Monday 29 November 2021

Spirituality, Philosophy and Psychedelics


Thomas, long time no hear. I was curious to get your take on something that I'm not sure what to make of, intellectually and emotionally: the increasingly popular idea that Western spirituality, but more concretely, Greek spirituality is rooted in psychedelic experience. It seems that the Eleusinian mysteries in particular are now being identified as quasi-mushroom cults, while Shamanic transformation is also more and more considered a product of substance use. Again, not sure what to make of it. I mean, would there be no Plato, Empedocles or Pythagoras without mushrooms? Is that the idea? Strange. Anyways, hope all is well. Johannes

...........,

Sorry for the delay in replying. I don't think that Greek spirituality is rooted in psychedelic experience, though you are right that scholars are trying to identify the opposite to be the case. They've been doing this for years, and particularly since the sixties. That's anthropology for you: just imagine how it must have been, rather than read the texts carefully. 

It is true that the ancient Greeks and Romans used drugs as part of religious ritual in some cases (there is a contributed chapter by Robert Graves in William Sargant's 'Battle for the Mind', which is worth a read) But that does not mean that religion or spirituality emerges from the use of psychedelics. The point of using drugs enables those who run the rituals to show that what you think you understand and what you think you see might be quite different. That was the significance of drug use all the way up to the romantic poets and beyond. Trying to understand Plato, Empedocles and Pythagoras  as the product of the use of psychedelic mushrooms however is a complete joke.

Hope this is useful.

Best, Thomas 

Sunday 25 July 2021

The Knower and the Known

 


A few years ago I had a disturbing conversation with an Egyptologist I'd known for many years. I'd mentioned a comment I'd made in public about the Pharaoh Akhenaten, to the effect that his heresy was no longer as unfathomable as it once seemed to be. Then, out of nowhere, my qualities as a scholar were attacked, with arguments which had no foundation at all. She knew me well enough to know that her charges were baseless, but nevertheless, the charges were made, and with force. 

One of the most puzzling experiences I've ever had. Though I'd seen the Egyptologist let fly in such an irrational way at a blameless librarian at the Oriental Institute in Oxford, years beforehand. 

I rebutted the charges on the same day. I wrote the following letter to her a week later (for which there was no reply), which represents my attempt to understand the nature and origin of the strange exchange we had. I have removed all names, except my own, and there is nothing in this text which identifies the recipient. I've made a couple of minor rewordings, but the argument of the letter is as it was. 

This letter has echoes in the text and theme of The Sacred History of Being' (aka SHB), where certain modes of irrationality are discussed. The relationship between the knower and what is known is one of the subsidiary themes of the book. This letter brings that theme to more prominence. 

***

Dear …….,

Hi. I've covered a lot of intellectual space over the past eight or so days, which has been a bit like a personal apocalypse. I'll try to keep it short. It will look a bit strange, but please bear with it.

It is one thing to write about a phenomenon: it is another thing to have it happen for real in front of you, and more than that, to realise what it is.

SHB is about a number of things, but one of the underlying themes is the ancient idea that knowledge is about the union between the knower and the known. This is an idea which exists within the frame of the idea that the divine is the source of all knowledge.

Since within this frame the divine is by definition unknowable as a complete entity, it can be accessed only in part, and through various forms of approach. Hence ritual and liturgy, hence images, etc.

These forms of approach can be through the gods, through the properties they exemplify. Using the Catholic model as an example, it would be via the saints, who are beatified according to their character and quality, etc.

In SHB I have argued that it is the contemplation and worship of the special excellences of the gods, often described in liturgical documents, which allows access to knowledge. Or at least that is how it was understood. I've argued this on the basis of Greek philosophical discussion, and according to Assyrian and Babylonian documents and liturgy.

This is the transactive route, in which the knower starts as separate from what is knowable. It is transitive in nature.

There is evidence from Mesopotamia however that the union of the knower and the known is sometimes intransitive, and not the result of ritual, or any kind of rational or intellectually reasoned process (though it may be built on such things). I'm thinking in particular of an account of a Mesopotamian temple official suddenly falling down and then speaking in another voice. The voice was of a Mesopotamian god. He spoke in the voice of more than one god during the occurrence. So it was understood that there was sometimes a subsurface connection between the knower and the known, and that sometimes there is no process involved - no invocation, no ritual, no inquiry, etc. The god is immanent. At least temporarily.

And the phenomenon doesn't have to be as dramatic as that: it can happen without anyone being aware of it - at least at the time.

One other thing: when this intransitive immanence is in place, the nature of conversation with the individual concerned necessarily changes. It isn't inquisitive. It is authorative. Or at least that is how it plays. Plato wrote about this phenomenon, rather coyly.

You should understand that my background, education, and inclination, is essentially empirical, and that I don't have a natural affinity with these concepts and ways of understanding the world. I'm a child abroad. SHB came about originally through the observation of evidential details which didn't fit the mainstream understanding of ancient ritual, art and thought. I found that close attention to the detail and argument in ancient sources provided a number of alternative ways of framing the  evidence, while doing less violence to that evidence.

This remoteness from the way of thinking sometimes results in a first reading of evidence being in some way faulty. I tend to operate on the basis that this is inevitable. 

***

You have retained a formal relationship with a religion, unlike me. I took the rather nihilistic approach of abandoning all relationship with religion when I found that none of them provided enough answers to what I assumed were important questions. Yours is probably the smarter choice. Though I have not been immune to religious experience despite having no intellectual affiliation with a formal religion.

I am now guessing. I'm guessing that you have had, at least once, an experience of some kind of contact with the divine (let's call it that here without getting more particular). This might be in one or a number of forms. Maybe by speech, maybe by consciousness of a moment of immanence. Or by a grasp of meaning beyond strictly reasoned thought. The detail of the mode of contact isn't important.

Some people are just better plugged in than others. I never thought of you like that before, though I did get an intimation of it at the time your first child was christened. The whole thing seemed to make much more sense to you than I could understand. But I was a million miles away then from where I am now, in terms of capacity to understand what is important. As I said, I am a child abroad.

***

I can see the trail of thoughts I had during the past few days, and can see now that I was going to get to where I got to last night, if I kept going. I kept going.

I needed to shift to another perspective on our exchange on Christmas Eve, which was maddening on a number of levels. It was as if I was not talking to you, but someone else, who knew more or less what you know. And whoever that was, was not directly talking to me, but past me, without a proper grasp of who I am, or any proper recall of anything I've said, and without any care as to how I would respond.  The order in the exchange was also disturbing. 

[…]

It looked as though I was being distantly engaged in a more or less disorganised discussion about the discipline of Egyptology, conducted in as few words as possible. A discussion not entirely aimed at me, since I am not wholly known by you (of course). But spoken with certain knowledge, as happens when the knower and the known (you and your discipline) have no intellectual distance between them, whether temporarily or permanently. This continued after the initial exchange was over, with (for me) the patently absurd advice about going mainstream (heterodox arguments never have that option!).

There are gods of Egypt, and gods of Egyptology. They are not the same. The gods of Egyptology are those of the discipline. The excellences of the discipline that is, as understood.

I seem to have been having an exchange with some of your gods. They brook no quarter. Why should they, since they know?

I've come to the conclusion (slightly unwillingly) that there is more to this idea of contact with, and participation in the divine (temporary and permanent) than I used to think.  And that it explains a lot of curious things. Even in what appears to be everyday life. It is just that there is no rational space for the idea in the modern world.

There is much more that could be said, but I will leave it there for now. Does this make any sense to you?

Best,

Thomas

July 25, 2021

Thursday 1 July 2021

Free books by Thomas Yaeger, from Smashwords during July




(This offer is now closed. Thanks to everybody who downloaded copies of my books).

13th annual July Smashwords Summer/Winter sale, running July 1 through July 31. Starts at midnight Pacific Time. Sale now open! All my books are free during the month. https://www.smashwords.com/profile/view/tpyaeger


Tuesday 27 April 2021

A Timeline of Texts



My intellectual history is quite complicated. I wrote half a million words between 1986 and 1989, very little of which is currently available (but all of it indexed). Meditations on the Egyptian Ka and Coelum Terrae were both written on an IBM golfball typewriter in 1988, but most other stuff was written in longhand.  A study of Henri Frankfort's view of Parmenides is however available in longhand on this site. 

I was always focussed on ancient history, but I spent a long time studying the English and Italian renaissances as well, which taught me many things which were useful in the study of antiquity. Particularly how to read images.This work was done before I went off to study at UCL in September 1989-92.

I was writing before the advent of a useful internet, and Tim Berners Lee’s World Wide Web. I was aware that what I was writing was not fitted to the contemporary market (which is what most writers and scholars write for these days). This is part of the explanation for the sequence of the following list.

 In 1993, who was going to publish J.G Frazer and the Platonic Theory of Being? Frazer had been heavily criticized since his death, but no-one was looking at his work from my point of view. Most scholars would have agreed with Frazer’s view that a reductionist interpretation of Plato was the right one, even if they disagreed with his methods, and sometimes his interpretations. So that book was finished (over many evenings) in a third floor office in Devonshire Street, London, in 1993, and then parked, because there was nothing I could do with it. For a while at least.

I first gained access to the Internet and the Web in March 1994, at the computing services building in Oxford..I'd learned about what was now possible through a number of Internet magazines on sale in the Science Fiction bookshop in Oxford Street. After that I was always looking for Internet related jobs. I ended up working in Oxford on a Leverhulme funded project focussed on making an author's work available via the web. I wrote a report for the funders and the stakeholders, which mentioned in passing the copyright issues which would arise. That pretty much killed the project as it was originally conceived. But I’d learned a great deal along the way, including how to get Mac files into Word files.

I then moved to a newly minted Encyclopedia company in plush modern offices in South West London, where I built their first proper website. It was an odd sort of company, which attracted the attention of the UK government by not having any visible income at the time. It did eventually get a return on the project, but was initially bankrolled by a member of the government in the United Arab Emirates. I spent a couple of weeks in the UAE along the way.  

In 1997 I moved to the University of Bath as an internet magazine editor and scribe, as well as a manager of web pages and builder of websites. All the staff had personal webspace available to them. I created a website focussed on a well-known poet, and built it up over a few years. It was in existence from 1998 to 2005. Lots of traffic, and questions from students. The files still exist. 

Then in late 1998 I decided to make the book on Frazer available on the Web, partly in response to a request from a Catalan friend, who was (and is) an anthropologist. I didn’t get much feedback from him, which was disappointing, but the access statistics (which I still have) were pretty good. My future course was set.

After that I spent eight years or so as a project manager in Edinburgh, mainly working on institutional repository development, including business analysis and system design. I departed the university in July 2013 in order to write full time.  

Here's the production sequence:

  

Henri Frankfort (et al) on Parmenides. 1987 Unpublished

Meditations on the Egyptian Ka 1987. Unpublished

Coelum Terrae 1988 Unpublished.

Mirrors of the Divine 1991-2 Unpublished

J. G. Frazer and the Platonic Theory of Being 1993. Unpublished on completion. This version was available on the web in html format between New Year’s Day 1999 till September 2005

Magic or Magia? Plato’s Sophist 1994 Unpublished on completion. Available on the Web from 2018 in jpeg format.

The Sacred History of Being 2003-5 initial draft. Unpublished.

Ontology and Representation in Assyria and The Ancient Near East 2005-9. Unpublished.

The Sacred History of Being 2011-14 Published as an ebook in November 2015

J. G. Frazer and the Platonic Theory of Being. Published as an ebook in 2016

Understanding Ancient Thought Published as an ebook in 2017

Man and The Divine Published as an ebook in 2018

Echoes of Eternity Published as an ebook in 2020 (contains a revised version of Mirrors of the Divine plus many other essays written between 2004 and 2020)

Meditations on the Egyptian Ka. 1987 Available on the web in jpeg format in 2020 

Henri Frankfort (et al) on Parmenides. 1987  Available on the web as jpeg files, 2017

Ontology and Representation in Assyria and The Ancient Near East 2005-9. First section published 2021

The Death of Pan  Publication as an ebook in 2021 

The Keys of the Kingdom..Contains new material and revised chapters from The Sacred History of Being 2015, and from later books. Publication as an ebook in 2021.

Items marked in orange are publicly available in some form.Try searching on this site. A number of chapters and articles are also available from institutional repositories, often full-text.

Sunday 25 April 2021

The Tedium of Immortality


Episode nine in the BBC R4 series (2016) 'A History of the Infinite' by the philosopher Adrian Moore) begins with a scene from the opera ‘The Makropulos Case’ by the Czech composer Janáček. The premise of the opera is simple: more than three hundred years earlier the heroine of the opera, Elina Makropulos, was given an elixir of life by her father, the court physician. She is now nearly three hundred and fifty years old. She has reached a state of utter indifference to everything, and her life has lost its meaning. In the opera excerpt she sings a lament: ‘Dying or living it is all one. It is the same thing. In me my life has come to a standstill. I cannot go on. In the end it is the same. Singing, and silence.’ Makropolos refuses to take the elixir again, and dies.

The opera raises some profound questions, about life, about death, about purpose, and about our finitude. But how should we understand our finitude? Human finitude has many facets. We live in a reality, which for the most part is quite independent of us. We are limited in what we can know, and in what we can do, but importantly, we also have temporal and spatial limits. Though it isn’t entirely clear what those actually are.  Moore asks, as an example, if he began to exist when he was born, or if he was himself when he was still a foetus. Another question concerns how big he is. He gives his dimensions and weight, but points out that you could cut his hair off, or even amputate his legs, without destroying him. Some philosophers would argue that who a person is, is represented principally by the brain of the individual in question.  And other philosophers might argue that we are not physical entities at all.

In any case, it is clear that human beings are not infinite in size.  And, unless there is an afterlife, there will come a time when we no longer exist. Is the prospect of our annihilation something we should fear, deplore, and does it reduce our lives to meaninglessness? The Greek philosopher Epicurus did not believe in an afterlife. But the Epicurians did not fear or deplore death. They did not see how they should be affected by something they would not be around to witness. They were of the view that death was not an evil to us, since we were not around to witness it. Lucretius, also an Epicurean, reinforced the point by saying that we didn’t exist before we were born, and the fact that we won’t exist after we are dead, is just a mirror image of that. Lucretius asked, ‘is there anything terrible there? Anything gloomy? It seems more peaceful than sleep.’

The twentieth century philosopher Bernard Williams went even further. Rather than dwelling on the innocuousness of being dead, he dwelt on the awfulness of being perpetually alive. He wrote a famous article which took both its theme and its title from the Makropolos Case. Its subtitle was ‘reflections on the tedium of immortality.’ He argued that a never-ending life would become what Elina Makropulous’s life had become – tedious to the point of unendurability. For Williams, it was about whether or not you could have a life of your own, if you could live for eternity. If you are going to live for eternity, it would seem that you would need to keep finding new things to do, or new ways to be satisfied doing the same things again and again.  Williams’ argument is that you can only talk about such a life as your own life if you remain reasonably close to how you started out. In other words, can it still be your life if it goes on for eternity? Williams’ answer was ‘no’. 

For some philosophers, it is straightforwardly obvious that annihilation, followed by nothingness, is a great and uncompensated evil. Moore quotes the American philosopher Thomas Nagel, who writes that being given the alternatives of living for another week or dying in five minutes would always (all things being equal) opt for living another week. If there were no other catastrophe which could be averted by his death. Which Nagel interprets as being tantamount to wanting to live for ever. He wrote that ‘there is little to be said for death: it is a great curse. If we truly face it, nothing can make it palatable.’ Moore suggests that the opposing points of view of Williams and Nagel may be the consequence of a temperamental difference, as much as an intellectual one.  Nagel also suggested the possibility that Williams might have been more easily bored than he is. Moore says this might have been the case. 

Wednesday 21 April 2021

Calculus and the Infinitesimals: 'The Ghosts of Departed Quantities'

 


In this  episode of Adrian Moore's 'A History of Infinity' (BBC R4, 2016), the subject is the nature and development of the calculus. It begins with the observation that to divide zero by zero, or zero into anything at all, makes no sense. If you know anything about the calculus, it is clear what is being talked about in this episode, but the way it is discussed is lacking in the kind of precise description you might expect. 
A train is used as an illustration. Travelling a distance of sixty miles over an hour means that the train had an average speed of sixty miles an hour. However, the train might have been travelling at a much higher speed for half of the journey, and have been delayed by signal failure during the second half of the journey. So if you measure the distance travelled and the speed at a particular point in the journey, the result may be misleading. If the time period measured is very short, say close to zero, and the distance travelled is close to zero, then you will know nothing useful about how fast the train is going, and how long it will take to complete its journey.  
Calculus enables the accurate measure of quantities which are subject to change (which is why the inventor of the calculus as we know it today, Isaac Newton, referred to it as ‘Fluxions’). The episode makes clear how important the development of the mathematics of change has been ever since, and that much of the modern world depends on the use of calculus. The term ‘integration’ makes no appearance in this episode. 
Much of the rest of the programme discusses the invention of calculus, and the bitter dispute which arose between Isaac Newton and the philosopher Leibniz, who developed a similar approach to the mathematics of change quite independently. Newton appears to have begun to develop the mathematics for ‘fluxions’ early on – perhaps as early as the 1660s. The chronology is not clearly established, but Leibniz may have developed his version some ten years later. 
Newton did not publish any information about the mathematics involved in the calculus until many years later, preferring to share a few details with his friends and colleagues. Newton was aware of Leibniz and his work, not least because he too was a member of the Royal Society. Eventually he wrote to Leibniz with some limited details of the calculus (Moore suggests that Leibniz could not have understood these details since they were in code). Newton became aware that Leibniz had developed similar mathematics to deal with change, and a long dispute ensued, mostly conducted via intermediaries. Leibniz was often travelling, and so correspondence sometimes took months to reach him. Newton launched attacks on the integrity of Leibniz, accusing him of plagiarizing his ideas. Leibniz was bemused by his attacks and the force with which they were made. But Newton had decided that Leibniz was his enemy, and that was that.
Eventually it was proposed that a report be prepared by the Royal Society to establish who had the prior claim to the invention of calculus. This sounds fair, except that the President of the Royal Society wrote the report, and the President was Isaac Newton. As Moore says, ‘not Newton’s finest hour’.
The philosopher George Berkeley makes another more substantial appearance in this episode, since he wrote a criticism of what he called ‘the analysts’ (The Analyst: a Discourse addressed to an Infidel Mathematician (1734)). His criticism was based on the general lack of rigour with which calculus was often used at the time, and argued that scholars who attacked religious and theological arguments for lack of rigour were being similarly careless. The criticism revolves around the limitations of the technique already  mentioned, when the quantities and measures chosen are too small to produce intelligible results.
The most famous quotation from this book describes infinitesimals as ‘the ghosts of departed quantities’. The book seems to have been aimed particularly at the mathematician Edmund Halley, who is reported to have described the doctrines of Christianity as ‘incomprehensible’, and the religion itself as an ‘imposture’. Moore references the fact that the technique of the calculus lacked technical rigour until the early nineteenth century, until the idea of the limit was introduced (in fact Cauchy, and later Riemann and Weierstrass redefined both the derivative and the integral using a rigorous definition of the concept of limit. But that is another story). 
Moore concludes the episode by saying that:
precisely what such precision and rigour show, is that the calculus can be framed without any reference to infinitely small quantities. There is certainly no need to divide zero by zero. What then remains is a branch of mathematics, which is regarded by many, in its beauty, depth and power, as one of the greatest ever monuments to mathematical excellence.

Tuesday 20 April 2021

A Sense of Divinity - Descartes and Kant


The fourth programme of Adrian Moore's 'A History of the Infinite' (BBC R4, 2016) discusses the views of Rene Descartes in the sixteenth century, and also the views of philosophers from the eighteenth-century Enlightenment. I haven’t added up the number of centuries of thought which have not been discussed at all, but so far argument has been drawn from the sixth century B.C.E. (Pythagoras) fourth century B.C.E. (Aristotle, Zeno), the third century C.E. (Plotinus), the 13th century C.E. (Aquinas), and the 16th century C.E. (Bruno). Which is a journey of around twenty centuries. 
It isn’t that there is nothing to say about the idea of infinity during those long centuries, but that where Moore is going determined his selection of evidence and argument. He wants to talk mainly about the role and history of infinity in mathematics and in physics, and the fascinating paradoxes and problems which later investigation has thrown up. And a little about religious faith and the infinite. The first episodes are therefore a necessary introduction to set the scene.  
As he puts it in the text introduction to this episode, 'we have arrived at a time where people think about these things as we now do.' A telling statement, which hints at the richness and strangeness of the unexplored territory between the sixth century B.C.E. and the sixteenth century C.E., and that most of it is best skipped over as quickly as possible. It also lets us know that he has a normative view of human thought, and that what he thinks is rational and reasonable is mostly to be found in modern times. His is the Enlightenment agenda, which he mentions during this episode. 
Descartes famous ‘Cogito Ergo Sum’ (‘I think therefore I am’) is mentioned in the context of Descartes massive reduction of all the ideas and beliefs which he could accept unequivocally as true. He engaged in this reduction in order not to rely on tradition and authority, but on the intellectual resources available to the finite human mind. The question of whether the infinite can be grasped at all by the human mind is discussed, since we cannot see it or touch it. It is hard for us to know it, because it is the infinite. Descartes is quoted as saying that you cannot put your arms around a mountain as you can around a tree. So our knowledge of the infinite is necessarily less intimate than our knowledge of finite things.  
In the next part, the relationship between Descartes confidence in his own existence and capacity to think (expressed in the ‘cogito’) and his understanding of the infinite nature of God, is less than clear. It is true that Descartes suggested that he might have an idea of an infinitely perfect, infinitely powerful God because God put that idea into his mind. That might be the case. Alternatively, it may be that you as a finite being do not have to have an intimate acquaintance with the infinite in order to understand what you are talking about.  
Moore does not use the expression which Descartes employed to explain why it was not necessary to have intimate knowledge of something in order to have a useful and intelligible idea of what it is. He used ‘clear and distinct’ idea to indicate when he had such a useful and intelligible notion of what he was talking about. Later, Bertrand Russell would reformulate the distinction between knowledge by acquaintance and knowledge by description (in his Problems of Philosophy). So, by ‘clear and distinct ideas’ about God Descartes is relying on a description of what is, which means that he could be sure what he meant, and that his idea of God was a rational idea.  
In fact, Descartes idea of his own finite reality was dependent on his certainty of the reality of an infinite God. If he could conceive of such a God clearly and distinctly, then it was likely that such a God was real. 
Moore skips on to the second half of the eighteenth century, mentioning Berkeley (‘there is no such thing as the 10,000 part of an inch’ is all that is said), and Hume also, in connection with the indivisibility of reality (the disappearing inkspot when seen from sufficient distance, which is a matter of perception and experience rather than indivisibility per se). Berkeley was an idealist philosopher, who held that the only reason the world is perceptible is because it is held in the mind of God. He also denied materiality, at least as a metaphysical concept. 
Finally Moore discusses a narrow aspect of Kant’s understanding of the idea of infinity. This final part of the episode represents a highly misleading understanding of Kant. 
Moore argues that Kant agreed with Descartes that we have a clear idea of the infinite (the nearest he gets to the Cartesian formulation ‘things which are clear and distinct’). But that our idea is limited to what we can experience and perhaps what we can invest faith in. Really? I don’t think it is.  Did Kant say that knowledge is confined to the five senses? And if we don’t understand knowledge this way, we leave solid ground and end up in metaphysics? That is what seems to be suggested at this point in the series. 
One of Kant’s principal interests was metaphysics, and how we apprehend things and have knowledge of them. Hume’s empiricism was one of the things which impelled Kant to write some of his most important works (The Critique of Pure Reason, and The Prolegomena to any Future Metaphysics which may Present itself as a Science). It isn’t the case that Kant thought our ideas are limited to what we can experience in terms of the senses, but instead what is intelligible to us is interpreted through the categories of our understanding. He sought to understand shape and form without these things being associated with form possessing scalar values and spatial angles, which are matters of experience. In that he was very close indeed to Plato’s understanding of the Platonic forms. 
Kant, a figure so important to the concept of reason, is quoted as saying that ‘I go beyond knowledge to make room for faith’. It is true that Kant had the idea that rational thought and reason did not have to exclude a life of faith. It had space in which to exist. But it does not mean that Kant thought that faith was important to the life of reason. For Kant, like Pythagoras and Plato, knowledge is not gained through knowledge of sensible things, but is acquired by the contemplation of things which have a transcendent reality. This isn’t something which everyone can do, or will ever be able to do. Since there is an equation between the Divine and the Infinite, what Kant is doing is leaving space for some sort of understanding of the Divine for those who will never have a genuine understanding of transcendental reality and the Infinite. He is not arguing that faith creates a functional connection with the Infinite.
Karl Lōwith wrote that, in his book Religion within the Limits of Reason Alone, Kant had
interpreted the whole history of Christianity as a gradual advance from a religion of revelation to a religion of reason…. It is the most advanced expression of the Christian faith for the very reason that it eliminates the irrational presupposition of faith and grace.    
Moore then turns to Kant’s conception of the moral law. Aspects of the life of the mind which put us in contact with the infinite are about our reason, our rationality. Our reason enables us to grasp the moral law, which gives us infinite dignity (since we are rational beings). He says that “the moral law is what ought to direct us in all we do, with infinite respect granted to fellow rational beings”.
Which explains little. The origin of Kant’s moral law may be the idea that the life of reason, and rationality itself (as he defined it) is about connecting with the infinite. If man is truly rational, then he is connected with the Infinite (the ancient concept of the soul, as discussed by Plato, is related to this idea). But we need to accept Kant’s understanding of what reason is, and not distort it by saying knowledge is obtained through the five senses. Through this distortion, what Moore is left with is the Calvinist notion of a ‘sensus divinitatis’ (sense of divinity).  Which is a poor substitute for the kind of engagement with divinity which was understood to be possible in the ancient world. Such engagement was not achieved through knowledge of the world of the five senses or space and time.

Monday 19 April 2021

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 19th September. The book is available in ePub format from leading retailers of eBooks, such as Barnes & Noble, Blio, Kobo, Itunes, Inktera, Smashwords, etc.

***

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 TimaeusThe SophistThe RepublicThe TheaetetusThe 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. 

Sunday 18 April 2021

Adrian Moore on Georg Cantor and the Size of Infinity

 



The sixth episode of Adrian Moore’s radio ‘A History of the Infinite’ is concerned with the infinitely big, considered not in terms of physical size, but in the context of mathematics. It focuses on the work of the German mathematician, Georg Cantor, who devised a way of distinguishing between different infinite sizes, and of calculating with infinite numbers. Cantor was the first to do such a thing.  One of the most interesting developments in modern mathematics, and as Moore says, his work was ‘utterly revolutionary.’ 

Everyone knows there is no such thing as the biggest number. No matter how far you travel along a sequence of numbers, you can always count further. Even Aristotle, who Moore suggested in an earlier episode was an arch-sceptic about the infinitely big, accepted the reality of the infinite only in terms of processes and sequences which were destined to go on for ever. 

This might be a little tendentious, since as Moore has already pointed out in the episode ‘Aristotle’s Rapprochment’, he divided the concept of the infinite into two things: the actual infinite, and a potential infinite. The world of numbers and calculation exists in the context of the potential infinite, in which change happens in space and time. The actual infinite, for the purposes of mathematics, is simply ignored, since it is (apparently) not possible to work with it. I make this point since there is much about Aristotle’s wider philosophical work which points to a strong concern with the actual infinite. He isn’t sceptical about the reality of the infinite.

Aristotle’s view prevailed for over two thousand years, and during that period there was hostility to the idea that the infinite itself could be the subject of mathematical study in its own right. This orthodoxy was not challenged until the late nineteenth century, when Cantor presented a systematic, rigorous, formal theory of the infinite. Moore is interested in what drove him, and at what cost.

Cantor had a very hard time in trying to have his ideas accepted by the mathematical community, partly because of the perception that there was a religious component to his work. Henri Poincaré said of his work that: ‘it was a disease, and there would be a cure.’ His teacher Leopold Kronecker, who might have been expected to support his pupil, was hostile to his work, and made it difficult for him to publish. Kronecker said ‘God made the integers, all the rest is the work of man’. Cantor suffered several nervous breakdowns, possibly because of the sheer perplexity of his work, and died in an asylum.

Moore now considers set theory. How do you count without actually counting, and know if a set or collection is the same size as another? You can assemble pairs of things, such as male and female, cats, dogs, etc. If they are paired, and there are no extra males, females, cats or dogs left over, then you know that they are the same size without counting the individuals in the sets.

Does this apply to the infinite? Cantor asked why not? But here things get a little weird. The set of what Moore refers to as ‘the counting numbers’ (positive integers) appears to be the same size as the set of the even numbers. Even though the first set includes all the numbers in the set of even numbers, plus all the odd numbers. If we want to show the number of counting numbers is the same as the number of even numbers, we can do this fairly easily by pairing the counting numbers with the even numbers which result from doubling them. There will be nothing left over, so we can say that these two sets are the same size as each other. Moore says that it is tempting to say that comparisons of size just don’t make sense in the infinite case. But Cantor accepted that they were the same size, despite the fact that the first set contained everything in the second set, plus more besides. 

Can we use this technique to show that all infinite sets are the same size, which might not be a counter-intuitive conclusion? In fact, some infinite sets are bigger than others, as Cantor discovered. Even if you start with an infinite set, it will always have more subsets than it does have members. You cannot pair numbers with the subsets: there will always be a subset left over. So there are different infinite sizes. Moore does not draw the conclusion that it is the unbounded nature of the infinite which makes the differently sized infinities true. What is infinite contains all things which are possible. It is not just something which is extremely large.

Cantor’s work polarized opinion in his lifetime, and it has continued to polarize opinion ever since. The mathematician David Hilbert famously said ‘No one shall be able to drive us from the paradise which Cantor has created for us’. To which Wittgenstein responded: 'I wouldn’t dream of trying to drive anyone from this paradise: I would do something quite different – I would try to show you that it is not a paradise, so that you leave of your own accord’

Moore concludes with a question: “Is Cantor’s work of any significance outside mathematics? Some would say that it is not. It certainly made its mark by creating as many problems as it solved.”

It can however be argued that many difficult questions are difficult for us as the result of an important concept dropping out of western philosophy, which is the concept of the plenum. This concept is not discussed by Moore in this series of programmes. The idea of the plenum is that reality itself is undifferentiated possibility, something which does not exist in time and space, but contains every possible aspect of time and space, and everything which might be contained in it as potential, as something which might be generated within physical reality. With the idea of such a transcendent reality, almost anything which can be imagined to exist, can have existence. But such things will inevitably point back to the nature of the initial plenum in some way, and be full of puzzles and paradoxes. In rejecting this view of infinity, and treating it as if it had no bearing on sensible reality, Aristotle and those who followed afterwards, effectively closed off the possibility of understanding why such paradoxes exist in the physical universe.

In the seventh episode there is a brief introductory recap, reminding us that Georg Cantor created a formal theory of the infinite in the late nineteenth century. The impact of his work on mathematics was large, and led to a period of unprecedented crisis and uncertainty. Subjecting the infinite to formal scrutiny, led to mathematicians confronting puzzles at the heart of their discipline. These puzzles indicate some basic limits to human knowledge.

Moore invites us to consider the issue of sets of sets. How can there be more sets of sets, than there are sets? He suggests at this point that our heads may begin to reel. But why shouldn’t we have, say the set of sets which have seven members? Enter Bertrand Russell, who, in trying to come to terms with some of these issues, arrived at what is known as Russell’s Paradox. He argued that once we have accepted that there are sets of sets, we can acknowledge sets which belong to themselves, and those which don’t. A set of apples is not a member of itself, for example, since it is not an apple.

The paradox arises in connection with the set of all sets which are not members of themselves. On the face of it, there should be such a set, but there is not. For the same reason that there cannot be a nun in a convent who prays for all those nuns in that convent who do not pray for themselves. This is a matter of logical rules. She is going to pray for herself, only if she does not pray for herself, which is impossible. Russell’s paradox seemed to indicate a crisis at the heart of mathematics, where sets play a pivotal role.

 Russell communicated his paradox to the German mathematician Gottlob Frege, which is a well-rehearsed incident in the history of philosophy and mathematics. Frege had been trying to put these mathematical issues on a sound footing in a three-volume work, which was two thirds completed. Russell’s paradox came like a bolt from the blue. Frege replied saying he was ‘thunderstruck’, since the paradox undermined his attempt to give a sure foundation to arithmetic, while he was engaged in writing and publishing his life’s work. Frege died embittered. 

Returning to Cantor, Moore discusses his work with the problem of the ‘counting numbers’, (1,2,3,4, etc), which constitutes a smaller group than the group of possible sets of the counting numbers. The question arose of how much smaller the first group was. Cantor’s hypothesis was that it was just one size smaller, and that there were no sets of intermediate size. But he was unable to confirm that this was the case, or to refute the idea. So he was in a state of uncertainty for a long time, and this exascerbated his lifelong problem with depression. This question was listed by David Hilbert as one of the 23 most important questions in mathematics to be addressed in the ensuing century. 

The matter is not settled, even now. Is this the result of mathematicians not being assiduous enough? Moore says that it has been shown that it is impossible, using all of the tools available to mathematicians, to resolve the issue. It looks as though we are stuck with an unanswerable question.  Perhaps not completely unanswerable, but it is with the toolkit of mathematical principles which are currently available. No new principle has been discovered in the decades since, so it looks as though we have stumbled on an inherent limitation on mathematical knowledge. 

The logician Kurt Gōdel showed that this limitation was in a sense unavoidable, in that, with a limited set of mathematical principles, there will always be truths which lie beyond their reach.

So there are many questions about the foundations of mathematics, and their security, or insecurity. Russell’s paradox of the set of all sets which don’t contain themselves, had revealed an inconsistency in the principles mathematician’s had been working with up to then. David Hilbert had said “how do we know there isn’t another inconsistency elsewhere in mathematics generating the problem?” He devised a programme to map mathematics with a limited but very precise set of principles, in order to discover if this was the case. Gōdel’s work however, made it unlikely that this programme would be a success. Is there a crisis in modern mathematics? It was suggested that modified versions of the Hilbert programme have proved that there are no other inconsistencies in basic mathematical principles. And that consequently the rest of mathematics is essentially reliable and consistent. Moore concludes that mathematical work on the infinite has left us acutely aware of what we do not know, and indeed what we cannot know

 



Tuesday 2 March 2021

The 'Hill of Many Stanes'




[An extract from a conversation with a correspondent in the US, from May and June, 2020, shortly after 'The Mathematics of the Megalithic Yard' was completed.] 

On Monday, June 1, 2020, 09:31:47 AM PDT, Thomas Yaeger [....] wrote:

[....], hi. Thanks for your mail. I'm going to respond to it in separate mails, since there is a lot to say. Interleaved, as usual (bad academic habit!)

At 06:03 29/05/2020, [....]  wrote:


Hi Thomas,
Sorry I haven't responded sooner. I've been working on a response to your article (& other emails) about the Megalithic Yard and didn' t want to write again until I had made some progress. I'm probably making it into too much of a project lol. [....} So, I'll send what I have for now (including other stuff I've been putting in a draft) and get it off to you. Sorry if it doesn't do justice to your arguments. 
[....] 
Your argument is very compelling and interesting. It seems like a real breakthrough although, naturally, I'm not enough of an expert to judge!

I think it is a real breakthrough, but it took a while to make it (as I said, the article was written in about a day and a half, after thinking it through for around two years). Developments are happening very fast now, which is interfering with my writing programme.


. I understand that math as such isn't the point of your argument, it's more about what Euler's number signified, right?

Yes. It's Euler's number, what it represents, and how they calculated it in the 2nd and 1st millennia BCE. I think I've changed my mind about how much Alexander Thom actually knew. I think he knew that it was a pointer towards the idea of the infinite. But he did not know that in those ancient days the ideas of the divine, the infinite, and reality itself were regarded as coterminous, and were just different ways of speaking about the same thing (which is an understanding which still survives in Hindu thought and religion). So for Thom, he could see the mathematics, but didn't understand the idea of reality itself as a primal fulness, or a plenum, and why that would engage ancient interest.

There is in Scotland a site near John O'Groats which is known as 'the hill of many stanes', which has remained uncleared since the neolithic. In the documentary he says he is impressed by what the builders of the circles were able to do without pen and paper, and logarithms. But that without such constructions (as the 'hill of many stanes') 'you can't really do it'.

What was he talking about in this short insert into the documentary? He doesn't explain what the small stones were for, or how they were used. I think I understand now that the field of stones was used to calculate Euler's number, in the context of an engineering construction. That site needs extensive re-evaluation.

Thom's book publications are very plain and not dogged with interpretation. I think he realised that what he could do, and get away with, was to draw attention to the fact that something very interesting and mathematically disciplined was happening in the Neolithic and Early Bronze Age, but the whole thing was just too big a pill to swallow for the academic community. He held back.


One thing that interests me is people's motivations, in particular, which of their psychological needs are being served by engaging in different courses of thought and action. I assume that people have always been curious about life and the world (some more than others, of course!), but what struck me about what you wrote is people's need for or a sense of order and structure in order to feel a degree of safety in a world that is challenging to fathom.

 It depends on where you are in society. Sometimes, as now people are told convenient lies (there is no money!), or circumspect evasions. Ancient priesthoods, because of their picture of the world, understood themselves to be dealing with the nature of reality itself. Neophytes would be chosen from all levels of society, since it was necessary to put a premium on intelligence, in order to join the worlds and make the incommensurate commensurate. Reality itself was the home of all knowledge, and all possibility. You can't deal with that without intelligence. The rest of society would have to make do with what Plato described as likelihoods, because they were too far from an understanding of reality.

Thom was not a classicist or a historian, so he did not know (as most modern scholars still don't) that ancient religion was about *knowledge* (scientia). The ancient priesthoods understood themselves to be dealing with knowledge, and that their activity was a science. That's all changed, but we continue to project modern religious intellectual weaknesses into the ancient past.

Thanks for the photographs.

More later,

Best,Thomas

Friday 5 February 2021

The Ontological Argument

 


[I've collected together all the chapters in The Sacred History of Being concerning the ontological argument. Most of what you need to know about the argument can be found here. It is still current among scholars, though it has many features which are problematic - these are discussed here at length. I've taken the opportunity to correct a typo which appeared in the published version. TY]. 

 

What is an ontological argument? In the introduction to Alvin Plantinga’s The Ontological Argument, written by Richard Taylor, the argument is defined simply as one which ‘purports to prove, simply from the concept of God as the supreme being, that God’s existence cannot rationally be doubted by anyone having such a concept of Him.’ He goes on to say that ‘it is thus a purely a priori argument, that is to say, one that does not appeal to any facts of experience but is concerned solely with the implications of concepts – in this case, the concept of God’.

 

Our modern understanding of the ontological argument is that it was first formulated by St. Anselm of Canterbury in the 11th century C.E. This is not disputed. But it is perfectly clear that some kind of ontological argument lies behind the arguments which are found in Plato’s semi-secularised discussions, in Aristotle (particularly in the Nicomachean Ethics), and, if Plato is to be considered an accurate historian of the views of Parmenides, also to be found in his dialogue Parmenides. What I intend to do here is to review the history of the ontological argument from St. Anselm onwards, and then to explore the likely nature of the ontological argument in antiquity. The range of questions which might be asked by a neophyte, or an advanced student, give many clues about the probable shape of such an argument. 


 

The Ontological Argument in Anselm

 

“Anselm… is rightly regarded as the inventor and perfecter of the ontological argument, though his philosophical inspiration was largely derived from St. Augustine. … His position is not that of a skeptic seeking some rational persuasion of God’s existence, but that of a believer seeking a single conception which would make manifest at once God’s existence and God’s attributes”.  [1]

 

The following is extracted from chapters 2-4 of St Anselm’s Proslogion, quoted from Alvin Plantinga’s The Ontological Argument. Plantinga takes his text from Anselm’s Basic Writings, translated by S. N. Deane, with an introduction by Charles Hartshorne, 2nd edition, 1962, Open Court Publishing Company.

 

Prosologion, Ch. II –

Truly there is a God, although the fool hath said in his heart, There is no God.

And so, Lord, do thou, who dost give understanding to faith, give me, so far as thou knowest it to be profitable, to understand that thou art as we believe; and that thou art that which we believe. And, indeed, we believe that thou art a being than which nothing greater can be conceived. Or is there no such nature, since the fool hath said in his heart, there is no God? (Psalm xiv. 1). But, at any rate, this very fool, when he hears of this being of which I speak – a being than which nothing greater can be conceived – understands what he hears, and what he understands is in his understanding; although he does not understand it to exist.

 

We might rephrase this thus: “Our belief is that God is a being greater than any other which can possibly be conceived. And it is this greatest of all beings which gives us understanding. A fool can understand the conception of this greatest of all beings as a conception, though he does not understand the existence of the greatest of all beings”.

 

This might be criticized by pointing out that two key elements in this argument are undefined. We have a definition of ‘God’ as the greatest of all beings.’ However we do not have a clear definition of the meaning of ‘greatest’ in this context, and neither do we have a clear definition of ‘existence.’ Both of these terms are made to do much work in this discussion.

 

For, it is one thing for an object to be in the understanding, and another to understand that the object exists. When a painter first conceives of what he will afterwards perform, he has it in his understanding, but he does not yet understand it to be, because he has not yet performed it. But after he has made the painting, he both has it in his understanding, and he understands that it exists, because he has made it.

 

Anselm makes it clear he understands the distinction between knowledge of a concept, and knowledge of the existence of something – in this case ‘God’. The illustration which he uses here is interesting. He likens the conceiving mind to the mind of a painter conceiving a representation of an object – before he begins to paint he has a conception in his mind of what he intends to paint, but does not understand it ‘to be’ ‘because he has not yet performed it’. But once the conception is painted, the painting has come to be (i.e., it ‘exists’).

 

However, a painter creates a representation by painting it, not an object itself. This is an important detail if the argument is designed to prove the ‘existence’ of God, rather than a physical object. It is fair to argue that the conception in the mind of the painter is also a representation, in that it is a conception rather than the thing itself. So the painting is a representation of a representation. The painting exists in the sense that it is a physical object existing in the world, containing an image which may or may not be a representation of an object which exists.

 

Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.

 

Rephrasing the first part of this, ‘even the fool can conceive that an idea in the understanding can be of something which is greater than anything other which can be conceived. He can understand this, and what is understood, has an existence in the understanding’.

 

It is true that the conception of something which is greater than anything other which can be conceived can be a concept, even in a foolish mind. But it does not follow that it is, as Descartes would say later on, a clear and distinct conception. ‘Great’ is a term which can mean many things, and to a fool, it is in the nature of foolishness for its meaning to be misunderstood.

 

Anselm then passes on to the suggestion that something which is greater than anything which can be conceived, cannot exist in the understanding alone. The reason he gives is that, if this conception exists only in the understanding, then to conceive it to exist in reality would be greater.

 

This requires deconstruction. If the conception, in the understanding of the fool, is unclear and indistinct, then it does not follow that what can be conceived in the understanding must exist in the world. If the conception is clear and distinct in the understanding of the wise man, does it follow that that which is conceived in the mind must also exist as a physical reality? The answer is no, in that, no matter how clear and distinct the conception of God is in the mind, it is a conception which describes what can be known or inferred of God by the mind of man. And man by his very nature, must participate in the quality of foolishness more than the quality of the divine.

 

A further criticism of this passage might be that ‘existence’ is used very loosely. Can we speak of God existing, rather than speaking of the reality of God? This is an important point if part of the definition of God is that the divine possesses a transcendent reality, rather than a physical one.

 

The only circumstance in which the concept of God in the understanding must also exist as a reality, is where that reality is transcendent - where the possessor of the understanding is also divine, and thus necessarily participates in the being of God through the clearest and most distinct understanding of the nature of God.

 

Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.

 

As already pointed out, that if there is a conception of that which nothing greater can be conceived in the understanding, and the understanding alone, it does not follow that there is no doubt that there ‘exists’ a being (or rather that a being of this nature has reality), and that it exists both in understanding and in reality.  J.G. Frazer suggested that Plato sometimes confused an epistemology with an ontology, and Anselm seems to be confusing the idea of naming, conceiving and describing a being with the necessity of the reality of such a being. Again, only if the scope of the understanding is as clear and distinct as the reality, would there be the impossibility of that understanding existing alone. And that is not a likely proposition. The ultimate nature of reality is always going to transcend our capacity to conceive of it, except in very special circumstances.

 

From Chapter III:

 

God cannot be conceived not to exist – God is that, than which nothing greater can be conceived. –That which can be conceived not to exist is not God.

 

And it assuredly exists so truly, that it cannot be conceived not to exist. For, it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist; and this being thou art, O Lord, our God.

 

Anselm has accepted his proof of the ‘reality’ of God, and is now building on it. I am not sure how one can argue that conceiving of a being which cannot be conceived not to exist, is necessarily ‘greater’ than one which can be conceived not to exist. Again, this only makes sense if the conception in the understanding is of the same nature as the being who exists in reality. He argues however that if the conception which is greater than anything which can be conceived, can be conceived not to be real, then it is not that which is greater than anything which can be conceived. And that this would be an irreconcilable contradiction. How so? We are talking in terms of the subjective powers of the mind here. In the mind of the fool, it is clearly possible to conceive in the understanding a being than which greater nothing can be conceived, and then to change opinion to that in which it can be conceived not to be real. But this is a fallible judgement, so for the most part this this does not throw up an irreconcilable contradiction.

 

So truly, therefore, dost thou exist, O Lord, my God, that thou canst not be conceived not to exist; and rightly. For, if a mind could conceive of a being better than thee, the creature would rise above the Creator; and this is most absurd. And, indeed, whatever else there is, except thee alone, can be conceived not to exist. To thee alone, therefore, it belongs to exist more truly than all other beings, and hence in a higher degree than all others. For, whatever else exists does not exist so truly, and hence in a less degree it belongs to it to exist. Why, then has the fool said in his heart, there is no God (Psalm xiv. 1), since it is so evident to a rational mind, that thou dost exist in the highest degree of all? Why, except that he is dull and a fool?

 

Anselm is here building on his conclusion that God cannot be conceived not to exist. It follows therefore that if a mind could conceive of something greater, that creature would rise above the Creator, which (to Anselm) would be ‘most absurd’. We can sense here that it is almost the case that the reality of the God he is discussing is dependent on whether or not the understanding of the believer is sufficiently acute to bring the God into being. But essentially here Anselm is looking for support for the faithful, and is not arguing for the power of an understanding of the divine, and of the word.

 

He argues that all other things excepting God can be conceived not to exist. This implies that they are part of the secular world rather than the divine reality. However the corollary is that the divine reality is qualitatively beyond mundane reality. But again, if the conception in the understanding of the faithful is less than perfect, then it does not follow that the conception of God cannot be conceived not to exist. And this would be true if the understanding was nearly at the highest degree of the spectrum which runs from foolish to wise.

 

From Chapter IV:

How the fool has said in his heart what cannot be conceived. – A thing may be conceived in two ways: (1) when the word signifying it is conceived; (2) when the thing itself is understood. As far as the word goes, God can be conceived not to exist; in reality he cannot.

 

But how has the fool said in his heart what he could not conceive; or how is it that he could not conceive what he said in his heart? Since it is the same to say in the heart, and to conceive.

 

But, if really, nay, since really, he both conceived, because he said in his heart; and did not say in his heart, because he could not conceive; there is more than one way in which a thing is said in the heart or conceived. For, in one sense, an object is conceived, when the word signifying it is conceived; and in another, when the very entity, which the object is, is understood.

 

In this fourth chapter it is as if Anselm has reflected on what he has written, and realizes he needs to deal with the objection that he is confusing (or conflating) an epistemology with an ontology. An object can be conceived in terms of words (what Bertrand Russell would say was ‘knowledge by description’), or in terms of a non-textual, intuitive understanding, (which Russell terms ‘knowledge by acquaintance’).

 

In the former sense, then, God can be conceived not to exist; but in the latter, not at all. For no one who understands what fire and water are can conceive fire to be water, in accordance with the nature of the facts themselves, although this is possible according to the words. So then, no one who understands what is can conceive that God does not exist, although he says these words in his heart, either without any, or with some foreign signification. For, God is that than which a greater cannot be conceived. And he who thoroughly understands this, assuredly understands that this being so truly exists, that not even in concept can it be non-existent. Therefore, he who understands that God so exists, cannot conceive that he does not exist.

 

Anselm acknowledges that in terms of description, a conception in the understanding may be imperfect, and consequently it is possible to conceive of the non-existence of God. But in terms of knowledge by acquaintance, to continue with Russell’s terminology, it is not possible to conceive of the non-existence of God. He uses the concrete images of fire and water, and argues that our understanding of those (which will include knowledge of their properties and characteristics), according to their differing natures, could not be be confused with one another; but that this might be possible in terms of their descriptions in words. He then argues that ‘no one who understands what is’ (i.e., what is real) can conceive that God does not exist, although it remains possible to express the notion in words, either words without signification, or with some signification which has no bearing on the question of the reality of God. He who has a thorough understanding of this, certainly understands that God so truly exists, that not even in concept can God not be real.

 

This is placing a great deal on non-textual and intuitive understanding. The fact remains that intuitive understanding can be as fallible and plain wrong as any other kind, and so Anselm has not made a watertight case for the reality of God. Though this is an argument which might please the faithful, who might be inclined to amplify their faith in line with what they believe intuitively to be the case. 

 

I thank thee, gracious Lord, I thank thee; because what I formerly believed by thy bounty, I now so understand by thine illumination, that if I were unwilling to believe that thou dost exist, I should not be able not to understand this to be true.

 

Richard Taylor writes that: “Anselm gives some background to how he came to construct his argument for the proof of the reality of God in the Proslogion.’ He was, he writes, seeking some single argument that would not only prove God’s existence but make evident God’s attributes as well. The central idea of the ontological argument, that perfection implies existence, kept forcing itself on him, but he rejected it as a specious and illusory basis for any argument until, finally, he realized he could find no rational ground for rejecting it any longer, whereupon he joyfully embraced it as providing the proof he had been seeking.”  [2]


 

The Ontological Argument in Descartes

 

The argument developed by Descartes differs from Anselm’s in a number of respects. He avoids the term ‘great’ (and notes the fact in the course of his argument). Instead he uses the concept ‘perfect’, so that God is described as the ‘supremely perfect Being’. He also uses variations on the phrase ‘clearly and distinctly’ in connection with his apprehension of the idea of God.  [3]

 

If just because I can draw the idea of something from my thought, it follows that all which I know clearly and distinctly as pertaining to this object does really belong to it, may I not derive from this an argument demonstrating the existence of God? It is certain that I no less find the idea of God, that is to say, the idea of a supremely perfect Being, in me, than that of any figure or number whatever it is; and I do not know any less clearly and distinctly that an actual and eternal existence pertains to this nature than I know that all that which I am able to demonstrate of some figure or number truly pertains to the nature of this figure or number, and therefore, although all that I concluded in the preceding Meditations were found to be false, the existence of God would pass with me as at least as certain as I have ever held the truths of mathematics to be.

 

To paraphrase: ‘If it follows that an idea in thought can be expressed, and all I know clearly and distinctly about it,  is the case, then may I not use this as the basis of an argument to prove the reality of God?’ He finds the idea of a ‘supremely perfect Being’ as real within himself as ideas of geometric figures, and numbers. He does not know any less clearly and distinctly that actual and eternal existence is a property of the supreme perfect Being, than he knows all which he can demonstrate in relation to geometrical figures or a number truly comprises the properties of these. And were everything else in the preceding Meditations to be found false, the reality of God would be as real for Descartes as he ever held the truths of mathematics to be.

 

However clear and distinct is Descartes idea of a ‘supremely perfect Being’, and that this idea can be expressed, it does not follow that it can be used as the basis of an argument to prove the reality of God. To follow his analogy, his knowledge of the properties of geometrical figures and numbers, may be extensive and even comprehensive, but it does not follow that his knowledge of these properties is complete. The properties of which he knows are just that. It is obvious that it is easier to circumscribe the properties and characteristics of geometrical figures and numbers than to have a clear and distinct idea of the properties and nature of a ‘supremely perfect Being’. What Descartes can have in his mind is a ‘notion’ of the properties and nature of such a perfect Being. He might think that the reality of God, the existence of God is at least as real as the truths of mathematics; this is a notion only, rather than something which can be established.

 

This indeed is not at first manifest, since it would seem to present some appearance of being a sophism. For being accustomed in all other things to make a distinction between existence and essence, I easily persuade myself that the existence can be separated from the essence of God, and that we can thus conceive God as not actually existing. But, nevertheless, when I think of it with more attention, I clearly see that existence can no more be separated from the essence of God than can its having its three angles equal to two right angles be separated from the essence of a rectilinear triangle, or the idea of a mountain from the idea of a valley; and so there is not any less repugnance to our conceiving a God (that is, a Being supremely perfect) to whom existence is lacking (that is to say, to whom a certain perfection is lacking), than to conceive of a mountain which has no valley.

 

Descartes defends himself against the possible charge that his argument is sophistry. He can ordinarily distinguish between the existence and the essence of something. And so he can easily persuade himself that the property ‘existence’ can be separated from the ‘essence’ of God. And thus that we can conceive of God as not possessing the property of something which exists. This however he says is the result of inattentive thinking, and more attention to the question allows him to clearly see that the existence of God cannot be separated from the essence of God any more than the properties of a right-angled triangle can be separated from the essence of it. Or any more than that the idea of a mountain can be separated from the idea of a valley. So the repugnance of the idea of conceiving a supremely perfect Being without the property of existence is no less than to conceive of a mountain without a valley.

 

The problem here is the conception of existence as a form or mode of perfection. In antiquity this equation would not have been made – rather the nature and properties of divinity would have been drawn in contrast with those of existence. There are many ways to express this difference – the secular world has existence, the world of coming-to-be and passing-away has existence, man has existence, the world of things and of representation has existence. The Divine and the eternal did not have existence in the same way in the ancient world. The world of reality was understood to be separate in essence from the secular world; this separate reality was the realm of the divine, and so existence would not be a property of the divine, even if the divine was (as it generally was) considered to be completely real. This is not to say that the divine could not manifest or act in the world of existence; but that existence is a species of imperfection, with which the divine could be (and was) contrasted. Descartes cannot mean that God is real in the sense of having a presence in the material world. And it is curious that later he treated God as if he was walled up in his own sphere. This was necessary to promote the idea that one could do mathematics without reference to God, and without concern that God would interfere with the purely mathematical workings of the world. 

 

But although I cannot really conceive of a God without existence any more than a mountain without a valley, still from the fact that I conceive of a mountain with a valley, it does not follow that there is such a mountain in the world; similarly although I conceive of God as possessing existence, it would seem that it does not follow that there is a God which exists; for my thought does not impose any necessity upon things, and just as I may imagine a winged horse, although no horse with wings exists, so I could perhaps attribute existence to God, although no God existed.

 

Here, Descartes concedes that though he can conceive of the supreme perfect Being as possessing existence, it does not necessarily follow that there is a God which exists, since his thought ‘does not impose any necessity upon things’. What he means by this is that the reality or otherwise or god is not dependent on his understanding of the nature of God.’ So Descartes might be attributing the property of existence to God, even if no God existed.

 

But a sophism is concealed in this objection; for from the fact that I cannot conceive a mountain without a valley, it does not follow that there is any mountain or any valley in existence, but only that the mountain and the valley, whether they exist or do not exist, cannot in any way be separated one from the other. While from the fact that I cannot conceive God without existence, it follows that existence is inseparable from Him, and hence He really exists; not that my thought can bring this to pass, or impose any necessity on things, but, on the contrary, because the necessity which lies in the thing itself, i.e., the necessity of the existence of God determines me to think in this way. For it is not within my power to think of God without existence (that is of a supremely perfect Being devoid of a supreme perfection) though it is in my power to imagine a horse either with wings or without wings.

 

Descartes argues that there is sophistry in this objection, before introducing a genuine sophism into the argument. He says that he cannot conceive a mountain without a valley, but agrees that it does not follow that there is any mountain or valley in existence. But, that whether they do or do not exist, the mountain and the valley cannot be separated from one another. He then says that since he cannot conceive of God without the property of existence, ‘it follows that existence is inseparable from him, and hence He really exists. Descartes has introduced the idea of the ‘necessity’ of the existence of God here, quite shamelessly: he argues that it is ‘not that my thought can bring this to pass, or impose any necessity on things, but, on the contrary, because the necessity which lies in the thing itself, i.e., the necessity of the existence of God determines me to think in this way’. That this remains a subjective understanding, rather than an objective property of God, is confirmed by the words which follow: ‘For it is not within my power to think of God without existence (that is of a supremely perfect Being devoid of a supreme perfection), though it is in my power to imagine a horse either with wings or without wings.’ Again the notion that existence is a form of perfection is called into play, and in conjunction with the necessity of the existence of God, because he is perfect, and the circular argument is complete.

 

Descartes then passes on to a discussion of the relationship between the matter of mathematical figures in his mind and in existence, as a comparison with his proof of the existence of God. The following large paragraph is split into four parts for convenience:

 

And we must not here object that it is in truth necessary for me to assert that God exists after having presupposed that He possesses every sort of perfection, since existence is one of these, but that as a matter of fact my original supposition was not necessary, just as it is not necessary to consider that all quadrilateral figures can be inscribed in the circle; for supposing I thought this, I should be constrained to admit that the rhombus might be inscribed in the circle since it is a quadrilateral figure, which, however, is manifestly false.

 

Descartes is arguing that it is not necessary to assert that God exists once he has presupposed (as part of the definition of the supreme perfect Being) that He possesses every sort of perfection (the property of existence being one of these), for the supposition was not necessary (in the sense that it is not necessary intellectually to assert this for the properties of things to be real), just as one does not have to think of facts such as ‘all quadrilateral figures can be inscribed in the circle’. Descartes here is referring to the strict definition of a figure being inscribed in a circle, which requires that each of the vertices should be in contact with the circle. The truth of what can be contained within a circle is not constrained by the looseness of a mathematician’s statement such as ‘all quadrilateral figures can be inscribed in the circle’. The rhombus is a quadrilateral figure, but it does not meet the requirement of each of the vertices being in contact with the circle.

 

We must not, I say, make any such allegations because although it is not necessary that I should at any time entertain the notion of God, nevertheless whenever it happens that I think of a first and a sovereign Being, and, so to speak, derive the idea of Him from the storehouse of my mind, it is necessary that I should attribute to Him every sort of perfection, although I do not get so far as to enumerate them all, or to apply my mind to each one in particular. And this necessity suffices to make me conclude (after having recognized that existence is a perfection) that this first and sovereign Being really exists; just as though it is not necessary for me ever to imagine any triangle, yet, whenever I wish to consider a rectilinear figure composed only of three angles, it is absolutely essential that I should attribute to it all those properties which serve to bring about the conclusion that its three angles are not greater than two right angles, even although I may not be then considering this point in particular.

 

Descartes here makes an interesting series of statements. These seem to be arguing that the notion (and Descartes uses this word here rather than ‘understanding’, which was used earlier in the argument) of God does not have to be conceived ‘at any time’, but that when it is conceived, he thinks first of ‘a first and sovereign Being’, and derives the idea of Him ‘from the storehouse of my mind’.  And it is necessary to attribute to this derived idea ‘every sort of perfection’. But, in the light of his frequent use of the phrase ‘clearly and distinctly’ in connection with his understanding of the properties of the supremely perfect Being, it is extraordinary to read the succeeding text. He says that does not ‘get so far as to enumerate them all, or to apply my mind to each one in particular’. So in what way is his understanding ‘clear and distinct’? I think here Descartes is emphasizing that his understanding or notion of God has nothing to do with the existence or otherwise of God. But if the understanding of God is actually just a notion, involving loose ideas of perfection, then in what way does this constitute a proof of the existence of the ‘supremely perfect Being’? In the text which follows Descartes emphasizes that he does not desire to accept anything which he cannot conceive clearly and distinctly.

 

But when I consider which figures are capable of being inscribed in the circle, it is in no wise necessary that I should think that all quadrilateral figures are of this number; on the contrary, I cannot even pretend that this is the case, so long as I do not desire to accept anything which I cannot conceive clearly and distinctly. And in consequence there is a great difference between the false superstitions such as this, and the true ideas born within me, the first and principal of which is that of God. 

 

Here Descartes is confronting loose definition, in this case the overgeneralization that all quadrilateral figures can be inscribed in a circle. The overgeneralization contradicts the need to conceive the understanding of God ‘clearly and distinctly’. And so there is a great difference between notions based on overgeneralisations such as ‘all quadrilaterals can be inscribed in a circle’, and the ideas born in the mind, the first of which is that of God.

 

For really I discern in many ways that this idea is not something factitious, and depending solely on my thought, but that it is the image of a true and immutable nature; first of all, because I cannot conceive anything but God himself to whose essence existence necessarily pertains; in the second place because it is not possible for me to conceive two or more Gods in this same position; and, granted that there is one such God who now exists, I see clearly that it is necessary that He should have existed from all eternity, and that He must exist eternally; and finally, because I know an infinitude of other properties in God, none of which I can either diminish or change.

 

To Descartes this idea of the supreme perfect Being is not something fabricated by the human mind, but it is the ‘image of a true and immutable nature’. Then he says something quite surprising - he says he cannot ‘conceive anything but God himself to whose essence existence necessarily pertains’.  What does he mean by this? Is he saying that he can doubt the existence of all other entities? Or perhaps he is saying that existence is not a necessary or essential property of all entities other than God? Descartes has subtly shifted his position here, by modifying his implicit definition of ‘existence’. Now it is an essential property of the divine, and perhaps an inessential property of all other entities and objects. The question arises therefore, is the modified definition of existence something which has aspects in common with the existence associated with entities and objects? Is it really the case in the mind of Descartes that ‘God’ possesses the property existence more than everyday objects which we are more accustomed to say exist?

 

And he cannot conceive two or more gods in the same position. Granted that this supremely perfect Being exists, it is necessary that He should have existed from all eternity, and that He must exist eternally.

 

 This is the end of the paragraph split into four parts . Descartes now concludes his argument:

 

For the rest, whatever proof or argument I avail myself of, we must always return to the point that it is only those things which we conceive clearly and distinctly that have the power of persuading me entirely. And although amongst the matters which I conceive of in this way, some indeed  are manifestly obvious to all, while others only manifest themselves to those who consider them closely and examine them attentively; still, after they have once been discovered, the latter are not esteemed as any less certain than the former. For example, in the case of every right-angled triangle, although it does not so manifestly appear that the square of the base is equal to the squares of the other two sides as that this base is opposite to the greatest angle; still, when this has once been apprehended, we are just as certain of its truth as of the truth of the other. And as regards God, if my mind were not preoccupied with prejudices, and if my thought did not find itself on all hands diverted by the continual pressure of sensible things, there would be nothing which I could know more immediately and more easily than Him. For is there anything more manifest than that there is a God, that is to say, a Supreme Being, to whose essence alone existence pertains?


 

The Nature of Reality in Berkeley

 

I’ve chosen to look initially at the philosophical outlook of Berkeley through public criticism by Bertrand Russell.  [4]  He was born in Ireland in 1685, and became a Fellow of Trinity College, Dublin when he was twenty-two years old. What was peculiar about his philosophy was that he denied the existence of matter, and in fact the reality of the objective world. He argued that material objects had existence only in so far as they are perceived by the viewer.

 

The obvious criticism of this theory is that if perception is the only thing which gives objects their reality, then when we are not looking at them, they should not exist.

 

To the objection that, in that case, a tree, for instance, would cease to exist if no-one was looking at it, he replied that God always perceives everything; if there were no God, what we take to material objects would have a jerky life, suddenly leaping into being when we look at them; but as it is, owing to God’s perceptions, trees and rocks and stones have an existence as continuous as common sense supposes. This is, in his opinion, a weighty argument for the existence of God.

 

His principal philosophical concerns were expressed in a small number of works written before he was twenty-eight years old. These concerns resemble remarkably those of ancient priestly interest. His works were A New Theory of Vision (1709); The Principles of Human Knowledge (1710); and The Dialogues of Hylas and Philonous (1713). The last of these is the one which presents the argument against matter. Russell considers that the first of these dialogues and the beginning of the second present the main aspects of the theory, and supplies a useful summary of the argument. This summary is reproduced here. Russell feels that Berkeley:

 

advances valid arguments in favour of a certain important conclusion, though not quite in favour of the conclusion he thinks he is proving. He thinks he is proving that all reality is mental; what he is proving is that we perceive qualities, not things, and that qualities are relative to the percipient.  [5]

 

There are only two characters in the dialogue, Hylas and Philonous.  [6]  The former represents educated common sense, and Philonous, represents Berkeley himself. Shortly after the opening remarks,

 

Hylas says that he has heard strange reports of the opinions of Philonous, to the effect that he does not believe in material substance. ‘Can anything,’ he exclaims, ‘be more fantastical, more repugnant to Common Sense, or a more manifest piece of Scepticism, than to believe there is no such thing as matter?’ Philonous replies that he does not deny the reality of sensible things, i.e. of what is perceived immediately by the senses, but that we do not see the causes of colours or hear the causes of sounds. Both agree that the senses make no inferences. Philonous points out that by sight we perceive only light, colour, and figure; by hearing, only sounds; and so on. Consequently, apart from sensible qualities ther is nothing sensible, and sensible things are nothing but sensible qualities or combinations of sensible qualities.

 

Philonous now sets to work to prove that ‘the reality of sensible things consists in being perceived’, as against the opinion of Hylas, that ‘to exist is one thing, and to be perceived is another’. That sense-data are mental is a thesis which Philonous supports by a detailed examination of the various senses. He begins with heat and cold. Great heat, he says, is a pain, and must be in a mind. Therefore heat is mental; and a similar argument applies to cold. This is reinforced by the famous argument about the lukewarm water. When one of your hands is hot and the other cold, you put both into lukewarm water, which feels cold to one hand and hot to the other; but the water cannot be at once hot and cold. This finishes Hylas, who acknowledges that ‘heat and cold are only sensations existing in our minds’. But he points out hopefully that other sensible qualities remain.

 

Philonous next takes up tastes. He points out that a sweet taste is a pleasure and a bitter taste is a pain, and that pleasure and pain are mental. The same argument applies to odours, since they are pleasant or unpleasant.

 

Hylas makes a vigorous effort to rescue sound, which, he says, is motion in air, as may be seen from the fact that are no sounds in a vacuum.  [7]  We must, he says, ‘distinguish between sound as it is perceived by us, and as it is in itself; or between the sound which we immediately perceive and that which exists without us’.  Philonous points out that what Hylas calls ‘real’ sound, being a movement, might possibly be seen or felt, but can certainly not be heard; therefore it is not sound as we know it in perception. As to this, Hylas now concedes that ‘sounds too have no real being without the mind’.

 

They now come to colours, and here Hylas begins confidently: ‘Pardon me: the case of colours is very different. Can anything be plainer than that we see them on the objects?’ Substances existing without the mind, he maintains, have the colours we see on them. But Philonous has no difficulty in disposing of this view. He begins with the sunset clouds, which are red and golden, and points out that a cloud, when you are close to it, has no such colours. He goes on to the difference made by a microscope, and to the yellowness of everything to a man who has jaundice. And very small insects, he says, must be able to see much smaller objects than we can see. Hylas thereupon says that colour is not in the objects, but in the light; it is, he says, a thin fluid substance. Philonous points out, as in the case of sound, that, according to Hylas, ‘real’ colours are something different from the red and blue that we see, and that this won’t do.

 

Hereupon Hylas gives way about all secondary qualities, but continues to say that primary qualities, notable figure and motion, are inherent in external unthinking substances. To this Philonous replies that things look big when we are near them and small when we are far off, and that a movement may seem quick to one man and slow to another.

 

At this point Hylas attempts a new departure. He made a mistake, he says, in not distinguishing the object from the sensation; the act of perceiving he admits to be mental, but not what is perceived; colours, for example, ‘have a real existence without the mind, in some unthinking substance’. To this Philonous replies: ‘That any immediate object of the senses – that is, any idea or combination of ideas – should exist in an unthinking substance, or exterior to all minds, is in itself an evident contradiction.’

 

Russell points out that the argument has now become a logical one, and is no longer empirical in nature. Berkeley has moved on to a discussion involving ideas, as expressed by Philonous a few pages later, where he says, ‘whatever is immediately perceived is an idea; and can any idea exist out of the mind?’

 

After a metaphysical discussion of substance, Hylas returns to the discussion of visual sensations, with the argument that he sees things at a distance. To this Philonous replies that this is equally true of things seen in dreams, which everyone admits to be mental; further, that distance is not perceived by sight, but judged as the result of experience, and that, to a man born blind but now for the first time able to see, visual objects would not appear distant.

 

At the beginning of the second Dialogue, Hylas urges that certain traces in the brain are the causes of sensations, but Philonous retorts that ‘the brain, being a sensible thing, exists only in the mind’.

 

Russell ends his summary of the argument here, and divides Philonous’ argument into two parts. The first is the argument that we do not perceive material things, but only their secondary qualities, such as colours, sounds, etc. These secondary qualities exist in the mind, and are mental in nature. Russell thinks that Berkeley’s reasoning is ‘completely cogent as to the first point,’ but as to the second, ‘it suffers from the absence of any definition of the word ‘mental’. He relies… upon the received view that everything must be either material or mental, and that nothing is both’. 

 

When he says that we perceive qualities, not ‘things’ or ‘material substances’, and that there is no reason to suppose that the different qualities which common sense regards as all belonging to one ‘thing’ inhere in a substance distinct from each and all of them, his reasoning may be accepted. But when he goes on to say that sensible qualities – including primary qualities – are ‘mental’, the arguments are of very different kinds, and of very different degrees of validity. There are some attempting to prove logical necessity, while others are more empirical.  [8]

 

Russell is not interested in Berkeley’s argument after this, as he explained. This is because he has exposed the same looseness of language which we saw employed by the most celebrated exponents of the ontological argument (and consequently the weakness of the argumentation), and the rest of Berkeley’s argument concerns a theological understanding of the world. We however shall press on, since Berkeley’s theological understanding is relevant to the subject of this book, and it also presents an alternative form of ontological argument, which Berkeley claims shows the reality of God.

 

The Second Dialogue opens with a discussion which functions to clarify whether the essentially skeptical view of Hylas is the correct response to Philonous’ argument.  Philonous ( p 166) asks to know ‘whether I rightly understand your hypothesis. You make certain traces in the brain to be the causes or occasions of our ideas. Pray tell me, whether by the brain you mean any sensible thing?’ Hylas confirms that this is his view, and that he cannot imagine what else Philonous thought he might mean. Philonous responds by defining that ‘sensible things are all immediately perceivable, are ideas; and these exist only in the mind.’ They both agree that Hylas has agreed to this much earlier in the argument.

 

Philonous then argues that, since the brain, being itself a sensible thing, ‘exists only in the mind’, and asks if Hylas would agree whether or not it is reasonable to suppose that ‘one idea or thing existing, occasions all other ideas.’ And that if this is his view, how does he account ‘for the origin of that primary idea of the brain itself?’  Hylas replies that he does not explain the origin of our ideas by a ‘brain which is perceptible to sense; rather he understands the brain being ‘only a combination of sensible ideas’, and that the explanation is by means of another brain which he imagines.

 

Philonous responds by suggesting that things imagined are as truly in the mind as things which are perceived. Hylas agrees. Philonous points out that Hylas has been ‘all this while accounting for ideas, by certain motions or impressions in the brain’ by means of ‘some alterations in an idea, whether sensible or imaginable,’ and that it does not matter which. Hylas is a little shaken by this, and says that he begins to suspect his own hypothesis.

 

A clue is presented as to where Philonous is going with this argument, since he says that ‘all we know or conceive are our own ideas,’ with the exception of ‘spirits.’ And if we do not conceive it, then we ‘talk unintelligibly,’ instead of forming a reasonable hypothesis’. Hylas now crumbles, and says that he ‘now clearly see it was a mere dream’ to argue in terms of motions or impressions in the brain. Philonous responds by saying that ‘this way of explaining things… could never have satisfied any reasonable man’ since ‘what connexion is there between a motion in the nerves and the sensations of sound or colour in the mind?’ He agrees with Philonous that he is satisfied that no sensible things have a real existence. He also agrees the he is clearly a skeptic.

 

Philolaus then embarks on a long paean to the glories of the sensible world and its orderliness:

 

Raise now your thoughts from this ball of earth, to all those glorious luminaries that adorn the high arch of heaven. The motion and situation of the planet, are they not admirable for use and order? Were those (miscalled erratic) globes ever known to stray, in their repeated journeys through the pathless void? Do they not measure areas around the sun ever proportioned to the times? So fixed, so immutable are the laws by which the unseen Author of Nature actuates the universe. How vivid and radiant is the lustre of the fixed stars! How magnificent and rich that negligent profusion, with which they appear to be scattered throughout the whole azure vault!

 

Philonous is appealing here to the heavens as a representation of the divine, whose uniformities point to something beyond the appearance. He says to Hylas that he ‘must call imagination to his aid,’ since ‘the feeble narrow sense cannot descry innumerable worlds revolving round the central fires the stars ; and in those worlds the energy of an all-perfect mind displayed in endless forms.’

 

This is not a metaphorical appeal. Berkeley has introduced the notion that reality as it is represented to us is not simply the more or less complex response of the human brain to sensory data, but is a series of representations which are associated with cosmic ‘all-perfect’ mind:

Neither sense nor imagination are big enough to comprehend the boundless extent with all its glittering furniture. Though labouring mind exert and strain each power to its utmost reach, there still stands out ungrasped a surplusage immeasurable. Yet all the vast bodies that compose this mighty frame, how distant and remote soever, are by some secret mechanism, some divine art and force linked in a mutual dependence and intercourse with each other, even with this earth, which was almost slipped from my thoughts, and lost in the crowd of worlds. Is not the whole system immense, beautiful, glorious beyond expression and beyond thought!

 

Both Philonous and Hylas by this point share the view that sensible things exist in mind only. Up to this point however, the view of Hylas has been a profound skepticism about reality, and our capacity to know it. By contrast, here Philonous shows, on the basis of the same evidence, that a quite different conclusion can be drawn, if the intellectual frame is changed. Philonous then attacks the skeptical position in general:

 

What treatment then do those philosophers deserve, who would deprive these noble and delightful scenes of all reality? How should those principles be entertained, that lead us to think all the visible beauty of the creation a false imaginary glare? To be plain, can you expect this skepticism of yours will not be thought extravagantly absurd by all men of sense?

 

Hylas is not impressed, and is not converted to Philonous’s outlook. He says that his comfort is that Philonous is ‘as much a sceptic as I am’. Philonous disagrees, which strikes Hylas as meaning that Philonous agreed all along to the premises of the argument, but is now denying the conclusion, leaving Hylas ‘to maintain those paradoxes’ which Philonous led him into.

Argument and evidence however do not by themselves lead to single and unambiguous conclusions. We arrive at conclusions only by the properties and processes of mind, and on the basis our notions and expectations. Philonous denies that he agreed with Hylas ‘in those notions that led to skepticism.’ He argues that Hylas ‘indeed said, the reality of sensible things consisted in an absolute existence out of the minds of spirits, or distinct from their being perceived.’

 

Consequent to this, Hylas is ‘obliged deny sensible things any real existence’. And that, according to his own definition, he is therefore a professed skeptic. But Philonous says that he ‘neither said nor thought the reality of sensible things was to be defined after that manner.’ Instead he says that to him it is evident, for the reasons that Hylas allows, ‘that sensible things cannot exist otherwise than in a mind or spirit.’ And so he concludes that it is not the case that they have no real existence, ‘but that seeing they depend not on my thought, and have an existence distinct from being perceived by me, there must be some other mind wherein they exist’  Berkeley’s emphasis . As sure therefore as the sensible world really exists, so sure is there an infinite omnipresent spirit who contains and supports it.’

 

This is an interesting proof of the reality of divine Being, which differs from the other arguments we have looked at. Berkeley clarifies that this is not the Christian notion that God knows and comprehends all things. He argues (as Philonous) that ‘men commonly believe that all things are known or perceived by God, because they believe the being of a God, whereas I on the other side, immediately and necessarily conclude the being of a God, because all sensible things must be perceived by him.’  [9]

 

Hylas objects that this is a footling distinction, saying ‘so long as we all believe the same thing, what matter is it how we come by that belief?  To which Philonous replies that they don’t believe the same thing. ‘For philosophers, though they acknowledge all corporeal beings to be perceived by God, yet they attribute to them an absolute subsistence distinct from their being perceived by any mind whatever, which I do not.’ He asks, ‘is there no difference between saying, there is a God, therefore he perceives all things: and saying, sensible things do really exist; and if they really exist, they are necessarily perceived by an infinite mind: therefore there is an infinite mind, or God. This furnishes you with a direct and immediate demonstration, from a most evident principle, of the being of a God.’

 

Again Berkeley returns to the judgement that men make about sense data, which is not always the same, though the evidence is the same. As Philonous he says that ‘Divines and philosophers had proved beyond all controversy, from the beauty and usefulness of the several parts of the creation, that it was the workmanship of God. But that setting aside all help of astronomy and natural philosophy, all contemplation of the contrivance, order, and adjustment of things, and infinite mind should be necessarily inferred from the bare existence of the sensible world, is an advantage peculiar to them only who have made this  easy reflexion: that the sensible world is that which we perceive by our several senses; and that nothing is perceived by the senses beside ideas; and that no idea or archetype of an idea can exist otherwise than in a mind.’

 

 

Berkeley regarded this as a powerful argument against atheism. Hylas says that ‘some eminent moderns’ entertain a notion of ‘seeing all things in God’, (a reference in particular to the French scholar Malebranche) and gives detail in response to questioning by Philonous. Hylas says that these men conceive that the soul being immaterial, ‘is incapable of being united with material things, so as to perceive them in themselves, but that she (the soul) by her union with the substance of God, which being spiritual is therefore purely intelligible, or capable of being the immediate object of a spirit’s thought. Besides, the divine essence contains in it perfections correspondent to each created being; and which are for that reason proper to exhibit or represent them to the mind.’

 

Philonous is not impressed with this argument, in that he argues it makes a created world ‘exist otherwise than in the mind of a spirit’. This is because, as he has said, ‘nothing is perceived by the senses besides ideas.’ He does not share the view with Malebranche that there is an absolute external world. According to Philonous, Malebranche ‘maintains that we are deceived by our senses, and know not the real natures or the true forms and figures of extended beings, of all which I hold the direct contrary.’ Hylas thinks however that what Philonous proposes comes near to ‘seeing all things in God’.

 

The response of Philonous is that ‘few men think, yet all will have opinions. Hence men’s opinions are superficial and confused. It is nothing strange that tenets, which in themselves are ever so different, should nevertheless be confounded with each other by those who do not consider them attentively.’  [10]  He says he is very remote from the view of Malebranche, because Malebranche builds on the most abstract general ideas… though he (Philonous) agrees with holy Scripture, in ‘that in God we live, and move, and have our being’. He explains briefly the difference between his view and that of Malebranche:

 

It is evident that the things I perceive are my own ideas, and that no idea can exist unless it be in a mind. Nor is it less plain that these ideas or things by me perceived, either themselves or their archetypes, exist independently of my mind, since I know myself not to be their author, it being out of my power to determine at pleasure, what particular idea I shall be effected with upon opening my eyes or ears. They must therefore exist in some other mind, whose will it is they should be exhibited to me. The things, I say, immediately perceived, are ideas or sensations, call them what you will. But how can any idea or sensation exist in, or be produced by, anything but a mind or spirit? This indeed is inconceivable; and to assert that which is inconceivable, is to talk nonsense….

 

It may be that the objection to the notion put forward by Malebranche is that it depicts reality as something which is perceived as outside the human mind by the human mind, whereas Berkeley does not make this distinction. For Berkeley it is as if his mind is a subset of the divine cosmic mind, perceiving a subset of the ideas in that mind.  If he perceives ideas, it is because the cosmic mind wills it.

 

The ideas which present themselves to Philonous, he argues, ‘it is very conceivable that they should exist in, and be produced by, a spirit; since this is no more than I daily experience in myself, inasmuch as I perceive numberless ideas; and by an act of my Will can form a great variety of them, and raise them up in my imagination: though it must be confessed, these creatures of the fancy are not altogether so distinct, so strong, vivid, and permanent, as those perceived by my senses, which latter are called real things. From all which I conclude, there is a mind which affects me every moment with all the sensible impressions I perceive. And from the variety, order, and manner of these, I conclude the Author of them to be wise, powerful, and good, beyond comprehension.

 

Philonous emphasizes here that he is not saying that he sees ‘things by perceiving that which represents in the intelligible substance of God. This I do not understand; but I say, the things by me perceived are known by the understanding, and produced by the will, of an infinite spirit.’ So his objection is as I suggested, and he is not simply seeing what is ‘in’ God.

 

Beyond this, the Second Dialogue deals with Malebranche’s occasionalism, which sees the physical world as a place where God has the occasion to create motion and change, and also deals with ideas of substance.

 

 


Hume and Kant on Reality

 

In his first work, the Treatise on Human Nature, published in 1739, when he was 29, Hume argued that he was introducing the scientific method into psychological subjects. That is, he was using an analytical and empirical approach to matters concerned with the mind, and human understanding. This was a large claim for his approach. It was certainly analytical, but its empirical content consists largely of appeals to experience and well-argued conjecture.

 

Hume argued on this basis that human understanding is based on sense data and empirical sense impressions. We have knowledge only of what we directly experience. He divided sense impressions into strong and weak, arguing that weak impressions are simply copies of strong impressions. The mind makes sense of these impressions in the context of what the mind believes it already knows and understands. He argued entirely against the notion of innate ideas, which had been part of the currency of philosophy in the preceding period.

 

There are two key and related areas where Hume’s inquiry into human nature threw up problems which cannot be satisfactorily resolved; these are:  a) whether it is really legitimate for us to perform inductive thought, and b) whether or not we can infer causality. Hume argued that we assume the constancy of the conjunction of things on the basis of experience, but have no actual knowledge of how these things are conjoined. Whatever might hold relationships together is obscure to us, and even our understanding of ourselves is no more than a complex bundle of sense impressions associated with the notion of the self. Of the self itself, we have no real knowledge. In essence Hume was arguing against the uniformitarian attitude to the world which developed after the publication of Newton’s Principia, which saw the apparent regularity and mathematical predictability in Newton’s description of the world as reliable proof of its consistency.

 

Hume used the example the example of colliding billiard balls to illustrate his point (Hume was clubbable, so the example is not a surprising one). Skilled players of the game know how the geometry of billiards works, and can infer the way a ball (B) will move when struck by ball (A). The skill of a good player relies on the consistency of the behaviour of the balls. We assume because of the consistency of this behaviour that there is an underlying and consistent causality at work. However Hume argued that, despite the apparent regularity of the behaviour of ball B when struck by ball A, we have no insight at all into the underlying process by which this behaviour is effected. Nor have we any reason beyond custom and expectation to believe that the balls will behave in the expected manner. Causality itself is a mystery wherever it is found, and we have no knowledge of how and why it works.

 

This is the reason why Hume is regarded as a sceptical philosopher – we have no certain knowledge about some things which we take very much for granted. This is true for both inductive thought, and our understanding of causality.

 

So Hume is left in an interesting position. On the one hand, he argued that what knowledge we have is based purely on experience, and this experience is mediated through sense impressions. On the other hand, he argued that we have no real understanding of how the knowledge we have is assembled, since the consistency we see in the relation between ideas is purely customary and a matter of expectation, which isn’t an understanding. This applies also to causal relations.

 

Hume’s point is not that the universe might at any moment start behaving in a different way; only that what we think we understand, we do not ‘understand’ at all. It is a matter of conjecture based on experience. What underlies these consistencies is wholly unknown to us.

 

Immanuel Kant responded to Hume’s challenge by inverting the line of argument. Where Hume argued that knowledge is acquired through experience, Kant argued that what we understand is shaped by what the human mind can understand. That is, it is reason itself which gives us understanding, and not simply sensory experience. We have to understand reason if we are to understand anything.

 

Not only did Kant argue that what we understand is shaped by properties and characteristics of reason, he also argued that the world of experience, the imagined source of sensory impressions received by the mind, might also be a product of human reason. In other words, we assume that the objective world we see as having existence outside ourselves in space and time, has objective reality. However without a proper understanding of human reason, it is as unreasonable to assume this to be the case, as it is for us to assume the consistent behaviour of billiard balls on a table.

 

This is not to assume the identity of, or to conflate processes occurring in the phenomenal world, with those operating in the mind. Precisely because we do not understand the processes and relations of things in the phenomenal world, there is no reason for them to always conform to our understanding.

 

Kant’s first major work was the Critique of Pure Reason. It had to be a critique rather than a dogmatic survey of pure reason, since reason remained to be understood.  Kant felt that, in pursuing this approach, he was making metaphysics anew, and that all previous writings on metaphysics were superseded, at least in terms of metaphysics as a science. He made this clear in the short work Prolegomena To Any Future Metaphysics That Will Be Able To Present Itself As A Science, which was published around Easter 1783, some two years after the publication of the Critique in the summer of 1781. The purpose of the Prolegomena was to make clear the radical nature of the Critique, and to explain his intent. Kant expected the Critique ‘to have a revolutionary effect and anxiously awaited its impact on the world of learning. In fact he found that it was being received in silence’.  [11]

 

A key argument of the Critique is that the reason does not apprehend things as they are, but only as they appear to us. Kant repeats the distinction made in classical times between the phenomena and the noumena. We can apprehend the phenomena, but the relationship between the phenomena and the noumena, or the ‘thing-in-itself’, is entirely unknown to us, and unknowable by means of the senses, and the mind. To Kant, only the ‘thing-in-itself,’ or ‘things-in-themselves,’ are real.

 

So how does Kant set about creating a scientific metaphysics? He tells us in the preamble to the Prolegomena that ‘If a field of knowledge is to be exhibited as a science, its differentia, which it has in common with no other science and which is thus peculiar to it, must first be capable of being determined exactly; otherwise the boundaries of all the sciences run into one another and none of them can be treading soundly according to its own nature.’  [12]

 

He continues by pointing out that ‘this peculiarity, whether it consists in the difference of the object, or of the sources of knowledge, or of the kind of knowledge, or of  some if not all of these together, is the basis of the idea of the possible science and of its territory’. Kant defines metaphysics very closely as something whose ‘fundamental propositions …  and  its fundamental concepts must never be taken from experience’, since metaphysical knowledge lies beyond experience. The ground of metaphysics will not be either ‘outer experience’, which he defines as the source of physics, nor ‘inner experience, which provides the basis for empirical psychology.’ In other words metaphysics is a priori knowledge, ‘out of pure understanding and pure reason’.

 

Kant recognizes the need to differentiate metaphysics from pure mathematics, and refers the reader to the Critique, where he says

 

Philosophical cognition is rational cognition from concepts. Mathematical cognition is rational cognition from the construction of concepts.’ [13]

 

He expands on this by saying that ‘to construct a concept means to exhibit a priori the intuition corresponding to it. Hence construction of a concept requires a non-empirical intuition. Consequently this intuition, as intuition, is an individual object; but as the construction of a concept, (a universal presentation), it must nonetheless express in the presentation its universal validity for all possible intuitions falling under the same concept.’

 

Kant uses the example of the construction of a triangle, arguing that this construction exhibits the object which corresponds to this concept ‘either through imagination alone, or in pure intuition.’ It can be drawn on paper of course, as a mathematical figure, but in such a case the representation is an empirical intuition, not a pure intuition, though both in the case of the pure intuition and the empirical intuition, Kant has exhibited the object a priori, without having used a model taken from experience (meaning that only the properties of a triangle have been used in its construction). Though the drawn figure is empirical, yet it serves to express the concept ‘without impairing the concept’s universality’.  Only those properties which it is necessary to consider for the construction of the triangle are involved – the many inconsequential details of a physical triangle – the length of the sides, and the angles of the triangle, are not involved in the abstraction. All such irrelevant details are removed from the concept, and the result is therefore wholly abstracted from any particular instance of a triangle.

 

Kant’s argument is therefore that ‘philosophical cognition contemplates the particular only in the universal’. By contrast, he says that mathematical cognition ‘contemplates the universal in particular, and indeed even in the individual’. This might seem at first sight to be a strange distinction, however Kant explains himself clearly, saying that even in the case of this mathematical cognition, the contemplation of it is ‘a priori, and by means of reason.’ And so, ‘just as this individual is determined under certain universal conditions of construction, so the object of the concept – to which this individual corresponds only as its schema – must be thought of as determined universally.  Thus the essential difference between these two kinds of rational cognition ‘consists in this difference of form, and does not rest on the difference of their matter or objects.’

 

He goes on to criticize those who ‘have meant to distinguish philosophy from mathematics by saying that philosophy has as its object merely quality but mathematics only quantity,’ He argues that ‘the form of mathematical cognition is the cause of the fact that mathematics can deal solely with quanta’ (i.e., magnitudes), and that ‘only the concept of magnitudes can be constructed, i.e., displayed a priori in intuition. Qualities, on the other hand, can be exhibited only in empirical intuition; hence a rational cognition of qualities can be possible only through concepts.’ He invokes the example of a conical shape, ‘which can be made intuitive without any empirical aid, merely according to the concept of a cone; but the colour of this cone will have to be given previously in some experience or other. However the cause of anything cannot be exhibited in intuition, since cause is presented by experience.

 

Again against those who have argued for a simplistic distinction between the objects of philosophy and mathematics, he points out that in fact ‘philosophy deals with magnitudes just as much as mathematics does – e.g., with totality, infinity, etc. Mathematics similarly is concerned not only with quantity but also with the difference between lines and planes considered as spaces of different quality, and with continuity as a quality of extension.

 


 

The End of the Ontological Argument

 

I did not write about the Ontological Argument in an earlier draft of this book. But I gained an understanding of its severe limitations while I was writing the paper in 2006 which was subsequently abandoned, due to the weakness of this mode of argument. Knowledge of these limitations informed the discussion of questions about reality in the two parts of the book which were under way, which looked at Greece and Assyria respectively. Once those two parts were largely constructed, I turned to the Ontological Argument sometime in 2012.

 

Ontological argument ought to be about the nature of reality itself, rather than a particular aspect of it. Attempting to prove the existence or reality of God on the basis of purely logical and a priori argument is about proof and existence within a known and perceived frame of reality, which is presumed to be real, though we have no knowledge of what it is and why it presents itself to us in the way that it does. So ontological argument for the most part isn't about reality at all, but some part of that reality, and argued in terms of the properties and attributes which that part may or may not have.

 

The concept of God is discussed within either the reality we know in terms of space and time, or else existing in some other place beyond the limitations of physical reality. In either case the physical frame of space and time is taken as a given.

 

In classical antiquity this would have seemed to be a barbarously crude way to argue about the divine. When they talked about reality, they meant reality itself, not some particular representation of it. And that reality was coterminous with Being. In other words, divine Being was presumed to be at the root of all the forms of reality which can be represented. It was reality.

 

Ancient ideas about divinity therefore need to be understood in their original context, or at least in as much of it as we can muster. A thorough understanding of the varieties of the ontological argument will not tell us much that is useful about ancient conceptions of the divine.

 

So this part of the book should be understood as a necessary demolition of the usefulness of the ontological argument, as we understand it. In the course of writing, I was reminded that there were ancient misunderstandings of the nature of divinity also, on the basis of the way in which the divine was spoken. If the divine is one and indivisible, for example, how is it that there are hundreds of gods, and not one?

 

Parts Two and Three can be read in a number of different ways. But essentially the discussion is of a common intellectual substrate, shared by Greece and Assyria, which lies beneath the strikingly different cultures. The nature of that substrate is explored initially through the writings of Plato, and the Greeks in general.

 

The contention is that Plato, in writing about the Forms or Ideas, was actually telling us something of extraordinary importance about Greek theology, and the role and function of divine images. The source of the idea of the nature of reality, of Being itself is referred to by Plato in many places, but never fully explained. And there is a related question he asks, about a most fundamental matter, but does not answer. The answer can be guessed, though professional philosophers are not in the business of guessing. So we have had nearly two hundred years of scholarship devoted to Plato, which has explained very little.

 

I guessed the answer, though as it turned out, I knew the answer already from a different context. It can be demonstrated that the same question lies beneath Mesopotamian ideas about the nature of reality, as expressed in the liturgy of their New Year Festival, and in other sources. It is the reason why there are two creations - the first chaotic, and the second, rational.

 




[1] Plantinga, A. Ontological Argument, p3, St Anselm (1033-1109).

[2] Plantinga, A. The Ontological Argument, from the introduction by Richard Taylor, pviii. Macmillan, 1968.

[3] Descartes, Rene, third Meditation. In The Philosophical Works of Descartes, Volume I, translated by Elizabeth S. Haldane and G.R.T. Ross.

[4] Russell, Bertrand, The History of Western Philosophy, Chapter XVI, p 623 ‘Berkeley’

[5] Op cit. p624

[6] ‘Philonous’ is a composite of two Greek words, meaning ‘lover of mind’.

[7]This information must have come from experimental data.

[8] Op. Cit, p 626

[9]  p 168

[10] p 169

[11] Kant, Immanuel, Prolegomena To Any Future Metaphysics That Will Be Able To Present Itself As A Science, p.ix, trans. Lucas, Peter G., Manchester University Press, 1953.

[12] Kant, Immanuel, Op. Cit., p15, 1953.

[13] Kant, Immanuel, Critique of Pure Reason,  (A 713. ff), unified edition, trans. Pluhar, Werner S., Hackett Publishing Company, Indianapolis/Cambridge, 1996.


[I've extracted the chapters in The Sacred History of Being which concern the ontological argument, as formulated in the middle ages, and which is still current among scholars. Most of what you need to know about the ontological argument is collected together in these chapters. One minor typo in the published text has been corrected. TY]

 

What is an ontological argument? In the introduction to Alvin Plantinga’s The Ontological Argument, written by Richard Taylor, the argument is defined simply as one which ‘purports to prove, simply from the concept of God as the supreme being, that God’s existence cannot rationally be doubted by anyone having such a concept of Him.’ He goes on to say that ‘it is thus a purely a priori argument, that is to say, one that does not appeal to any facts of experience but is concerned solely with the implications of concepts – in this case, the concept of God’.

 

Our modern understanding of the ontological argument is that it was first formulated by St. Anselm of Canterbury in the 11th century C.E. This is not disputed. But it is perfectly clear that some kind of ontological argument lies behind the arguments which are found in Plato’s semi-secularised discussions, in Aristotle (particularly in the Nicomachean Ethics), and, if Plato is to be considered an accurate historian of the views of Parmenides, also to be found in his dialogue Parmenides. What I intend to do here is to review the history of the ontological argument from St. Anselm onwards, and then to explore the likely nature of the ontological argument in antiquity. The range of questions which might be asked by a neophyte, or an advanced student, give many clues about the probable shape of such an argument. 


 

The Ontological Argument in Anselm

 

“Anselm… is rightly regarded as the inventor and perfecter of the ontological argument, though his philosophical inspiration was largely derived from St. Augustine. … His position is not that of a skeptic seeking some rational persuasion of God’s existence, but that of a believer seeking a single conception which would make manifest at once God’s existence and God’s attributes”.  [1]

 

The following is extracted from chapters 2-4 of St Anselm’s Proslogion, quoted from Alvin Plantinga’s The Ontological Argument. Plantinga takes his text from Anselm’s Basic Writings, translated by S. N. Deane, with an introduction by Charles Hartshorne, 2nd edition, 1962, Open Court Publishing Company.

 

Prosologion, Ch. II –

Truly there is a God, although the fool hath said in his heart, There is no God.

And so, Lord, do thou, who dost give understanding to faith, give me, so far as thou knowest it to be profitable, to understand that thou art as we believe; and that thou art that which we believe. And, indeed, we believe that thou art a being than which nothing greater can be conceived. Or is there no such nature, since the fool hath said in his heart, there is no God? (Psalm xiv. 1). But, at any rate, this very fool, when he hears of this being of which I speak – a being than which nothing greater can be conceived – understands what he hears, and what he understands is in his understanding; although he does not understand it to exist.

 

We might rephrase this thus: “Our belief is that God is a being greater than any other which can possibly be conceived. And it is this greatest of all beings which gives us understanding. A fool can understand the conception of this greatest of all beings as a conception, though he does not understand the existence of the greatest of all beings”.

 

This might be criticized by pointing out that two key elements in this argument are undefined. We have a definition of ‘God’ as the greatest of all beings.’ However we do not have a clear definition of the meaning of ‘greatest’ in this context, and neither do we have a clear definition of ‘existence.’ Both of these terms are made to do much work in this discussion.

 

For, it is one thing for an object to be in the understanding, and another to understand that the object exists. When a painter first conceives of what he will afterwards perform, he has it in his understanding, but he does not yet understand it to be, because he has not yet performed it. But after he has made the painting, he both has it in his understanding, and he understands that it exists, because he has made it.

 

Anselm makes it clear he understands the distinction between knowledge of a concept, and knowledge of the existence of something – in this case ‘God’. The illustration which he uses here is interesting. He likens the conceiving mind to the mind of a painter conceiving a representation of an object – before he begins to paint he has a conception in his mind of what he intends to paint, but does not understand it ‘to be’ ‘because he has not yet performed it’. But once the conception is painted, the painting has come to be (i.e., it ‘exists’).

 

However, a painter creates a representation by painting it, not an object itself. This is an important detail if the argument is designed to prove the ‘existence’ of God, rather than a physical object. It is fair to argue that the conception in the mind of the painter is also a representation, in that it is a conception rather than the thing itself. So the painting is a representation of a representation. The painting exists in the sense that it is a physical object existing in the world, containing an image which may or may not be a representation of an object which exists.

 

Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.

 

Rephrasing the first part of this, ‘even the fool can conceive that an idea in the understanding can be of something which is greater than anything other which can be conceived. He can understand this, and what is understood, has an existence in the understanding’.

 

It is true that the conception of something which is greater than anything other which can be conceived can be a concept, even in a foolish mind. But it does not follow that it is, as Descartes would say later on, a clear and distinct conception. ‘Great’ is a term which can mean many things, and to a fool, it is in the nature of foolishness for its meaning to be misunderstood.

 

Anselm then passes on to the suggestion that something which is greater than anything which can be conceived, cannot exist in the understanding alone. The reason he gives is that, if this conception exists only in the understanding, then to conceive it to exist in reality would be greater.

 

This requires deconstruction. If the conception, in the understanding of the fool, is unclear and indistinct, then it does not follow that what can be conceived in the understanding must exist in the world. If the conception is clear and distinct in the understanding of the wise man, does it follow that that which is conceived in the mind must also exist as a physical reality? The answer is no, in that, no matter how clear and distinct the conception of God is in the mind, it is a conception which describes what can be known or inferred of God by the mind of man. And man by his very nature, must participate in the quality of foolishness more than the quality of the divine.

 

A further criticism of this passage might be that ‘existence’ is used very loosely. Can we speak of God existing, rather than speaking of the reality of God? This is an important point if part of the definition of God is that the divine possesses a transcendent reality, rather than a physical one.

 

The only circumstance in which the concept of God in the understanding must also exist as a reality, is where that reality is transcendent - where the possessor of the understanding is also divine, and thus necessarily participates in the being of God through the clearest and most distinct understanding of the nature of God.

 

Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.

 

As already pointed out, that if there is a conception of that which nothing greater can be conceived in the understanding, and the understanding alone, it does not follow that there is no doubt that there ‘exists’ a being (or rather that a being of this nature has reality), and that it exists both in understanding and in reality.  J.G. Frazer suggested that Plato sometimes confused an epistemology with an ontology, and Anselm seems to be confusing the idea of naming, conceiving and describing a being with the necessity of the reality of such a being. Again, only if the scope of the understanding is as clear and distinct as the reality, would there be the impossibility of that understanding existing alone. And that is not a likely proposition. The ultimate nature of reality is always going to transcend our capacity to conceive of it, except in very special circumstances.

 

From Chapter III:

 

God cannot be conceived not to exist – God is that, than which nothing greater can be conceived. –That which can be conceived not to exist is not God.

 

And it assuredly exists so truly, that it cannot be conceived not to exist. For, it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist; and this being thou art, O Lord, our God.

 

Anselm has accepted his proof of the ‘reality’ of God, and is now building on it. I am not sure how one can argue that conceiving of a being which cannot be conceived not to exist, is necessarily ‘greater’ than one which can be conceived not to exist. Again, this only makes sense if the conception in the understanding is of the same nature as the being who exists in reality. He argues however that if the conception which is greater than anything which can be conceived, can be conceived not to be real, then it is not that which is greater than anything which can be conceived. And that this would be an irreconcilable contradiction. How so? We are talking in terms of the subjective powers of the mind here. In the mind of the fool, it is clearly possible to conceive in the understanding a being than which greater nothing can be conceived, and then to change opinion to that in which it can be conceived not to be real. But this is a fallible judgement, so for the most part this this does not throw up an irreconcilable contradiction.

 

So truly, therefore, dost thou exist, O Lord, my God, that thou canst not be conceived not to exist; and rightly. For, if a mind could conceive of a being better than thee, the creature would rise above the Creator; and this is most absurd. And, indeed, whatever else there is, except thee alone, can be conceived not to exist. To thee alone, therefore, it belongs to exist more truly than all other beings, and hence in a higher degree than all others. For, whatever else exists does not exist so truly, and hence in a less degree it belongs to it to exist. Why, then has the fool said in his heart, there is no God (Psalm xiv. 1), since it is so evident to a rational mind, that thou dost exist in the highest degree of all? Why, except that he is dull and a fool?

 

Anselm is here building on his conclusion that God cannot be conceived not to exist. It follows therefore that if a mind could conceive of something greater, that creature would rise above the Creator, which (to Anselm) would be ‘most absurd’. We can sense here that it is almost the case that the reality of the God he is discussing is dependent on whether or not the understanding of the believer is sufficiently acute to bring the God into being. But essentially here Anselm is looking for support for the faithful, and is not arguing for the power of an understanding of the divine, and of the word.

 

He argues that all other things excepting God can be conceived not to exist. This implies that they are part of the secular world rather than the divine reality. However the corollary is that the divine reality is qualitatively beyond mundane reality. But again, if the conception in the understanding of the faithful is less than perfect, then it does not follow that the conception of God cannot be conceived not to exist. And this would be true if the understanding was nearly at the highest degree of the spectrum which runs from foolish to wise.

 

From Chapter IV:

How the fool has said in his heart what cannot be conceived. – A thing may be conceived in two ways: (1) when the word signifying it is conceived; (2) when the thing itself is understood. As far as the word goes, God can be conceived not to exist; in reality he cannot.

 

But how has the fool said in his heart what he could not conceive; or how is it that he could not conceive what he said in his heart? Since it is the same to say in the heart, and to conceive.

 

But, if really, nay, since really, he both conceived, because he said in his heart; and did not say in his heart, because he could not conceive; there is more than one way in which a thing is said in the heart or conceived. For, in one sense, an object is conceived, when the word signifying it is conceived; and in another, when the very entity, which the object is, is understood.

 

In this fourth chapter it is as if Anselm has reflected on what he has written, and realizes he needs to deal with the objection that he is confusing (or conflating) an epistemology with an ontology. An object can be conceived in terms of words (what Bertrand Russell would say was ‘knowledge by description’), or in terms of a non-textual, intuitive understanding, (which Russell terms ‘knowledge by acquaintance’).

 

In the former sense, then, God can be conceived not to exist; but in the latter, not at all. For no one who understands what fire and water are can conceive fire to be water, in accordance with the nature of the facts themselves, although this is possible according to the words. So then, no one who understands what is can conceive that God does not exist, although he says these words in his heart, either without any, or with some foreign signification. For, God is that than which a greater cannot be conceived. And he who thoroughly understands this, assuredly understands that this being so truly exists, that not even in concept can it be non-existent. Therefore, he who understands that God so exists, cannot conceive that he does not exist.

 

Anselm acknowledges that in terms of description, a conception in the understanding may be imperfect, and consequently it is possible to conceive of the non-existence of God. But in terms of knowledge by acquaintance, to continue with Russell’s terminology, it is not possible to conceive of the non-existence of God. He uses the concrete images of fire and water, and argues that our understanding of those (which will include knowledge of their properties and characteristics), according to their differing natures, could not be be confused with one another; but that this might be possible in terms of their descriptions in words. He then argues that ‘no one who understands what is’ (i.e., what is real) can conceive that God does not exist, although it remains possible to express the notion in words, either words without signification, or with some signification which has no bearing on the question of the reality of God. He who has a thorough understanding of this, certainly understands that God so truly exists, that not even in concept can God not be real.

 

This is placing a great deal on non-textual and intuitive understanding. The fact remains that intuitive understanding can be as fallible and plain wrong as any other kind, and so Anselm has not made a watertight case for the reality of God. Though this is an argument which might please the faithful, who might be inclined to amplify their faith in line with what they believe intuitively to be the case. 

 

I thank thee, gracious Lord, I thank thee; because what I formerly believed by thy bounty, I now so understand by thine illumination, that if I were unwilling to believe that thou dost exist, I should not be able not to understand this to be true.

 

Richard Taylor writes that: “Anselm gives some background to how he came to construct his argument for the proof of the reality of God in the Proslogion.’ He was, he writes, seeking some single argument that would not only prove God’s existence but make evident God’s attributes as well. The central idea of the ontological argument, that perfection implies existence, kept forcing itself on him, but he rejected it as a specious and illusory basis for any argument until, finally, he realized he could find no rational ground for rejecting it any longer, whereupon he joyfully embraced it as providing the proof he had been seeking.”  [2]


 

The Ontological Argument in Descartes

 

The argument developed by Descartes differs from Anselm’s in a number of respects. He avoids the term ‘great’ (and notes the fact in the course of his argument). Instead he uses the concept ‘perfect’, so that God is described as the ‘supremely perfect Being’. He also uses variations on the phrase ‘clearly and distinctly’ in connection with his apprehension of the idea of God.  [3]

 

If just because I can draw the idea of something from my thought, it follows that all which I know clearly and distinctly as pertaining to this object does really belong to it, may I not derive from this an argument demonstrating the existence of God? It is certain that I no less find the idea of God, that is to say, the idea of a supremely perfect Being, in me, than that of any figure or number whatever it is; and I do not know any less clearly and distinctly that an actual and eternal existence pertains to this nature than I know that all that which I am able to demonstrate of some figure or number truly pertains to the nature of this figure or number, and therefore, although all that I concluded in the preceding Meditations were found to be false, the existence of God would pass with me as at least as certain as I have ever held the truths of mathematics to be.

 

To paraphrase: ‘If it follows that an idea in thought can be expressed, and all I know clearly and distinctly about it,  is the case, then may I not use this as the basis of an argument to prove the reality of God?’ He finds the idea of a ‘supremely perfect Being’ as real within himself as ideas of geometric figures, and numbers. He does not know any less clearly and distinctly that actual and eternal existence is a property of the supreme perfect Being, than he knows all which he can demonstrate in relation to geometrical figures or a number truly comprises the properties of these. And were everything else in the preceding Meditations to be found false, the reality of God would be as real for Descartes as he ever held the truths of mathematics to be.

 

However clear and distinct is Descartes idea of a ‘supremely perfect Being’, and that this idea can be expressed, it does not follow that it can be used as the basis of an argument to prove the reality of God. To follow his analogy, his knowledge of the properties of geometrical figures and numbers, may be extensive and even comprehensive, but it does not follow that his knowledge of these properties is complete. The properties of which he knows are just that. It is obvious that it is easier to circumscribe the properties and characteristics of geometrical figures and numbers than to have a clear and distinct idea of the properties and nature of a ‘supremely perfect Being’. What Descartes can have in his mind is a ‘notion’ of the properties and nature of such a perfect Being. He might think that the reality of God, the existence of God is at least as real as the truths of mathematics; this is a notion only, rather than something which can be established.

 

This indeed is not at first manifest, since it would seem to present some appearance of being a sophism. For being accustomed in all other things to make a distinction between existence and essence, I easily persuade myself that the existence can be separated from the essence of God, and that we can thus conceive God as not actually existing. But, nevertheless, when I think of it with more attention, I clearly see that existence can no more be separated from the essence of God than can its having its three angles equal to two right angles be separated from the essence of a rectilinear triangle, or the idea of a mountain from the idea of a valley; and so there is not any less repugnance to our conceiving a God (that is, a Being supremely perfect) to whom existence is lacking (that is to say, to whom a certain perfection is lacking), than to conceive of a mountain which has no valley.

 

Descartes defends himself against the possible charge that his argument is sophistry. He can ordinarily distinguish between the existence and the essence of something. And so he can easily persuade himself that the property ‘existence’ can be separated from the ‘essence’ of God. And thus that we can conceive of God as not possessing the property of something which exists. This however he says is the result of inattentive thinking, and more attention to the question allows him to clearly see that the existence of God cannot be separated from the essence of God any more than the properties of a right-angled triangle can be separated from the essence of it. Or any more than that the idea of a mountain can be separated from the idea of a valley. So the repugnance of the idea of conceiving a supremely perfect Being without the property of existence is no less than to conceive of a mountain without a valley.

 

The problem here is the conception of existence as a form or mode of perfection. In antiquity this equation would not have been made – rather the nature and properties of divinity would have been drawn in contrast with those of existence. There are many ways to express this difference – the secular world has existence, the world of coming-to-be and passing-away has existence, man has existence, the world of things and of representation has existence. The Divine and the eternal did not have existence in the same way in the ancient world. The world of reality was understood to be separate in essence from the secular world; this separate reality was the realm of the divine, and so existence would not be a property of the divine, even if the divine was (as it generally was) considered to be completely real. This is not to say that the divine could not manifest or act in the world of existence; but that existence is a species of imperfection, with which the divine could be (and was) contrasted. Descartes cannot mean that God is real in the sense of having a presence in the material world. And it is curious that later he treated God as if he was walled up in his own sphere. This was necessary to promote the idea that one could do mathematics without reference to God, and without concern that God would interfere with the purely mathematical workings of the world. 

 

But although I cannot really conceive of a God without existence any more than a mountain without a valley, still from the fact that I conceive of a mountain with a valley, it does not follow that there is such a mountain in the world; similarly although I conceive of God as possessing existence, it would seem that it does not follow that there is a God which exists; for my thought does not impose any necessity upon things, and just as I may imagine a winged horse, although no horse with wings exists, so I could perhaps attribute existence to God, although no God existed.

 

Here, Descartes concedes that though he can conceive of the supreme perfect Being as possessing existence, it does not necessarily follow that there is a God which exists, since his thought ‘does not impose any necessity upon things’. What he means by this is that the reality or otherwise or god is not dependent on his understanding of the nature of God.’ So Descartes might be attributing the property of existence to God, even if no God existed.

 

But a sophism is concealed in this objection; for from the fact that I cannot conceive a mountain without a valley, it does not follow that there is any mountain or any valley in existence, but only that the mountain and the valley, whether they exist or do not exist, cannot in any way be separated one from the other. While from the fact that I cannot conceive God without existence, it follows that existence is inseparable from Him, and hence He really exists; not that my thought can bring this to pass, or impose any necessity on things, but, on the contrary, because the necessity which lies in the thing itself, i.e., the necessity of the existence of God determines me to think in this way. For it is not within my power to think of God without existence (that is of a supremely perfect Being devoid of a supreme perfection) though it is in my power to imagine a horse either with wings or without wings.

 

Descartes argues that there is sophistry in this objection, before introducing a genuine sophism into the argument. He says that he cannot conceive a mountain without a valley, but agrees that it does not follow that there is any mountain or valley in existence. But, that whether they do or do not exist, the mountain and the valley cannot be separated from one another. He then says that since he cannot conceive of God without the property of existence, ‘it follows that existence is inseparable from him, and hence He really exists. Descartes has introduced the idea of the ‘necessity’ of the existence of God here, quite shamelessly: he argues that it is ‘not that my thought can bring this to pass, or impose any necessity on things, but, on the contrary, because the necessity which lies in the thing itself, i.e., the necessity of the existence of God determines me to think in this way’. That this remains a subjective understanding, rather than an objective property of God, is confirmed by the words which follow: ‘For it is not within my power to think of God without existence (that is of a supremely perfect Being devoid of a supreme perfection), though it is in my power to imagine a horse either with wings or without wings.’ Again the notion that existence is a form of perfection is called into play, and in conjunction with the necessity of the existence of God, because he is perfect, and the circular argument is complete.

 

Descartes then passes on to a discussion of the relationship between the matter of mathematical figures in his mind and in existence, as a comparison with his proof of the existence of God. The following large paragraph is split into four parts for convenience:

 

And we must not here object that it is in truth necessary for me to assert that God exists after having presupposed that He possesses every sort of perfection, since existence is one of these, but that as a matter of fact my original supposition was not necessary, just as it is not necessary to consider that all quadrilateral figures can be inscribed in the circle; for supposing I thought this, I should be constrained to admit that the rhombus might be inscribed in the circle since it is a quadrilateral figure, which, however, is manifestly false.

 

Descartes is arguing that it is not necessary to assert that God exists once he has presupposed (as part of the definition of the supreme perfect Being) that He possesses every sort of perfection (the property of existence being one of these), for the supposition was not necessary (in the sense that it is not necessary intellectually to assert this for the properties of things to be real), just as one does not have to think of facts such as ‘all quadrilateral figures can be inscribed in the circle’. Descartes here is referring to the strict definition of a figure being inscribed in a circle, which requires that each of the vertices should be in contact with the circle. The truth of what can be contained within a circle is not constrained by the looseness of a mathematician’s statement such as ‘all quadrilateral figures can be inscribed in the circle’. The rhombus is a quadrilateral figure, but it does not meet the requirement of each of the vertices being in contact with the circle.

 

We must not, I say, make any such allegations because although it is not necessary that I should at any time entertain the notion of God, nevertheless whenever it happens that I think of a first and a sovereign Being, and, so to speak, derive the idea of Him from the storehouse of my mind, it is necessary that I should attribute to Him every sort of perfection, although I do not get so far as to enumerate them all, or to apply my mind to each one in particular. And this necessity suffices to make me conclude (after having recognized that existence is a perfection) that this first and sovereign Being really exists; just as though it is not necessary for me ever to imagine any triangle, yet, whenever I wish to consider a rectilinear figure composed only of three angles, it is absolutely essential that I should attribute to it all those properties which serve to bring about the conclusion that its three angles are not greater than two right angles, even although I may not be then considering this point in particular.

 

Descartes here makes an interesting series of statements. These seem to be arguing that the notion (and Descartes uses this word here rather than ‘understanding’, which was used earlier in the argument) of God does not have to be conceived ‘at any time’, but that when it is conceived, he thinks first of ‘a first and sovereign Being’, and derives the idea of Him ‘from the storehouse of my mind’.  And it is necessary to attribute to this derived idea ‘every sort of perfection’. But, in the light of his frequent use of the phrase ‘clearly and distinctly’ in connection with his understanding of the properties of the supremely perfect Being, it is extraordinary to read the succeeding text. He says that does not ‘get so far as to enumerate them all, or to apply my mind to each one in particular’. So in what way is his understanding ‘clear and distinct’? I think here Descartes is emphasizing that his understanding or notion of God has nothing to do with the existence or otherwise of God. But if the understanding of God is actually just a notion, involving loose ideas of perfection, then in what way does this constitute a proof of the existence of the ‘supremely perfect Being’? In the text which follows Descartes emphasizes that he does not desire to accept anything which he cannot conceive clearly and distinctly.

 

But when I consider which figures are capable of being inscribed in the circle, it is in no wise necessary that I should think that all quadrilateral figures are of this number; on the contrary, I cannot even pretend that this is the case, so long as I do not desire to accept anything which I cannot conceive clearly and distinctly. And in consequence there is a great difference between the false superstitions such as this, and the true ideas born within me, the first and principal of which is that of God. 

 

Here Descartes is confronting loose definition, in this case the overgeneralization that all quadrilateral figures can be inscribed in a circle. The overgeneralization contradicts the need to conceive the understanding of God ‘clearly and distinctly’. And so there is a great difference between notions based on overgeneralisations such as ‘all quadrilaterals can be inscribed in a circle’, and the ideas born in the mind, the first of which is that of God.

 

For really I discern in many ways that this idea is not something factitious, and depending solely on my thought, but that it is the image of a true and immutable nature; first of all, because I cannot conceive anything but God himself to whose essence existence necessarily pertains; in the second place because it is not possible for me to conceive two or more Gods in this same position; and, granted that there is one such God who now exists, I see clearly that it is necessary that He should have existed from all eternity, and that He must exist eternally; and finally, because I know an infinitude of other properties in God, none of which I can either diminish or change.

 

To Descartes this idea of the supreme perfect Being is not something fabricated by the human mind, but it is the ‘image of a true and immutable nature’. Then he says something quite surprising - he says he cannot ‘conceive anything but God himself to whose essence existence necessarily pertains’.  What does he mean by this? Is he saying that he can doubt the existence of all other entities? Or perhaps he is saying that existence is not a necessary or essential property of all entities other than God? Descartes has subtly shifted his position here, by modifying his implicit definition of ‘existence’. Now it is an essential property of the divine, and perhaps an inessential property of all other entities and objects. The question arises therefore, is the modified definition of existence something which has aspects in common with the existence associated with entities and objects? Is it really the case in the mind of Descartes that ‘God’ possesses the property existence more than everyday objects which we are more accustomed to say exist?

 

And he cannot conceive two or more gods in the same position. Granted that this supremely perfect Being exists, it is necessary that He should have existed from all eternity, and that He must exist eternally.

 

 This is the end of the paragraph split into four parts . Descartes now concludes his argument:

 

For the rest, whatever proof or argument I avail myself of, we must always return to the point that it is only those things which we conceive clearly and distinctly that have the power of persuading me entirely. And although amongst the matters which I conceive of in this way, some indeed  are manifestly obvious to all, while others only manifest themselves to those who consider them closely and examine them attentively; still, after they have once been discovered, the latter are not esteemed as any less certain than the former. For example, in the case of every right-angled triangle, although it does not so manifestly appear that the square of the base is equal to the squares of the other two sides as that this base is opposite to the greatest angle; still, when this has once been apprehended, we are just as certain of its truth as of the truth of the other. And as regards God, if my mind were not preoccupied with prejudices, and if my thought did not find itself on all hands diverted by the continual pressure of sensible things, there would be nothing which I could know more immediately and more easily than Him. For is there anything more manifest than that there is a God, that is to say, a Supreme Being, to whose essence alone existence pertains?


 

The Nature of Reality in Berkeley

 

I’ve chosen to look initially at the philosophical outlook of Berkeley through public criticism by Bertrand Russell.  [4]  He was born in Ireland in 1685, and became a Fellow of Trinity College, Dublin when he was twenty-two years old. What was peculiar about his philosophy was that he denied the existence of matter, and in fact the reality of the objective world. He argued that material objects had existence only in so far as they are perceived by the viewer.

 

The obvious criticism of this theory is that if perception is the only thing which gives objects their reality, then when we are not looking at them, they should not exist.

 

To the objection that, in that case, a tree, for instance, would cease to exist if no-one was looking at it, he replied that God always perceives everything; if there were no God, what we take to material objects would have a jerky life, suddenly leaping into being when we look at them; but as it is, owing to God’s perceptions, trees and rocks and stones have an existence as continuous as common sense supposes. This is, in his opinion, a weighty argument for the existence of God.

 

His principal philosophical concerns were expressed in a small number of works written before he was twenty-eight years old. These concerns resemble remarkably those of ancient priestly interest. His works were A New Theory of Vision (1709); The Principles of Human Knowledge (1710); and The Dialogues of Hylas and Philonous (1713). The last of these is the one which presents the argument against matter. Russell considers that the first of these dialogues and the beginning of the second present the main aspects of the theory, and supplies a useful summary of the argument. This summary is reproduced here. Russell feels that Berkeley:

 

advances valid arguments in favour of a certain important conclusion, though not quite in favour of the conclusion he thinks he is proving. He thinks he is proving that all reality is mental; what he is proving is that we perceive qualities, not things, and that qualities are relative to the percipient.  [5]

 

There are only two characters in the dialogue, Hylas and Philonous.  [6]  The former represents educated common sense, and Philonous, represents Berkeley himself. Shortly after the opening remarks,

 

Hylas says that he has heard strange reports of the opinions of Philonous, to the effect that he does not believe in material substance. ‘Can anything,’ he exclaims, ‘be more fantastical, more repugnant to Common Sense, or a more manifest piece of Scepticism, than to believe there is no such thing as matter?’ Philonous replies that he does not deny the reality of sensible things, i.e. of what is perceived immediately by the senses, but that we do not see the causes of colours or hear the causes of sounds. Both agree that the senses make no inferences. Philonous points out that by sight we perceive only light, colour, and figure; by hearing, only sounds; and so on. Consequently, apart from sensible qualities ther is nothing sensible, and sensible things are nothing but sensible qualities or combinations of sensible qualities.

 

Philonous now sets to work to prove that ‘the reality of sensible things consists in being perceived’, as against the opinion of Hylas, that ‘to exist is one thing, and to be perceived is another’. That sense-data are mental is a thesis which Philonous supports by a detailed examination of the various senses. He begins with heat and cold. Great heat, he says, is a pain, and must be in a mind. Therefore heat is mental; and a similar argument applies to cold. This is reinforced by the famous argument about the lukewarm water. When one of your hands is hot and the other cold, you put both into lukewarm water, which feels cold to one hand and hot to the other; but the water cannot be at once hot and cold. This finishes Hylas, who acknowledges that ‘heat and cold are only sensations existing in our minds’. But he points out hopefully that other sensible qualities remain.

 

Philonous next takes up tastes. He points out that a sweet taste is a pleasure and a bitter taste is a pain, and that pleasure and pain are mental. The same argument applies to odours, since they are pleasant or unpleasant.

 

Hylas makes a vigorous effort to rescue sound, which, he says, is motion in air, as may be seen from the fact that are no sounds in a vacuum.  [7]  We must, he says, ‘distinguish between sound as it is perceived by us, and as it is in itself; or between the sound which we immediately perceive and that which exists without us’.  Philonous points out that what Hylas calls ‘real’ sound, being a movement, might possibly be seen or felt, but can certainly not be heard; therefore it is not sound as we know it in perception. As to this, Hylas now concedes that ‘sounds too have no real being without the mind’.

 

They now come to colours, and here Hylas begins confidently: ‘Pardon me: the case of colours is very different. Can anything be plainer than that we see them on the objects?’ Substances existing without the mind, he maintains, have the colours we see on them. But Philonous has no difficulty in disposing of this view. He begins with the sunset clouds, which are red and golden, and points out that a cloud, when you are close to it, has no such colours. He goes on to the difference made by a microscope, and to the yellowness of everything to a man who has jaundice. And very small insects, he says, must be able to see much smaller objects than we can see. Hylas thereupon says that colour is not in the objects, but in the light; it is, he says, a thin fluid substance. Philonous points out, as in the case of sound, that, according to Hylas, ‘real’ colours are something different from the red and blue that we see, and that this won’t do.

 

Hereupon Hylas gives way about all secondary qualities, but continues to say that primary qualities, notable figure and motion, are inherent in external unthinking substances. To this Philonous replies that things look big when we are near them and small when we are far off, and that a movement may seem quick to one man and slow to another.

 

At this point Hylas attempts a new departure. He made a mistake, he says, in not distinguishing the object from the sensation; the act of perceiving he admits to be mental, but not what is perceived; colours, for example, ‘have a real existence without the mind, in some unthinking substance’. To this Philonous replies: ‘That any immediate object of the senses – that is, any idea or combination of ideas – should exist in an unthinking substance, or exterior to all minds, is in itself an evident contradiction.’

 

Russell points out that the argument has now become a logical one, and is no longer empirical in nature. Berkeley has moved on to a discussion involving ideas, as expressed by Philonous a few pages later, where he says, ‘whatever is immediately perceived is an idea; and can any idea exist out of the mind?’

 

After a metaphysical discussion of substance, Hylas returns to the discussion of visual sensations, with the argument that he sees things at a distance. To this Philonous replies that this is equally true of things seen in dreams, which everyone admits to be mental; further, that distance is not perceived by sight, but judged as the result of experience, and that, to a man born blind but now for the first time able to see, visual objects would not appear distant.

 

At the beginning of the second Dialogue, Hylas urges that certain traces in the brain are the causes of sensations, but Philonous retorts that ‘the brain, being a sensible thing, exists only in the mind’.

 

Russell ends his summary of the argument here, and divides Philonous’ argument into two parts. The first is the argument that we do not perceive material things, but only their secondary qualities, such as colours, sounds, etc. These secondary qualities exist in the mind, and are mental in nature. Russell thinks that Berkeley’s reasoning is ‘completely cogent as to the first point,’ but as to the second, ‘it suffers from the absence of any definition of the word ‘mental’. He relies… upon the received view that everything must be either material or mental, and that nothing is both’. 

 

When he says that we perceive qualities, not ‘things’ or ‘material substances’, and that there is no reason to suppose that the different qualities which common sense regards as all belonging to one ‘thing’ inhere in a substance distinct from each and all of them, his reasoning may be accepted. But when he goes on to say that sensible qualities – including primary qualities – are ‘mental’, the arguments are of very different kinds, and of very different degrees of validity. There are some attempting to prove logical necessity, while others are more empirical.  [8]

 

Russell is not interested in Berkeley’s argument after this, as he explained. This is because he has exposed the same looseness of language which we saw employed by the most celebrated exponents of the ontological argument (and consequently the weakness of the argumentation), and the rest of Berkeley’s argument concerns a theological understanding of the world. We however shall press on, since Berkeley’s theological understanding is relevant to the subject of this book, and it also presents an alternative form of ontological argument, which Berkeley claims shows the reality of God.

 

The Second Dialogue opens with a discussion which functions to clarify whether the essentially skeptical view of Hylas is the correct response to Philonous’ argument.  Philonous ( p 166) asks to know ‘whether I rightly understand your hypothesis. You make certain traces in the brain to be the causes or occasions of our ideas. Pray tell me, whether by the brain you mean any sensible thing?’ Hylas confirms that this is his view, and that he cannot imagine what else Philonous thought he might mean. Philonous responds by defining that ‘sensible things are all immediately perceivable, are ideas; and these exist only in the mind.’ They both agree that Hylas has agreed to this much earlier in the argument.

 

Philonous then argues that, since the brain, being itself a sensible thing, ‘exists only in the mind’, and asks if Hylas would agree whether or not it is reasonable to suppose that ‘one idea or thing existing, occasions all other ideas.’ And that if this is his view, how does he account ‘for the origin of that primary idea of the brain itself?’  Hylas replies that he does not explain the origin of our ideas by a ‘brain which is perceptible to sense; rather he understands the brain being ‘only a combination of sensible ideas’, and that the explanation is by means of another brain which he imagines.

 

Philonous responds by suggesting that things imagined are as truly in the mind as things which are perceived. Hylas agrees. Philonous points out that Hylas has been ‘all this while accounting for ideas, by certain motions or impressions in the brain’ by means of ‘some alterations in an idea, whether sensible or imaginable,’ and that it does not matter which. Hylas is a little shaken by this, and says that he begins to suspect his own hypothesis.

 

A clue is presented as to where Philonous is going with this argument, since he says that ‘all we know or conceive are our own ideas,’ with the exception of ‘spirits.’ And if we do not conceive it, then we ‘talk unintelligibly,’ instead of forming a reasonable hypothesis’. Hylas now crumbles, and says that he ‘now clearly see it was a mere dream’ to argue in terms of motions or impressions in the brain. Philonous responds by saying that ‘this way of explaining things… could never have satisfied any reasonable man’ since ‘what connexion is there between a motion in the nerves and the sensations of sound or colour in the mind?’ He agrees with Philonous that he is satisfied that no sensible things have a real existence. He also agrees the he is clearly a skeptic.

 

Philolnous then embarks on a long paean to the glories of the sensible world and its orderliness:

 

Raise now your thoughts from this ball of earth, to all those glorious luminaries that adorn the high arch of heaven. The motion and situation of the planet, are they not admirable for use and order? Were those (miscalled erratic) globes ever known to stray, in their repeated journeys through the pathless void? Do they not measure areas around the sun ever proportioned to the times? So fixed, so immutable are the laws by which the unseen Author of Nature actuates the universe. How vivid and radiant is the lustre of the fixed stars! How magnificent and rich that negligent profusion, with which they appear to be scattered throughout the whole azure vault!

 

Philonous is appealing here to the heavens as a representation of the divine, whose uniformities point to something beyond the appearance. He says to Hylas that he ‘must call imagination to his aid,’ since ‘the feeble narrow sense cannot descry innumerable worlds revolving round the central fires the stars ; and in those worlds the energy of an all-perfect mind displayed in endless forms.’

 

This is not a metaphorical appeal. Berkeley has introduced the notion that reality as it is represented to us is not simply the more or less complex response of the human brain to sensory data, but is a series of representations which are associated with cosmic ‘all-perfect’ mind:

Neither sense nor imagination are big enough to comprehend the boundless extent with all its glittering furniture. Though labouring mind exert and strain each power to its utmost reach, there still stands out ungrasped a surplusage immeasurable. Yet all the vast bodies that compose this mighty frame, how distant and remote soever, are by some secret mechanism, some divine art and force linked in a mutual dependence and intercourse with each other, even with this earth, which was almost slipped from my thoughts, and lost in the crowd of worlds. Is not the whole system immense, beautiful, glorious beyond expression and beyond thought!

 

Both Philonous and Hylas by this point share the view that sensible things exist in mind only. Up to this point however, the view of Hylas has been a profound skepticism about reality, and our capacity to know it. By contrast, here Philonous shows, on the basis of the same evidence, that a quite different conclusion can be drawn, if the intellectual frame is changed. Philonous then attacks the skeptical position in general:

 

What treatment then do those philosophers deserve, who would deprive these noble and delightful scenes of all reality? How should those principles be entertained, that lead us to think all the visible beauty of the creation a false imaginary glare? To be plain, can you expect this skepticism of yours will not be thought extravagantly absurd by all men of sense?

 

Hylas is not impressed, and is not converted to Philonous’s outlook. He says that his comfort is that Philonous is ‘as much a sceptic as I am’. Philonous disagrees, which strikes Hylas as meaning that Philonous agreed all along to the premises of the argument, but is now denying the conclusion, leaving Hylas ‘to maintain those paradoxes’ which Philonous led him into.

Argument and evidence however do not by themselves lead to single and unambiguous conclusions. We arrive at conclusions only by the properties and processes of mind, and on the basis our notions and expectations. Philonous denies that he agreed with Hylas ‘in those notions that led to skepticism.’ He argues that Hylas ‘indeed said, the reality of sensible things consisted in an absolute existence out of the minds of spirits, or distinct from their being perceived.’

 

Consequent to this, Hylas is ‘obliged deny sensible things any real existence’. And that, according to his own definition, he is therefore a professed skeptic. But Philonous says that he ‘neither said nor thought the reality of sensible things was to be defined after that manner.’ Instead he says that to him it is evident, for the reasons that Hylas allows, ‘that sensible things cannot exist otherwise than in a mind or spirit.’ And so he concludes that it is not the case that they have no real existence, ‘but that seeing they depend not on my thought, and have an existence distinct from being perceived by me, there must be some other mind wherein they exist Berkeley’s emphasis . As sure therefore as the sensible world really exists, so sure is there an infinite omnipresent spirit who contains and supports it.’

 

This is an interesting proof of the reality of divine Being, which differs from the other arguments we have looked at. Berkeley clarifies that this is not the Christian notion that God knows and comprehends all things. He argues (as Philonous) that ‘men commonly believe that all things are known or perceived by God, because they believe the being of a God, whereas I on the other side, immediately and necessarily conclude the being of a God, because all sensible things must be perceived by him.’  [9]

 

Hylas objects that this is a footling distinction, saying ‘so long as we all believe the same thing, what matter is it how we come by that belief?  To which Philonous replies that they don’t believe the same thing. ‘For philosophers, though they acknowledge all corporeal beings to be perceived by God, yet they attribute to them an absolute subsistence distinct from their being perceived by any mind whatever, which I do not.’ He asks, ‘is there no difference between saying, there is a God, therefore he perceives all things: and saying, sensible things do really exist; and if they really exist, they are necessarily perceived by an infinite mind: therefore there is an infinite mind, or God. This furnishes you with a direct and immediate demonstration, from a most evident principle, of the being of a God.’

 

Again Berkeley returns to the judgement that men make about sense data, which is not always the same, though the evidence is the same. As Philonous he says that ‘Divines and philosophers had proved beyond all controversy, from the beauty and usefulness of the several parts of the creation, that it was the workmanship of God. But that setting aside all help of astronomy and natural philosophy, all contemplation of the contrivance, order, and adjustment of things, and infinite mind should be necessarily inferred from the bare existence of the sensible world, is an advantage peculiar to them only who have made this  easy reflexion: that the sensible world is that which we perceive by our several senses; and that nothing is perceived by the senses beside ideas; and that no idea or archetype of an idea can exist otherwise than in a mind.’

 

 

Berkeley regarded this as a powerful argument against atheism. Hylas says that ‘some eminent moderns’ entertain a notion of ‘seeing all things in God’, (a reference in particular to the French scholar Malebranche) and gives detail in response to questioning by Philonous. Hylas says that these men conceive that the soul being immaterial, ‘is incapable of being united with material things, so as to perceive them in themselves, but that she (the soul) by her union with the substance of God, which being spiritual is therefore purely intelligible, or capable of being the immediate object of a spirit’s thought. Besides, the divine essence contains in it perfections correspondent to each created being; and which are for that reason proper to exhibit or represent them to the mind.’

 

Philonous is not impressed with this argument, in that he argues it makes a created world ‘exist otherwise than in the mind of a spirit’. This is because, as he has said, ‘nothing is perceived by the senses besides ideas.’ He does not share the view with Malebranche that there is an absolute external world. According to Philonous, Malebranche ‘maintains that we are deceived by our senses, and know not the real natures or the true forms and figures of extended beings, of all which I hold the direct contrary.’ Hylas thinks however that what Philonous proposes comes near to ‘seeing all things in God’.

 

The response of Philonous is that ‘few men think, yet all will have opinions. Hence men’s opinions are superficial and confused. It is nothing strange that tenets, which in themselves are ever so different, should nevertheless be confounded with each other by those who do not consider them attentively.’  [10] He says he is very remote from the view of Malebranche, because Malebranche builds on the most abstract general ideas… though he (Philonous) agrees with holy Scripture, in ‘that in God we live, and move, and have our being’. He explains briefly the difference between his view and that of Malebranche:

 

It is evident that the things I perceive are my own ideas, and that no idea can exist unless it be in a mind. Nor is it less plain that these ideas or things by me perceived, either themselves or their archetypes, exist independently of my mind, since I know myself not to be their author, it being out of my power to determine at pleasure, what particular idea I shall be effected with upon opening my eyes or ears. They must therefore exist in some other mind, whose will it is they should be exhibited to me. The things, I say, immediately perceived, are ideas or sensations, call them what you will. But how can any idea or sensation exist in, or be produced by, anything but a mind or spirit? This indeed is inconceivable; and to assert that which is inconceivable, is to talk nonsense….

 

It may be that the objection to the notion put forward by Malebranche is that it depicts reality as something which is perceived as outside the human mind by the human mind, whereas Berkeley does not make this distinction. For Berkeley it is as if his mind is a subset of the divine cosmic mind, perceiving a subset of the ideas in that mind.  If he perceives ideas, it is because the cosmic mind wills it.

 

The ideas which present themselves to Philonous, he argues, ‘it is very conceivable that they should exist in, and be produced by, a spirit; since this is no more than I daily experience in myself, inasmuch as I perceive numberless ideas; and by an act of my Will can form a great variety of them, and raise them up in my imagination: though it must be confessed, these creatures of the fancy are not altogether so distinct, so strong, vivid, and permanent, as those perceived by my senses, which latter are called real things. From all which I conclude, there is a mind which affects me every moment with all the sensible impressions I perceive. And from the variety, order, and manner of these, I conclude the Author of them to be wise, powerful, and good, beyond comprehension.

 

Philonous emphasizes here that he is not saying that he sees ‘things by perceiving that which represents in the intelligible substance of God. This I do not understand; but I say, the things by me perceived are known by the understanding, and produced by the will, of an infinite spirit.’ So his objection is as I suggested, and he is not simply seeing what is ‘in’ God.

 

Beyond this, the Second Dialogue deals with Malebranche’s occasionalism, which sees the physical world as a place where God has the occasion to create motion and change, and also deals with ideas of substance.

 

 


Hume and Kant on Reality

 

In his first work, the Treatise on Human Nature, published in 1739, when he was 29, Hume argued that he was introducing the scientific method into psychological subjects. That is, he was using an analytical and empirical approach to matters concerned with the mind, and human understanding. This was a large claim for his approach. It was certainly analytical, but its empirical content consists largely of appeals to experience and well-argued conjecture.

 

Hume argued on this basis that human understanding is based on sense data and empirical sense impressions. We have knowledge only of what we directly experience. He divided sense impressions into strong and weak, arguing that weak impressions are simply copies of strong impressions. The mind makes sense of these impressions in the context of what the mind believes it already knows and understands. He argued entirely against the notion of innate ideas, which had been part of the currency of philosophy in the preceding period.

 

There are two key and related areas where Hume’s inquiry into human nature threw up problems which cannot be satisfactorily resolved; these are:  a) whether it is really legitimate for us to perform inductive thought, and b) whether or not we can infer causality. Hume argued that we assume the constancy of the conjunction of things on the basis of experience, but have no actual knowledge of how these things are conjoined. Whatever might hold relationships together is obscure to us, and even our understanding of ourselves is no more than a complex bundle of sense impressions associated with the notion of the self. Of the self itself, we have no real knowledge. In essence Hume was arguing against the uniformitarian attitude to the world which developed after the publication of Newton’s Principia, which saw the apparent regularity and mathematical predictability in Newton’s description of the world as reliable proof of its consistency.

 

Hume used the example the example of colliding billiard balls to illustrate his point (Hume was clubbable, so the example is not a surprising one). Skilled players of the game know how the geometry of billiards works, and can infer the way a ball (B) will move when struck by ball (A). The skill of a good player relies on the consistency of the behaviour of the balls. We assume because of the consistency of this behaviour that there is an underlying and consistent causality at work. However Hume argued that, despite the apparent regularity of the behaviour of ball B when struck by ball A, we have no insight at all into the underlying process by which this behaviour is effected. Nor have we any reason beyond custom and expectation to believe that the balls will behave in the expected manner. Causality itself is a mystery wherever it is found, and we have no knowledge of how and why it works.

 

This is the reason why Hume is regarded as a sceptical philosopher – we have no certain knowledge about some things which we take very much for granted. This is true for both inductive thought, and our understanding of causality.

 

So Hume is left in an interesting position. On the one hand, he argued that what knowledge we have is based purely on experience, and this experience is mediated through sense impressions. On the other hand, he argued that we have no real understanding of how the knowledge we have is assembled, since the consistency we see in the relation between ideas is purely customary and a matter of expectation, which isn’t an understanding. This applies also to causal relations.

 

Hume’s point is not that the universe might at any moment start behaving in a different way; only that what we think we understand, we do not ‘understand’ at all. It is a matter of conjecture based on experience. What underlies these consistencies is wholly unknown to us.

 

Immanuel Kant responded to Hume’s challenge by inverting the line of argument. Where Hume argued that knowledge is acquired through experience, Kant argued that what we understand is shaped by what the human mind can understand. That is, it is reason itself which gives us understanding, and not simply sensory experience. We have to understand reason if we are to understand anything.

 

Not only did Kant argue that what we understand is shaped by properties and characteristics of reason, he also argued that the world of experience, the imagined source of sensory impressions received by the mind, might also be a product of human reason. In other words, we assume that the objective world we see as having existence outside ourselves in space and time, has objective reality. However without a proper understanding of human reason, it is as unreasonable to assume this to be the case, as it is for us to assume the consistent behaviour of billiard balls on a table.

 

This is not to assume the identity of, or to conflate processes occurring in the phenomenal world, with those operating in the mind. Precisely because we do not understand the processes and relations of things in the phenomenal world, there is no reason for them to always conform to our understanding.

 

Kant’s first major work was the Critique of Pure Reason. It had to be a critique rather than a dogmatic survey of pure reason, since reason remained to be understood.  Kant felt that, in pursuing this approach, he was making metaphysics anew, and that all previous writings on metaphysics were superseded, at least in terms of metaphysics as a science. He made this clear in the short work Prolegomena To Any Future Metaphysics That Will Be Able To Present Itself As A Science, which was published around Easter 1783, some two years after the publication of the Critique in the summer of 1781. The purpose of the Prolegomena was to make clear the radical nature of the Critique, and to explain his intent. Kant expected the Critique ‘to have a revolutionary effect and anxiously awaited its impact on the world of learning. In fact he found that it was being received in silence’.  [11]

 

A key argument of the Critique is that the reason does not apprehend things as they are, but only as they appear to us. Kant repeats the distinction made in classical times between the phenomena and the noumena. We can apprehend the phenomena, but the relationship between the phenomena and the noumena, or the ‘thing-in-itself’, is entirely unknown to us, and unknowable by means of the senses, and the mind. To Kant, only the ‘thing-in-itself,’ or ‘things-in-themselves,’ are real.

 

So how does Kant set about creating a scientific metaphysics? He tells us in the preamble to the Prolegomena that ‘If a field of knowledge is to be exhibited as a science, its differentia, which it has in common with no other science and which is thus peculiar to it, must first be capable of being determined exactly; otherwise the boundaries of all the sciences run into one another and none of them can be treading soundly according to its own nature.’  [12]

 

He continues by pointing out that ‘this peculiarity, whether it consists in the difference of the object, or of the sources of knowledge, or of the kind of knowledge, or of  some if not all of these together, is the basis of the idea of the possible science and of its territory’. Kant defines metaphysics very closely as something whose ‘fundamental propositions …  and  its fundamental concepts must never be taken from experience’, since metaphysical knowledge lies beyond experience. The ground of metaphysics will not be either ‘outer experience’, which he defines as the source of physics, nor ‘inner experience, which provides the basis for empirical psychology.’ In other words metaphysics is a priori knowledge, ‘out of pure understanding and pure reason’.

 

Kant recognizes the need to differentiate metaphysics from pure mathematics, and refers the reader to the Critique, where he says

 

Philosophical cognition is rational cognition from concepts. Mathematical cognition is rational cognition from the construction of concepts.’ [13]

 

He expands on this by saying that ‘to construct a concept means to exhibit a priori the intuition corresponding to it. Hence construction of a concept requires a non-empirical intuition. Consequently this intuition, as intuition, is an individual object; but as the construction of a concept, (a universal presentation), it must nonetheless express in the presentation its universal validity for all possible intuitions falling under the same concept.’

 

Kant uses the example of the construction of a triangle, arguing that this construction exhibits the object which corresponds to this concept ‘either through imagination alone, or in pure intuition.’ It can be drawn on paper of course, as a mathematical figure, but in such a case the representation is an empirical intuition, not a pure intuition, though both in the case of the pure intuition and the empirical intuition, Kant has exhibited the object a priori, without having used a model taken from experience (meaning that only the properties of a triangle have been used in its construction). Though the drawn figure is empirical, yet it serves to express the concept ‘without impairing the concept’s universality’.  Only those properties which it is necessary to consider for the construction of the triangle are involved – the many inconsequential details of a physical triangle – the length of the sides, and the angles of the triangle, are not involved in the abstraction. All such irrelevant details are removed from the concept, and the result is therefore wholly abstracted from any particular instance of a triangle.

 

Kant’s argument is therefore that ‘philosophical cognition contemplates the particular only in the universal’. By contrast, he says that mathematical cognition ‘contemplates the universal in particular, and indeed even in the individual’. This might seem at first sight to be a strange distinction, however Kant explains himself clearly, saying that even in the case of this mathematical cognition, the contemplation of it is ‘a priori, and by means of reason.’ And so, ‘just as this individual is determined under certain universal conditions of construction, so the object of the concept – to which this individual corresponds only as its schema – must be thought of as determined universally.  Thus the essential difference between these two kinds of rational cognition ‘consists in this difference of form, and does not rest on the difference of their matter or objects.’

 

He goes on to criticize those who ‘have meant to distinguish philosophy from mathematics by saying that philosophy has as its object merely quality but mathematics only quantity,’ He argues that ‘the form of mathematical cognition is the cause of the fact that mathematics can deal solely with quanta’ (i.e., magnitudes), and that ‘only the concept of magnitudes can be constructed, i.e., displayed a priori in intuition. Qualities, on the other hand, can be exhibited only in empirical intuition; hence a rational cognition of qualities can be possible only through concepts.’ He invokes the example of a conical shape, ‘which can be made intuitive without any empirical aid, merely according to the concept of a cone; but the colour of this cone will have to be given previously in some experience or other. However the cause of anything cannot be exhibited in intuition, since cause is presented by experience.

 

Again against those who have argued for a simplistic distinction between the objects of philosophy and mathematics, he points out that in fact ‘philosophy deals with magnitudes just as much as mathematics does – e.g., with totality, infinity, etc. Mathematics similarly is concerned not only with quantity but also with the difference between lines and planes considered as spaces of different quality, and with continuity as a quality of extension.

 


 

The End of the Ontological Argument

 

I did not write about the Ontological Argument in an earlier draft of this book. But I gained an understanding of its severe limitations while I was writing the paper in 2006 which was subsequently abandoned, due to the weakness of this mode of argument. Knowledge of these limitations informed the discussion of questions about reality in the two parts of the book which were under way, which looked at Greece and Assyria respectively. Once those two parts were largely constructed, I turned to the Ontological Argument sometime in 2012.

 

Ontological argument ought to be about the nature of reality itself, rather than a particular aspect of it. Attempting to prove the existence or reality of God on the basis of purely logical and a priori argument is about proof and existence within a known and perceived frame of reality, which is presumed to be real, though we have no knowledge of what it is and why it presents itself to us in the way that it does. So ontological argument for the most part isn't about reality at all, but some part of that reality, and argued in terms of the properties and attributes which that part may or may not have.

 

The concept of God is discussed within either the reality we know in terms of space and time, or else existing in some other place beyond the limitations of physical reality. In either case the physical frame of space and time is taken as a given.

 

In classical antiquity this would have seemed to be a barbarously crude way to argue about the divine. When they talked about reality, they meant reality itself, not some particular representation of it. And that reality was coterminous with Being. In other words, divine Being was presumed to be at the root of all the forms of reality which can be represented. It was reality.

 

Ancient ideas about divinity therefore need to be understood in their original context, or at least in as much of it as we can muster. A thorough understanding of the varieties of the ontological argument will not tell us much that is useful about ancient conceptions of the divine.

 

So this part of the book should be understood as a necessary demolition of the usefulness of the ontological argument, as we understand it. In the course of writing, I was reminded that there were ancient misunderstandings of the nature of divinity also, on the basis of the way in which the divine was spoken. If the divine is one and indivisible, for example, how is it that there are hundreds of gods, and not one?

 

Parts Two and Three can be read in a number of different ways. But essentially the discussion is of a common intellectual substrate, shared by Greece and Assyria, which lies beneath the strikingly different cultures. The nature of that substrate is explored initially through the writings of Plato, and the Greeks in general.

 

The contention is that Plato, in writing about the Forms or Ideas, was actually telling us something of extraordinary importance about Greek theology, and the role and function of divine images. The source of the idea of the nature of reality, of Being itself is referred to by Plato in many places, but never fully explained. And there is a related question he asks, about a most fundamental matter, but does not answer. The answer can be guessed, though professional philosophers are not in the business of guessing. So we have had nearly two hundred years of scholarship devoted to Plato, which has explained very little.

 

I guessed the answer, though as it turned out, I knew the answer already from a different context. It can be demonstrated that the same question lies beneath Mesopotamian ideas about the nature of reality, as expressed in the liturgy of their New Year Festival, and in other sources. It is the reason why there are two creations - the first chaotic, and the second, rational.

 




[1] Plantinga, A. Ontological Argument, p3, St Anselm (1033-1109).

[2] Plantinga, A. The Ontological Argument, from the introduction by Richard Taylor, pviii. Macmillan, 1968.

[3] Descartes, Rene, third Meditation. In The Philosophical Works of Descartes, Volume I, translated by Elizabeth S. Haldane and G.R.T. Ross.

[4] Russell, Bertrand, The History of Western Philosophy, Chapter XVI, p 623 ‘Berkeley’

[5] Op cit. p624

[6] ‘Philonous’ is a composite of two Greek words, meaning ‘lover of mind’.

[7] This information must have come from experimental data.

[8] Op. Cit, p 626

[9]  p 168

[10] p 169

[11] Kant, Immanuel, Prolegomena To Any Future Metaphysics That Will Be Able To Present Itself As A Science, p.ix, trans. Lucas, Peter G., Manchester University Press, 1953.

[12] Kant, Immanuel, Op. Cit., p15, 1953.

[13] Kant, Immanuel, Critique of Pure Reason,  (A 713. ff), unified edition, trans. Pluhar, Werner S., Hackett Publishing Company, Indianapolis/Cambridge, 1996.