ラッセルが自分の著作を後から見直すこと(→ work backwards 後ろ向きに作業する)をしないために生じたもうひとつの結果は、- 一方の用法が他方の用法と異なることをはっきりさせずに- 彼が別々の著作で言葉を少し違った意味で使うことによって(through 使うことを通して)、外見上の矛盾が起こる可能性があるということである。敵意をもつ批評者なら誰でも、このようにして言葉上の矛盾を容易に収集することが可能である。 そういったただ単なる(purely 純粋に)言語的な混乱を、ひとつの語の,ラッセルのある時期の用法を他の時期の用法に翻訳する一種の辞書を用意する(provide 提供する)ことによってとり除くことは、評者の義務であると言ってよいかも知れない。そのような辞書の編集(編纂)は G.E, ムーアの『倫理学原理』以来、哲学研究の第一歩であると当然のように考えられるようになっている。そしてラッセル自身も、哲学的議論を始める前に、自分が使う述語(用語)を定義しようとしばしば試みている。 しかし、ラッセルが正しくも(rightly 適切にも)主張したように、それ(辞書編纂)は、日常言語では避けられないところの不明確さを避けるための最上の方法だとは、私は思わない。* * たとえば、P. A. Schilpp (ed.):Philosophy of Bertrand Russell, 1944, p.690
Cautionary notes, n.04 Another result of Russell’s refusal to work backwards is that apparent inconsistencies can arise through his use of words in slightly different senses in different books, without his being explicit about how one usage differs from the other. Any hostile critic can collect an easy crop of verbal inconsistencies in this way. It might be said that it was the duty of a commentator to remove such purely verbal confusion by providing a kind of dictionary, whereby Russell’s use of a word at one time can be translated in terms of his use of it at another. Such lexicography has appeared an obvious first step in philosophical scholarship ever since Moore’s Principia Ethica; and Russell himself frequently prefaces a philosophical discussion with an attempt to define his terms. But I do not think this is the best way of trying to avoid the kind of vagueness which, as Russell rightly insisted, is unavoidable in ordinary language.*1 *1 1 e.g. P. A. Schilpp ed.: Philosophy of Bertrand Russell, p.690. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_cautionary-notes_04.html
ラッセルの仕事の仕方についてある程度知ることは、彼の著作を理解するために不可欠である*。 激しい思考の(猛烈に考える)時期が続き(successive periods of intense thinking)、それぞれの時期に考えたものは、最終的に、それぞれ、急いで執筆された、一冊の本に結実した(culminated in)。ラッセルは自分が(過去に)書いたものを後に改訂(修正)することはほとんどせず、 また、出版後、読みかえすこともほとんどなかった。(それを示す十分な証拠が小さな誤植の数々の中にあり、彼の著書は何度版を重ねても(edition after edition )、それらの誤植は残り続けている)。彼は自ら思索(思考)におい て新たな前進を始める時にはいつも(過去にしばられない)新鮮な精神(気持ち)で開始した。彼は、自分の新しいアイデア(考え)と前回言ったこととの関係を気にすることはめったになかった。 たとえば、ヴィットゲンシュタインは『哲学的探究』(Philosophical Investigations)を執筆している時に常に『論理哲学論考』(Tractatus)を念頭においていたように(は、ラッセルは気にすることはなかった)。 * Portraits from Memory, pp.195-6. その結果、(ラッセルの思想が)初期と後期との(思想の)間に実際にある不一致(矛盾)よりももっと大きな不一致が存在しているかのような印象を与えることとなった。一見すると矛盾が存在しているように見えるのは、ラッセルがひとつの問題を全く新たな見地から論じているから、あるいは、異なる論敵に対して議論しているからである。外見上の不一致(矛盾)を示すことはある。(しかし)反対の方向からの攻撃に対して(自分の)同じ立場(ground 根拠、立場)を弁護するとき、異なったやり方(方法)で対峙することに(facing 直面することに)矛盾(inconsistency 不一致)はまったく存在していない。ラッセルの著作のこのような論争的な側面(this polemic aspect )は極めて重要であり、そうして、彼の論敵が何を言っているかを知らずにラッセルの主張を理解することは不可能である場合が多い、と私は信じている。
II Cautionary notes, n.03 Some knowledge of Russell’s method of working is essential to understanding his writings.* There were successive periods of intense thinking, each of which culminated in a book which, in the end, was written rapidly. Russell hardly ever revised anything he had written, and almost never re-read a book after it had been published. (There is sufficient evidence for this in the number of small misprints which survived edition after edition of his work.) When he began each new advance in his thinking he did so with a fresh mind. He rarely concerned himself with the relation between his new ideas and what he had said the last time; in the way that Wittgenstein, for instance, always had the Tractatus in mind when writing his Philosophical Investigations. * Portraits from Memory, pp.195-6. The result is to give an impression of greater inconsistency than really existed between earlier and later years. There are apparent contradictions because he is discussing a problem from a completely different point of view, or arguing against a different opponent. There was no inconsistency in Russell facing in different ways when defending the same ground against attacks from opposite directions. I believe this polemic aspect of many of Russell’s writings is of great importance, and that it is often impossible to understand his position without knowing what his opponents were saying. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_cautionary-notes_03.html
ホワイトヘッドは例外にしなければいけないかも知れないが、 ラッセルは恐らく他のどの同時代の哲学者よりも広範に本を読んだ人であるだろう。 ラッセルの哲学に対する最大の貢献のいくつかは、多数の情報源から数多くのアイデア(思想/考え)を手に入れてそれらをひとつの十分仕上げられた体系(a fully-wrought system)にまとめ上げる能力から生じている(生じた)。 (それは)ニュートンのプリンキピヤがガリレイに発するいくつかの根本的な概念をまとめ上げた方法と同じである*1。しかし、それらの思想(アイデア)が他の人々によって最初に暗示された場合でさえ、ラッセルは、自分自身の精神(知性)の生み出したものしか書かなかったのである。その最も明白な証拠は、(たとえば中性的一元論の場合のように)他の哲学者の視点(見解)を彼が受けいれるまでの長いタイムラグ(時間上の遅れ)があった事例の数々である。(訳注:「The most obvious evidence is in the number of cases」:そういった事例の数がそこそこある、といったニュアンスでしょうか?) *1 自分の業績は「根気強さと執拗さ(一徹さ)」のおかげであるというラッセルの発言(アラン・ウッドとの対話における)は、 ニュートンの「私には特別な洞察力(sdagacity)があったわけではない。ただ辛抱強い思考力があっただけである」という発言と比較することができる。 また、ラッセルが他の人が同様の結論を出したことを知らずに自らの結論にいたったという、全くの偶然の一致という事例も多かった。 (たとえば)ライプニッツとニュートンによる微積分の発見や、ヴェルディ(作曲)の 「オテロ」(訳注:ヴェルディが作曲した全4幕からなるオペラ)とグノー(作曲)の「ロメオとジュリエット」とにおける4つの小節(the four identical bars)の一致の場合のように(である)。 ラッセルの場合、最も明らかな例は、言うまでもなく、彼とフレーゲが全く独立に到達した数学の理論がそれである。 ラッセルが比較的生涯の遅くまで、哲学の知識を -他の哲学者の著作を研究するという通常のアカデミックな意味で- 大して獲得しなかったということにも注目しても多分よいであろう。彼は ケンブリッジの第4学年になるまでは正式に哲学の本を読まなかったので(訳注:1年から3年までは数学専攻/4年時に哲学専攻)、ケンブリッジにおける彼の研究過程にはいくつかの重要なギャップ(空隙/くうげき=すきま)があった。 少年時代にラッセルは、まだデカルトを読まない前にデカルトの二元論に似たものに達している。(また)ヒュームを読む前にヒーム的な懐疑を抱いた(抱いている)*2 。 彼が体系的な哲学教育を受けなかったことが有利に働いたのであり、あまり若い時から過去の哲学者について行きとどいた知識を得ることほど独創的な思考を窒息させるものはない、と私は考える傾向がある(考えたい気がする)。 なぜなら、そうすることは、自分の思いつく観念がたいていすでに誰かによって考えられていることに気づくという、意気消沈をもたらす(やる気をなくしてしまう)からである。(もしかすると、無知がよい結果を生んだ典型的な(classic 第1級の)例はヴィットゲ ンシュタインだったかも知れない。) *2 「私の知的発展」(シルプ(編)『バートランド・ラッセルの哲学』及び「論理的原子論」(『現代英国哲学』)
Cautionary notes, n.02 Russell probably read more widely than any other contemporary philosopher, with the possible exception of Whitehead. Some of his greatest contributions to philosophy arose through his ability to take a multitude of ideas from many sources and combine them into a fully-wrought system; in the same way that Newton’s Principia brought together a number of fundamental concepts originated by Galileo.*1 *1 Russell’s remark (in conversation with Alan Wood) that he owed his achievements to ‘pertinacity and obstinacy’ can be compared with Newton’s: ‘I had no special sagacity-only the power of patient thought.”‘ But even when ideas were suggested in the first place by others, Russell wrote nothing which was not the product of his own mind. The most obvious evidence is in the number of cases (for instance, with neutral monism) where there was a long time-lag before came to accept another philosopher’s point of view. There were also many cases of pure coincidence, where Russell reached his conclusion in ignorance of similar conclusions by others; like the discovery of the calculus by Leibniz and Newton, or like the four identical bars in Verdi’s Otello and Gounod’s Romeo et Juliette. In Russell’s case, of course, the most obvious example is the theory of mathematics which he and Frege arrived at completely independently. It may also be noticed that Russell did not acquire much knowledge of philosophy-in the usual academic sense of studying the writings of other philosophers-until comparatively late in life. He did not read philosophy officially until his fourth year at Cambridge, and his course of study at Cambridge had some important gaps. As a boy, Russell arrived at something like Descartian dualism before he read Descartes; he had Humean doubts before he read Hume*2. I am inclined to think that his lack of systematic philosophical education was an advantage, and that nothing can do more to stultify original thinking than a thorough knowledge of past philosophers acquired too early in life; because it brings with it the deadening discouragement of realizing that most of the ideas one thinks up have been thought of by someone else before. (Perhaps the classic example of the advantages of ignorance was Wittgenstein.) *2 *2 My Mental Development, in: Philosophy of Bertrand Russell, p.7 and ‘Logical Atomism, in Contemporary British Philosophy, p.323 Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_cautionary-notes_02.html
ラッセルの思想の発展を論じはじめる前に、いくつかの予備的な注記(メモ)が必要である。 彼の思想(Russell’s ideas)があれこれの結論(such-and-such a conclusion.)に達したいという彼の欲求から彼の思考(his thoughts)はある一定の方向に推し進められたと、私は今後たびたび書く機会があるかも知れない。しかし、このことはこの動機が、意識的にせよ無意識的にせよ、彼の思索(his thinking:)の結果に影響したと意味しているととられては決していけない。この区別は、終始明確に、絶対に維持されなければならない。すでに示されたように、彼のこの思考の一般的な傾向(the general trend of this thought)が、彼が到達したいと望んだものとは正反対の結果に導いたのである。そしてこの区別は、私がその時々に述べるの(彼の)他の動機についてもあてはまるのである。 ラッセルの思想と彼の先行者(先達者)及び彼の同時代人の思想との関連を追う時に、彼の思想が 事実そうであったよりも独創的ではなかったかのような印象が与えられかも知れないという危険性がある。 この印象は、 彼自身が他人に負うところを認める時の気前のよすぎる態度(his own over-generosity)によっても強められるかも知れない(可能性がある)。彼はかつて、一つの発見を他人よりも自分が先にしたと主張するような哲学者は株屋の水準にまで落ちた者だ、と書いた。
Cautionary Notes 01 Some preliminary notes are necessary before beginning to discuss the development of Russell’s ideas. I may often have occasion to write that his thoughts were impelled in a certain direction because of his desire to reach such-and-such a conclusion. This must never be taken as implying that this motive, consciously or unconsciously, affected the results of his thinking: the distinction must be kept absolutely clear cut throughout. It has already been pointed out that the general trend of this thought led to results directly opposite to those he hoped to reach; but the distinction also applies to other motives I may mention incidentally. There is a danger that, in tracing connections between Russell’s ideas and those of his predecessors and contemporaries, an impression may be given that his thought was not so original as it was. This impression may also be fostered by his own over-generosity in acknowledging his debts to others; he once wrote that a philosopher who claimed priority for a discovery was descending to the level of a stock-jobber. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_cautionary-notes_01.html
Summary and Introduction n.14 The philosopher has the choice to-day of advancing precise thinking as far as possible, while recognizing spheres remaining separate outside it, or else attempting a grand synthesis in which his emotions and his mystic yearnings are brought in to muddle up his thinking. Russell followed in the first course. In short, I believe that analysis is abundantly justified as a method, but can be misleading if it comes to be regarded as a metaphysic. There are hints in Russell’s writings that he himself may have felt this: for instance (my italics): ‘Speaking generally, scientific progress has been made by analysis and artificial isolation.”* * Human Knowledge, p.49 In at least one passage he emphasized the distinction I have in mind between a metaphysic and a method. He wrote of Meinong (in 1904): ‘Although empiricism as a philosophy does not appear to be tenable, there is an empirical method of investigating, which should be applied in every subject-matter.” Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_14.html
Summary and Introduction n.13 As Russell himself said in criticism of Santayana, a smooth literary form is rarely compatible with original ideas, which are more likely to be marked – at least in their first expression – by ‘uncouth jargon’. Russell himself kept remarkably free from ‘uncouth jargon’; but his philosophy was far from ‘simple’.*1 It is right that any study of a philosopher should be prefaced by a statement of the author’s own views, so that the reader can allow for any unconscious bias. *1 B. R. on George Santayana By temperament I am a mystic Bergsonian; I cannot be satisfied with the static analytic approach of Russell. In fact my main aim, in studying his philosophy, was to find some way of getting round his conclusions; but in this, so far, I have been completely unsuccessful; and I do not believe that anyone else has produced any answer to his philosophy which can be accepted with intellectual integrity. As I have said, it is hard to be sure about exactly what point is at issue between Russell and the monists. Russell could hardly quarrel with Bradley’s statement that ‘Since what I start with in fact is this, and what analysis leaves to me instead is that – I therefore cannot but reject, at least in part, the result of analysis.”*2 To the question ‘Does analysis mean falsification?” I believe the only correct answer is ‘Yes, if you don’t know what you are doing.” A physicist is obviously wrong if he thinks that, after carrying out the electrolysis of water, he can still get a cooling drink from the products of his analysis; but the fact remains that analysis is the proper method of increasing our knowledge of water. A physiologist who dissects a living body cannot expect to be able to put the body together again, or (I believe) to discover what makes the body live and breathe. But most major advances in medicine have come from accepting the materialistic view of the human body as a working hypothesis; even though some doctors in recent years have tended to go astray through regarding the materialistic view as sufficient in itself. In the same way, I believe that Russell was right, as a method of increasing knowledge, in pushing the philosophy of analysis as far as it will go; in his case he came up against its furthest present-day limits, and could not really feel satisfied with his conclusions, when he came to ethical theory. *2 F. H. Bradley: Philosophy of Logic, p.693. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_13.html
ラッセルの著作がなぜ複雑で微妙で込み入っているか(ややこしいか)、なぜホワイトヘッドはラッセルをプラトン的対話そのものだ(訳注:複数のラッセルがラッセルの著書のなかで対話・議論をしている)と呼んだかが、今や一層容易に理解できるであろう。実際、ブラトン以後の偉大な哲学者で、その見解を短く(in a short space)要約することが(これほど)困難な哲学者はいない。 ラッセルの哲学は、彼が自分自身に対して負け戦(まけいくさ)を戦った戦場であった。(即ち)ある時はある方向へ向い、ある時には別方向に向かい、結論 - 通常の場合、彼が当初期待したものとは正反対の(diametrically)結論 - に達するまでには問題の全領域を網羅していた(のである)。 ラッセルとその最初期の哲学上の論敵との間の主な論争点を要約することは、- どちらの側もある意味では正しかったと述べることをしないでは、非常に困難である。しかし、「内的関係(internal relations)」についてのラッセルとブラッドリとの論争における根本的な争点は、ブラッドリの側での一種の想定(assumption)、即ち、ひとつの存在が事実上ある関係をもつ場合それはその関係を必然的にもっていなければならない(持っているに違いない)という想定であると、私は考える(訳注:たとえば、AとBが関係がある場合、その関係というものが外にあると考えるのが外的/外面的関係説、内的にあるというのが内的/内面的関係説)。恐らく、我々はラッセルのディレンマを次のように言うことによって最もよく説明できるであろう。(即ち)彼は、ほとんどの場合、充足理由の法則(注:「どんな出来事にも、そうであるためには十分な理由がなくてはならない」という原理)を信じたかった、(しかし)彼の知的誠実さはそれを拒否し、そうしてそのゆえに、ラッセルには、いかにして科学的知識が可能であるかを説明する問題が残されたのである。 かなり逆説めいているが(逆説的な言い方だが)、ラッセルのいつものスタイル(文体)が非常に明確であることは、彼の議論(主張)の常なる(絶え間のない)繊細さと独創性とを不明瞭にしている(覆い隠してきている)。論争的な誇張(表現)や(眼の前のものを)一掃するような警句は誰でもよくわかるので繰り返し引用されてきたが、彼がある主張から別の主張へと骨折って取り組んでいるあるいは自問自答している著書は、しばしば読まれないままとなる。現代のある評判の解説者によれば、ラッセルの書くものは「最も困難な主題についても常に容易である」とのことであるが、そのことから、その解説者は(ラッセルの)『数学の原理』や、さらには『人間の知識』をさえ、一度も読んだことがないと推論(演繹)しても、誤りではないように思われる。
Summary and Introduction n.12 It may now be easier to understand why Russell’s writings are so complex, subtle and intricate, and why Whitehead called him a Platonic dialogue in himself. In fact there is no great philosopher since Plato whose ideas are harder to sum up in a short space. His philosophy was a battleground on which he fought a losing battle against himself; sometimes going one way, sometimes another; and he covered the whole field before reaching conclusions usually diametrically opposed to those which he had hoped for. It is very difficult to sum up the main point at issue, between Russell and his earliest philosophical opponent, without making it appear that both sides were, in a sense, right. But I think the fundamental point at issue, in Russell’s controversy with Bradley over internal relations, was some sort of assumption, on Bradley’s part, that an entity must have the relations which it has. Perhaps we can best sum up Russell’s dilemma by saying that for the most part he wanted to believe in a Law of Sufficient Reason; his intellectual integrity made him reject it; and he was therefore left with the problem of explaining how scientific knowledge could be possible. Paradoxically enough, the very clarity of Russell’s usual style has obscured the continual subtlety and originality of his arguments. The polemic overstatements and sweeping epigrams which anyone can understand have been quoted again and again; the books where he is painfully working his way from one position to another, or arguing with himself, often remain unread. According to a modern commentator of some repute, Russell ‘even on the most difficult topics is always simple, easy’; from which it would seem a fair deduction that the commentator in question has never read The Principles of Mathematics, nor even Human Knowledge. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_12.html
Summary and Introduction n.11 What is involved might variously be described as love of aesthetic elegance, love of unity, love of system, or profundity. (In the only sense of the word ‘profundity’ which I think has any meaning.) It was a passion partly connected with, and partly at variance with, his passion for impersonal and certain truth. And it proved just as impossible to attain. In an early article he described how, in the greatest mathematical works, ‘unity and inevitability are felt as in the unfolding of a drama…. The love of system, of interconnection … is perhaps the inmost essence of the intellectual impulse’.*1 He was later forced to the conclusion that the love of system was the greatest barrier to honest thinking in philosophy; just as he decided that ‘the demand for certainty is one which is natural to man, but is nevertheless an intellectual vice’.*2 He put his conclusions in their most extreme form when he wrote in 1931: ‘Academic philosophers, ever since the time of Parmenides, have believed that the world is a unity. . . . The most fundamental of my intellectual beliefs is that this is rubbish. I think the universe is all spots and jumps, without unity, without continuity, without coherence or orderliness or any of the other properties that governesses love. Indeed, there is little but prejudice and habit to be said for the view that there is a world at all. *3 “The external world may be an illusion, but if it exists, it consists of events, short, small and haphazard. Order, unity, and continuity are human inventions, just as truly as are catalogues and encyclopaedias.”*4 To appreciate the force of such a passage, it must not be regarded as simply a sweeping attack on most ‘academic philosophers’. It was an attack on a position which Russell held himself; and one which he always, in a sense, wanted to hold as intellectually possible. *1 Mysticism and Logic, p.66, cf. Our Knowledge of the External World, p.238 *2 Unpopular Essays, p.42 *3 Scientific Outlook, 98 *4 ibid., p.101 Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_11.html
Summary and Introduction n.10 What he would not say about himself he said about Einstein. He gave a better clue to his real feelings when he wrote that the Theory of Relativity ‘is possessed by that sort of grandeur that is felt in vast results achieved with the very minimum of material’. Occam’s Razor is not just a kind of philosophical economy campaign; that is like describing a sculptor as a man who gets rid of unnecessary chips of marble. It is not, as suggested by Wittgenstein, a rule of symbolism. It is not even merely a rule for securing a greater chance of accuracy in philosophical calculations. Russell’s use of Occam’s Razor was not only a means to an end but part of something which was a motive in itself; a passion which had almost as much force in Russell’s mind as his passion for impersonal truth. It is a passion known to every writer who whittles away unnecessary words from his manuscript, and to every mathematician and scientist in the search for the most elegant proofs and most general laws. It is easier to give illustrations of it than to attempt to define or explain it.*1 *1 cf. Mysticism and Logic, p.70 Russell wrote in 1906 that, when choosing among the different alternative systems of primitive propositions for mathematical logic, ‘that one is to be preferred, aesthetically, in which the primitive propositions are fewest and most general; exactly as the Law of Gravitation is to be preferred to Kepler’s three Laws’ (my italics). *2 He recalled that he had ‘a sense almost of intoxication’ when he first studied Newton’s deduction of Kepler’s Second Law from the Law of Gravitation.*3 He told of his delight when he discovered for himself, as a boy, the formula for the sum of an arithmetic progression, and his delight in such a concise formula as Eiπ=-1. In such instances he gave a much truer picture, but when he wrote, for example, “then the justification for the utmost generalization in mathematics was not to “waste our time” proving in a particular case what can be proved generally’.*4 *2 Philsophy of Leibniz, p.8 *3 On Education, p.203. *4 Introduction to Mathematical Philosophy, p.197-8. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_10.html
Summary and Introduction 09 The fact that philosophical argument consists of ‘exhortation’ accounts for much of the informal flavour of his writing, and the use of different popular illustrations of his ideas, in which critics can find contradictions. It is as though Russell were saying ‘if that way of putting it won’t convince you, perhaps this will’.*1 *1 Perhaps it is of interest to note that A. D. Lindsay made a similar remark about Kant.) Since Russell reached the above views on philosophy over fifty years ago, there has been time for them to be forgotten, and they have been presented again in recent years as though they were new discoveries due to Wittgenstein and his school. (For instance, Dr Waismann in the latest volume of Contemporary British Philosophy: “There is a notion that philosophical questions can be settled by argument, and conclusively if one only knew how to set about it…. I incline to come to a new and somewhat shocking conclusion: that the thing cannot be done. No philosopher has ever proved anything (because) philosophical arguments are not deductive.’)*2 *2 VOL.III, p.471 I have referred above to Occam’s Razor as a part of Russell’s philosophical method inspired by his passion for certain knowledge. This was how Russell himself justified its use. (“That is the advantage of Occam’s Razor, that it diminishes your risk of error.)*3 *3 Philosophy of Logical Atomism, in Logic and Knowledge But much more was involved than this; and we must beware of Russell’s habit of describing his own work in terms of belittlement. Source: My Philosophical Development, 1959, by Bertrand Russell. More info.: https://russell-j.com/beginner/wood_br_summary-and-introduction_09.html