Chapter 17 Chapter 17 Abandoning Pythagoras

Since the beginning of this century, the development of my philosophy can be roughly described as gradually abandoning Pythagoras.In former times, the disciples of Pythagoras had a special kind of mysticism, which was closely related to mathematics.This mysticism has had a great influence on Parker, and I think it has had a greater influence on him than is recognized.There was a time when I had a similar opinion.At that time I found something in what I thought was the nature of mathematical logic that made me emotionally satisfying in some ways. As a teenager, my interest in mathematics was relatively simple and mundane.Of the two, Thales and Pythagoras, my interest in mathematics is closer to Thales.I found out that things in the real world follow the principles of mathematics, and I was very happy then.I love levers and tackle.I also like that falling objects follow a parabola.I don't know how to play pool, but I like the mathematics of how pool balls work.Once a new tutor came, and I transferred money.He said: "Why is that money transferred?" I replied: "Because I used my fingers to make a force".He was surprised and said, "How much do you know about Ooli?" I replied briskly, "Oh, there's nothing I don't know about Ooli."

Once, I had to draw my own tennis court, and I used the Pythagorean theorem to make sure the lines were at right angles. My uncle took me to visit the famous physicist Tyndall.While they were talking, I had to find some entertainment for myself.I took two walking sticks, each with a curved handle.I balance the two canes on my fingers so that they are angled in opposite directions, thus crossing at a point.Tyndall looked back and asked what I was doing. I replied that I wanted to find a practical way of estimating the center of gravity, since the center of gravity of each stick must be on a vertical line below my fingers, and therefore at the point where the sticks cross.Probably because of what I said, Tyndall gave me one of his books, The Form of Water.At that time, I wanted all sciences to be as serious as mathematics, including psychology.The parallelogram of force proves that if an object has two forces acting on it at the same time, it must take the middle route and favor the side with the greater force.I was hoping that maybe there was a similar "Mobile Quad".This is a kind of confused thinking, because if a person comes to a fork in the road and wants to take this road and that road, he does not walk in the middle of the two roads.

Back then science hadn't discovered "there is or isn't a principle".The importance of this principle was not discovered until this century. When I was young, I thought that if two gravitational forces run counter to each other, the result would be a Democratic-style compromise.It was later discovered that often one of the two completely prevailed.This gave Dr. Johnson the reason that, in his opinion, the first Democrat was the devil, not God. My interest in the applications of mathematics was gradually superseded by an interest in the principles which form the basis of mathematics.This shift was due to a desire to refute mathematical skepticism.There are many arguments that I am asked to accept that are clearly false.

I read every book I could find that seemed to strengthen my faith in mathematics.This kind of research gradually led me farther and farther away from applied mathematics, more and more into the abstract field, and finally into mathematical logic.Later I had an idea that mathematics is basically not a tool for understanding and manipulating the world of senses, but an abstract system that exists in the heaven in the sense of Plato's philosophy, and only in an impure and depraved form of it Come to the world of feeling.In the early years of this century, my general view was one of profound escapism.I loathe this real world, and want to seek refuge in a world beyond time, where there is no change, no decline, and no will-o'-the-wisp of progress.Although this view is serious and sincere, I sometimes express it in a careless way.My brother-in-law Luo Gan Pisao Smith has a set of questions that he often asks people.One of the questions was: "What is your favorite?"

My answer was: "Mathematics and the ocean, theology and heraldry. I like the first two because they are inhuman, and the last two because they are ridiculous." This form is adopted, but it is to get the approval of the person who asked the question. My attitude towards mathematics at that time was expressed in an article of mine entitled "A Study of Mathematics", published in the New Quarterly in 1907 and reprinted in the Philosophical Papers (1910).Quoting a few passages in this article can illustrate my opinion at that time: Mathematics, if viewed correctly, not only possesses truth, but also has supreme beauty, just like the beauty of sculpture, which is a cold and serious beauty, A beauty that does not appeal to the feebler aspects of our nature, a beauty free from the ornate ornamentation of painting or music, capable of sublime purity, of that exacting perfection which only the greatest art can reveal. .A spirit of true joy, a spiritual growth, a sense of being superior to man (these are the standards of the highest good) can be found in poetry, and indeed in mathematics.The best things in mathematics should not only be learned as a job, but should also be made a part of daily thought, often brought to mind by repeated encouragement.For most people, real life is a long, secondary thing, a constant compromise between the ideal and the possible; but the purely rational world knows no compromise, no practical limit, no obstacle to creative activity. thing. (The activity of creation embodies the passionate desire for perfection in magnificent buildings, and all great achievements originate from the desire for perfection).Far removed from human emotion, and even from the poor facts of nature, the generations have gradually created a well-ordered universe.Pure thought seems to live in its own home in this universe.At least one of our nobler impulses can escape the dreary wanderings of the real world in this universe.

※ ※ ※Meditate on things that have nothing to do with people, and find that our hearts can deal with materials that are not made by the mind. More importantly, we know that beauty belongs to the inner world, but it does not belong to the outside world. These are all ways to overcome the terrible The main method of feeling powerless, weak, can overcome the feeling of exile among hostile forces.The reason for this dreadful feeling is the recognition of the almost omnipotence of external powers.The so-called destiny is nothing but the personification of these forces in literature.It is the task of tragedy to bring out the awe-inspiring beauty of fate and make us content with it.But mathematics takes us a step further than human affairs, takes us to the realm of absolute necessity.Not only the real world cannot but obey this necessity, but every possible world has to obey it; mathematics even builds a dwelling here (or rather, it finds a permanent dwelling), where There our ideals are fully gratified and our highest hopes are not thwarted.

※ ※ ※It is often said that there is no absolute truth, only opinions and personal judgments; each person is limited in his world view by his own characteristics, tastes and prejudices; that outside world that we can enter with patience and training In the realm of truth there is no truth, only my truth, your truth, and the truth of individual people.By this habit of the mind one of the chief ends of human endeavor is negated, and the supreme virtue of candor, that which is not afraid to admit existence, is lost from our moral ideal. ※ ※ ※In a world full of disasters and pains, retreating to contemplation and enjoying some pleasures (however noble these pleasures must always be for a few) cannot be regarded as selfish, refusing to share the burden of disasters. There is no justice in these calamities of burdening others.Let us ask, do we have the right to ignore the present disaster and not to help our kind?And we lead a life which, though austere and serious, is good obviously by its very nature.

All of this, while I still remember the joy I had when I believed it, now seems largely absurd, partly for technical reasons and partly because my worldview has changed.I no longer think that mathematics has nothing to do with personnel in terms of subject matter.I have come to believe (albeit reluctantly) that mathematics is made of tautologies.I am afraid that to a person of sufficient intelligence the whole of mathematics would appear as insignificant as saying that a quadruped is an animal.I think the super-temporal nature of mathematics does not have the kind of sublime and solemnity I thought it had before, but only because pure mathematicians do not talk about time.I no longer experience any mystical satisfaction in contemplating mathematical truth.

The aesthetic feeling born of an exquisite mathematical deduction is still there.But there are also disappointments here.The resolution of some contradictions was mentioned in the previous chapter. These contradictions seem to be resolved only by adopting a theory that is true but not beautiful.I then felt about contradictions as a sincere Catholic must feel about bad bishops.The magnificent certainty I had always hoped for in mathematics was lost in a bewildering bewilderment.All this would have made me sad were it not for the recluse which I had then begun to lose.That sense of escapism seized me so strongly that I found Dante's "New Life" to be psychologically natural, and the strange symbolism in it appealed to me. A kind of satisfaction can be obtained.But the mood began to fade, and was finally dispelled by the First World War.

The effect of that war was that I could no longer live in an abstract world. At that time I saw young people board the army train, and then they were massacred at Somme because of the stupidity of the generals.I feel a painful pity for these young people.I found myself in a painful union with the actual world.Seeing the pain around me, all my old grandiose thoughts about the world of abstract concepts, I felt empty and insignificant.The impersonal world is still sometimes a place of escape, but not a realm where permanent dwellings are built. In this change of mood, there are also losses and gains.What is lost is the hope for fullness, finality and certainty.What was gained was a new surrender to some truths I loathed.But I have not completely abandoned my former beliefs.Some things I believed then and still believe now.I still believe that truth depends on a relation to facts which are generally speaking irrelevant to man; I still believe that man is cosmicly unimportant; "Present" prejudices look at the universe without mentioning man, except perhaps in a footnote at the end of the volume; but I no longer wish to drive the human element out of its field; I no longer feel Reason is higher than feeling, and no longer feel that only Plato's ideal world is close to the "real" world.

I used to think that feeling, and thought based on feeling, was a prison from which we could be set free by thought free of feeling.Now I don't think so.I regard sensations and thoughts built upon them as windows, not prisons.I think we can (though not quite) reflect the world like Leibniz's monad; I think it is the philosopher's job to make himself as even a mirror as possible.But it is also his duty to recognize the inevitability of the distortion of the mirror by our nature.The most important of these distortions is that we learn from "here" Looking at the world from the perspective of "this time" is not looking at the world with the kind of impartiality that theists think comes from God. This kind of impartiality is impossible for us, but we can go a distance.It is the philosopher's supreme duty to show the way towards this goal.