Disclosing Truth
The photograph is of the sculpture of Pythagoras in the Incarnation Portal of the west façade of Chartres Cathedral.
"Everything proceeding from the profound nature of things shows the influence of the law of number; for this is the highest prototype contained in the mind of the Founder. From this are derived the four elements, the succession of the seasons, the movement of the stars, and the course of the heavens".
Boethius
The basis of medieval arithmetic is a qualitative and not merely quantitative conception of number, and is not so much a method of reckoning as a way of understanding the nature of things, their properties and relations.
“God invented and gave us sight to the end that we might behold the courses of intelligence in the heaven, and apply them to the courses of our own intelligence which are akin to them.”
Plato, Timaeus 3:46
The Timaeus is the only text by Plato that the Chartrains knew directly, in an incomplete fourth century Latin translation by Calcidius. Other works by Plato were, however, known to them through the likes of St. Augustine, Macrobius, Boethius and others.
"Talent hits a target no one else can hit; Genius hits a target no one else can see."
(Schopenhauer, Vol. II, Ch. III, para. 31 (On Genius), 1844)
You can only find truth with fact and logic if you have already know the truth without them. There is, in other words, a moral truth that impels the search for truth, that causes human beings to seek and value truth. I am thinking of an argument made by G.K. Chesterton here:
“You can only find truth with logic if you have already found truth without it.”
Fact and logic can take us so far. But all "truth" is based on assumptions for which there is neither proof nor evidence. The statement upon which materialists base their arguments is one such example: matter exists. That’s a statement that can only be assumed, not proven, since we have no way of conceptualizing it otherwise. The scholastics were wise in premising their arguments on axioms, self-evident truths that are incapable of being proven: Know the ground you stand on and you will never fear of falling.
I see links and make connections, and I keep trying to "hit" them. I tend to labour the same points, approaching them from slightly different angles. I once gave a general introduction to philosophy to a group of non-philosophers. I took the opportunity to elaborate upon the theme of ‘rational freedom’ which runs throughout my work. I cited a lot of philosophers in my talk. One perceptive soul shouted when I introduced a new thinker, ‘they’re all saying the same thing!’ To be fair, I did have lots of thinkers giving their particular versions of the same idea – human beings are social beings and the freedom of each is conditional upon the freedom of all. I had the oddest collection of thinkers, from Pythagoras, Plato, and Aristotle, to Augustine and Aquinas, Thomas More and Erasmus, to Leibniz, Spinoza, and Descartes, to Rousseau, Kant, Hegel, and Marx, to Weber, Antonio Gramsci, Max Weber, and Foucault. I inhabit the thoughts of others in order to expose important aspects of their thoughts and spin them in my direction. ‘Are you sure Marx said this,’ my Director Jules Townshend asked me once, ‘or is this you saying that this is what Marx should have said?’ An awful lot of thinkers maybe should have said things other than they did, in order to be as good as the claims they made. So I say it for them. It is me in the guise of others.
I was once heavy on praxis-based truth and projection, seeing human beings as co-authors of their own world. I still work in the contentious area that sees the world as "humanly objective," as in some part human. I have no doubt that I could be criticized as anthropocentric. I make absolutely no apologies for this. When human beings talk, they talk about themselves in some way, and those who pretend otherwise are deluding themselves, to the detriment of what may be their very valid principles. We see this most of all in environmental ethics, with a demand for the almost complete eclipse of human interests and concerns in favour of a worship of and sacrifice to some external indifferent Nature. This human self-immolation is self-contradictory and self-defeating. If, as ecologists repeat endlessly, human beings are a part of nature, then human agency is both legitimate and natural. To read some accounts, everything is entitled to act in nature except human beings. The challenge is to ensure human actions that are in tune with nature within and nature without. If you cut human affairs, interests and needs out in the concern to preserve Nature, proceeding to make an appeal to humans to act on a non-human, even anti-human truth, then don't be surprised to meet with a complete lack of response. Human beings are most certainly concerned and interested in their own affairs and very much have a stake. The challenge is to devise an ethic and a practice that does indeed involve humans as active agents within the creative unfolding of nature. The world is not objective in the sense of being some external datum, it is humanly objective. I argue here that the world is divinely and humanly objective. This is the significance of the personal God. Human beings need to conform their will to a reality that is greater than their wilful self-projection. The divine spark within impels us to seek union with God, the personal God, the God of love and inter-relation. This is the appeal to something greater than the human self that will gain a response from human beings.
I now see human creation as sub-creation, an agency that is operative within a greater reality. The world is more than a human self-creation, the self-created order is itself enfolded within the greater God/Nature. Human freedom and happiness thus depends on the appreciation of a reality that can only be apprehended rationally to a certain extent; beyond logical and fact, the understanding of this reality requires musical metaphors and modes of (mystic) revelation - of just "be-ing". Knowing and being proceed hand in hand. This ‘necessary freedom’ also requires reason with its ethical component in place, also an emotional as well as a cognitive intelligence. Philosophy/science/religion are not antagonistic human modes of knowledge and understanding but entirely complementary, and those who remain within antagonistic relations here are merely trading shadows as blows between themselves. That’s neither entertaining nor enlightening, only irrelevant and irritating. I argue for complementarity, whilst acknowledge that even this yields only a partial vision. Even philosophy/science/religion working together in unison amounts only to humanity pointing its grubby little fingers at the sun, the moon, and the stars and all that they encompass and making its best guesses; it is the finite in pursuit of the infinite. The worst is when we come to see our necessarily limited knowledge as giving us the right to get our grubby grasping hands on things that are beyond our reach, attempting to appropriate the order of the world and make it subservient to our own ends through the technical manipulation of things – and people.
Of course, the more fact and logic we have on our side, then the less of a guess, and less of a leap, we will have to make. But there's always a leap to be made, and to ensure a safe landing on the other side you need faith of a kind that would allow you to leap long before all the proof and evidence were in. That’s precisely the point about fact and logic – to find truth by way of fact and logic, you need to have found it without them: it is that prior truth that motivates truth-seeking in the first place and makes you willing to take that first leap of faith.
Hence I refer continuous to the anarchic surplus that escapes the enclosure of a totalizing reason and shuns a manipulative and exploitative technics. That surplus is an excess that isn’t ephemeral. It is excessive only in the sense that it is beyond the grasp of the rational and technological mind: that denotes a surplus that is the core of our being. Anarchic here doesn't mean accidental or arbitrary, the very opposite in fact. Anarchic here means that there is a reality beyond our rational tools, to which we still need to conform our will. That conforming can only be a matter of faith. Logic and fact can take us so far; faith and courage take us further. Love takes up where knowledge leaves off, to paraphrase Aquinas. It is faith and courage that make us value truth in the first place, it is faith and courage that make us want to leap. Fact and logic will bring you to truth only if you are impelled to find truth in the first instance – faith and courage are required to impel us into living forwards into mystery, embracing a reality for which no proof and evidence are possible or required. That’s what intelligent beings in an intelligible universe do.
Chesterton was bang on target when he wrote, “Logic is not necessarily an instrument for finding truth; on the contrary, truth is necessarily an instrument for using logic — for using it, that is, for the discovery of further truth… Briefly, you can only find truth with logic if you have already found truth without it.” There is a moral knowledge and truth which we need to set alongside logic and fact. Plato argued for the rule of philosopher, or the philosopher-rule, but was wise in knowing that reason does not rule alone; he therefore he put the True, the Good, and the Beautiful together so that humans came to order their existence through the full use of all of their faculties.
Plato emphasized dialectic. This is an important point to grasp. In statements on truth and statements on ‘why truth matters,’ the question of the dissemination and assimilation of truth is frequently overlooked. Plato held that the human senses are incapable of perceiving the Forms, but human beings can nevertheless approach the truth through reasoning and intelligence. For Plato, the world that human beings are capable of knowing can only be an imperfect likeness or copy of the ‘real’ world. In the world perceptible to human beings, things resemble the higher realm of the 'Forms,' but are never fully real in the sense of being perfect and eternal. These things are forever changing and in the process of becoming and are therefore subject to passions and opinions that can never be the full and whole truth, only copies or imitations of the Forms. Plato therefore required dialectic to bring humans closer to the truth. It requires intellectual effort and discipline on the part of human beings to approximate the ‘real’ world of the Forms, a combination stimulated and sustained through dialogue and debate, hence the emphasis on 'dialectic.’ The characters in Plato’s dialogues engage in dialectic. The truth cannot just passively given by the philosopher, but must be both teased out by the teacher and sought after by the taught, hence Socrates' question-and-answer lessons. Genius doesn’t require any great intelligence, just the ability to see the way things are, and make a difference for the better in the world. One of the things I love about the ‘rational’ tradition I work within is that it values and seeks to stimulate the genius that all human beings have; all have a genius, a particular spirit that is innate to each of us, a particular quality that we bring to the party. That's what Socrates emphasised when he made a point of drawing out the innate knowledge possessed by those who had claimed not to know. By Socratic questioning, we come to realize how much we do know, despite thinking that we knew nothing.
There are outstanding issues to be settled. I shall end by noting a divergence between the Platonist and the Pythagorean view. The short and simple take on this is:
In Plato’s tower, the staircase from the human-experience level doesn’t quite ascend to the level of the Forms. Plato's staircase to the top is incomplete, human intelligence can never reach to the Forms, it can only achieve copies. Numbers and mathematics can take you up quite a few flights indeed, high enough, you may say. You could go even higher by use of dialectic, dialogue, engagement in the yes/no world, reasoning, logic. But you’ll never reach the realm of the Forms, and will never know if the unreachable peak was mathematical or not. The music suggests it may be.
In the Pythagoreans’ tower, the staircase goes to the very top. Pythagoreans can propose a complete staircase of numbers and mathematics, connecting ground level to the heights. Convinced that they know mathematics and numbers to constitute the rationality of the universe, Pythagoreans claim to have the key to complete understanding and reunion with the divine level of reality. Human beings can climb those stairs and, in reaching the top, would find the peak to be mathematical.
There are tricky issues for Platonists and Pythagoreans here. The complete staircase of numbers and mathematics implies that the Forms could come to be completely known. In coming to be completely known, beware of appropriation. The eternal plan of Justice is not for human hands. Humans are meant to conform their will to that plan, not to take possession of it and turn it to human ends: you cannot have your transcendent cake and eat it too, once that cake is eaten it is eaten for good, and humans cannot digest it. I run a mile from the 'men as gods' delusion. Numbers and mathematics can take you up quite a few flights indeed, high enough, many may say. You could go even higher by use of dialectic, dialogue, and engagement in the yes/no world. Or risk being forever plunged into the murk and bias of the inherently contested social and political world in which humans live. But that’s what we are, all too human, with stakes and interests, not gods. Reasoning and logic can take us far. But humans will never reach the realm of the Forms, and are not meant to. Instead of soaring to the heavens as gods, humans are charged with drawing the transcendent down to earth, at least the norms and standards of that realm. The problems that Plato had in spanning the divide between contemplation and action is fascinating to ponder. The contemplative life is the best, but Plato was nevertheless deeply concerned with political affairs, laws and good governance.
'Knowing' in this sense is problematic for a Platonist, in that it contradicts the view that the Forms could never be fully known. It brings us into a completely knowable universe. The Pythagoreans have something that Platonists lack. Whether we call it a faith or a knowledge, it is certainly rational: the belief, backed by discovery, that mathematical logic and pattern underlie nature. Mathematics and numbers are therefore the rational, unconditional principles of the universe, awaiting disclosure on the part of human intelligence.
In this short piece, I'm interested in what makes human beings step forward as truth-seekers in the first place - because there are evolutionary reasons for saying humans are rationalizers and deceivers rather than truth-seekers. In what way are human beings enjoined to disclose the truth of the universe? The idea that humans seek truth is inherently theological - God made the world intelligible to stimulate intellectual and ethical inquisitiveness on the part of human beings as intelligent beings.
“I think that modern physics has definitely decided in favour of Plato. In fact, the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.”
Werner Heisenberg
I do so love Plato's notion of a well-tempered order but, poor me, I can't count and so can't express truths in unambiguous, unanswerable terms. I therefore have to leave the eternal realm of the Forms and enter the "ambiguous" world of politics and ethics, the field of practical reason, the place where human beings are, social beings with interests and concerns, a characteristic which they share with others, even if they conflict over the particulars. That’s the difficult problem. A truth that is clear and unambiguous at the transcendent level is many-sided and multi-faceted in its concrete particulars. The task is to reconcile multiplicity in unity through the convergence of different elements in concord. Plato sought to move to the ethical and political terrain, developing the implications of the transcendent forms in practical life, as Pythagoras had done before him. This means taking up the dialectic in an attempt to tease out the truth through dialogue and engagement with others in the ambiguous terrain of the social world. I have always been a dialectical thinker, and did great work on Marx in this area. It means I am not always easy to pin down, since my views exist in the unfolding and intertwining).
I’m fairly courageous, I’d say, in eschewing the certainty I crave to enter the world of uncertainty, conflict, friction, and endless questioning. With my character traits, I'm supposed to be a genius with numbers, but was always a dunce in arithmetic and maths. I'm a Pythagorean who can't count! You can't get more different than that! Although, as I note above, numbers are as much about the qualitative as they are the quantitative in this tradition. I am certainly Pythagorean and Platonist in that sense, and am certainly with the Chartrians.
I have always fancied a job in conservation, counting puffins in Anglesey or Skomer Island: the innumerate counting the innumerable! Theologians trying to describe God the ineffable call it eternity; I call it a job for life.
Despite not being able to do basic arithmetic, I have always been fascinated by numbers. It's the idea of order and harmony. But the world of philosophical argumentation, dialogue, ethics, politics, society, and human psychology is nothing less than extremely complicated. I eschewed the peace that would come with certainty and "went straight for the most complex of networks and structures" (as my dear friend Helene Domon said of me). That is it in a nutshell.
I still worry that I am missing something, and that I am wasting time in endless debate, adrift in the world where people cancel each other out with their ‘yeses’ and ‘noes.’ But whenever I address this issue, I keep drawing the same conclusion – the truth cannot just be given, passively, in unanswerable form – it has to be assimilated and absorbed through the clash of 'yes' and 'no' in the dialectic. So I proceed from transcendent truth to deal in the ambiguous world of ethics and politics, trying to get the 'yeses' and 'noes' to conform their answers to standards greater than the assertive ego. I do seek harmony and order, the reconciliation of multiplicity in unity, but I try to achieve it the hard way, involving people and dialectic. I write on the social dialectic. Here, in the world of ambiguity and the friction of competing views and values, human beings come to disclose truth practically. In the unambiguous world of unanswerable truth, you lose friction, you lose the dialectic. Truth exists, but it is on ice, frozen and immobilized. Truth needs to live and breath. You have to enter the ambiguous world, however frustrating, however annoying - it's where people are, however frustrating, however annoying. I say this as an Aspie who struggles mightily with social communication and social interaction. And here I so recognize Wittgenstein's emotional and intellectual turmoil in dealing with truth and the world. This notion of dialectic is something that Wittgenstein understood well:
“To convince someone of the truth, it is not enough to state it, but rather one must find the path from error to truth."
Wittgenstein, Philosophical Occasions 1912-1951 (1993) Ch. 7 : Remarks on Frazer's Golden Bough, p. 119
I would much prefer to remain in the realm of certain, the world of fact and logic, where the truths seem unanswerable. But that’s only part of the world. There is friction and conflict in the world. We cannot put politics and people on ice – such a thing can never realize truth, only freeze and immobilize it, as if locked forever at the pit of Dante’s Inferno:
“I must plunge into the water of doubt again and again.”
Wittgenstein, Philosophical Occasions 1912-1951 (1993), Edited by James Carl Klagge and Alfred Nordmann, Ch. 7 : Remarks on Frazer's Golden Bough, p. 119
If you put politics on ice, and people on ice too, then the truth remains passive and inert. Stating truth is the easy part. It is the people who work in the world of language, humanities, society, psychology, ethics, and politics who do the hard stuff in trying to body forth the truth. In Dante's Enamoured Mind, I wrote on how Dante sought 'to make shadow substance', to 'incarnate' and 'body forth' the truth. I have nothing against people who work in systems, design and technology and such like - ideals without their means of realization are impotent - but insofar as they advance the means in an attempt to ‘workaround’ addressing ends enjoined upon the hard and ambiguous human material, then they will fail on account of their irrelevance. Technics will be drawn back into prevailing arrangements and misfire as a result.
Coming out a philosophical tradition of ‘rational freedom,’ where I sought to ground the good in reason, I veered close in reaction to situating God in the unambiguous order I have been seeking. That’s an error. I now see that the search for such certainty is a modernist delusion encouraged by a loss of nerve on the part of ethics and philosophy in face of the advances of natural science. There are no such grounds for God and no theologian worth their salt ever said that there were. They are wise in their axioms. The same cannot be said of the moderns, whose philosophical reason undercuts itself and leaves their claims for certainty empty. I try now to write of the anarchic excess that evades capture by a totalizing Reason.
I sense this view also cuts me off from environmentalists, those who talk “Nature” as “boss”, some unanswerable authority or deity, as if people are a blight and unimportant. Although they repeat that human beings are a part of nature, they seem to show little understanding or liking of what human beings naturally do. You get the impression that everything is a legitimate agent in nature apart from human beings. Of course, human beings are destructive; they are also creative. It is that relative moral autonomy that has always been the key issue to resolve, getting humans to conform their will to something greater than their own egoistic desires. Whether you call that something greater Nature or God, that need to conform to reality is the same. I’d just say that the personal God has the advantage here, in that it denotes a partnership with humans, a personal interest in human concerns, relationships and love. A cold, indifferent nature could care less, and therefore cannot motivate and inspire action in the same way. Humans could easily turn such a nature into a tool-box; to do the same to God is the plainest abomination and self-immolation, a form of self-abuse.
Helene Domon told me this:
“Language seemed like an infinite system for producing meaning, and even better, for revealing meaning.”I even see God essentially in linguistic relationship with the world. Love those "And God said..." "And Jesus said..."He said let there be light, and there was light. Superb.
This God is personal and relational, and that is the key point. I'm still debating with myself where the balance lies between theology and literary ecology, whether reality is a metaphorical physics, and whether God is a writer and poet as well as a mathematician. We may be talking of eco-poetic creation and invention here. Dante himself does define his purpose as 'to make shadow substance', to 'incarnate' and 'body forth' the truth of fiction. He states that this purpose can be realized only by God, the verace autore (Paradiso 26: 40).
Creation through name and number. I’m not sure I ever much liked naming and framing, although I do love the idea of an intelligible world, that God made humans as intelligent beings who are not only capable of knowing the intelligible world, but are morally enjoined so to do. The notion of humans as truth-seekers is a theological concept, in my view. The evolutionary view is that humans are deceivers, manipulators and rationalizers, of others, of themselves, and of reality.
I started with Pythagoras, Plato, Boethius, number, and harmony, and I'd like to end with these.
In keeping with ancient Greek tradition, Boethius identified three kinds of proportions: the arithmetical, the geometrical, and the harmonic.
In the arithmetical proportion the same interval obtains between all members of the series. The difference between one term and the next is a constant in an arithmetic sequences, the same value each time is added infinitely, as in, for example: 1, 3, 5, 7, 9, 11, ... We could write an arithmetic sequence like this: (a, a+d, a+2d, a+3d, ... ).
The geometrical sequence progresses by means of a constant multiplication, as in: 1, 3, 9, 27, 81. Note that the next term after the term before is obtained by multiplying the preceding element by 3. We could write a geometric sequence like this: (a: c=c: b).
The harmonic sequence (harmonic progression) unites the arithmetic and the geometric according to the formula a: c=a—b: b—c. The harmonic sequence is a sequence of numbers in which the reciprocals of all terms form a arithmetic sequence. Thus (1, 1/2, 1/3, 1/4, . . .) is a harmonic sequence, since the reciprocals of all terms (1, 2, 3, 4, . . .) can form an arithmetic sequence. The harmonic sequence or progression is the most perfect proportion: in geometry it is made manifest as the “golden cut,” and in music as harmony. The regular relationship of different movements to one another is rhythm. The day, the year, the lunar cycle are the great rhythms which measure all change.
Number, proportion, rhythm, and harmony are clear manifestations of unity in diversity which also give clear indications as to how to return to unity from diversity. Boethius argued that the essence of things is in intimate connection with unity: the more unity that a thing possesses in itself, the more profoundly it participates in being. Knowledge in such a science is less a concern with knowing many things than with taking a holistic view of existence as “whole.” The method of this science was concerned with neither the investigation of the material world through breaking it down and analysing it in discrete parts nor the technological manipulation of nature, the very opposite in fact: its aim was a spiritualism of the senses, opening the spiritual ear to the music of the spheres and the spiritual eye to the beauty of mathematical proportions underlying the universe as a whole.
That's the idea I shall be developing through my Dante book. I am somewhat arithmetically challenged. Which is to say I can't count. But I do understand the significance of numbers, and I do think numbers have a meaning. I am very comfortable with the qualitative side of life. And I get the music.
This is rather the point of my Wittgenstein piece - the world of quantity is the easy part, it is the qualitative dimension that is much more interesting:
“The positivists have a simple solution: the world must be divided into that which we can say clearly and the rest, which we had better pass over in silence. But can anyone conceive of a more pointless philosophy, seeing that what we can say clearly amounts to next to nothing? If we omitted all that is unclear, we would probably be left with completely uninteresting and trivial tautologies.”
Werner Heisenberg
Tautologies have their role. Tautology is probably my most favourite logical fallacy. In the end, when all the questions are in, and remain mostly unanswered, we are here because we are here, and whatever works, works because it works, and we are going somewhere because we are going somewhere. Kant was careful to set up his ‘necessary presuppositions’ for moral action only after he had established the universality of reason. His rational ethics are contestable. His necessary presupposition seem fine to me. They can neither be proven nor refuted. They inspire moral action and, in doing so, prove their worth. Human beings must prove the truth in practice, said Marx in the Theses on Feuerbach. Then we can come to the axiomatic, irreducible truths of the scholastics. People still believe the prejudice that the Scholastics idled their time away discussing how many angels danced on the head of a pin. That was a lie spread by the theologically dumb. The Scholastics were far deeper than that. And they developed a philosophy that was eminently practical – who do you think built the cathedrals? And civilization? If you think them misguided, then the converging crises of the modern world are calling upon you to do better.