Retreat from Pythagoras

“We here in Cambridge all keep each other going by the unquestioned assumption that what we do is important, but I often wonder if it really is. What is important, I wonder? Scott and his companions dying in the blizzard seem to me impervious to doubt – and his record of it has a really great simplicity. But intellect, except at white heat, is very apt to be trivial.”

“Sometimes, things inside me are in such a ferment that I think I’m going mad; then the next day I am totally apathetic again. But deep inside me there’s a perpetual seething, like the bottom of a geyser, and I keep on hoping that things will come to an eruption once and for all, so that I can turn into a different person. Perhaps you regard this thinking about myself as a waste of time, but how can I be a logician before I am a human being? Far the most important thing is to settle accounts with myself.”

“What’s the good of sticking in the damned ship and haranguing the merchant pilgrims in their own language? Why don’t you drop overboard? Why don’t you clear out of the whole show?...You said in your lecture on education that you didn’t set much count by the unconscious. This is sheer perversity. The whole of consciousness and the conscious content is old hat – the millstone around your neck.”

“We are sometimes accused of being arrogant scientists,” wrote Alan Sokal and Jean Bricmont, in their classic critique of postmodernism, Intellectual Impostures, “but our view of the hard sciences’ role is in fact rather modest. Wouldn’t it be nice (for us mathematicians and physicists, that is) if Gödel’s theorem or relativity theory did have immediate and deep implications for the study of society? Or of the axiom of choice could be used to study poetry? Or if topology had something to do with the human psyche? But alas, it is not the case.”[iv]

Sokal and Bricmont were concerned, by their own account, with exposing intellectual charlatanism, precisely so that reason could be applied critically, effectively and progressively to our common social and political, cultural and psychological concerns. How that is to be done has been a fundamental concern of inquirers into reason and truth at least since the time of the Greek philosophers. It is often called ‘the Enlightenment project’, as if it commenced in the modern era; but its roots are classical.

The very real problems with which this project has collided, in the classical world and in the modern world, have again and again led to suggestions that it is inherently flawed; that either metaphysical reality or human nature are not, ultimately, accessible to the dictates of reason and that some other form of understanding is necessary. The practitioners of reason themselves, from Plato to Wittgenstein, have often espoused a kind of mysticism which leaves both reason and practical concerns behind it.

In the past century, ‘the Enlightenment project’ came in for round after round of criticism or outright rejection. The sources of such criticism or rejection were, broadly speaking, of three kinds: psychological, ideological and philosophical. The psychological critique of reason stemmed from the claim that human behaviour was inescapably rooted in the drives of the unconscious, not in a free or rational consciousness. The ideological critique stemmed from assertions that human beings needed religious revelation, symbolic culture or group identity and that these made claims which trumped those of reason. The philosophical critique stemmed from the disconcerting sense that the claims of reason, whether of logic or of mathematics, could not themselves be anchored in a bedrock of demonstrable truth.

That all these critiques took place against the background of utterly unprecedented advances in pure and applied physical science, quantitative social science and economic analysis did less than one might have thought to dispel their appeal. Indeed, such advances were often described as either irrelevant to the fundamental problems in question, or as symptoms of the problems themselves. Just as nineteenth century industrialism had led to Romantic critiques of the proverbial ‘dark Satanic mills’, even as those mills first generated unparalleled material prosperity and then underwrote ameliorative social reform; so twentieth century science was often seen as ominous rather than exhilarating, because it was seen as creating a cultural and possibly ecological wasteland.

Perhaps the most famous psychological critiques of reason were those of the psychoanalysts, Sigmund Freud and Carl G. Jung; but they were anticipated by Friedrich Nietzsche and others in the nineteenth century.[v] Human sexual and aggressive drives, they argued, suffered repression under the constraints of civilization, leading to discontent and neurosis. The ideological critique, though it came from many quarters, was perhaps most gloomily articulated by Theodor Adorno and Max Horkheimer in The Dialectic of Enlightenment, in the 1940s. Reason itself, they reflected, seemed to be producing a reductionist, consumerist and militarist order of things which was itself a disaster.[vi]

The philosophical critique of reason was the most subtle and ingenious of all. Its roots, like those of the Enlightenment project itself, are classical. Among the Greeks themselves, skepticism and atomism developed alongside geometry and formal logic. The Enlightenment itself consisted not in a unitary scheme for the rational reconstruction of the natural and human order, but of increasingly strenuous inquiries into the roots of reason, truth and meaning. It was Immanuel Kant, one of the towering figures of the Enlightenment epoch, who, at one and the same time, urged human beings to reason boldly and engaged in a searching Critique of Pure Reason.

The bedrock of reason as a means to truth has always been mathematics. The late classical Neo-Platonist philosopher Iamblichus (245-325 CE) summed up an attitude first articulated by Pythagoras, when he wrote, at the beginning of the Christian era, “The Pythagoreans, having devoted themselves to mathematics, and admiring the accuracy of its reasonings, because it alone among human activities knows of proofs…deemed these (facts of mathematics) and their principles to be, generally, causative of existing things, so that whoever wishes to comprehend the true nature of existing things should turn his attention to…numbers…and proportions, because it is by them that everything is made clear.”[vii]

The great philosophical quest of the modern era has been for the deepest foundations of truth – the bedrock of reason itself. The quest was self-consciously in a direct lineage from Pythagoras and Plato, Aristotle and the great mathematician Euclid.[viii] The problem was that, the deeper the most relentless thinkers delved, the more elusive they found that bedrock. The philosophical critique of ‘the Enlightenment project’ derives from this disconcerting collective experience. The confusions of postmodernism have arisen against this very real background.

The quest might be seen, in shorthand, as extending from the discovery by Carl Friedrich Gauss and Janos Bolyai, in 1829, that the axioms of geometry articulated by Euclid and believed for more than two thousand years to have constituted a solid piece of the bedrock, were not as solid as they had been thought to be; to the demonstration by Kurt Gödel (1906-1978), in 1931, “that, in various axiomatic systems for the foundations of mathematics…there are arithmetical propositions whose truth cannot be settled by the axioms, one way or the other, assuming that the system in question is consistent.”[ix]

What was at stake here? What the great 20^th century philosopher Rudolf Carnap called ‘the logical structure of the world’.[x] To even set out on the quest for such a ‘structure’ in earnest required a serious grasp of what reason and mathematics were capable of doing.[xi] To demonstrate that the structure was ‘incomplete’, in the way that Gauss and Gödel did, required reasoning of the most exacting and exquisite nature. Yet it seemed to generate the paradox that reason at its most intense could not provide a secure foundation for itself.

Where, then, did this leave ‘the Enlightenment project’? On what secure basis were the proponents of reason now to respond to the psychological and ideological critics of the project? What were the implications for practical judgment in regard to the study of society, where such critiques were sheeted home; in relation to poetry and the life of the imagination; or in relation to the nature and emotional workings of the human psyche? Where did the acute reasonings of the reasoners leave them in relation to the claims of ideology and religion?[xii]

To keep our bearings here, it may help to refer back to the classical beginnings of the great quest; for it goes back to Pythagoras (582-507 BCE). Few aspects of human experience seem more expressive of the ‘irrational’ element in the human psyche than our enjoyment of music. Yet it was precisely in music that Pythagoras first saw the possibility of analyzing reality in terms of numbers. What he discovered was that “the differences in vibration that characterize the notes of a musical scale can be calculated. Each individual tone is determined by the number of times a particular sound-producing medium – such as the strings of a lyre or guitar – oscillates in a given time.”[xiii]

His remarkable insight was that numbers enabled us to grasp a hidden, but rigorous and demonstrable order. ‘If in music, then why not in other matters?’ he wondered. He and his disciples came to think that one could “construct the whole universe out of numbers”, as Aristotle put it 200 years later.[xiv] One could now apprehend the order of things as a ‘cosmos’, a harmonious order, rather than as a chaos. One could tune one’s mind to the very music of the spheres and grasp, through the mathematical structure of this cosmos the very mind of God.

Here is the origin of the quest that Carnap was engaged in 2,500 years later. Yet Aristotle had already sounded a cautionary note, so to speak, in observing of the Pythagoreans that, being intoxicated by the idea of numerical harmony, “if there was any gap anywhere, they readily made additions, so as to make their whole theory coherent. For example, as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth – the ‘counter-earth’.”[xv]

Whereas the Pythagoreans believed they had discovered in number the key to a complete theory of reality and the mind of God, others grasped logic, less portentously, as a method for clarifying the mind of man. How to ascertain something as true, rather than merely superstitious or plausible was their quest. Parmenides of Elea (circa 500 BCE) was, perhaps, the founder of this variant of the quest. It was his judgment that, provided one followed certain rules and techniques, mere opinion could be sifted from true belief by the detection of fallacies and contradictions.

This tradition did not apprehend or seek completeness or harmony in quite the same way as did Pythagoras. Rather, it rested on a sceptical sense that human beings are highly prone to error and that true opinion could only be separated from false opinion by a careful, logical and provisional testing of evidence and a clear use of language. To be free from an error was not, in itself, to have discovered the truth, but it was nonetheless an epiphany and a good thing in its own right.

This tradition was perhaps most famously represented in the twentieth century by the philosopher Karl Popper (1902-1994), with his insistence on the need for falsifiability criteria in serious claims and his abiding interest in how human beings can be set free to engage in conjectures and refutations. Seen in the context of this sceptical tradition, the work of Gauss and Gödel was not demoralizing at all, but extraordinary and liberating.

Popper is possibly most famous for his critique of all those philosophers, beginning with Plato, who sought ‘completeness’ in their systems, since he saw this as constituting a leaning toward totalitarianism. His polemical mid-20^th century work, The Open Society and Its Enemies, directed at all myths of origin and destiny, whether Platonist, Nazi or Marxist, remains a classic philosophical response to the critics of ‘the Enlightenment project’.[xvi] It was in honour of Popper’s work that George Soros, in the late 20^th century, created his Open Society Foundations around the world.[xvii]

One possible response, therefore, to the whole set of critiques of ‘the Enlightenment project’ is the ‘Parmenidean’ or Popperian one: that reason is best exercised not in discovering ‘the mind of God’, but in overcoming illusion and working free of prejudice, naiveté and fundamental error. The open society, then, is liberal in a classical sense, as defined by John Stuart Mill: customary ways and conventional opinion keep life workable and stable, but are open to debate and correction by careful, piecemeal, peaceful and rational means.

There may be no better case study in how all of these profoundly important matters played out during the last century than the life of Bertrand Russell (1872-1970).[xviii] Born to parents who came from a long line of Whiggish (which is to say, made-by-the-English-Reformation) aristocrats and were close personal friends to John Stuart Mill, Russell was given the best education available in his day, quested strenuously for the bedrock of logic and mathematics and tried all his life to apply his philosophical ideas to practical reality.

The life of Russell stands out, in the context I have sketched out, for several reasons. What made him famous was the monumental three volume work he co-authored with Alfred North Whitehead, at Cambridge University, Principia Mathematica (1910-1913). Yet the key to understanding his life is what he himself called “the retreat from Pythagoras”[xix] that he felt compelled to undertake in the wake of this great labor – because it did not succeed in its quest.

He was, in any case, ambivalent about metaphysical and purely intellectual pursuits all his life, because of unresolved inner conflicts about his emotions and passions. Finally, he longed to make a practical difference in political and geopolitical affairs, but nothing that he wrote or did in this domain had the intellectual distinction that characterized his technical philosophic work with Whitehead in his youth.[xx] Indeed, his political and geopolitical thinking were erratic and tended to veer toward extremes, such as radical pacifism in the 1930s, pre-emptive nuclear war advocacy in the late 1940s and Guevarist revolutionism in the 1960s.

What makes it possible for his life to be seen as a case study in the relationship between logic and practical judgment, however, is not simply that he wrestled with that relationship for most of his very long life, but that he left behind an immense documentary record, which enables the scrupulous scholar to explore in detail how he thought and how he exercised his formidable powers of reason in the study of society, the appreciation of literature and, above all, the life of his own psyche.

The scrupulous scholar who has examined this documentary record to provide us with the case study in digestible form is Ray Monk, professor of philosophy at the University of Southampton. The biography, which runs to 1,269 pages in two solid volumes, makes deeply absorbing reading. It makes disconcerting reading, however, for anyone who would prefer to believe that the exercise of critical reason can readily deal with the enduring and intractable matters of the emotional life of the psyche and the tensions and troubles of political and geopolitical affairs.

Monk shows that Russell’s youthful interest in the philosophy of mathematics and the quest for the bedrock of truth was inspired by the same ancient intoxicants that had inspired Pythagoras and Plato long before: the hunger for certainty and wonder at the sheer beauty of ‘eternal forms’. He shows, also, that Russell sought in such certainty and beauty both a refuge from the messiness of the social world and a defense against his own emotional needs and fears. Finally, he shows that Russell floundered when it came to applying his reason to politics and geopolitics.

By a curious parallelism, Russell’s three volume autobiography, published at the end of his life, approximates in bulk the three volume magnum opus he co-authored in his youth. The two parallel one another in a second respect: Principia Mathematica fails to complete its task and the Autobiography does the same. Autobiographies, whether confessional or apologetic, tend to omit or bend much of the less flattering truth about the author. But only the very best biographies do much better. Ray Monk’s biography of Russell, like his earlier biography of Wittgenstein, does do better than both Russell’s autobiography and any earlier biography of the man.

It does so because Monk, himself deeply conversant with the philosophic issues with which the young Russell was engaged, set out to explore the relationship between Russell’s philosophical development and his personal and public life. What he created in the process was an account at once lucid and illuminating of how an enormously intelligent human being struggled without final success to both get his mind around the foundations of reason and to live a passionate, humane and politically responsible existence. His judgment is neither censorious nor sparing of Russell’s failings; and in both respects it is a monument of rational inquiry.

It takes something to register the sheer mass of writing that Bertrand Russell left behind him when he died. Monk discovered some 40,000 letters, for example, written by Russell himself over some eighty or more years. Apart from the letters, of course, there were the massive three volume works, the Principia and the Autobiography and, in between, more than two dozen books, from German Social Democracy (1896) to Logic and Knowledge (1956). Merely to have sorted through this huge archive was a monumental achievement. To have crafted from it a narrative at once dispassionate and deeply reflective is a quite extraordinary accomplishment.

The concern at the centre of Monk’s reflections is the implicit relationship between Russell’s commitment to abstract reason and the way his mind actually worked psychologically and politically. Three kinds of concern run right through the biography: the lifelong fears Russell harbored of descending into madness; the deep conflicts he experienced between his passion for abstract reason and his emotional needs; and the floundering efforts he made to take his reason out of the cloisters of Cambridge University and apply it in the ‘real world’ of English politics and international affairs. Each is worth briefly illustrating.

The second volume of the biography is sub-titled ‘The Ghost of Madness’. It centres on Russell’s fear that, like his Uncle William, who suffered a nervous breakdown in 1874 and was confined to an asylum for the rest of his long life, dying in 1933, he would lapse into madness himself or have children who were mad. In addition, throughout his life, Russell oscillated between writing of hope, peace, enlightenment and progress, on the one hand; and feeling that both he himself and mankind in general was, beneath a veneer of civility, barbarous and cruel.

He admired the novels of Fyodor Dostoevsky and, even more, those of Joseph Conrad, because they explored the psychology of moral corruption, existential vertigo and madness with such insight and artistry. When he met Conrad, in September 1913, he thought he had met a rare kindred spirit. Immediately afterwards, he wrote to the great love of his life, Ottoline Morrell:

“At our very first meeting, we talked with continually increasing intimacy. We seemed to sink through layer after layer of what was superficial, till gradually both reached the central fire. It was an experience unlike any other that I have known. We looked into each other’s eyes, half appalled and half intoxicated to find ourselves together in such a region. The emotion was as intense as passionate love and at the same time all-embracing. I came away bewildered and hardly able to find my way among ordinary affairs.”[xxi]

The contrast between this experience and view of the world and that of the abstract purity of the Pythagorean or Platonist world he inhabited at Cambridge could hardly be greater. And whereas the Platonist in him longed to see metaphysical truths as reality, in his encounter with Conrad it was as if such truths were merely a layer of the ‘superficial’, beneath which lay true reality – the ‘central fire’.

The remarkable thing is that Russell never came close to reconciling these discordant themes in his mental life. One can imagine them being reconciled in various ways, but Russell did not embrace any of them.[xxii] The chief way in which they have been reconciled by human beings has been in the form of religion, but Russell had a deep ambivalence toward religion and seems never to have been able to fully come to terms with it. Writing to another of his great loves, Constance Malleson, in 1916, Russell confessed:

“The centre of me is always and eternally a terrible pain…a searching for something beyond what the world contains, something transfigured and infinite – the beatific vision – God…I can’t explain it or make it seem anything but foolishness…I have known others who had it – Conrad especially – but it is rare – it sets one oddly apart and gives a great sense of isolation” [xxiii]

The author of Why I Am Not a Christian (1927) and Religion and Science (1935) saw himself, in other words, as ‘oddly set apart’ by precisely those things which characterized the Christian view of the human condition.

Why was his reason so unable to work through all of this? The answers, Monk suggests, have to do with his psychological character – personality traits deeply ingrained in him and not readily amenable to being overcome by his own reason. But if this is so; if one of the most gifted and rational minds of the 20^th century was left stranded in this manner, must not significant concessions be made to the psychological critique of ‘the Enlightenment project’? Must we not concede that human beings have psychological needs which, be they ever so ‘irrational’, are substantially ineradicable and need to be addressed on their own terms, rather than being dismissed or neglected?

Similar questions arise in regard to Russell’s emotional life. All his life he felt a terrible sense of loneliness and a profound need for passionate intimacy. Both of these things are common enough, of course. What is striking is the Russell’s intense rationalism not only did not enable him to deal with them better than most others; it actually served to compound the loneliness and inhibit the intimacy. The repressive sexual upbringing he went through cannot have helped and his desolate first marriage, to Alys Pearsall Smith, accentuated all the problems he brought into it; but he appears never to have been able to find the kind of balance and happiness he craved.

This is shown by Monk in Russell’s relationships with his first three wives, a number of lovers and various friends and colleagues; but it is especially well illuminated by his relationship with the greatest love of his life, the aristocratic Ottoline Morrell, and by his encounter with D. H. Lawrence. Morrell was both fascinated by Russell and repelled by him. They had known each other six years when she recorded in her diary, in July 1915:

“He gets dreadfully on my nerves, he is so stiff, so self-absorbed, so harsh and unbending in mind or body, that I can hardly look at him, but have to control myself and look away. And of course he feels this and it makes him harsher and more snappy and crushing to me. What can I do? I feel I must be alone and go my own way to develop my life, my own internal life. Bertie crushes it out; he would remake me and the effort of resisting him and of protecting myself makes me desperate. It is far better to be alone than to be false.” [xxiv]

This was not merely a late development or an experience peculiar to Morrell. It ran through Russell’s life and caused him intense anguish.[xxv] He loved the poetry of Shelley, especially his great love poem Epipsychidion[xxvi], and Shakespeare’s sonnets. Yet he could never overcome the tendency to coldness and self-absorption that Morrell saw in him when he was 43.[xxvii]

The encounter with Lawrence, brokered by Morrell, as the encounter with Conrad had been, brought all this violently to the surface for Russell. He was immensely impressed by Lawrence and told Morrell, “He is amazing. He sees through and through one.” For once it was Morrell who played the sceptic. “But do you think he sees correctly?” “Absolutely,” Russell replied. “He sees everything and is always right.”[xxviii] When this ‘infallible’ seer wrote to him denouncing his anti-war activism as arrant hypocrisy and telling him he was “simply full of repressed desires”, Russell was stunned and depressed to the point where he contemplated committing suicide. Nor was this a passing mood. He remained convinced throughout his life that he was barely containing inner demons.

The politics of D. H. Lawrence, of course, were barely coherent and verged on a phantasmagorical form of communism. They were ancestral to some of the wilder versions of New Leftism in the 1960s and after. Russell, perhaps in part because of his repressive and rationalistic character, never allowed himself to wallow in the kind of wild rhetoric in which the novelist freely indulged. He did, however, indulge in some remarkably errant political reasoning throughout his life, which neither his Whig background, nor his wide and deep education, nor his formidable training in philosophical logic and mathematics corrected.

The most admirable moments in Russell’s rather quixotic political life were, surely, his intelligent reflections on German social democracy in 1896; his recoil from anti-German racism during the First World War; the writing of Principles of Social Reconstruction during the same years; and his horrified reaction to Bolshevism during his 1920 visit to the new Soviet Union, which were captured in his book The Practice and Theory of Bolshevism, published that same year. After that, however, his brilliant capacity for formal logic was less and less converted into anything resembling sound, practical judgment.

Against his better efforts must be set his naïve reflections on China, in 1921; his espousal of unconditional pacifism in the 1930s, even as the Nazi menace rose; his call for a pre-emptive nuclear war against the Soviet Union in the late 1940s, should it fail to bow to an American ultimatum to disarm; his espousal, conversely, of unilateral nuclear disarmament in Britain, in the 1950s; and his lapse into Guevarist anti-Americanism in his last decade. What astonishes one again and again is not simply the extravagance of Russell’s opinions and public statements over the last forty years of his life, but the wild inconsistencies, morally and strategically, in his thinking.[xxix]

What are we to make of all this? Monk quotes John Maynard Keynes, a man who had much in common with Russell philosophically, but a far more practical cast of mind, as remarking, in his Essays in Biography, “Bertie held two ludicrously incompatible beliefs: on the one hand, he believed that all the problems of the world stemmed from conducting human affairs in a most irrational way; on the other hand that the solution was simple, since all we had to do was to behave rationally.”[xxx] Instead of being corrected both by reflection and experience over the course of his life, these incompatible beliefs of Russell’s seem to have become entrenched, with more and more lamentable consequences, in terms of the substantive foolishness and superficiality of his political and geopolitical judgments.[xxxi]

But let us reflect a little more closely on the implications of Keynes’s remark. For he was himself convinced that human affairs were often conducted in a most irrational manner and was committed, in intensely practical ways, to ameliorating this often appalling state of affairs by rational means. He was very much a man of ‘the Enlightenment project’ and stood in a grand tradition of practical economic reason going back via Alfred Marshall to Adam Smith. He, like Popper, saw reason as an instrument for solving tangible problems in imaginative new ways and not merely as a way to discover and contemplate eternal truths.

I have, throughout this essay, placed ‘the Enlightenment project’ between inverted commas. I have done so not because it is something of which I am sceptical, but because it is a somewhat ill-defined something. The truth is that it has never been a single or coordinated project. Rather, it is a broad label for a general ferment of inquiry, which took hold in Europe in the seventeenth century and has since opened up to common understanding the natural world and the world of the human species to a completely unprecedented depth. In doing so, it has presented us with both astonishing opportunities and daunting challenges.

Perhaps the greatest of those challenges is how to integrate our social and psychological needs with what our reason tells us is so about the world.[xxxii] How do we maintain even a semblance of cultural and social cohesion amidst the ferment of ideas? How do we avoid errant kinds of ‘integration’ in the form of religious fundamentalism or ideological fanaticism and, at the same time, avoid the kinds of disintegration implicit in ‘postmodernism’? You will, perhaps, already have guessed my answer: through the application of both prudence and imagination to the challenges we face as evolved beings in a complex world. That much our reason surely tells us. As for precisely how to accomplish such ends, it tells us, also, that the hopes of Pythagoras were excessive and that incompleteness, rather than mathematical exactness will always attend our schemes. Should that dismay us? Not of any necessity. It keeps the horizon open and the day after tomorrow provocatively uncertain.

[i] Bertrand Russell, writing to Goldie Lowes Dickinson, 13 February 1913. Ray Monk Bertrand Russell: The Spirit of Solitude, Jonathan Cape, London, 1996, p. 292.

[ii] Ludwig Wittgenstein writing to Bertrand Russell, January 1914. Ibid. p. 340.

[iii] D. H. Lawrence writing to Bertrand Russell 19 February 1916. Ibid. p. 452.

[iv] Alan Sokal and Jean Bricmont Intellectual Impostures, Profile Books, London, 1998, Preface, p. x.

[v] The most representative works of Freud in this regard are Civilization and Its Discontents and Beyond the Pleasure Principle. For a brief introduction to Jung’s outlook on the problem, see his The Undiscovered Self, first published in German in 1957, published Routledge Classic in 2002.

[vi] A classic philosophic response to such trends and critiques, written at the same time as The Dialectic of Enlightenment, is Friedrich A. Hayek’s The Road to Serfdom (1944), Routledge Classics, 2001.

[vii] Quoted in Arnold Hermann To Think Like God: Pythagoras and Parmenides, Parmenides Publishing, 2004, p. 101. Iamblichus was the chief representative of Neoplatonism in the last decades before the Emperor Constantine made Christianity the state religion in the Roman Empire. The events of his life and the details of his creed are very imperfectly known, but the main tenets of his belief can be worked out from his extant writings, chief among which are the surviving fragments of his ten book treatise on the teachings of Pythagoras. He was the son of a rich and illustrious family and studied under Porphyry, a pupil of Plotinus, the founder of Neoplatonism. In 304, he founded his own school near Antioch, in Syria, and designed a curriculum for studying Plato and Aristotle, writing grand commentaries on the two that survive only in fragments. He regarded Pythagoras, however, as the supreme authority. He is known to have written the Collection of Pythagorean Doctrines, in ten books, of which only the first four books, and fragments of the fifth, survive. Indeed, only a fraction of his books have survived, most of them having been destroyed during the Christianization of the Roman Empire.

[viii] Euclid of Alexandria (325-265 BCE) was the most prominent mathematician of antiquity and is best known for his treatise on mathematics, The Elements. Proclus, the last major Greek philosopher, who lived around 450 CE recorded a famous anecdote about Euclid, to the effect that Ptolemy, the Greek ruler of Egypt in the early 3^rd century BCE, once asked him if there were a shorter way to study geometry than The Elements, to which Euclid is said to have replied that there was “no royal road to geometry”. Euclid considered himself a Platonist.

[ix] Anita Burdman Feferman and Solomon Feferman Alfred Tarski: Life and Logic, Cambridge University Press, 2004, p. 84.

[x] Rudolf Carnap (1891-1970) was powerfully influenced by Kant’s Critique of Pure Reason and Alfred North Whitehead and Bertrand Russell’s Principia Mathematica. He was a founding member of the so-called Vienna Circle in the 1920s, which espoused the philosophy of logical positivism. He published two important books in 1928, which established him as a major philosopher: The Logical Structure of the World and Pseudo-problems in Philosophy. Working at the University of Prague, he wrote The Logical Syntax of Language in 1934, then emigrated to the United States, in 1935, because as a socialist and pacifist he dreaded what the Nazis were about to unleash on Europe.

[xi] For an engaging reflection on this question by two mathematicians, see Philip J. Davis and Reuben Hersh Descrates’ Dream: The World According to Mathematics, Dover, New York, 1986.

[xii] The precise implications of Godel’s work are the subject of an impressive monograph by Torkel Franzen, Godel’s Theorem: An Incomplete Guide to Its Use and Abuse, A. K. Peters, Wellesley, Massachusetts, 2005. See especially Ch 4 ‘Incompleteness Everywhere’, pp. 77-95.

[xiii] Arnold Hermann To Think Like God: Pythagoras and Parmenides, Parmenides Publishing, 2004, p. 101.

[xiv] Richard McKeon (ed) The Basic Works of Aristotle, Random House, New York, 1941, p. 898; Metaphysics 1080b19.

[xv] Ibid. p. 698, op. cit. 986a 2-12. See also the beginning of Book II of Aristotle’s treatise De Caelo (On the Heavens) 293a19-26, McKeon p. 428: “It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. As to its position, there is some difference of opinion. Most people – all, in fact who regard the whole of heaven as finite – say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and he earth s one of the stars, creating night and day y its circular motion about the centre. They further construct another earth in opposition to ours to which they give he name counter-earth. In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observation and trying to accommodate them to certain theories and opinions of their own.”

[xvi] Karl Popper The Open Society and Its Enemies, fifth edition, one volume hardback, Routledge, London 2002. The book was first published by Routledge and Kegan Paul, London, 1945, and went through many new editions and reprintings over the following six decades.

[xvii] Charles Freeman The Closing of the Western Mind: The Rise of Faith and the Fall of Reason, William Heinemann, London, 2002, reflected on the opposite process occurring in late classical antiquity with the triumph of Christianity over the sceptical and empirical philosophies of the Greeks. He cites the Church Fathers on the importance of faith and the triviality or even danger of rational inquiry. We must, declared St John Chrysostom, “restrain our own reasoning, and empty or mind of secular learning, in order to provide a mind swept clear for the reception of divine words.” Basil of Caesarea, similarly: “Let us Christians prefer the simplicity of our faith to the demonstrations of human reason…For to spend much time on research about the essence of things would not serve the edification of the church.” Lactantius, another of the towering figures of the early church, declared: “What purpose does knowledge serve – for as to knowledge of causes, what blessing is there for me if I should know where the Nile rises, or whatever else under the heavens the ‘scientists’ rave about?” p. 322.

[xviii] Ray Monk Bertrand Russell 1872-1921: The Spirit of Solitude, Jonathan Cape, London, 1996; and Bertrand Russell 1921-1970: The Ghost of Madness, Jonathan Cape, London, 2000.

[xix] This was Russell’s own characterization of his philosophical development, in his History of Western Philosophy, George Allen & Unwin, London, 1946. In a summation of Russell’s philosophy for the Royal Society, Ray Monk observes that, having discovered Euclidean geometry through his older brother Frank’s tutoring, as a boy of eleven, Russell conceived “the hope that all knowledge could be like that: ‘I liked to think of the applications of mathematics to the physical world, and I hoped that in time there would be a mathematics of human behaviour as precise as the mathematics of machines. I hoped this because I liked demonstrations, and at most times this motive outweighed the desire, which I also felt, to believe in free will.’… This conception of philosophy is exemplified by the figure of Pythagoras, around whom Russell built a kind of myth that reveals much about his attitude to the subject. Pythagoreanism, on Russell’s understanding, was a reformed version of Orphism, which was, in turn, a reformed version of the worship of Dionysus. Central to all three was the exaltation of ecstasy, but, in the cult of Pythagoras, this ecstasy is to be achieved, not by Bacchanalian revelries, but by the exercise of the intellect. The highest life, on this view, is that devoted to ‘passionate sympathetic contemplation’. It is with such passages in mind that one should understand Russell’s characterisation of his own philosophical development as a ‘retreat from Pythagoras’.” Interestingly, in 1943, Kurt Gödel, who still took a Platonist view of mathematics, attempted to suggest a reversal of Russell’s retreat from Pythagoras, but Russell did not engage him in the debate. Ray Monk Bertrand Russell 1921-1970: The Ghost of Madness, Jonathan Cape, London, 2000, p. 269.

[xx] “Though Wittgenstein never lost his admiration for Russell’s early work in logic,” Monk wrote, “he vehemently disapproved of Russell’s popular writing of the inter-war period. ‘Russell’s books should be bound in two colours’, he once said, ‘those dealing in mathematical logic in red – and all students of philosophy should read them; those dealing with ethics and politics in blue – and no-one should be allowed to read them.’.” Perhaps his most famous book is his History of Western Philosophy (1946), was, in Monk’s words, “greeted with almost universal disdain by the academic philosophers who reviewed it. Even C. D. Broad, an ex-pupil and admirer of Russell’s…could not bring himself to overlook the book’s outrageous and cavalier superficialities and si9mplifications.” Yet “despite its many flaws (or perhaps to some extent because of them), the book became a runaway best seller and placed Russell’s finances on a secure footing for the rest of his life.” (2000) pp. 278-79.

[xxi] Ray Monk Bertrand Russell 1872-1921: The Spirit of Solitude, Jonathan Cape, London, 1996, p. 315.

[xxii] The philosophy of Spinoza clearly appealed to Russell from quite an early age, but he never made of it or saw in it what Antonio Damasio has recently discovered: the vital co-existence of feeling and emotion with reason in the brain. See his Looking for Spinoza: Joy, Sorrow and the Feeling Brain, Harcourt, 2003.

[xxiii] Ray Monk (1996) . pp. 316-17.

[xxiv] Ibid. pp. 436-37.

[xxv] His first marriage, to Alys Pearsall, was all but celibate, childless and ended in divorce; his second marriage, to Dora Black, produced two children, but ended in alienation, divorce and a complete refusal of Russell to communicate with Dora; his third wife, Patricia Spencer, withdrew from him, attempted suicide and, as Monk expresses it, “For the third time in his life, Russell found himself living in a hollow shell of a marriage, in which love, passion and affection were replaced by a fragile and brittle courtesy” (2000, p. 260) – and which ended, also, in a bitter divorce.

[xxvi] The poem is quite a long one and concludes, “…The winged words on which my soul would pierce/Into the height of love’s rare Universe/Are chains of lead around its flight of fire. - /I pant, I sink, I tremble, I expire.” For the complete text, see Shelley, Everyman Library Pocket Poets, Alfred Knopf, New York, 1993, pp. 167-189.

[xxvii] When Morrell died, in April 1938, after a long illness, Russell wrote to her husband, Philip, “The news is a terrible blow. A great part of my life…is gone dead with her. I do not know anything consoling to say.” Monk (2000, p. 212)

[xxviii] Ray Monk (1996). p. 403.

[xxix] “In a series of speeches and journalistic articles, beginning in September 1945, Russell argued passionately that, in order to preserve peace, America had to act firmly and immediately to impose its will on the rest of the world and, in particular, on the Soviet Union. From the very beginning, these articles had a bellicosity that contrasted markedly with the pacifist views he had expressed in the 1930s.” Ray Monk (2000) p. 298.

[xxx] Ibid., p. 177.

[xxxi]Monk writes of the “self-delusion to which Russell was prone whenever he wrote on social, political or historical subjects.” He believed his books, such as Power (1938) or Freedom and Organization (1934) to be of very great importance, when in fact they were light weight pieces of reflection, lacking in serious scholarly weight or conceptual originality. Ibid. p. 212.

[xxxii] “There is increasing scientific evidence that reason and emotion need to live side by side in the healthy mind. It appears that some degree of irrationality acts as healthy corrective to the aridity of narrowly logical thought”, writes Charles Freeman, towards the end of his defense of the classical tradition, The Closing of the Western Mind (2002), p. 327.