcendental thought is however the lynchpin of religious thought and practice in the ancient Near East. The denial of the presence of transcendental thought in the ANE has very little to do with the evidence which we have, and much more to do with the way the evidence is approached by us.

Further details concerning transcendentalism in the ANE can be found by following the links in the article Babylon the Great. There is also an article describing detail of the Babylonian creation which suggests a transcendentalist outlook: The Idea of the Plenum in Babylon. The importance of the idea of limit in Assyria is discussed in: The Threshold in Ancient Assyria. Links to articles on the importance of limit in general can be found in: At the very Edge: Marking Transition and Transformation in Antiquity. The properties and atributes of  Mesopotamian kingship are discussed in The Fifty Names of Marduk.

A book, The Origins of Transcendentalism in Ancient Religion, was originally slated for publication in 2019, but will now appear either late in 2020, or early 2021.


TY, September 11, 2018, and January 9, 2020.

Pythagorean Triples and the Generation of Space

The traditional formulation of the theorem of Pythagoras is that the square on the hypotenuse of a right angled triangle is equal to the sum of the squares on the other two sides. This is the Greek formulation, but we know that some of the properties of Pythagorean triangles were known in earlier cultures, such as in Babylonia.

The triangles of most interest were those constructed using integral values, such as the 3,4,5 triangle. These values were commensurable, and not irrational.

If we consider this in terms of the construction of the version of the triangle constructed using the square values, we can see that it is not a geometrical figure in two dimensions at all, but a line, built out of the three squared values (9, 16, and 25), exactly 25 integral units in length, with the three sides subsumed into one dimension.

This understanding of the geometrical arrangement perhaps tells us something about the ancient perception of space, and why it exists.

There are several possible Pythagorean triangles which exist, all of which exhibit the same properties, but with different combinations of integral values.

There are 16 primitive Pythagorean triples with c ≤ 100:

(3, 4, 5)  (5, 12, 13)  (8, 15, 17)  (7, 24, 25)

(20, 21, 29)  (12, 35, 37)  (9, 40, 41)  (28, 45, 53)

(11, 60, 61)  (16, 63, 65)  (33, 56, 65)  (48, 55, 73)

(13, 84, 85)  (36, 77, 85) (39, 80, 89) (65, 72, 97)

Additionally these are the 29 primitive Pythagorean triples with 100 < c ≤ 300:

(20, 99, 101) (60, 91, 109) (15, 112, 113) (44, 117, 125)

(88, 105, 137) (17, 144, 145) (24, 143, 145) (51, 140, 149)

(85, 132, 157) (119, 120, 169) (52, 165, 173) (19, 180, 181)

(57, 176, 185) (104, 153, 185) (95, 168, 193) (28, 195, 197)

(84, 187, 205) (133, 156, 205) (21, 220, 221) (140, 171, 221)

(60, 221, 229) (105, 208, 233) (120, 209, 241) (32, 255, 257)

(23, 264, 265) (96, 247, 265) (69, 260, 269) (115, 252, 277)

(160, 231, 281)

All of these Pythagorean triples when squared, represent mathematical and geometrical constructions which do not exist in Euclidean space as geometries: they are lines existing in one dimension.

We tend to look at the phenomenon of Pythagorean triangles as just that: something which has practical usage, but no further implications for the nature of the world in which we live, or our understanding of it. This is not likely to have been the case in the ancient world, in which number was venerated as something belonging to the divine and knowledge of the divine. The triples meant something profound.

What might be the meaning of the existence of these triangles and their properties?

In antiquity, it was obvious to anyone interested in number, mathematics and geometry, that there were several aspects of the physical world that involved irrationality, long before it was possible to provide logical proof of such irrationality. One of these irrationalities was the relationship between the diameter and the circumference of the circle. We know that irrationality (understood as an absence of commensuration) was a major concern in antiquity, since the existence of it seemed to undermine the idea that the world was rational, and constructed by the divine on rational principles. In other words, the existence of irrational things served to undermine the idea that the world made sense, and that it was good.

What we understand as Pythagoreanism is actually a way of approaching the world and reality on the basis of number, mathematics and geometry. We have lost a grasp of this, particularly since the close of the ancient world. Pythagorean ideas are not the creation of Pythagoras in the sixth century B.C.E., but a range of ideas about the world, focussing particularly on numbers and geometry, and the puzzles which the study of these throws up (the Greek name for these puzzles is ‘aporia’). As such, these ideas and puzzles belong to any culture which chooses to address the divine in terms of how the universe is constructed. As already suggested, the Babylonians had a sense of this, though they were also interested in the practical applications. It is also the case that the inhabitants of Britain in the late Neolithic and the early Bronze Age had such a sense.

The engineer Alexander Thom surveyed many of the megalithic circles across Britain from the 1930s into the 1970s, and established that the circles were constructed on the basis of a number of different Pythagorean triangles, and that these circles were not in fact circular.  The circumferences of these circles were modified in order to make their lengths commensurate with the length of the sides of the underlying triangles.  These modifications testify to the contemporary idea in ancient times that the incommensurate nature of diameter and circumference shouldn’t be the case.

I’ve written elsewhere that Pythagoreanism, whether in the sixth century or long before, was a transcendentalist view of the world. Meaning that the world of physics and appearance in which we live, is not reality itself, but simply a presentation of it. And the presentation of it is, in a number of ways, crooked. So some aspects of physical reality are not rational. 

This does not mean that the ancient Pythagoreans were pitching themselves against the workings of the divine, but rather that they were trying to understand why what they saw, experienced and understood, was not rational. The answer was that their place of refuge was not reality itself, but a false representation of it.

In the physical world, they could therefore not expect rationality to be woven all through it. Thom identified the obsessive concern of the ancient Britons with whole numbers, and as a consequence (though this was not understood at the time he was studying the megaliths), we know that they were looking to a world beyond the puzzles and paradoxes, in which the relationships of one thing to another were rational in nature.

The theorem of Pythagoras, however it was articulated in the late Neolithic and the early Bronze Age, provided the answer to this. The relationship between the sides of a 3, 4, 5 triangle is irrational in nature, but by squaring the sides, the result is rational and commensurate. This would have been understood to point to a world which transcended space, in that it indicated a one-dimensional reality.

 In that world, some things which are incommensurate here,  were commensurate. Which they might have taken to indicate that, beyond that limited form of reality, there was another reality with no dimensions at all, in which all irrational values existed as commensurate with one another.

Plato echoed a range of Pythagorean ideas in his work, including that reality itself exists in no particular place, has no form or shape or colour. He also suggested that forms existed beyond geometrical figures existing in space, and that these were to be accessed in the mind alone.

The Pythagoreans may have understood physical reality to have been generated as the square root of mathematical values in a higher reality. The resulting incommensuration would necessarily generate space. We could not possibly live in a reality which embraced only one dimension, or even none at all. In which case physical reality might have been understood by the ancient Pythagoreans as a compromise of sorts, which made it possible for mankind to live.