Tuesday, 23 February 2016

Physics and the Origins of the Universe (III)

This is the third in the series of posts on Physics and the Origins of the Universe, and contains a discussion of the Kaluza-Klein hypothesis, which is a hypothesis which brings Einstein's field equations together with Maxwell's equations for Electrodynamics. Its proposition, that there are five dimensions of space and time, not four, and that it is hard to characterise the fifth spatial dimension in terms of size, may point to the presence of a plenum beneath physical reality. 

The Plenum and its Properties (II)

How many dimensions are there? It depends on what you are doing and how many you need to describe and understand physical reality. The number will change according to what phenomenon is being explored.

We are accustomed to thinking that, for most of recorded history, the human race has made do with three dimensions of space, plus time, in order to make sense of the world. If we treat time as a dimension, that gives us four dimensions. Three separate dimensions in which things can exist, and in which they can move. And whether these things are motionless or moving, they are also moving through time, at the same rate, irrespective of whether they are travelling left or right, backwards or forwards, or up or down.

In fact four dimensions is an inadequate number to explain how the world of physical reality actually works, and how its component parts fit together. For the most part, our understanding of what physically exists is described in scalar and vector terms within four dimensions, because that seems to work. Most of the time. Unless you are working in Fermilab or CERN, where their descriptions of physical reality concern the quantum level of physical reality, and things are more complicated there. But even at the anthropic scale, sometimes four dimensions can be found wanting. A description is not an explanation, and some things are therefore not explained.

I will borrow a little from the Wikipedia article on the Kaluza-Klein theory, which has been described as a unified theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the standard four of space and time. The article describes how this five dimensional theory was developed, and breaks it down into three steps.

The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919,[1] and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The five-dimensional metric has 15 components. Ten components are identified with the four-dimensional spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified scalar field.

This extension to five dimensions for Einstein’s equations yields

 …the four-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field.

Now that is pretty interesting, and it is surprising that physicists were not falling over themselves at the time to understand the mechanics of this mathematical description which tied electromagnetic vector potential with Space and Time.

It would be intriguing to know what was in Theodor Kaluza’s mind when he came up with this five dimensional model, which involved an unidentified scalar field.  His model involved a hypothesis which is described as the ‘cylinder condition’, which means that

 that no component of the five-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of five-dimensional relativity are enormously more complex.

In other words, the five dimensional model of physical reality has two potential states – one of which results in impossibly difficult field equations. The cylinder condition is the other state for the model, which results in relatively simple and intelligible equations.

The article suggests that

 standard four-dimensional physics seems to manifest the cylinder condition.

Which may be the case, or it may be that there is a fundamental problem with the five dimensional model, and that it is a conception which doesn’t reflect physical reality. Kaluza

… set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.

Meaning that Kaluza knew how the equations should turn out, and he knew how to characterise the unknown scalar field in order for the equations to turn out correctly.

The second step in the development of Kaluza’s theory was a quantum interpretation, supplied by Oskar Klein in 1926. This to enable the theory to

accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, [my emphasis] to explain the cylinder condition. Klein also calculated a scale for the fifth dimension based on the quantum of charge.

The third step happened in the 1940s, when the classical theory was completed, and the
full field equations including the scalar field were obtained by three independent research groups

The introduction to the article concludes by saying that even under the cylinder condition the full Kaluza equations are quite complex, and that

The complete Kaluza equations were evaluated using tensor algebra software in 2015

Here is a section from the main body of the Wikipedia page. I can understand the concepts involved, but I’m not remotely competent to evaluate the equations.  I’ve left the links to the Wikipedia references intact. [this version of the document presents the Wikipedia text as graphics, so the links are not functional. The original article is at: https://en.wikipedia.org/wiki/Kaluza-Klein_theory]

I’ll pick out some parts of the text -

So far, this decomposition is quite general and all terms are dimensionless. Kaluza then applies the machinery of standard general relativity to this metric. The field equations are obtained from five-dimensional Einstein equations, and the equations of motion are obtained from the five-dimensional geodesic hypothesis. The resulting field equations provide both the equations of general relativity and of electrodynamics; the equations of motion provide the four-dimensional geodesic equation and the Lorentz force law, and one finds that electric charge is identified with motion in the fifth dimension.

It has been an objection to the original Kaluza hypothesis to invoke the fifth dimension only to negate its dynamics. But Thiry argued that the interpretation of the Lorentz force law in terms of a 5-dimensional geodesic mitigates strongly for a fifth dimension irrespective of the cylinder condition. Most authors have therefore employed the cylinder condition in deriving the field equations.

…It shows that the electromagnetic field is a source for the scalar field. Note that the scalar field cannot be set to a constant without constraining the electromagnetic field. The earlier treatments by Kaluza and Klein did not have an adequate description of the scalar field, and did not realize the implied constraint on the electromagnetic field by assuming the scalar field to be constant.

In the Kaluza theory, the gravitational constant can be understood as an electromagnetic coupling constant in the metric. There is also a stress-energy tensor for the scalar field. The scalar field behaves like a variable gravitational constant, in terms of modulating the coupling of electromagnetic stress energy to spacetime curvature. The sign of phi in the metric is fixed by correspondence with 4D theory so that electromagnetic energy densities are positive. This turns out to imply that the 5th coordinate is spacelike in its signature in the metric.


So what are we actually looking at with this five dimensional model of physical reality? The theory unifies Einstein’s field equations, and Maxwell’s equations, and does appear to be describing physical reality, even if there are problematic aspects to it.

The fifth dimension is invoked, and then dismissed as a functional component in the model, which reduces it to a dimension on a par with the other four. But it is very small, and may be rolled up. It is practical to treat it as if it is on a par with the other dimensions, which is what physicists generally do. But ignoring the complexity the model may have beyond the cylinder condition – one of the two states of the model - doesn’t mean that it does not have this complexity, and that the fifth dimension does not have an important role in how the physical world functions.

It is possible that what has been identified in the course of the development of the theory is in fact the plenum, and not simply another dimension on a par with the other four.

Thomas Yaeger, 22 February 2016.

Physics and the Origins of the Universe (II)

Current popular understanding of how the universe came into physical existence depends on some improbable ideas, such as the existence of physics where physics cannot be present, and that there was a physical explosion of something into a place which did not yet exist. This doesn't seem to trouble the popular understanding. More importantly, it does not seem to trouble most physicists. 

I've written elsewhere about how we got into this difficulty. In short, the west ditched certain ideas about reality between the time of Newton and the Enlightenment, and consequently also ditched the intellectual tools necessary to understand how and why we have physics and a physical existence.

What follows is a description of creation as it might have been framed, if the west had not offloaded the concepts and tools which enable an understanding of the origins of the universe not requiring us to believe several impossible things before breakfast.  

Essentially this argument proposes that physical existence is the consequence of an underlying plenum, whose nature transcends our understanding of what is real. The nature of this plenum is what gives rise to physics and the physical world, through the necessity of retaining its own nature. As a result, the physical world has a logical origin, rather than an origin requiring a strange pre-existence of physical laws.  

The second part of this discussion (Physics and the Origins of the Universe III) concerns the Kaluza-Klein hypothesis, whose implications suggest that the idea of a plenum, in the form of a fifth dimension, is critically important in connecting Einstein's field equations, and Maxwell's equations for electrodynamics. 

The Plenum and its Properties (I)

The Plenum is, as it is, undefined in any way. We can say that it is what it is, and that its properties are those which can be said to characterise the plenum: it has no shape or form, or size. It does not move (there is as yet no space), and it has no age (there is as yet no time, which is a vector of change).

What are the properties of the plenum? It is one undivided thing, which has no physical existence, no location, and is something which remains unaltered and unalterable. It is literally eternal. It is utterly transcendent of the categories of our understanding, and is not subject to the laws of physics. Though it is one undivided thing, it is beyond characterisation as one undivided thing. It is just that which is, before dimensions and time, and categories of understanding.

It is neither one thing nor another.  It can be understood as a fullness, since it is not an absence. But in itself, it is not a presence either. It has potential. This does not mean that its nature will change, but that there is potential within its nature for the appearance and perception of change, size, form and shape.

So we are building up a picture of the plenum, or the initial state of the cosmos. It is one not two, (there is no ‘two’). It is beyond definition. It is unmoving and is not subject to change. It contains the potential for all of these things, including time and space, since it is undefined. It can contain these things as entities which appear, in the context of other things which can perceive entities which appear. At the earliest stages, perception can mean as little as detection of, and response to, things which appear. Not consciousness of any sort that we would understand.

All physical reality that may ever have existence is, in a sense, already present within the plenum. That is, physical reality is already present in potential.

All possibility is present in the plenum. Nothing is fixed or determined, at least initially (we are looking back at the initial conditions, so ‘initially’ references our own point of view, not that of the plenum. It is not in development. It does not change).

So the plenum is, conceived from the outside, is a formless, churning and foaming potency.

What other things can we say of the Plenum? It is infinite, in that it not finite, since it is undefined. It is also infinitesimal, for the same reason.

The parameters in which the apparent realities of the physical world can have their existence include binary opposites.  We can oppose the ideas of the infinite and the infinitesimal, but we can also oppose the ideas of the infinite and the finite. These are different oppositions involving the same concept. We can do the same with other oppositions, such as the unlimited and the limited, and the limitless and the limited. These may appear to be the same, but the unlimited is something which has not been subject to limit. The limitless is simply that which is without limit.  Likewise with the ideas of great and small. But the great can be contrasted with the not-great, which is not limited to the idea of small.

These may appear to be footling distinctions between abstractions, but the abstractions are the earliest things which can be present in the plenum, before the plenum can give rise to the appearance of a physical reality (abstractions are by definition beyond particular physical instances). So the churn in the plenum is in a sense a logical one, rather than anything resembling a physical reality. It is a chaos of logical possibilities, and also of logical contradictions. The Plenum does not have a consciousness, at this level of the creation.

The plenum has been defined as one, and itself. What may the one be contrasted with? The many? Or the absence of the oneness of anything? The idea of the many can be contained within the plenum as an abstract idea, without compromising the oneness of the plenum. Likewise, the absence of oneness. Each of these opposing abstractions within the plenum represents a potential subdivision of its nature, by which a physical creation increasingly becomes a possibility. All of this is present in the plenum from the beginning. This chaos of conflicting abstractions is eternal.  For a physical and ordered world to exist the conflicting abstractions need to marshalled.

The formless abstractions are ideas, which are subject to the power of other ideas. This stage can be understood as a second creation, in which logical decisions are made. At this point we could speak of the presence of a consciousness, though all that is meant is that an ordering process begins to take place, replacing a senseless churn of abstractions and oppositions.

The oppositions represent the sameness of the plenum with its difference. In the case of the infinite and the finite, the infinite is the sameness, and the finite is the difference. In both cases, the same and the different are the same plenum, understood differently, and looked at with different categories of understanding.  In a sense the plenum begins to understand itself after the second creation. The idea of finitude is crucial to the creation of physical reality, and is created as a qualifier of the idea of infinity.

Another property of the plenum is the completeness of what it is. But completeness can imply boundedness, rather than the boundless. Is the plenum bounded and therefore limited and finite because it is complete? Again, it is a matter of the categories of understanding which are brought to bear.

With finitude, and the idea of the many, physical reality becomes possible. The abstractions can be understood in terms of number, while still being abstract.  With the presence of number, all kinds of processes and constructs become possible.  But we are still (from our point of view) before space and time in any sense we would understand. 

The unmoving abstract concept of the plenum gives rise to the idea of a possible opposite, which is a cosmos of movement. So space and time become abstractions by which numbers and their interactions may be represented. Once you have space and time, the representation of numbers can move beyond points to geometrical shapes, and eventually three dimensional form.

Space and time are generated by the same process of opposing the same and the different. Ultimately they are both representations of understandings of the plenum.

So what populates the cosmos? The earliest occupant of the newly generated physical cosmos will be hydrogen, since it is the simplest element, made up of two different electrical charges. These charges will have been created as a consequence of the same principle of opposing the same and the different. A myriad of representations of one or more of the original polarities contained (as a possibility) in the plenum. 

It is possible to see opposing electrical charges as a representation of the same and the different in the context of finitude.  Whereas the raw state of the plenum is foaming and churning (from our point of view), hydrogen represents a stable opposition of electrical charges in a dynamical relation. The foaming and churning has, in this representation, been reduced to a resonance. Order has emerged from chaos.


There was a well-known toy for drawing complex patterns when I was a child (Spirograph). It had its limitations as a toy, but it taught me that a simple ratio could imply something very complex, depending on how that ratio was expressed. Similarly so with the development of patterns in animal fur, which Alan Turing investigated at the end of his life – the underlying mathematics were often simple, but the process could produce startlingly complex patterns.  The complexity we see in physical reality can have its roots in something very simple, such as the generation of numbers (real or imaginary).

I learned to use log tables and a slide rule while at school. That taught me that a process such as multiplication could be represented as addition, depending on the adopted point of view.  In the case of logarithms, through the use of reciprocal numbers.  Again, the same, represented in both form and process, by the different.  And patterns emerge from the encounters of the same with the different. So interaction between the plenum itself with its difference, and the representations of its relationship with its difference, can be understood in terms of ratio. The old sense of what is rational descends from this idea – what accords, what is consonant, etc. 

Two logical modalities underpin the descent of aspects of the plenum into physical reality. One can be understood in terms of entities possessing identity with itself, of not being something else while it is itself, and not partaking of itself and something else while it is itself. The other logical modality is startlingly different, but it is a completely rational modality. Since the encounter of the same with the different is happening within the underlying plenum, and is in a sense powered by the properties of the plenum, it is the case that all things can pass into one another. That is, what is the same as itself, can pass into what is different from itself.

It is not possible however for the same to always pass directly into something which is different from it. It must pass from itself to what is different through a rational process. It is possible for the same to do this, since it necessarily shares aspects of its nature with the plenum within which it has its reality. This is how this logical modality is rational, and not chaotic.

When I learned music, I found that the possible scales were patterns within the octave which reflected mathematical ratios based on the octave itself. That is, each of the notes possessed a relationship with the root note of the octave which expressed a ratio which existed outside the octave. Music works because we are hearing the intervals, and the progressions of the intervals, all of which are in a sense beyond the actual notes played. So we are appreciating the rationality of the relationship of one to the other.  The expression of those relationships can be understood as a rational and logical interplay between what is the same, and what is its difference; multiplied, and in different sequences, both horizontally and vertically.

One particular ratio, is defined by ‘the smaller is to the larger, as the larger is to the whole’. This is of course the golden ratio, where each of the parts bears a relationship to the whole, and, is not dependent at all on any scalar values. So it has a reality which exists apart from any particular instance in which this ratio may be expressed. It refers to itself, without necessary reference to anything which has physical reality. It is an abstraction which refers only to sameness, and to difference. It is therefore a conception of great importance, and we should expect to find it often represented in the continuum of reality. And we do.  It is the plenum, the thing which is itself, reminding us of how the world of physical reality came into existence.


The two logical modalities both draw their natures from the properties and characteristics of the plenum. They appear to be contradictory, but then the nature of the plenum contains a number of apparent contradictions. Nevertheless, it must be itself, whatever itself is. But it must also share its identity with every aspect of itself, since, in reality, there is nothing other than the plenum. Accordingly, the world of appearances is just that – the world of abstractions and concrete instances, of ideas, number and physical form, is just an array of different perspectives on the plenum. The plenum is the one true thing, and all that there is.


The plenum is complete, and whole. Every other thing which has reality has it because it participates in the plenum through its completeness. Anything which is whole participates in wholeness, and wholeness is an abstraction which provides connection with the ultimate abstraction of wholeness, which is the plenum. All parts of things also participate in the plenum through the wholeness they share as the parts of things which are whole. If they are whole or completed parts, they again participate in the wholeness of the plenum. So in sense, the part and the whole are not entirely separable concepts. They can be understood as the same and the different. They may also pass into and out of one another.

Because nothing can have reality or existence, or come to be and pass away, change, or move, without the underlying ground of reality, it can be argued that the plenum must be real for the illusion of these finite things to function.


This is an account of a creation from abstractions, which have no firm location in time or space, even where there is time and space present. So it is possible to conceive of them having reality before time and space came to be.  The need to explain the presence of the physical world in terms of a physical creation is removed, which is plainly a species of category mistake: the presence of the physical world does not need to be explained in terms of a physical creation, which approach has saddled our understanding with the need to find a prime mover.

There is also no need for the idea of a creation ex nihilo. The presence of a plenum (which is neither presence nor absence) allows for a rational creation from the interplay of abstractions. The plenum contains all things which may be thought, and which may come into existence. Hence we can understand reality by studying its properties, as well as come to understand why the physical world is the way it is. This approach is not the opposite of a scientific understanding of reality, it is the root of a scientific understanding of reality, and of its subset, the physical world.

Thomas Yaeger, 21-2 February 2016.

Thursday, 18 February 2016

Understanding Ancient Thought

New book, 'Understanding Ancient Thought' now being edited into shape. It deals with a number of important issues which obstruct our understanding of ancient thought. It also provides introductory materials for the 'The Sacred History of Being', and explores the history of the twenty year plus project, through documentation recently recovered from imprisonment in obsolete software formats.

Questions explored include the ancient model of reality; the intellectual basis of Greek theology; Aristotle and the early history of philosophy; sociology and the evolutionary view of religious thought; magic and ontology in ancient Greece; the four causes; the understanding of the ancient world in the high Renaissance; the understanding of the ancient world in the European Enlightenment;   and the role of intention in ancient religion.

The final text will be around 60 thousand words. It will be published by the Anshar Press, in early summer 2016. Illustrated. Details of the publication date and availability will be published on this blog.

Thomas Yaeger

Wednesday, 10 February 2016

Logic, Sophistry and the Esoteric in Ancient Education

We are inclined to treat ancient argument at face value, except where we do not understand the significance of the argument. Then engagement with the material is difficult to maintain, because  what we need to know isn't present. The argument is dependent on an esoteric interpretation long lost to us. Or at least that the consensus view.

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. One translator of Plato's Philebus (Robin Waterfield) confessed in his preface that even after translating the work, he didn't know what it was about.

Sometimes the clues to the meaning of arguments are present elsewhere in the canons of both writers, even for the ones which 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. As if one work is unconnected to the others.

Sometimes arguments are unsatisfactory at a logical level. It would be easy to write these examples off as sloppy instances of argument. But we may be too quick to do this. Both Plato and Aristotle taught students, and we need to explore something of their approaches to the education of their students.

We can begin by considering Aristotle's laws of thought, which are the ancestor of most later systems of non-paradoxical logical modalities. They aren't as sound as they would seem to be, and his approach to the education of his students may have something to do with this.

Aristotle’s laws of thought are as follows:

A thing is itself and not something else. Which is known as the law of identity.

There is also the law of non-contradiction – a thing cannot be a thing other than itself, at least at the same time. Aristotle gives three definitions in his Metaphysics: Ontological: "It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect." (1005b19-20). Psychological: "No one can believe that the same thing can (at the same time) be and not be." (1005b23-24). Logical: "The most certain of all basic principles is that contradictory propositions are not true simultaneously." (1011b13-14)

The third is the law of the excluded middle. Meaning that a thing is either itself, or something else, not something in between. He states it as a principle in the Metaphysics book 3, saying that it is necessary in every case to affirm or deny, and that it is impossible that there should be anything between the two parts of a contradiction.

This is not part of Aristotle’s manual of logical procedure, known as the Organon. The Organon codifies how the human understanding should deal with identifying and differentiating aspects of reality, reasoning, deduction, detecting false or misleading conclusions and specious modes of argument (the text on Sophistical Refutations is part of the Organon). This work is based on the ancient practice of collection and division, of identifying the same, and what is different. We normally think of dialectic as what the Greeks did in the course of philosophical argument, but its original scope was much wider than that. They were engaged in the practice of collection and division in Babylonia and elsewhere in the second millennium B.C.E. Which is why the Babylonians and the Assyrians created lexical lists of objects which had something in common, such the property of whiteness (the purpose of which scholars initially found puzzling, and most still do).

The law of non-contradiction, as stated by Aristotle, isn’t actually provable, though he tried to demonstrate it. Many later philosophers have tinkered with the law, but its main use is as a guide to thinking, and it is useful to know, even if it is possible to give instances where it does not hold.

I've said elsewhere that Aristotle practised sophistry. I do not mean that he was a liar or that he was trying to make 'the worse cause appear better' (Plato’s accusation against the sophists). But he did create fictions. I used the conclusion of his Nicomachean Ethics as an example, in which he states that the gods cannot move or interact with the world, and that their function is restricted to contemplation. Which must have seemed like a denial of the role of the divine in the world, current at the end of the fourth century B.C.E.

I studied the Nicomachean Ethics in some depth as a student, and noticed that a part of his argument is repeated, in slightly different words (in Book 8 I think). It has been observed before that the cramped and compacted wording of Aristotle’s treatises is reminiscent of lecture notes taken down in the classroom. And that’s what we have here - someone has collated notes from at least two different hands, and added two passages which repeat the same section of one of Aristotle’s classes (there are three ethical treatises which are attributed to Aristotle, so this may have been a popular series of classes, perhaps repeated on different occasions, and in slightly different forms).

My point is that Aristotle was a teacher, and was creating lectures which weren’t simply to be absorbed whole as the final word on the subject by a great teacher. He was expecting his students to think. Some of the students would ask questions, query points, or perhaps argue against the main pillar of the argument, though most wouldn’t.

Both Plato and Aristotle had the concept of an inner and outer knowledge. Plato referred to these grades of knowledge as ta eso and ta exo. We know that students at Aristotle’s Lyceum attended two different sets of classes, one in the morning, and the second set in the afternoon. Exoteric knowledge was taught in the morning, and the esoteric understanding of things was reserved for those who attended in the afternoon.

Esoteric knowledge is by definition obscure in nature, and/or difficult to understand. Which is what the story of the prisoners in the cave in Plato’s Republic is all about. They see the shadows of reality on the wall before them, but not the reality itself. When they are released with suddenness, their reason is deranged by the experience. Instead they should have been released gradually, being shown details of reality first, without the whole of the shocking truth of reality being given to them all at once.

So both Plato and Aristotle were dealing in what they understood to be esoteric knowledge. In Mesopotamia there was a similar division of the types of knowledge. We are told by the Assyrian king Esarhaddon (Seventh century B.C.E.) that the common run of men are ‘deaf and blind throughout their lives’. Exoteric knowledge of divine things would consist of the names of the gods, their epithets, and stories told of the gods. This superficial knowledge could be imparted by fathers to sons, and could be taught in the schoolroom, as sometimes is said in tablet colophons. The esoteric knowledge was kept secret by the initiates and the priesthood, and tablets relating to the mysteries of the gods would state that they were not to be read by the uninitiated.

Aristotle’s Lyceum can therefore be thought of as a combination of school and college, with the classes in the morning providing a steady flow of students who had shown sufficient intelligence and independence of mind to be suitable for the classes which imparted esoteric knowledge in the afternoon. They could show this intelligence by challenging the sophistical arguments embedded in Aristotle’s lectures (as I’ve said, he attempted to prove some of his arguments, but didn’t always succeed. The students were supposed to spot when what he said was not soundly based).

Aristotle often begins from what people commonly believe – from common opinion. Common opinion as we know is usually wrong. It has been suggested that he attempts in the course of argument to lead the students from what they think they already know, to something closer to what Plato would have called true opinion. In short, to release them gradually from their imprisonment with the shadows of true knowledge. He isn’t always doing that, as the Nicomachean Ethics shows. So it is possible that this series of lectures, and perhaps also his Metaphysics, belong to the morning sessions, where the purpose was not to impart true knowledge, but to detect the sharpest and most critical students. For example, from the Metaphysics:

"First then this at least is obviously true, that the word 'be' or 'not be' has a definite meaning, so that not everything will be 'so and not so'. Again, if 'man' has one meaning, let this be 'two-footed animal'; by having one meaning I understand this:-if 'man' means 'X', then if A is a man 'X' will be what 'being a man' means for him. It makes no difference even if one were to say a word has several meanings, if only they are limited in number; for to each definition there might be assigned a different word. For instance, we might say that 'man' has not one meaning but several, one of which would have one definition, viz. 'two-footed animal', while there might be also several other definitions if only they were limited in number; for a peculiar name might be assigned to each of the definitions. If, however, they were not limited but one were to say that the word has an infinite
number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning our reasoning with one another, and indeed with ourselves, has been annihilated; for it is impossible to think of anything if we do not think of one thing; but if this is possible, one name might be assigned to this thing."

— Aristotle, Metaphysics, Book IV, Part 4

He cannot mean this. All poetry, literature and art collapses at this point, where Aristotle claims that, in order to eliminate ambiguity in thought, there should be a one to one correspondence between words and definitions. This would have made no sense to the Babylonians and to the Assyrians, whose literature is woven all through with wordplay - homonyms, synonyms, ideograms, logograms, phonograms, metaphor, metonomy, and a litany of interchangeable signs and signifiers.

This is a good place to pass on to a discussion of the kind of logic invoked by Plato to understand the nature of reality. There are intimations in his canon that he understood pretty well the laws of thought that we find in Aristotle, but there is another logic present and discussed at length, which entirely cuts across the three laws, and enables a quite different picture of reality. Whereas Aristotle’s laws of thought provide guidance for understanding what exists in the world of physical existence, what Plato tells us about is an esoteric doctrine, which explains what is hidden and obscure, and relates to the gods, and what is divine. As one might expect, the rules for the gods are different.

Pleroma, Cosmos, and Physical Existence

As suggested elsewhere, there isn’t much we can say about the initial state of physical reality at a notional time of its emergence, if the various parameters of what can be said of it don’t have any existence. That’s the problem physics has when it is looking for causes and mechanisms.

However it is possible to talk about the initial state of reality in terms of logical argument, which is how it was done in antiquity. They were familiar with talking about reality in terms of extreme states: does it exist? What is it? Is it one or two? If it is two is reality other than itself? Is reality complete in itself? Is physical existence a copy based on the pattern of reality itself? If it is a copy, has the nature of reality itself been compromised?

Whatever the initial conditions might have been, we can say that those conditions are at the edge of physical existence. Which is not to suggest that they actually occupy some kind of space at the edge of physical existence. Just that, since the initial conditions don’t participate in the conditions of our physical existence (extension, vectors, time, etc), then these conditions will, to us, appear to be something which we can find at the extremes of physical existence.

This is the root of the idea of the telos. It is about beginnings and endings – how things start and finish. When what is ultimately real is considered in this way, it is susceptible to logical analysis, and an idea of a prime mover beyond the properties of the telos itself is not required.

A discussion of this conception of the telos should be untarnished by the general deprecation of teleological argument in any kind of scientific analysis. We aren’t looking for purpose. But we are looking for the beginning, and how things might have unfolded from that beginning. The concept of the telos as a plenum, a pleroma undefined by the kind of parameters we find in our physical existence, as opposed to the idea that physical existence just appeared ex nihilo, can be discussed. Nothing as absence is very hard to discuss, except in the context of its opposite. In fact it cannot reasonably be conceived without that context.

The discussion of Aristotle (elsewhere) places his laws of thought into a wider context. The laws represent tools in the Greek dialectical armoury. So do the techniques used by Plato. But they are quite different and produce different kinds of argument and result in different conclusions. They belong to the same armoury (a discussion for another time). It is possible to understand some things with Plato’s approach which would not be possible with a rigorous application of Aristotle’s laws of thought. It isn’t the case that one logical approach is correct, and the other not. But they are appropriate to different contexts.

A plenum can be understood as identical with itself, and so, in that sense, can be thought of as consistent with the first of the laws of thought. But its properties, as understood from the point of view of physical reality, cannot be self-consistent, since it is beyond definition in physical terms. So the plenum must have a paradoxical aspect (literally meaning it is beyond human understanding), and therefore must breach the other two laws of thought (it can be one thing or its opposite; and it may also be neither one thing or its opposite).

There are several ways an argument about an initial and ever-present plenum can be taken forward. One is to take the view that physical reality represents a partial view of the plenum. Or can be understood as an assemblage of partial views of the plenum. It contains consistencies and regularities, but at a granular level (particularly), it behaves with apparent inconsistency, being best understood in terms of probability. That is how the plenum is, or at least the best way it can be understood by us. It isn’t one thing or the other. But occasionally its granularity looks like one thing or the other. And sometimes both at the same time. We can describe what is going on in terms of probabilities, which is how physics handles it, but it is not understood except in terms of mathematical description. The idea of the plenum, as established through a purely logical analysis, gives us insight into how the universe is actually operating.

It could be argued that physical reality behaves as it does at the quantum level because, for all practical purposes, the plenum has no size. So, at the quantum level, we are looking more closely at the nature of the plenum as it is, or rather as it must, on account of its nature, look to us.

Quantum entanglement might have a similar basis, on the ground that what is happening is actually happening in the plenum, rather than in physical space. Despite it having no size, it must necessarily be (in a sense) distributed throughout space and time.

In future I will be discussing Bell’s Theorem; Einstein, Podolsky, Rosen; and Klein-Kaluza. Also about the fact that Maxwell’s equations can be derived from Klein-Kaluza, and why the maths of Klein-Kaluza has two states.

Post-Enlightenment Plato, and That Which Cannot Move

The Plato we have we look at differently from the way he was understood in antiquity. For most of the middle ages all that was available to scholars was the first part of the Timaeus. So it is not the case that a way of understanding Plato has been handed down to us, except via the neoplatonists. But the neoplatonist understanding of Plato is deprecated as a way of understanding his work, with the consequence that modern scholars approach Plato virtually naked, with a very modern set of intellectual baggage. This can be a problem.

I wrote in SHB that:

In parallel with the changing scholarly assessment of Egyptian civilisation in the eighteenth century, Greek philosophy itself was undergoing a re-evaluation. This was essentially the first since the renaissance, when Plato was generally understood to be writing about theological matters, rather than purely philosophical questions. Now Plato needed to be co-opted into the life of reason.

Karl Friedrich Herman (1804 1855) wrote what von Wilemovitz-Moellendorff regarded as an important 'Life of Plato.' This life was 'the first to understand the development of Plato's thought.'

Well there you have problem number one: the idea of a development in Plato. So, what Plato was writing about had nothing to do with a background in cultic life, and therefore he could be approached as a writer on all fours with modern philosophers. Modern philosophers, principally after the foundation of the University of Gottingen, do research, and what they do is a secular activity.

Martin Bernal wrote that:

Gottingen can well be considered the embryo of all later, modern, diversified and professional universities. It was established in 1734 by George II, King of England and Elector of Hanover, was well endowed, and as a new foundation was able to escape many of the medieval religious and scholastic constraints that persisted in other universities. With its British connections it was a conduit for Scottish Romanticism as well as for the philosophical and political ideas of Locke and Hume.

Bernal writes about one of the founders of the University of Gottingen, Kristophe August Heumann. He says that: “As a pioneer of the new professionalism Heumann established a scholarly journal, Acta Philosophorum, in the first issue of which, in 1715, he argued that although the Egyptians were cultivated in many studies they were not ‘philosophical’.

This claim – which his contemporaries Montesquieu and Bruckner… did not dare to make – was both striking and daring in the light of the strong ancient association between philosophia and Egypt." Bernal mentions that 'three of the earliest four references to philosophia are associated with Egypt'. Isokrates specifically associated philosophy with Egypt (Bousiris, 28).

Bernal points out that modern scholars have difficulty in accepting this ancient association, and mentions one author, who, writing in 1961, consistently translated 'philosophia' as the civilisation of Egypt' (Black Athena p 216) .

Further, he writes that: “Heumann’s categorical distinction between Egyptian ‘arts and studies’ and the Greek ‘philosophy’ is rather difficult to comprehend, as his definition of the latter was ‘the
research and study of useful truths based on reason.’ Nevertheless its very imprecision made, and makes, the claim that the Greeks were the first ‘philosophers’ almost impossible to refute."

It is in fact not so difficult to comprehend, when Heumann's view is considered in its cultural context. At the time this distinction was made, Newton's mechanical philosophy and mathematics were in the ascendant. A reaction had long since set in across Europe against magic, alchemy, astrology, and other pseudo-sciences of the time. Leibniz, Newton's rival in mathematics, had, toward the end of the seventeenth century begun to distance himself from both people he knew in these fields, and from the kind of language they used to describe and understand ideas and phenomena. He became modern. 1

Egypt, being undoubtedly a place of magic and other unreasonable practices, experienced collateral damage. It could no longer be seen by proponents of reason as a place of philosophy, since philosophy was to be understood as the exercise of human reason, and not something which could co-exist with magic, prophecy, divination, etc. Irrespective of the fact that magic and the other unreasonable practices co-existed with philosophy in Greece.

So there has been a very strong effort by scholars, particularly since the enlightenment, to break with earlier understandings of both the basis of Greek philosophy, and its relationship to other cultures in the ancient world. In the interest of establishing the life of reason.

Hence SHB is, as a work of scholarship, as near anathema as it is possible to imagine, since one of its principal aims is to break up the post-enlightenment consensus about what philosophy is, where it came from, and its cultural context, by showing its roots in a ‘cultus deorum’ - among those who speculated on the nature of Divinity, the Creation, and the nature of Reality itself. In short, among those who sought to answer the question, ‘why is there something rather than nothing?’

I will now turn to the kind of argument Plato used in addressing the nature of reality itself. Some of the most interesting passages are well known, but apparently impenetrable to the modern mind. They come from three dialogues in particular – the Timaeus, the Sophist, and the Republic. Other important information is scattered through other dialogues, but it is possible to understand Plato’s thought on the basis of these three dialogues alone (though reading the Theatetus as well is recommended).

I’m now going to quote from the chapter in SHB on Plato’s theory of Being:

The Timaeus contains a famous passage which discusses the manner in which the forms are conjoined with body:

...it is not possible that two things alone should be conjoined without a third; for there must needs be some intermediary bond to connect the two. And the fairest of bonds is that which most perfectly unites into one both itself and the things which it binds together; and to effect this in the fairest manner is the natural property of proportion. 2

The context of this passage is an attempt to explain water and air as intermediary between fire and earth, but what Plato is giving us is more general: a theory of participation which has been the root of the western tradition in art and architecture ever since:

For whenever the middle term of any three numbers, cubic or square, is such that as the first term is to it, so is it to the last term - and again, conversely, as the last term is to the middle, so is the middle to the first.

- then the middle term becomes in turn the first and the last, while the first and last become in turn middle terms, and the necessary consequence will be that all the terms are interchangeable, and being interchangeable they all form a unity. 3

Why is it a necessary consequence that all the terms are interchangeable? Each of the terms bears a relation to the others, a proportionate similitude, and each can become first, middle and last terms in an extended sequence, but they are not the same as each other. They are conjoined with one another, but in sequence. They bear likeness to each other in the proper sequential order but not otherwise. It depends on the arrangement. Given the proper arrangement, one may pass through the sequence and establish degrees of similitude between all the different terms. But they are still not the same. They participate in each other, but their proportionate similitude is not identity, and that is essentially what Plato is claiming here.

I think that there is no doubt that this is what Plato means, and it is up to us to explain it. Clearly it underpins the description of the activity of the philosopher in the Republic, where it is said that the process of argument:

...treats assumptions not as principles, but as assumptions in the true sense, that is, as starting points and steps in the ascent to something which involves no assumption and is the first principle of everything; when it has grasped that principle it can again descend, by keeping to the consequences that follow from it, to a conclusion. The whole procedure involves nothing in the sensible world but moves solely through forms to forms, and finishes with forms. 4

What Plato is arguing is that, by systematic dialectical enquiry, we can rise from the realms of likelihood and opinion, where we encounter only similitudes, to the realm in which certain knowledge is possible. This is to be achieved by passing through the similitudes, on account of their similitude, to their ultimate origin, the Form of the Good.

End of the section from SHB. When Plato speaks of ‘something which involves no assumption and is the first principle of everything’, he is speaking of the root of creation, as well as an intellectual apprehension of Reality itself. Plato sees a parallel between the acquisition of knowledge of what lies behind the world of appearance, and the inverse process by which that world of appearance is created, though he speaks only of an intellectual descent: ‘when it (the mind) has grasped that principle it can again descend, by keeping to the consequences that follow from it, to a conclusion. The whole procedure involves nothing in the sensible world but moves solely through forms to forms, and finishes with forms.’

Another section from SHB, which explores the attempt to define what Reality itself is in the Sophist:

… the ideas, formerly aloof from the world of sensibles and incapable of interaction turn out to be entities capable of participation in each other. And thus, like objects apprehended by opinion, are compounded both of Being and Not-being.

At 244c the Eleatic stranger asks whether the Real is "the same thing as that to which you give the name one? Are you applying two names to the same thing...?" And continues: "it is surely absurd for him Parmenides to admit the existence of two names, when he has laid down that there is no more than one thing..." Thus in attempting to define the One Parmenides cannot state it at all "without recognising three real things." 5

At 244d the Stranger questions the notion of the reality as wholeness: is "whole" other than the one real thing or identical with it? For

... if it is a whole - as indeed Parmenides says 6 "Every way like the mass of a well-rounded sphere, evenly balanced from the midst in every direction; for there must not be something more nor something less here than there" - If the Real is like that, it has a middle and extremities, and consequently it must have parts, must it not? 7

The Stranger observes that if a thing is divided into parts it may have the property of unity in terms of an aggregate of its parts, "being a sum or whole". However, "the thing which has these properties cannot be just Unity itself... Unity in the true sense and rightly defined must be altogether without parts." 8

Thus, how are we to define the Real - is it one and whole? The property of unity is not unity itself, and alternatively, if the Real is not a whole by virtue of having this property of unity, while at the same time Wholeness itself is real, it follows that the Real falls short of itself... and further... all things will be more than one since Reality on the one side and Wholeness on the other have now each a distinct nature. 9

The Real cannot come to be if wholeness does not exist, for "whenever a thing comes into being, at that moment it has come to be as a whole; accordingly, if you do not reckon unity or wholeness amongst real things, you have no right to speak of either Being or coming into being as having any existence." 10 The Eleatic stranger (probably representing Plato himself) concludes by observing that "countless other difficulties, each involved in measureless perplexity, will arise, if you say that the Real is either two things or only one." 11

In the Timaeus the fully knowable is defined as the eternal and the unchanging, i.e., that which fully "is". However the discussion at Sophist 248-249d seems to jettison this definition. The Eleatic stranger observes that the Idealists (the "Friends of Forms," 248a) distinguish between "Becoming" and "Real being": the definition of the former involving the sensible world, and the latter communing via the soul through reflection. And whereas Real being is defined as unchanging, Becoming is subject to change (the word used is koinonein: "to be in touch with". The same word is used of our communion or participation with both change and the changeless).

The Eleatic stranger recalls an earlier proposition that the "sufficient mark of real things is the presence in a thing of the power of being acted upon or of acting in relation to however insignificant a thing." 12 The Friends of Forms do not accept this argument and reply that: "a power of acting and being acted upon belongs to Becoming, but neither of these powers is compatible with Real being." 13

Thus apparently is distinguished the material world subject to causal relations from the world of Forms and those objects which participate in them, clearly by acausal means; the division would seem to be absolute.

The Friends of Forms acknowledge that the soul knows, and that Real being is known, it is agreed; and then the stranger asks if it is agreed that

knowing or being known is an action, or is it experiencing an effect, or both? Or is one of them experiencing an effect, the other an action? Or does neither of them come under either of these heads at all? 14

It can of course be neither action or effect, as the text makes clear, 15 if the Friends of Forms are to avoid contradicting their earlier remarks, for: if knowing is to be acting upon something, it
follows that what is known must be acted on by it; and so, on this showing, Reality when it is being known by the act of knowledge must, in so far as it is known, be changed owing to being so acted upon; and that, we say, cannot happen to the changeless. 16

Cornford's translation of the remainder of 248e is unsatisfactory, since it obscures one of the most interesting allusions in Plato. It may be translated thus:

Before God - that we might be easily persuaded that truly motion, life, soul and wisdom are not completely real - neither life itself nor thought, but revered and sacred, it has no mind, if it put on existence unmoved. 17

The allusion, semnon kai hagion, is, as Campbell noted in his edition of the Sophist, to the statues of the gods. This phrase might be written off as of no great moment, but I think it unwise to do so. Reality has been spoken of as revered and sacred, using a phrase of specific application to the images of the gods. We catch here (I think) a glimpse of the true scope of this argument and its consequences: it concerns the logic underpinning the patterns of understanding among the Greeks. 18

End of this section of SHB. The absurdity of the argument concerning the gods (that they cannot move) in Aristotle’s Nicomachean Ethics (discussed elsewhere) is now perfectly clear. What is being discussed in the Sophist is the nature of a Reality which completely transcends the world of appearance, and so can be considered to be the root from which the physical creation emerged. This reality is the telos; the Ur-Reality. Its nature, properties and attributes have been established by logical argument. The result however is paradoxical. It must remain one to be itself (elsewhere Plato ‘conjectures’ that the world of appearance is a copy of the Ur-Reality. That too cannot be the case, without compromising the nature of the Ur-Reality). It cannot move because it is the undifferentiated all. But without movement there is no mind. Without movement there is no life.

Yet there is thought and life. So at the least, the created world enshrines a paradox.

1 This phenomenon is discussed in Leibniz, Mysticism and Religion, ed. by Allison P. Coudert, et al, Kluwer, 1998.
2 Tim 31b-c
3 Tim 31c-32a
4 Rep. 511b-c
5 Cornford, F.M. Plato's Theory of Knowledge, p221.
6 Frag. 8.43
7 244d-e
8 245a
9 245c
10 245d
11 245e
12 Soph.248c.
13 Soph. 248c
14 248d
15 There is a minor textual problem concerning the identity of the speaker at this point in the dialogue which does not affect the sense of the argument - see L. Campbell, Sophistes, p128
16 248e.
17 Soph. 248e-249a. Lewis Campbell comments, in addition to noting the allusion to the statues of the gods, that there is a striking passage in the Laws (967 a-e) ‘where it is said that the deepest study of astronomy, instead of encouraging the notion of a blind necessity, leads directly to the supposition of a celestial mind or minds.’ Sophistes and Politicus, Oxford, 1867, p129. Reprinted by the Arno Press, New York, 1973.
18 We are not generally accustomed to imagine that belief is something for which sound arguments can be supplied, though christian religious history provides numerous examples of the use of philosophy to support the foundation of these.

Thursday, 4 February 2016

Physics and the Origins of the Universe (I)

Most arguments in physics take for granted a frame of space and time, and the reality of physical existence. Such things need to be explained, not assumed for the purposes of description and analysis. Otherwise physics is a multi-million dollar parlour game (I stood inside the fantastically complex Atlas detector in CERN three times, while it was under construction. The cafeteria cutlery was magnetised, which was impressive).

I covered a wide range of subjects in writing The Sacred History of Being (hereafter ‘SHB’ as my friends now generally refer to it). Not everything the book explores is reflected in the blog postings however.  This range is not the consequence of a lack of focus, but because the implications of the core argument impact on many subjects, including logic, mathematics, physics, cosmology, religion, etc. I was also interested in why we had arrived at where we are, culturally speaking, so that the central argument of SHB can seem to be without meaning.

There are two principal logical modes present in antiquity:  Aristotle’s laws of thought, upon which most everything since has been built, up until the late nineteenth and early twentieth century (things became interesting with Cantor’s work relating to the infinite and transfinite groups, and with Russell’s paradox). And the other is a mode of logic present in Plato, but also connected with Pythagoras, and with the Babylonians, from whom Pythagoras is supposed to have received it, when he was present at the fall of Babylon in 510 BCE. The second modality has not been the focus of thorough scholarship over the past two hundred years, and is scarcely recognised for what it is. These two modalities are so different from each other, that they provide radically different understandings of the world. Taking account of the second modality was a major part of SHB. I still haven’t dealt with it properly.

We have turned our understanding of the world upside down during the past three hundred years in the west, without really knowing what we were doing, and what the consequences would be. What that means is that the ancient picture of the world was always built on the idea that there was a question behind its understanding. That question is one which has often been repeated since – it is ‘why should there be anything rather than nothing?’ The question goes nowhere in the modern world, because we have no way of answering it.

In the ancient world, a possible answer would be that our physical reality exists as part of a plenum; as a consequence of the reality and the properties of that plenum. Arthur Lovejoy wrote a book on how important that way of looking at reality was for the history of western culture from the ancient Greeks up until relatively recent times (The Great Chain of Being, published in 1936). In a sense SHB is designed to knock the bottom out of the notion that the idea of a plenum, a plenitude, or Being itself, began with the Greeks. It used to be the natural place to start. Now our understanding is different. A premise of the argument is that the idea can be traced back at least until the 14th century B.C.E. So I wrote a kind of prequel to Lovejoy’s book.

Why a plenum? The power of this idea is that it allows us to accept that there is nothing, rather than anything, at the root of our reality. It is just that it so transcends the common sense idea of nothing, in that it is neither something, nor nothing. It has no presence, and no absence: it is just what it is. A field of possibility, if you like. Undefined, and without limit.

This is the essence of the teleological world view, in which the end and the beginning, the idea of limit itself, is a matter of some significance. This idea was dominant in antiquity. It is very prominent in Aristotle’s writings, but he did not invent it. Solon expresses the idea very clearly in the account of his conversation with Croesus in Herodotus, some two centuries earlier. It underpins the Assyrian picture of the world, and also the Babylonian account of the creation, as expressed in the liturgy of their New Year Festival, the Enuma Elish (‘When on High’).

Originally the idea of the telos was intimately associated with the gods, and with religious cult. The gods were understood to be a product, a consequence of the telos, and of the initial plenum. Later, this association was less well understood, so that the concept of the telos became reified into an intellectual frame in which things had purpose, function, and value (one of my teachers of philosophy once said that ‘a teleological universe is one in which fact and value interpenetrate’, meaning that everything has a meaning in such a universe). For Aristotle, in his writings, everything was ‘rowing towards its end’. Without the idea of an initial plenum, the idea of the telos is insupportable and without meaning. It isn’t a secular idea, though nevertheless it does have a range of presences in time and space, since reality does not adjust itself to suit our point of view. If it is there, it continues to function.

We have let all of the transcendent nature of the telos slip, and we deprecate what we currently understand as teleology, outside religion, poetry and literature, because it is a view of the world which sees purpose and direction in processes and things, which cannot be present. It has for us no meaning, no significance. It lasted longest in biology, perhaps because of Aristotle’s massive legacy for the study of the subject, but it is now nowhere to be seen in any of the sciences. At least not explicitly.

I could take an excursion here into Aristotle’s doctrine of the four causes, since we are talking about the final cause. I will stay on course by saying that one of the four causes is the efficient or physical cause. This is now, since Newton, the only cause the west recognises. This is physical force, physical determinism, energy, power, action and reaction, etc. Why only the efficient cause? Because Newton made such a good job of his explanation of the universe in terms of the mathematical description of the consequences of physical force, and of inertia. His work was so profoundly impressive that even the Divines wanted to be part of the new dispensation, in which the universe could be understood in terms of a certain uniformity, a clockwork precision. They presented this uniformity as evidence for the existence and controlling power of god, which was not of course Newton’s intention. This uniformitarian view of the universe has persisted (in various forms) until the present day. The efficient cause rules.

So, when a physicist or a cosmologist is asked: how did the universe come into being, it is hard to give any kind of answer beyond the ‘Big Bang’. The efficient cause always presumes a mover, and when the beginning of the universe is considered, there is no obvious prime mover. And in any case, identifying a prime mover simply moves the question of the start another stage back (‘it’s turtles all the way down!’).The idea of the ‘Big Bang’ exists only because an expanding universe suggests that a primordial explosion might have taken place. It’s an inference. It isn’t a very sophisticated notion, and doesn’t have exclusive explanatory rights. Why did it explode?  What was there to explode, and why was it there? What was there for it to explode into?

The questions have expanded, without the possibility of answers, which is often a sign that the critical model in which something is being examined is crippled.

We can conceive an alternative kind of physics which considers initial cosmological conditions, the idea of creation, the properties and attributes of the plenum and of the creation of visible reality, and the implications of the two opposing logical and inferential frames promoted by Plato and Aristotle.

I’m drawing up something on Plato and Aristotle’s respective modes of logic. I outlined Plato’s views on the logical relations of the Forms with each other in SHB (he’s only interested in the abstract cases), but I haven’t written much about Aristotle’s laws of thought. We think of them as enshrining common sense. 

But Aristotle practiced sophistry (he wrote a text on sophistical refutation - De Sophisticis Elenchis). What he is saying therefore depends on the context in which he is saying it; on who he is talking to and why. Aristotle’s writings on the soul (De Anima) mirror Plato’s closely, which suggests that they are not far apart in their understanding, but chose to come to different conclusions elsewhere. The absurd conclusion of the Nicomachean Ethics, where it is concluded that the gods are unmoving, and limited to contemplation, is a case in point. It would have looked profoundly odd at the time, since it means that the gods cannot act.