### In the spring of 1899 Bertrand Russell envisions an enormous treatise The Fundamental Ideas and Axioms of Mathematics . He believes that he can derive all of Mathematics from 4 irreducible notions : 'number ' ; 'order' ; 'whole' ; and 'part' .
### By the following year he has changed his mind. Now he plans what will eventually become The Principles of Mathematics ( not to be confused with Principia Mathematica ). the concept, 'order' , he decides, is redundant: Mathematics will be founded only on 'number' , 'whole' and 'part'. In the summer of 1900 he begins writing with his customary application and energy.
### A month later he throws out everything he has done to date. In a burst of energy extending over 3 months he sets out a new version. All former notions are rejected: Mathematics is to be built on one idea: the 'class' . As he writes in a letter " ...In October I invented a new subject, which turned out to be all of mathematics ..." (Monk, Vol I. ,pg 133 )
### The Russell Paradox, his claim to immortality, is discovered in 1901. Continual brooding on the paradox will lead to collaboration with Whitehead.
### In May ,1901 Russell once again sets out to completely rewrite The Principles of Mathematics . He brings in the additional notion of 'propositional function' .In the course of working out the consequences of this he invents 'types' , together with a 'theory of types'. His system quickly becomes entangled in a jungle of new expressions: 'terms' ; 'classes of terms'; ' classes of classes of terms'; etc. etc., completely destroying the austere monistic ( or shall we say 'monastic') simplicity he'd envisioned for his reconstruction of Mathematics.
It is around the same time, deeply depressed by the stubborn refusal of Mathematics to bend to his need for simplicity and absolute certainty, (and by the worsening nightmare of his marriage with Alys Pearsall Smith) , that he writes A Free Man's Worship . This hymn to intellectual courage in the face of total despair is adumbrated in grandiloquent Ruskinian prose. Despite its' stylistic beauty, it is more than obvious that he didn't adhere to its conclusions, because he never lived them.
### It is now October , 1902: in response to a letter from Frege, Russell recycles the debates of the medieval scholastics over Universals and Individuals. Positing a notion he calls the 'complex', he blurs the distinction between the objects denoted by a proposition and the proposition itself: " ...when pressed to clarify this notion of a 'complex', Russell .... completely astonished Frege by cheerfully accepting what Frege had regarded as self-evidently absurd. 'Mont Blanc with its snowfields', Frege wrote ....' is not itself a component part of the thought that Mont Blanc is more than 4,000 meters high' . ' On the contrary', Russell wrote , (Monk, Vol I, page. 166) ' I believe that in spite of all its snowfields Mont Blanc itself is a component part of what is actually asserted in the proposition ' Mont Blanc is more than 4,000 meters high ...'"( I invite the reader to come to my assistance in figuring out the significance of this distinction.)
### In May, 1903, Russell throws out 'classes' altogether, retaining only 'propositional function'. This solution is quickly run to ground.
### In July, 1905 he writes the essay On Denoting . Ray Monk calls this Russell's indisputable masterpiece. It may well be. To my mind, its ideas are straight out of Abelard, ascribing meaning to meaningful things, and linguistic convention to linguistic conventions. I don't think it 'solves' the Paradox. The analysis of the many ways in which the statements ' Scott is Scott ' , and 'The author of Waverley is Scott ' are alike and different, does not impress me as powerful enough to dispose of it. To my understand, the Russell Paradox cannot be solved; it can only be mined for treasures.
### Apparently Russell felt the same way. By the end of 1905 he completely throws out everything he's done, replacing 'classes' , 'concepts', and 'propositional functions' by the single notion of 'proposition' .
### December, 1905 . Enter the 'substitution theory' - which he scraps in April, 1906, as 'rubbish' .
### In response to criticism from Henri Poincare, Russell conceives of the Axiom of Reducibility . This important idea, which he will scrap in the 2nd Edition of the Principia, asserts that two propositions that have the same extension are identical at every meta-level. Simply stated, although "The author of Waverley " and "The author of Ivanhoe " are not the same statement, their extension, namely Sir Walter Scott , is the same. The Axiom of Reducibility then says that all statements, at all levels, made about the author of Waverly, will be identical to those made about the author of Ivanhoe.
Anyone who has seen Don Siegel's Invasion of the Body Snatcherswill recall the scene in which the medical doctor, Miles Bennell, who does not yet know that something is seriously wrong in the town of Santa Mira , pays a visit to the house of Wilma , a former schoolmate of his girl-friend. Wilma is suffering from a strange delusion. She is certain that her uncle Ira, ( seen making intermittent appearances running a lawn mower ) , is not the same person she's known all her life. When pressed to explain why she believes this, she replies that he is the same in all particulars, down to the tiniest details - yet she just knows in her heart of hearts that he is different.
Wilma : That's it. There is no difference. He looks, sounds, acts like Uncle Ira.
Dr. Bennell: So - he is your uncle Ira.
Wilma : But he isn't! ... Miles; am I going crazy?
Dr. Bennell : Even these days it's not so easy to go crazy as you think. Had Miles Bennell read the first edition of the Principia Mathematica he would have known how to deal with this situation.
### Influenced by the ideas of Harold Joachim, Russell writes A Multiple Relation Theory of Judgments . ( Monk calls this paper 'notorious'.) According to this theory only mental acts are real. Introduces 'ramified theory of types'; 'hierarchies of judgments' ; 'levels of truth'. These are such things as 'judgments on individuals' , 'judgments on classes of individuals' , 'judgments on classes of classes of individuals' , etc .... Statements about numbers depend on statements about classes, which depend on the theory of propositional functions, which depends on the theory of types of judgments which depends on .......
### November 1906 : Russell scraps 'propositions' ! " With a characteristic readiness to abandon views he had previously considered definitely correct, Russell now declared that there were, after all, no such 'things' as propositions . " ( Monk, Vol I, page 188 ) 'Propositions' are entirely replaced by 'judgments' that is to say, 'mental acts'. Hegel's detested 'Idealism in Logic' , which seems to have been the primary motivation for Russell's decision to embark on this fateful journey , has come in, like Dracula, through a window left open in the basement! On page 88, Volume I, Ray Monk summarizes the effect on the Principia Mathematica of this extraordinary daredevil act lasting over half a decade:
" If the theory of The Principles of Mathematics had had the impressive simplicity of a modernist building, this new theory was more like a baroque cathedral, with one complex structure piled on top of another. The analysis it offers of even the simplest mathematical equation is therefore extraordinarily convoluted: the proposition that '1 +1 = 2' for example, is arrived at only half-way through Volume II of Principia , by which time it has been shown to be analyzable into, and founded upon, a murky morass of definitions, propositional functions and, ultimately, judgments."
It is my understanding that, to the present day, it is not known if the generally accepted belief that 1+1 = 2, is satisfactorily established in either the first or the second edition of the Principia
. Herein one finds yet another sobering reminder that Philosophy and Science are autonomous enterprises: it is rare that people argue over what Newton, Galileo, Pasteur, Josiah Willard Gibbs or Crick and Watson are actually saying in their scientific writings. Even the geologists who disputed the evidence for Wegener's hypothesis of tectonic plate dynamics for half a century, did not disagree as to what he was actually saying. A scientific theory may be shown to contain errors, or to fall short of the evidence, or to be superceded by later discoveries.
Yet, to this very day , 2500 years later, people are still arguing about what Parmenides really meant, or discovered, or if his arguments are valid, or if they matter. Here is Russell's opinion of Parmenides, circa 1945:
" Parmenides assumes that words have a constant meaning; that is really the basis of his argument, which he supposes unquestionable. " ( History of Western Philosophy, page 50 )
This is Karl Jaspers' take on him : " It was Parmenides who first explicitely stated that thinking is being, or being thinking. Only when this thesis had been stated thus radically did it become possible to oppose it and to ask whether being and thinking must not, on the contrary, be conceived as separate if we are to discern the relation between them ( It was Kant who stated this position in full clarity) . " ( Jaspers, The Great Philosophers, pgs. 31-32)
David J. Furley has this opinion : " It has often been said that Parmenides' attack on the reality of the physical world depends on his confusion of two senses of the word 'to be' -the existential and the copulative ...... the surviving text does not bear this out.... " ( Macmillan Encyclopedia of Philosophy, Vol 6, page 50 )
Plato himself, in the Theatetus Dialogue, asserts that Parmenides' thought is so noble and profound that he dares not claim to understand it. From the full exposition that it receives in the Parmenides Dialogue , we understand that he was not being sarcastic.
Once again, what we are seeing was typical of Russell's style, though what he said and thought in his 30's at the height of his powers, and his ramblings in his 70's , his intellect enfeebled by 4 decades of promiscuous debauchery, should not be placed on the same level. It is not all that surprising to find that the philosopher who maintained that he could transform philosophy into a natural science, would be the same person who could dismiss the legacy of Parmenides, and all his other contemporaries who have excited controversies over thousands of years , with a trite comment about a mistake in linguistics .
This attitude, furthermore, seems to have set its stamp on the entire English school of philosophy of the 20th century. Although a better knowledge of what the exponents of this school have done, should have been one of my prerequisites for writing this review, I do not, and probably never will learn enough about them to satisfy myself or others. My extreme distaste for this very manner of thinking has made it difficult, even impossible, to fully explore their legacy.
Among them, Russell is the most accessible and interesting for me, as I have always been intrigued by the problems associated with the foundations of mathematics. My personal objections to the analytic philosophy invented by Russell and Moore are the following. As I understand it , after one grants that an external world independent of anyone's thinking has real existence ( including the world of number and relations), one subjects one's thinking, and above all one's language, to a extended critical analysis for the purpose of separating out what is external from what is mental or a mental construction in one's thought . Ideally, one ends up with a list of 'logical atoms' : subject-predicate propositions standing in 1-to-1 correspondence with the world that science reveals to us:
Summing up my appraisal of Monk's treatment of Bertrand Russell's work on philosophy,( particularly in Logic and the Foundations of Mathematics) , it appears to me to be more than adequate for a book intended for the general public. His account of Russell's ideas on the philosophy of physics is less satisfactory, however I doubt that there is a physicist throughout the whole previous century who altered even one hypothesis or experiment on the basis of any idea put forth by Russell. The impact of his thought on mathematics, however, was, and continues to be, considerable.
Mathematicians and philosophers reading these volumes would no doubt require a more extended treatment of Russell's thought. The thoroughness of Monk's chronology makes it relatively easy to search out primary sources and fill in the missing parts which, for the sake of a wider public accessibility, ( and no doubt acting on 'sage advice' from his publishers), he had to pass over .
B. Russell's Popular Writing
Our introductory analysis of the role of contingency in the definition of "professionalism" in philosophy accords with the further observation that an unbroken continuum extends from the academic philosopher to the cracker-barrel philosopher. As one end of this continuum, in the rarefied heights of privileged discourse, stand the descendants of Kant. At the other, addressing the vulgar herd, are gathered the promulgators of cant. Because of the limitations imposed upon him by a highly technical vocabulary, the academic philosopher speaks to the One, or at least to the Few. The cracker-barrel philosopher, from his rocking chair on the porch of the general store, speaks to the Many. It has become apparent once more that Parmenides will always be with us.
Bertrand Russell the man of letters , and it is as such that he is best known to the general public, struts gleefully back and forth along this continuum, stopping the full gamut of harmonics on his Pythagorean monochord. Through long practice, education and singular talent he became something of a virtuoso on this instrument. Like Xenophanes with his lyre or Abelard with his lute, Russell performed on the street corners of the world, though his plectrum was his pen, his resonance the eternal craving of mankind for authoritative clues as to the meaning of life.
At his best Russell is one of the finest exponents in the English language of a certain prose style much cultivated in the post- Macaulay era. Ruskin himself would have been moved to tears by the power of his impassioned threnody to inexorable pessimism , " A Free Man's Worship". This masterly command of a certain sort of learnŠd-literary tone carries him through the Autobiography, which even the disparaging Ray Monk calls a literary masterpiece. Even in the Principia, it is only the content of what he is saying that is obscure, not his way of saying it.
It was a Genius for the Articulate that Bertrand Russell imbibed from his childhood environment, the frosty, demoralizing , yet loving and boundlessly secure world of his grandparents' estate, Pembroke Lodge. While the imaginations of the majority of today's children are nurtured by TV sitcoms, moronic flicks , swinish rock, screaming newspaper headlines, and indoctrination by an educational system based on fad, fashion and functional illiteracy, Bertrand Russell grew up reading and listening to the works of the members of his family's social set : The Arnolds, John Stuart Mill, the Brownings, Tennyson, and scores of other eminent literary, political and scientific figures of the century.
" My mother and her sister ,Mrs. George Howard , ( afterwards Lady Carlisle), had rival salons. At Mrs. Howard's salon were to be seen all the Pre-Raphaelite painters, and at my mother's all the British philosophers from Mill downwards. " ( Autobiography, Vol I, page 9 )
Speaking of his grandmother's cultivation, he writes, ( perhaps with some pardonable exaggeration in his recollection ) :
" She could speak French, German and Italian faultlessly, without the slightest trace of accent. She knew Shakespeare, Milton and the eighteenth-century poets intimately.. She had a minute knowledge of English history according to the Whig tradition. French, German and Italian classics were familiar to her ...Turgeniev once gave her one of his novels... " ( op. cit., pg. 8 )
" I read with her Shakespeare, Milton, Dryden, Cowper's Task, Thompson's Castle of Indolence, Jane Austen and a host of other books. " (op. cit., pg. 29 )
When he became independent in his 20's, he found no difficulty fitting into the milieu of Bloomsbury, or Ottoline Morrell's literary zoo, Garsington Manor. Among his friends( later, in some instances , bitter enemies) were numbered D.H. Lawrence, Joseph Conrad, Lytton Strachey, the Huxleys, and T.S. Eliot.
The mastery of literary style that came out of this background eventually became as natural to Russell as composition was to Mozart. For that very reason it proved, in all too many instances, to be something of a handicap. To explain why this is so, one needs to says a few words about the underlying insecurity of his finances throughout his life. After reaching maturity he was no longer rich, and even the moderate comfort derived from being on the wrong side of primogeniture of one of the wealthiest aristocratic families of England did not sustain him beyond the First World War:
" As the child of an aristocratic family he had inherited enough to live on without an earnt income, but he had given this inheritance away, some of it to the London School of Economics and some of it to T.S. Eliot. " (Monk,Vol II, page 7 )
As part of his divorce settlement with Dora Black in 1935 he was required to give her 1/3 of his income , as well as keeping up the support payments to the widow, ( Elizabeth von Arnim ) , of his elder brother, Frank. The sums consumed by his political activities, the cost of supporting his next two wives, his son child Conrad, and ultimately his 3 grandchildren by the marriage of his schizophrenic son John Conrad to Susan Lindsay ( daughter of Vachel Lindsay) , placed him under a heavy financial burden, rarely relieved save through the odd miraculous intervention like George Santayana's decision , in 1937 to grant him1000 pounds a year.
The world of ideas did not benefit from the fact that Bertrand Russell possessed a skill which, when applied commercially , could bring in sufficient income at all times : the production, in any amount, of polished, urbane, sophisticated and witty Edwardian/Cantabridgean prose on any topic under the sun. Russell's privileged access , ( from both aristocratic and university connections) to publication outlets made it all too easy for him to spout off the top of his head whatever passing fancy came into his mind. Constrained by time and money ( which, by a celebrated theorem of Benjamin Franklin have the same extension) , it became habitual for him to dispense with the dreary labor of re-reading the contents of his writing for sense, consistency, sanity or silliness. The wisdom in the books, articles, columns and letters which Russell churned out in princely quantities could therefore vary from deep philosophy, great poetry or learned counsel, to straight drivel, intemperate abuse, ignorant pseudo-science, puerile infatuation and things on a similar level - all written in the same high-sounding intellectual tone, and bearing the imprint of an eminent sage.
A small sampling of some of his cruder scintillations bears this out:
Ray Monk, Volume I:
### pg 126 : In defence of the English cause during the Boer War: " If you had read anthropology books you would know what a truly savage country is, and what are the benefits which result from civilized government... Now, the stronger nation, the less fear it has of insurrections by the savages ... "
### pg 347: Commenting on Boston society shortly before World War I he writes : " {Bostonians are] the kind of people who are frightfully proud of their ancient lineage because they go back to 1776 .... rich, over-eating, selfish, feeble pigs... "
About his house servants during his stay in Cambridge : " I find the coloured people friendly and nice, they seem to have something of a dog's liking for the white man - the same kind of trust and ungrudging sense of inferiority.... "
### pg 352 : " [Princeton University is] ..full of new Gothic, and ... as like Oxford as monkeys can make it... "
### pg 383: "...The conflicts of Europeans with American-Indians , Maoris and other aborigines in temperate regions ....if we judge by the results we cannot regret that such wars have taken place.... the process by which the American continent has been acquired for European civilization [ was entirely justified because] there is a very great and undeniable difference between the civilization of the colonizers and that of the dispossessed natives... " From 'The Ethics of War", January 1915
### pg 576 . A propos of the Russian Revolution : " There has been nothing comparable since the France of the Revolution, and for my part I cannot but think that what the Bolsheviks are doing is of even greater importance for the future of the world that what was accomplished in France by the Jacobins... "
### pg 536 . On chemical mind control : " If Beethoven could have been turned into a quiet well-behaved person, the loss to music would have outweighed the gain to the cook. " ...
" The education authority will decide what form of character is most virtuous and the medical officers will produce this type of character... "
### pg 593 : On the miraculous Chinese government, after being feted and flattered by Chinese officials during a teaching appointment there in the 20's: " Imagine the British Empire ruled by Augustus John and Lytton Strachey, and you will have some idea of how China has been governed for 2,000 years.... "
Ray Monk, Volume II :
### pg 10 : On the application of Behaviorist psychology to child-raising : " If existing knowledge were used and tested methods applied we could, in a generation, produce a population almost wholly free from disease, malevolence and stupidity.... "
### pg 36 : Commenting on being the guest of the social historian H.M. Kallen during his American lecture tour of 1924 : " ..... A Jew, whose friends are all Jews. All were kind, but I began to long for the uncircumcised..." (!!x??)
### pg 92 : On his reaction to being taken to a jazz club in Harlem: " I left the place and went home. I couldn't bear the jazz music or the futurist walls or the negro ladies got up like Americans....I just felt jungle poison invading my soul... " ( Russell is 52 )
### pg 104 Quotations from Marriage and Morals , arguably his worst book :
" Women are on the average stupider than men... "
" It seems on the whole fair to regard negroes as on the average inferior to white men.. " This was later changed, but what follows was not: " ..although for work in the tropics they are indispensable, so that their extermination ( apart from the question of humanity) would be highly undesirable... "
" The sterilization of the unfit is within the scope of immediate practical politics in England.... " ( Ray Monk is so shocked by the paragraph following this statement that it takes him half a page of commentary to come to terms with it. )
### pg 176 : " Among all the successors of Hume, sanity has meant superficiality, and profundity has meant some degree of madness... " Written in 1936 ( Russell is 64)
### pg 182. Excerpts taken from "Which Way To Peace", 1936 " Suppose England and France were to disarm... If the Nazis endeavour to continue their military parades and their glorification of war they would cease to look heroic and become ridiculous; their own compatriots would laugh at them... Is it not clear that this is the really effective way of fighting militarism?..... "
Arguing that it is in the interests of humanity and the progress of civilization that Britain and France should accede to Germany's desire to conquer Russia: "After a successful campaign against Russia, the Germans would feel satisfied and grow less warlike.... "