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1897年夏天,意大利经济学家帕累托(Pareto)在研究英国社会分配的时候发现，百 分之二十的人控制着百分之八十的财富。后人在现实世界里形形色色 的分布里也看到了类似“少多众寡”的现象：大段文字里单词出现的频率、都市城镇的人口、沙 粒的大小，甚至林火烧过的面积。比如，把全世界每个人拥有的财富 从大到小排起来，一边是一个纤细但高耸入云的头，另一边是漫长的一望无际，低矮的让人 绝望的尾。这样的分布在经济学里被灌名为“帕累托分布”，只是一直不 为大众所知。但是有一个简单的版本一直在商业世界里传诵, 就是今天的“80/20原则”。 1982年春天，托夫勒的 《第三次浪潮》在 中国登岸。我们刚开始憧憬大工业生产的时候，托夫勒就不识时务地预言它的灭亡。“不再 有大规模生产。不再有大众消费。不再有大众娱乐”。取而代之的是个性 化到每个人的生产、创造和消费。为什么要有重样的产品？难道生产和消费不能是一件事吗？遗 憾的是，大家激动过后，发现还没有见识过真正大众消费的时候就琢 磨它的消亡实在需要太多的想像力。二十年后大众娱乐终于到来的时候，托夫勒早已经被多 数人抛在了脑后。 到了2004年的秋天，终于有人把这两件事扯在了一起。美国 《联线》(Wired)杂志发表了总编克里斯・安德森(Chris Anderson)的文章： 长尾。 副标题是“别老掂着从榜顶的几个巨无霸里多榨几百万出来。娱乐的未来在码流低浅的那头 无数个细微市场那儿”。“低浅的那头”，其实就是帕累托分布的尾巴； “无数个细微市场”，其实也就是托夫勒的全民个性化消费。安德森的神来之笔，是在极其 正确的时间，在极其正确的媒体上，用一个简单响亮的词向大众描绘了互 联网下面高涨涌动之中的暗流。安德森一发不可收拾，开始在 Long Tail Blog上公开编撰书稿。两年后，《 长尾理论》(The Long Tail)问世了。 沿袭记者擅长的悬疑开局，安德森用真实发生的几件事向我们直接勾画出了长尾现象：一本 六年无人过问的冷门书突然窜上《纽约时报》的排行榜，因为有人在评论类似话题的新书的 时候提到了它；在线音乐店 Rhapsody里下载排行十万名以后的那些歌，在任何一家最最专业的唱片店都找不到，每月下载次数只 有几次、几十次，加起来却占了所有下载次数的15%；在线DVD租赁店 Netflix销量占末尾21%的碟片在任何一家线下碟店都找不到。这些“多出来”的冷僻产品每样都 卖得可怜，但因为品种数目庞大，加起来却能带来不小的销售。这就是长尾了。 如果你想在一刻种内比较精准地把握可能是下一个流行的谈资，读到这里也就差不多够了。对 更好奇或者多疑的读者来说，有些个问题还是值得探究的。比方 说，为什么线下商店没有长尾？长尾和以前说的80/20原则有什么关系? 那些长尾产品既然不畅销，会不会都是垃圾? 长尾对畅销排行榜有什么影响？长尾的泛滥会导致个人中心主义吗？还有些更功利的问题：长 尾带来什么样的机会？怎样去利用它？这本书剩下来95%的篇幅里， 用简单直观的方式给出了这些问题的答案。总的来说，长尾无处不在，无时不在。只是有了 网络以后，各个环节的成本都大大降低，长尾的东西才有了广泛产生、传 播和获取的可能。 和《 引爆流行》、《 世界是平的》 一样，作者倾向于在讲清楚核心命题以后，开始多角度、多行业反复引申和描述。要是你和 我一样对渲染容易感到困倦，看到第六章的时候我建议你提起神来。承认 长尾里鱼目混杂以后，安德森用“过滤器”的概念来解释为什么直到现在长尾才开始重要起 来。长尾里选择过多，所以要为每个人挑出合适的东西，需要更强大的过 滤器。编辑、星探、营销者、广告是传统的“事前过滤器”。博客、评论、推荐、草根意见 是“事后过滤器”，只有这些能应对长尾的低信噪比和极端个人化的兴趣 取向。网络发展到今天，终于有了搜索、推荐这些强大的信息技术，可以为单个消费者提供 有效的过滤。这是长尾现象和Web 2.0产生在同样年代的原因。 《 长尾理论》生动、易读、及时，面面俱到，这些决定了这会是一本对很多行业影响深远的书。期望更 深入理解和指引的读者可能会觉得不过瘾。不过长尾是此时此刻正在发生的事情，有机会参 与其中，比起任何单纯的脑力享受来，我认为是更加幸运的。 powered by performancing firefox
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NATURAL HISTORY For THE BUILDING UP OF PHILOSOPHY Francis Bacon (1607)
bacon
PHENOMENA OF THE UNIVERSE
Or
NATURAL HISTORY
For
THE BUILDING UP OF PHILOSOPHY
Source: Natural History for the Building Up of Philosophy, 1609, 19th Century English edition; first 5 pages from the Preface.
PREFACE
Since it seems to me that people do not keep strictly to the straight and narrow when forming their opinions or putting things to the test, I have decided to use all the means at my disposal to remedy this misfortune. For in nothing else does the aspiration to deserve well show itself than it things are so arranged that people, freed both from the hobgoblins of belief and blindness of experiments, may enter into a more reliable and sound partnership with things by, as it were, a certain literate experience. For in this way the intellect is both set up in safety and in its best state, and it will besides be at the ready and then come upon harvests of useful things.
Now the beginnings of this enterprise must in general be drawn from natural history; for the whole body of Greek philosophy with its sects of all kinds, and all the other philosophy we possess seem to me to be founded on too narrow a natural-historical basis, and thus to have delivered its conclusions on the authority of fewer data than was appropriate. For having snatched certain things from experience and tradition, things sometimes not carefully examined or ideas nor securely established, they leave the rest to meditation and intellectual agitation, employing Dialectic inspire greater confidence in the matter.
But the chemists and the whole pack of mechanics and empirics, should they have the temerity to attempt contemplation and philosophy, being accustomed to meticulous subtlety in a few things, they twist by extraordinary means all the rest into conformity with them and promote opinions more odious and unnatural than those advanced by the very rationalists. For the latter take for the matter of philosophy very little out of many things, the former a great deal out of a few, but in truth those courses are weak and past cure. But the Natural History which has been accumulated hitherto may seem abundant on casual inspection, while in reality it is sketchy and useless, and not even of the kind I am seeking. For it has not been stripped of fables and ravings, and it rushes into antiquity, philology and superfluous narratives, neglectful and high-handed in matters of weight, overscrupulous and immoderate in matters of no importance. But the worst thing about this abundance is that it has embraced the inquiry into things natural but largely spurned that into things mechanical. Now the latter are far better than the former for examining nature's recesses; for nature of its own accord, free and shifting, disperses the intellect and confuses it with its variety, but in mechanical operations the judgement is concentrated, and we see nature's modes and processes, not just its effects. Yet, on the other hand, all the subtlety of mechanics stops short of what I am seeking. For the craftsman, intent on his work and its end, does not direct his mind or put his hand to other things, things which perhaps do more for the inquiry into nature.
Therefore we need more meticulous care and handpicked trials, not to mention funding and the utmost patience besides. For it has ruined everything in the experimental field that right from the beginning men have continually aimed at Experiments of Fruit not ones of Light, and have devoted their energies entirely to producing some splendid work, not to revealing nature's oracles, which is the work of works and encompasses in itself all power. It also comes about from men's misguided conceit that they have mostly applied themselves to things hidden and rare, and put their efforts and inquiry into those while spurning common experiments and observations, and this seems to have come about either because they sought admiration and fame, or because they fell for the belief that the function of philosophy lies in accommodating and reducing rarer events to those which occur familiarly, not equally to unearthing the causes of these common things themselves and deeper causes of those causes.
But the main point of the whole accusation against natural history is that men have gone astray not only in the work, but in its very plan. For the natural history which is in existence seems to have been composed either for the usefulness of the experiments themselves, or for the agreeableness of their narratives, and to have been made for their own sake, not so as to furnish the makings of philosophy and the sciences and as it were breast-feed them.
Thus, as far as it is within my power, I do not wish to fail to do my duty in this matter. For I have long since decided how much I should grant to abstract philosophies. Indeed, I believe that I hold fast to the ways of true and good induction, in which all things lie, and which can help the frail and crippled faculty of human intellect towards the sciences, as by mechanical aids or by some thread to guide it through a labyrinth. Nor am I unaware that if I had been willing to restrict that instauration of the sciences which I have in mind to any of the greater inventions, I could perhaps have harvested a greater crop of honour. But since God has given me a mind which knows how to submit itself to things and which readily rejects the specious out of a sense of what is right and from confidence that things will turn out well, I have also taken upon myself that part of the work which I think others have wanted either to avoid entirely, or to treat in a way different from my idea of it.
But there are two things which I wish to warn people about in this connection both for the future and, since I am girding myself for the very thing itself, for now especially. The first is to get rid of that idea which, though it be utterly false and harmful, easily invades and takes hold of men's minds, namely that the inquiry into particulars is something infinite and without end, when it would be truer to say that the way of opinions and disputations is the trifling one; but in fact these vain imaginings are condemned to perpetual errors and infinite disturbances, whereas particulars and the informations of the sense (which, when individuals and the gradations of things have been left out, is sufficient for the inquiry into truth) allow understanding for certain, and that, to be sure, neither forlorn nor hopeless.
The second is that I would have men never forget what is involved and, when they have come across troops of thoroughly vulgar things, things slight and to all appearances frivolous, even vile, and which (as the man says) must be brought in with an apology, they do not think I am trifling, or reducing the human mind to things beneath its dignity. For these things are neither examined nor described for their own sake, but in fact there is simply no other alternative open to the human intellect, and the grounds of the work are left insecure without them. I am then certainly undertaking the most serious business of all and most worthy of the human mind, that nature's light, pure and quite unclouded by vain imagination (that light whose name has sometimes been mentioned thus far, while people have known nothing about the thing itself), may be lit in this age of ours by a torch furnished and brought near by the Divine Will.
For I do not hide the fact that I believe that preposterous subtlety of argument and thought can by no means put things right again, though all the intellects of all ages be gathered together, when, at the proper time, the subtlety and truth of the basic information or true induction have been overlooked or incorrectly established, but that nature, like fortune, is long-haired at the front and bald at the back. It remains, therefore, for the matter to be attempted anew, and that with better help and with the zeal of opinions laid aside, so that we may enter into the kingdom of philosophy and the sciences (in which human power is situated, for nature is conquered only by obeying it) in the way that we gain access to the Kingdom of Heaven, which none may enter save in the likeness of a little child. Yet I do not wholly despise the base and indiscriminate custom of working by experiments themselves (for it may doubtless suggest very many useful things to men's knowledge and invention, according to the variety of their arts and capacities), nevertheless I think it is something very trivial in comparison with that entrance into human knowledge and power which I hope for from the Divine Mercy, which indeed I again humbly beseech to allow me to endow the human family with new alms through my efforts.
The nature of things is either free, as in species, or disturbed, as in monsters, or confined, as in experiments of the Arts; yet its deeds of whatever kind are worthy of report and history. But the History of Species currently available, as for example of plants, animals, metals and fossils, is puffed up and full of curiosities; the History of Marvels empty and based on rumour; the History of Experiments detective, attempted piecemeal, dealt with carelessly, and entirely for practical not philosophical use.
Therefore it is my resolve to curb the History of Species, to shake our and purify the History of Marvels, but to our special effort into Mechanical and Artificial Experiments where nature gives in to human intervention. For what are the sports and frivolities of nature to us? That is, the tiny differences of species as to shape, which contribute nothing to works but in which Natural History none the less abounds. Now knowledge of Marvels certainly pleases me, if it be purified and sifted; but why in the final analysis is it pleasing? Not for the fun of being astonished, but because it often reminds Art of its duty to lead nature knowingly where it has itself sometimes gone before of its own accord.
In general I assign the leading roles in shedding light on nature to artificial things, not only because they are most useful in themselves, but because they are the most trustworthy interpreters of natural things. Can it be said that anyone had just happened to explain the nature of lightning or a rainbow as clearly before the principles of each had been demonstrated by artillery or the artificial simulacra of rainbows on a wall? But if they are trustworthy interpreters of causes, they will also be sure and fertile indicators of effects and of works. However, I do not think it appropriate to divide my history in accordance with this threefold partition, so as to deal with singular instances separately, but I shall mix the three kinds, joining things natural with artificial. ordinary with extraordinary, and paying very close attention to all the most useful ones.
Now it would be more usual to begin with the phenomena of the ether. But I, sacrificing nothing of the seriousness of my undertaking, shall give priority to things which make up and answer to a nature more general, in which both globes share. I shall begin in fact with a history of bodies according to the difference which seems the simplest, that is, the abundance or paucity of the matter contained and spread out within the same space or boundaries, seeing indeed that none of the pronouncements about nature is truer than that double proposition. Nothing comes from nothing, nor is anything reduced to nothing, but the very quantum of nature, or the whole sum of matter always remains and stays the same, and is in no way increased or diminished. Moreover, it is no less certain. even though not so clearly noted or asserted (whatever stories people make up about the impartial potential of matter towards forms) that more or less of this quantity of matter is contained in the same volumes of space according to the diversity of the bodies which occupy them, bodies some of which we find to be very obviously more compact, others more extended or diffuse. For a vessel or cauldron filled with water and air does not hold an equal portion of matter, but more of the one and less of the other. Therefore if someone claimed that a given amount of water could be made from the same amount of air, it would be the same as saying that something can come from nothing. For what you deem to be lacking from the quantity of matter would have to have been made up from nothing. On the other hand, if someone claimed that a given amount of water could be turned into the same amount of air, it would be the same as saying that something can be reduced to nothing. For what you deem to be extra in the quantity of matter would likewise have to have vanished into nothingness. There is no doubt in my mind that this business is capable of being reduced to calculation, to indefinite proportions perhaps in some things, but to ones precise and certain in others, and known to nature. As, for example, if someone said that the concentration of matter in a body of gold exceeded than of a body of spirit of wine by a factor of twenty to one or thereabouts, he would nor be wrong. So as I now mean to present the history I mentioned concerning the abundance and paucity of matter, and its coming together and expansion, things from which the notions of Dense and Rare (if properly understood) take their origin, I shall so order matters that I shall draw up the relative figures for different bodies (as of gold, water, oil, air and flame) first. Then after examining these, I shall record with calculations or ratios the retreats and expatiations of each particular body. For a given body, even without anything being added to it or taken away, or at least nor in proportion to its contraction and extension, allows itself to be gathered by various impulses both external and internal into a larger or smaller sphere. Sometimes the body struggles and strives to restore itself into its old sphere, sometimes it clearly goes beyond that and does not try to revert. Here I shall first record the courses, differences and proportions of any natural body (as to its extent) compared with its openings and closings up, that is, with its powders, its calces, its virrifications, its dissolutions, its distillations, vapours and breaths, its exhalations and inflammations; then I shall set out the actions and motions themselves, the progressions and the limits of contraction and dilatation, and when bodies restore themselves and when they go beyond than in respect of their extent; but I shall especially note the efficient causes and media by means of which such contractions and dilatations of bodies come about; and meanwhile I shall in passing append the virtues and actions which bodies get and take on from such compressions and dilatations.
And since I know well how difficult a thing it is, in the present climate of opinion, to familiarise oneself with nature right from the very beginning, I shall add my own observations to gain men's attention and arouse them to contemplation. Now as far as the demonstration or revealing of the density and rarity of bodies is concerned, I have no doubt or hesitation that as to dense and palpable bodies the motion of gravity (as they call it) may be taken as the best and most ready test, for the more compact the body, the heavier it is. But when it comes to the level of airy and spiritual things, then scales will for sure be of no use to me, and I shall need another kind of industry. I shall begin, however, with Gold: which of all the things we have (for philosophy has nor grown up enough for us to say anything for certain about the bowels of the Earth) is the heaviest and contains the most matter in the smallest space, and I shall relate the ratios of the rest to the sphere of this body, with the reminder that I am not dealing here with the history of weights except in so far as it sheds light for demonstrating the space or dimensions of bodies. ... powered by performancing firefox
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MIA Philosophy Resource from Andy Blunden G W F Hegel (1817/30)
from The Shorter Logic
The Critical Philosophy
Source: From “Hegel’s Logic”, translated by William Wallace, with Foreword by J N Findlay, Clarendon Press 1975. First published 1873. The additions by the original editors have been omitted to bring out the line of argument more clearly.
§40
In common with Empiricism the Critical Philosophy assumes that experience affords the one sole foundation for cognitions; which however it does not allow to rank as truths, but only as knowledge of phenomena.
The Critical theory starts originally from the distinction of elements presented in the analysis of experience, viz. the matter of sense, and its universal relations. Taking into account Humes's criticism on this distinction as given in the preceding section, viz. that sensation does not explicitly apprehend more than an individual or more than a mere event, it insists at the same time on the fact that universality and necessity are seen to perform a function equally essential in constituting what is called experience. This element, not being derived from the empirical facts as such, must belong to the spontaneity of thought; in other words, it is a priori. The Categories or Notions of the Understanding constitute the objectivity of experiential cognitions. In every case they involve a connective reference, and hence through their means are formed synthetic judgements a priori, that is, primary and underivative connections of opposites.
Even Hume's scepticism does not deny that the characteristics of universality and necessity are found in cognition. And even in Kant this fact remains a presupposition after all; it may be said, to use the ordinary phraseology of the sciences, that Kant did no more than offer another explanation of the fact.
§ 41
The Critical Philosophy proceeds to test the value of the categories employed in metaphysic, as well as in other sciences and in ordinary conception. This scrutiny however is not directed to the content of these categories, nor does it inquire into the exact relation they bear to one another: but simply considers them as affected by the contrast between subjective and objective. The contrast, as we are to understand it here, bears upon the distinction (see preceding §) of the two elements in experience. The name of objectivity is here given to the element of universality and necessity, i.e. to the categories themselves, or what is called the a priori constituent. The Critical Philosophy however widened the contrast in such a way, that the subjectivity comes to embrace the ensemble of experience, including both of the aforesaid elements; and nothing remains on the other side but the 'thing-in-itself'.
The special forms of the a priori element, in other words, of thought, which in spite of its objectivity is looked upon as a purely subjective act, present themselves as follows in a systematic order which, it may be remarked, is solely based upon psychological and historical grounds.
§ 42
(a) The Theoretical Faculty. Cognition qua cognition. The specific ground of the categories is declared by the Critical system to lie in the primary identity of the 'I' in thought what Kant calls the 'transcendental unity of self-consciousness'. The impressions from feeling and perception are, if we look to their contents, a multiplicity or miscellany of elements: and the multiplicity is equally conspicuous in their form. For sense is marked by a mutual exclusion of members; and that under two aspects, namely space and time, which, being the forms, that is to say, the universal type of perception, are themselves a priori. This congeries, afforded by sensation and perception, must however be reduced to an identity or primary synthesis. To accomplish this the 'I' brings it in relation to itself and unites it there in one consciousness which Kant calls 'pure apperception'. The specific modes in which the Ego refers to itself the multiplicity of sense are the pure concepts of the understanding, the Categories.
Kant, it is well known, did not put himself to much trouble in discovering the categories. 'I', the unity of selfconsciousness, being quite abstract and completely indeterminate, the question arises, how are we to get at the specialised forms of the 'I', the categories? Fortunately, the common logic offers to our hand an empirical classification of the kinds of judgement. Now, to judge is the same as to think of a determinate object. Hence the various modes of judgement, as enumerated to our hand, provide us with the several categories of thought. To the philosophy of Fichte belongs the great merit of having called attention to the need of exhibiting the necessity of these categories and giving a genuine deduction of them. Fichte ought to have produced at least one effect on the method of logic. One might have expected that the general laws of thought, the usual stock-in-trade of logicians, or the classification of notions, judgements, and syllogisms, would be no longer taken merely from observation and so only empirically treated, but be deduced from thought itself. If thought is to be capable of proving anything at all, if logic must insist upon the necessity of proofs, and if it proposes to teach the theory of demonstration, its first care should be to give a reason for its own subject.
§ 43
The Categories may be viewed in two aspects. On the one hand it is by their instrumentality that the mere perception of sense rises to objectivity and experience. On the other hand these notions are unities in our consciousness merely: they are consequently conditioned by the material given to them, and having nothing of their own they can be applied to use only within the range of experience. But the other constituent of experience, the impressions of feeling and perception, is not one whit less subjective than the categories.
§ 44
It follows that the categories are no fit terms to express the Absolute the Absolute not being given in perception and Understanding, or knowledge by means of the categories, is consequently incapable of knowing the Things-in-themselves.
The Thing-in-itself (and under 'thing' is embraced even Mind and God) expresses the object when we leave out of sight all that consciousness makes of it, all its emotional aspects, and all specific thoughts of it. It is easy to see what is left utter abstraction, total emptiness, only described still as an 'other-world' the negative of every image, feeling, and definite thought. Nor does it require much penetration to see that this caput mortuum is still only a product of thought, such as accrues when thought is carried on to abstraction unalloyed: that it is the work of the empty 'Ego', which makes an object out of this empty self-identity of its own. The negative characteristic which this abstract identity receives as an object is also enumerated among the categories of Kant, and is no less familiar than the empty identity aforesaid. Hence one can only read with surprise the perpetual remark that we do not know the Thing-in-itself. On the contrary there is nothing we can know so easily.
§ 45
It is Reason, the faculty of the Unconditioned, which discovers the conditioned nature of the knowledge comprised in experience. What is thus called the object of Reason, the Infinite or Unconditioned, is nothing but self-sameness, or the primary identity of the 'Ego' in thought (mentioned in § 42). Reason itself is the name given to the abstract 'Ego' or thought, which makes this pure identity its aim or object (cf. note to the preceding §). Now this identity, having no definite attribute at all, can receive no illumination from the truths of experience, for the reason that these refer always to definite facts. Such is the sort of Unconditioned that is supposed to be the absolute truth of Reason what is termed the Idea; while the cognitions of experience are reduced to the level of untruth and declared to be appearances.
§ 46
But it is not enough simply to indicate the existence of the object of Reason. Curiosity impels us to seek for knowledge of this identity, this empty thing-in-itself. Now knowledge means such an acquaintance with the object as apprehends its distinct and special subject-matter. But such subject-matter involves a complex interconnection in the object itself, and supplies a ground of connection with many other objects. In the present case, to express the nature of the features of the Infinite or Thing-in-itself, Reason would have nothing except the categories: and in any endeavour so to employ them Reason becomes over-soaring or 'transcendent'.
Here begins the second stage of the Criticism of Reason which, as an independent piece of work, is more valuable than the first. The first part, as has been explained above, teaches that the categories originate in the unity of self-consciousness; that any knowledge which is gained by their means has nothing objective in it, and that the very objectivity claimed for them is only subjective. So far as this goes, the Kantian Criticism presents that 'common' type of idealism known as Subjective Idealism. It asks no questions about the meaning or scope of the categories, but simply considers the abstract form of subjectivity and objectivity, and that even in such a partial way that the former aspect, that of subjectivity, is retained as a final and purely affirmative term of thought. In the second part, however, when Kant examines the application, as it is called, which Reason makes of the categories in order to know its objects, the content of the categories, at least in some points of view, comes in for discussion: or, at any rate, an opportunity presented itself for a discussion of the question. It is worth while to see what decision Kant arrives at on the subject of metaphysic, as this application of the categories to the unconditioned is called. His method of procedure we shall here briefly state and criticise.
§47
[a] The first of the unconditioned entities which Kant examines is the Soul (see above, § 34). 'In my consciousness', he says, 'I always find that I (1) am the determining subject; (2) am singular or abstractly simple; (3) am identical, or one and the same, in all the variety of what I am conscious of; (4) distinguish myself as thinking from all the things outside me.'
Now the method of the old metaphysic, as Kant correctly states it, consisted in substituting for these statements of experience the corresponding categories or metaphysical terms. Thus arise these four new propositions: (a) the Soul is a substance; (b) it is a simple substance; (c) it is numerically identical at the various periods of existence; (d) it stands in relation to space
Kant discusses this translation, and draws attention to the Paralogism or mistake of confounding one kind of truth with another. He points out that empirical attributes have here been replaced by categories; and shows that we are not entitled to argue from the former to the latter, or to put the latter in place of the former.
This criticism obviously but repeats the observation of Hume (§ 39) that the categories as a whole ideas of universality and necessity are entirely absent from sensation; and that the empirical fact both in form and contents differs from its intellectual formulation.
If the purely empirical fact were held to constitute the credentials of the thought, then no doubt it would be indispensable to be able precisely to identify the 'idea' in the 'impression'.
And in order to make out, in his criticism of the metaphysical psychology, that the soul cannot be described as substantial, simple, self-same, and as maintaining its independence in intercourse with the material world, Kant argues from the single ground that the several attributes of the soul, which consciousness lets us feel in experience, are not exactly the same attributes as result from the action of thought thereon. But we have seen above that according to Kant all knowledge, even experience, consists in thinking our impressions in other words, in transforming into intellectual categories the attributes primarily belonging to sensation.
Unquestionably one good result of the Kantian criticism was that it emancipated mental philosophy from the 'soul-thing', from the categories, and, consequently, from questions about the simplicity, complexity, materiality, etc., of the soul. But even for the common sense of ordinary men, the true point of view, from which the inadmissibility of these forms best appears, will be not that they are thoughts, but that thoughts of such a stamp neither can nor do retain truth.
§47
If thought and phenomenon do not perfectly correspond to one another, we are free at least to choose which of the two shall be held the defaulter. The Kantian idealism, where it touches on the world of Reason, throws the blame on the thoughts; saying that the thoughts are defective, as not being exactly fitted to the sensations and to a mode of mind wholly restricted within the range of sensation, in which as such there are no traces of the presence of these thoughts. But as to the actual content of the thought, no question is raised.
§ 48
[b] The second unconditioned object is the World (§ 35). In the attempt which reason makes to comprehend the unconditioned nature of the World, it falls into what are called Antinomies. In other words it maintains two opposite propositions about the same object, and in such a way that each of them has to be maintained with equal necessity. From this it follows that the body of cosmical fact, the specific statements descriptive of which run into contradiction, cannot be a self-subsistent reality, but only an appearance. The explanation offered by Kant alleges that the contradiction does not affect the object in its own proper essence, but attaches only to the Reason which seeks to comprehend it.
In this way the suggestion was broached that the contradiction is occasioned by the subject-matter itself, or by the intrinsic quality of the categories. And to offer the idea that the contradiction introduced into the world of Reason by the categories of Understanding is inevitable and essential was to make one of the most important steps in the progress of Modern Philosophy. But the more important the issue thus raised the more trivial was the solution. Its only motive was an excess of tenderness for the things of the world. The blemish of contradiction, it seems, could not be allowed to mar the essence of the world; but there could be no objection to attach it to the thinking Reason, to the essence of mind. Probably nobody will feel disposed to deny that the phenomenal world presents contradictions to the observing mind; meaning by 'phenomenal' the world as it presents itself to the senses and understanding, to the subjective mind. But if a comparison is instituted between the essence of the world and the essence of the mind, it does seem strange to hear how calmly and confidently the modest dogma has been advanced by one, and repeated by others, that thought or Reason, and not the World, is the seat of contradiction. It is no escape to turn round and explain that Reason falls into contradiction only by applying the categories. For this application of the categories is maintained to be necessary, and Reason is not supposed to be equipped with any other forms but the categories for the purpose of cognition. But cognition is determining and determinate thinking: so that, if Reason be mere empty indeterminate thinking, it thinks nothing. And if in the end Reason be reduced to mere identity without diversity (see next §), it will in the end also win a happy release from contradiction at the slight sacrifice of all its facets and contents.
It may also be noted that his failure to make a more thorough study of Antinomy was one of the reasons why Kant enumerated only four Antinomies. These four attracted his notice, because, as may be seen in his discussion of the so-called Paralogisms of Reason, he assumed the list of the categories as a basis of his argument. Employing what has subsequently become a favourite fashion, he simply put the object under a rubric otherwise ready to hand, instead of deducing its characteristics from its notion. Further deficiencies in the treatment of the Antinomies I have pointed out, as occasion offered, in my Science of Logic. Here it will be sufficient to say that the Antinomies are not confined to the four special objects taken from Cosmology: they appear in all objects of every kind, in all conceptions, notions, and Ideas. To be aware of this and to know objects in this property of theirs makes a vital part in a philosophical theory. For the property thus indicated is what we shall afterwards describe as the Dialectical influence in Logic.
§ 49
[c] The third object of the Reason is God (§ 36): he also must be known and defined in terms of thought. But in comparison with an unalloyed identity, every defining term as such seems to the understanding to be only a limit and a negation: every reality accordingly must be taken as limitless, i.e. undefined. Accordingly God, when he is defined to be the sum of all realities, the most real of beings, turns into a mere abstract. And the only term under which that most real of real things can be defined is that of Being itself the height of abstraction. These are two elements, abstract identity, on one hand, which is spoken of in this place as the notion; and Being on the other which Reason seeks to unify. And their union is the Ideal of Reason.
§ 50
... The organic structures, and the evidence they afford of mutual adaptation, belong to a higher province, the province of animated nature. But even without taking into consideration the possible blemish which the study of animated nature and of the other teleological aspects of existing things may contract from the pettiness of the final causes, and from puerile instances of them and their bearings, merely animated nature is, at the best, incapable of supplying the material for a truthful expression to the idea to God. God is more than life: he is Spirit. And therefore if the thought of the Absolute takes a starting-point for its rise, and desires to take the nearest, the most true and adequate starting-point will be found in the nature of spirit alone.
§ 51
The other way of unification by which to realise the Ideal of Reason is to set out from the abstractum of Thought and seek to characterise it: for which purpose Being is the only available term. This is the method of the Ontological proof. The opposition, here presented from a merely subjective point of view, lies between Thought and Being; whereas in the first way of junction, being is common to the two sides of the antithesis, and the contrast lies only between its individualisation and universality. Understanding meets this second way with what is implicitly the same objection as it made to the first. It denied that the empirical involves the universal; so it denies that the universal involves the specialisation, which specialisation in this instance is being. In other words it says: Being cannot be deduced from the notion by any analysis.
The uniformly favourable reception and acceptance which attended Kant's criticism of the Ontological proof was undoubtedly due to the illustration which he made use of. To explain the difference between thought and being, he took the instance of a hundred sovereigns, which, for anything it matters to the notion, are the same hundred whether they are real or only possible, though the difference of the two cases is very perceptible in their effect on a man's purse. Nothing can be more obvious than that anything we only think or conceive is not on that account actual; that mental representation, and even notional comprehension, always falls short of being. Still it may not unfairly be styled a barbarism in language, when the name of notion is given to things like a hundred sovereigns. And, putting that mistake aside, those who perpetually urge against the philosophic Idea the difference between Being and Thought might have admitted that philosophers were not wholly ignorant of the fact. Can there be any proposition more trite than this ? But after all, it is well to remember, when we speak of God, that we have an object of another kind than any hundred sovereigns, and unlike any one particular notion, representation, or however else it may be styled. It is in fact this and this alone which marks everything finite: its being in time and space is discrepant from its notion. God, on the contrary, expressly has to be what can only be 'thought as existing'; his notion involves being. It is this unity of the notion and being that constitutes the notion of God.
If this were all, we should have only a formal expression of the divine nature which would not really go beyond a statement of the nature of the notion itself. And that the notion, in its most abstract terms, involves being is plain. For the notion, whatever other determination it may receive, is at least reference back on itself, which results by abolishing the intermediation, and thus is immediate. And what is that reference to self, but being? Certainly it would be strange if the notion, the very inmost of mind, if even the 'Ego', or above all the concrete totality we call God, were not rich enough to include so poor a category as being, the very poorest and most abstract of all. For, if we look at the thought it holds, nothing can be more insignificant than being. And yet there may be something still more insignificant than being that which at first sight is perhaps supposed to be, an external and sensible existence, like that of the paper lying before me. However, in this matter, nobody proposes to speak of the sensible existence of a limited and perishable thing. Besides, the petty stricture of the Kritik that 'thought and being are different' can at most molest the path of the human mind from the thought of God to the certainty that he is: it cannot take it away. It is this process of transition, depending on the absolute inseparability of the thought of God from his being, for which its proper authority has been revindicated in the theory of faith or immediate knowledge whereof hereafter.
§ 52
In this way thought, at its highest pitch, has to go outside for any determinateness; and although it is continually termed Reason, is out-and-out abstract thinking. And the result of all is that Reason supplies nothing beyond the formal unity required to simplify and systematise experiences; it is a canon, not an organon, of truth, and can furnish only a criticism of knowledge, not a doctrine of the infinite. In its final analysis this criticism is summed up in the assertion that in strictness thought is only the indeterminate unity and the action of this indeterminate unity.
§ 53
(b) The Practical Reason is understood by Kant to mean a thinking Will, i.e. a Will that determines itself on universal principles. Its office is to give objective, imperative laws of freedom laws, that is, which state what ought to happen. The warrant for thus assuming thought to be an activity which makes itself felt objectively, that is, to be really a Reason, is the alleged possibility of proving practical freedom by experience, that is, of showing it in the phenomenon of selfconsciousness. This experience in consciousness is at once met by all that the Necessitarian produces from contrary experience, particularly by the sceptical induction (employed among others by Hume) from the endless diversity of what men regard as right and duty i.e. from the diversity apparent in those professedly objective laws of freedom.
§ 54
What, then, is to serve as the law which the Practical Reason embraces and obeys, and as the criterion in its act of selfdetermination? There is no rule at hand but the same abstract identity of understanding as before: there must be no contradiction in the act of self-determination. Hence the Practical Reason never shakes off the formalism which is represented as the climax of the Theoretical Reason.
But this Practical Reason does not confine the universal principle of the Good to its own inward regulation: it first becomes practical, in the true sense of the word, when it insists on the Good being manifested in the world with an outward objectivity, and requires that the thought shall be objective throughout, and not merely subjective. We shall speak of this postulate of the Practical Reason afterwards.
§ 55
(c) The Reflective Power of Judgment is invested by Kant with the function of an Intuitive Understanding. That is to say, whereas the particulars had hitherto appeared, so far as the universal or abstract identity was concerned, adventitious and incapable of being deduced from it, the Intuitive Understanding apprehends the particulars as moulded and formed by the universal itself. Experience presents such universalised particulars in the products of Art and of organic nature.
The capital feature in Kant's Criticism of the Judgement is, that in it he gave a representation and a name, if not even an intellectual expression, to the Idea. Such a representation, as an Intuitive Understanding, or an inner adaptation, suggests a universal which is at the same time apprehended as essentially a concrete unity. It is in these apercus alone that the Kantian philosophy rises to the speculative height. Schiller, and others, have found in the idea of artistic beauty, where thought and sensuous conception have grown together into one, a way of escape from the abstract and separatist understanding. Others have found the same relief in the perception and consciousness of life and of living things, whether that life be natural or intellectual. The work of Art, as well as the living individual, is, it must be owned, of limited content. But in the postulated harmony of nature (or necessity) and free purpose in the final purpose of the world conceived as realised, Kant has put before us the Idea, comprehensive even in its content. Yet what may be called the laziness of thought, when dealing with the supreme Idea, finds a too easy mode of evasion in the 'ought to be': instead of the actual realisation of the ultimate end, it clings hard to the disjunction of the notion from reality. Yet if thought will not think the ideal realised, the senses and the intuition can at any rate see it in the present reality of living organisms and of the beautiful in Art. And consequently Kant's remarks on these objects were well adapted to lead the mind on to grasp and think the concrete Idea.
§ 56
We are thus led to conceive a different relation between the universal of understanding and the particular of perception, than that on which the theory-of the Theoretical and Practical Reason is founded. But while this is so, it is not supplemented by a recognition that the former is the genuine relation and the very truth. Instead of that, the unity (of universal with particular) is accepted only as it exists in finite phenomena, and is adduced only as a fact of experience. Such experience, at first only personal, may come from two sources. It may spring from Genius, the faculty which produces 'aesthetic ideas'; meaning by aesthetic ideas, the picture-thoughts of the free imagination which subserve an idea and suggest thoughts, although their content is not expressed in a notional form, and even admits of no such expression. It may also be due to Taste, the feeling of congruity between the free play of intuition or imagination and the uniformity of understanding.
§ 57
The principle by which the Reflective faculty of Judgement regulates and arranges the products of animated nature is described as the End or final cause the notion in action, the universal at once determining and determinate in itself. At the same time Kant is careful to discard the conception of external or finite adaptation, in which the End is only an adventitious form for the means and material in which it is realised. In the living organism, on the contrary, the final cause is a moulding principle and an energy immanent in the matter, and every member is in its turn a means as well as an end.
§ 58
Such an Idea evidently radically transforms the relation which the understanding institutes between means and ends, between subjectivity and objectivity. And yet in the face of this unification, the End or design is subsequently explained to be a cause which exists and acts subjectively, i.e. as our idea only: and teleology is accordingly explained to be only a principle of criticism, purely personal to our understanding.
After the Critical philosophy had settled that Reason can know phenomena only, there would still have been an option for animated nature between two equally subjective modes of thought. Even according to Kant's own exposition, there would have been an obligation to admit, in the case of natural productions, a knowledge not confined to the categories of quality, cause and effect, composition, constituents, and so on. The principle of inward adaptation or design, had it been kept to and carried out in scientific application, would have led to a different and a higher method of observing nature.
§ 59
If we adopt this principle, the Idea, when all limitations were removed from it, would appear as follows. The universality moulded by Reason, and described as the absolute and final end or the Good, would be realised in the world, and realised moreover by means of a third thing, the power which proposes this End as well as realises it that is, God. Thus in him, who is the absolute truth, those oppositions of universal and individual, subjective and objective, are solved and explained to be neither self-subsistent nor true.
§ 60
But Good which is thus put forward as the final cause of the world has been already described as only our good, the moral law of our Practical Reason. This being so, the unity in question goes no further than make the state of the world and the course of its events harmonise with our moral standards. Besides, even with this limitation, the final cause, or Good, is a vague abstraction, and the same vagueness attaches to what is to be Duty. But, further, this harmony is met by the revival and reassertion of the antithesis, which it by its own principle had nullified. The harmony is then described as merely subjective, something which merely ought to be, and which at the same time is not real a mere article of faith, possessing a subjective certainty, but without truth, or that objectivity which is proper to the Idea. This contradiction may seem to be disguised by adjourning the realisation of the Idea to a future, to a time when the Idea will also be. But a sensuous condition like time is the reverse of a reconciliation of the discrepancy; and an infinite progression which is the corresponding image adopted by the understanding on the very face of it only repeats and re-enacts the contradiction.
A general remark may still be offered on the result to which the Critical philosophy led as to the nature of knowledge; a result which has grown one of the current 'idols' or axiomatic beliefs of the day. In every dualistic system, and especially in that of Kant, the fundamental defect makes itself visible in the inconsistency of unifying at one moment what a moment before had been explained to be independent and therefore incapable of unification. And then, at the very moment after unification has been alleged to be the truth, we suddenly come upon the doctrine that the two elements, which, in their true status of unification, had been refused all independent subsistence, are only true and actual in their state of separation. Philosophising of this kind wants the little penetration needed to discover, that this shuffling only evidences how unsatisfactory each one of the two terms is. And it fails simply because it is incapable of bringing two thoughts together. (And in point of form there are never more than two.) It argues an utter want of consistency to say, on the one hand, that the understanding only knows phenomena, and, on the other, assert the absolute character of this knowledge, by such statements as 'Cognition can go no further'; 'Here is the natural and absolute limit of human knowledge.' But 'natural' is the wrong word here. The things of nature are limited and are natural things only to such extent as they are not aware of their universal limit, or to such extent as their mode or quality is a limit from our point of view, and not from their own. No one knows, or even feels, that anything is a limit or defect, until he is at the same time above and beyond it. Living beings, for example, possess the privilege of pain which is denied to the inanimate: even with living beings, a single mode or quality passes into the feeling of a negative. For living beings as such possess within them a universal vitality, which overpasses and includes the single mode; and thus, as they maintain themselves in the negative of themselves, they feel the contradiction to exist within them. But the contradiction is within them only in so far as one and the same subject includes both the universality of their sense of life, and the individual mode which is in negation with it. This illustration will show how a limit or imperfection in knowledge comes to be termed a limit or imperfection, only when it is compared with the actually present Idea of the universal, of a total and perfect. A very little consideration might show that to call a thing finite or limited proves by implication the very presence of the infinite and unlimited, and that our knowledge of a limit can only be when the unlimited is on this side in consciousness.
The result however of Kant's view of cognition suggests a second remark. The philosophy of Kant could have no influence on the method of the sciences. It leaves the categories and method of ordinary knowledge quite unmolested. Occasionally, it may be, in the first sections of a scientific work of that period, we find propositions borrowed from the Kantian philosophy; but the course of the treatise renders it apparent that these propositions were superfluous decoration, and that the few first pages might have been omitted without producing the least change in the empirical contents.
We may next institute a comparison of Kant with the metaphysics of the empirical school. Natural plain Empiricism, though it unquestionably insists most upon sensuous perception, still allows a supersensible world or spiritual reality, whatever may be its structure and constitution, and whether derived from intellect, or from imagination, etc. So far as form goes, the facts of this supersensible world rest on the authority of mind, in the same way as the other facts embraced in empirical knowledge rest on the authority of external perception. But when Empiricism becomes reflective and logically consistent, it turns its arms against this dualism in the ultimate and highest species of fact; it denies the independence of the thinking principle and of a spiritual world which develops itself in thought. Materialism or Naturalism, therefore, is the consistent and thoroughgoing system of Empiricism. In direct opposition to such an Empiricism, Kant asserts the principle of thought and freedom, and attaches himself to the first mentioned form of empirical doctrine, the general principles of which he never departed from. There is a dualism in his philosophy also. On one side stands the world of sensation, and of the understanding which reflects upon it. This world, it is true, he alleges to be a world of appearances. But that is only a title or formal description; for the source, the facts, and the modes of observation continue quite the same as in Empiricism. On the other side and independent stands a self-apprehending thought, the principle of freedom, which Kant has in common with ordinary and bygone metaphysic, but emptied of all that it held, and without his being able to infuse into it anything new. For, in the Critical doctrine, thought, or, as it is there called, Reason, is divested of every specific form, and thus bereft of all authority. The main effect of the Kantian philosophy has been to revive the consciousness of Reason, or the absolute inwardness of thought. Its abstractness indeed prevented that inwardness from developing into anything, or from originating any special forms, whether cognitive principles or moral laws; but nevertheless it absolutely refused to accept or indulge anything possessing the character of an externality. Henceforth the principle of the independence of Reason, or of its absolute self-subsistence, is made a general principle of philosophy, as well as a foregone conclusion of the time. powered by performancing firefox
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powered by performancing firefox MIA Philosophy Resource from Andy Blunden 3
The Copenhagen Interpretation of Quantum Theory
THE Copenhagen interpretation of quantum theory starts from a paradox. Any experiment in physics, whether it refers to the phenomena of daily life or to atomic events, is to be described in the terms of classical physics. The concepts of classical physics form the language by which we describe the arrangements of our experiments and state the results. We cannot and should not replace these concepts by any others. Still the application of these concepts is limited by the relations of uncertainty. We must keep in mind this limited range of applicability of the classical concepts while using them, but we cannot and should not try to improve them.
For a better understanding of this paradox it is useful to compare the procedure for the theoretical interpretation of an experiment in classical physics and in quantum theory. In Newton's mechanics, for instance, we may start by measuring the position and the velocity of the planet whose motion we are going to study. The result of the observation is translated into mathematics by deriving numbers for the co-ordinates and the momenta of the planet from the observation. Then the equations of motion are used to derive from these values of the co-ordinates and momenta at a given time the values of these co-ordinates or any other properties of the system at a later time, and in this way the astronomer can predict the properties of the system at a later time. He can, for instance, predict the exact time for an eclipse of the moon.
In quantum theory the procedure is slightly different. We could for instance be interested in the motion of an electron through a cloud chamber and could determine by some kind of observation the initial position and velocity of the electron. But this determination will not be accurate- it will at least contain the inaccuracies following from the uncertainty relations and will probably contain still larger errors due to the difficulty of the experiment. It is the first of these inaccuracies which allows us to translate the result of the observation into the mathematical scheme of quantum theory. A probability function is written down which represents the experimental situation at the time of the measurement, including even the possible errors of the measurement.
This probability function represents a mixture of two things, partly a fast and partly our knowledge of a fact. It represents a fact in so far as it assigns at the initial time the probability unity (i.e., complete certainty) to the initial situation: the electron moving with the observed velocity at the observed position; 'observed' means observed within the accuracy of the experiment. It represents our knowledge in so far as another observer could perhaps know the position of the electron more accurately. The error in the experiment does - at least to some extent - not represent a property of the electron but a deficiency in our knowledge of the electron. Also this deficiency of knowledge is expressed in the probability function.
In classical physics one should in a careful investigation also consider the error of the observation. As a result one would get a probability distribution for the initial values of the co-ordinates and velocities and therefore something very similar to the probability function in quantum mechanics. Only the necessary uncertainty due to the uncertainty relations is lacking in classical physics.
When the probability function in quantum theory has been determined at the initial time from the observation, one can from the laws of quantum theory calculate the probability function at any later time and can thereby determine the probability for a measurement giving a specified value of the measured quantity. We can, for instance, predict the probability for finding the electron at a later time at a given point in the cloud chamber. It should be emphasised, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. l he probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. Only then does the probability function allow us to calculate the probable result of the new measurement. The result of the measurement again will be stated in terms of classical physics.
Therefore, the theoretical-interpretation of an experiment requires three distinct steps: (I) the translation of the initial experimental situation into a probability function; (2) the following up of this function in the course of time; (3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function. For the first step the fulfilment of the uncertainty relations is a necessary condition. The second step cannot be described in terms of the classical concepts; there is no description of what happens to the system between the initial observation and the next measurement. It is only in the third step that we change over again from the 'possible' to the 'actual'.
Let us illustrate these three steps in a simple ideal experiment. It has been said that the atom consists of a nucleus and electrons moving around the nucleus; it has also been stated that the concept of an electronic orbit is doubtful. One could argue that it should at least in principle be possible to observe the electron in its orbit. One should simply look at the atom through a microscope of a very high revolving power, then one would see the electron moving in its orbit. Such a high revolving power could to be sure not be obtained by a microscope using ordinary light, since the inaccuracy of the measurement of the position can never be smaller than the wave length of the light. But a microscope using ~~-rays with a wave length smaller than the size of the atom would do. Such a microscope has not yet been constructed but that should not prevent us from discussing the ideal experiment.
Is the first step, the translation of the result of the observation into a probability function, possible? It is possible only if the uncertainty relation is fulfilled after the observation. The position of the electron will be known with an accuracy given by the wave length of the y-ray. The electron may have been practically at rest before the observation. But in the act of observation at least one light quantum of the y-ray must have passed the microscope and must first have been deflected by the electron. Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations. Therefore, there is no difficulty with the first step.
At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus. The second step shows a wave pocket moving not around the nucleus but away from the atom, because the first light quantum will have knocked the electron out from the atom. The momentum of light quantum of the y-ray is much bigger than the original momentum of the electron if the wave length of the e-ray is much smaller than the size of the atom. Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense. The next observation - the third step - will show the electron on its path from the atom. Quite generally there is no way of describing what happens between two consecutive observations. It is of course tempting to say that the electron must have been somewhere between the two observations and that therefore the electron must have described some kind of path or orbit even if it may be impossible to know which path. This would be a reasonable argument in classical physics. But in quantum theory it would be a misuse of the language which, as we will see later, cannot be justified. We can leave it open for the moment, whether this warning is a statement about the way in which we should talk about atomic events or a statement about the events themselves, whether it refers to epistemology or to ontology. In any case we have to be very cautious about the wording of any statement concerning the behaviour of atomic particles.
Actually we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus. Such a description would directly contradict the other description if one does not pay attention to the limitations given by the uncertainty relations. Through the limitations the contradiction is avoided. The use of 'matter waves' is convenient, for example, when dealing with the radiation emitted by the atom. By means of its frequencies and intensities the radiation gives information about the oscillating charge distribution in the atom, and there the wave picture comes much nearer to the truth than the particle picture. Therefore, Bohr advocated the use of both pictures, which he called 'complementary' to each other. The two pictures are of course mutually exclusive, because a certain thing cannot at the same time be a particle (i.e., substance confined to a very small volume) and a wave (i.e., a field spread out over a large space), but the two complement each other. By playing with both pictures, by going from the one picture to the other and back again, we finally get the right impression of the strange kind of reality behind our atomic experiments. Bohr uses the concept of 'complementarity' at several places in the interpretation of quantum theory. The knowledge of the position of a particle is complementary to the knowledge of its velocity or momentum. If we know the one with high accuracy we cannot know the other with high accuracy; still we must know both for determining the behaviour of the system. The space-time description of the atomic events is complementary to their deterministic description. The probability function obeys an equation of motion as the coordinates did in Newtonian mechanics; its change in the course of time is completely determined by the quantum mechanical equation, but it does not allow a description in space and time. The observation, on the other hand, enforces the description in space and time but breaks the determined continuity of the probability function by changing our knowledge of the system.
Generally the dualism between two different descriptions of the same reality is no longer a difficulty since we know from the mathematical formulation of the theory that contradictions cannot arise. The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The formalism is normally written to resemble Newtonian mechanics, with equations of motion for the coordinates and the momenta of the particles.
But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary three-dimensional matter wave. Therefore, this possibility of playing with different complementary pictures has its analogy in the different transformations of the mathematical scheme; it does not lead to any difficulties in the Copenhagen interpretation of quantum theory.
A real difficulty in the understanding of this interpretation arises, however, when one asks the famous question: But what happens 'really' in an atomic event? It has been said before that the mechanism and the results of an observation can always be stated in terms of the classical concepts. But what one deduces from an observation is a probability function, a mathematical expression that combines statements about possibilities or tendencies with statements about our knowledge of facts So we cannot completely objectify the result of an observation, we cannot describe what 'happens' between this observation and the next. This looks as if we had introduced an element of subjectivism into the theory, as if we meant to say: what happens depends on our way of observing it or on the fast that we observe it. Before discussing this problem of subjectivism it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations.
For this purpose it is convenient to discuss the following ideal experiment: We assume that a small source of monochromatic light radiates toward a black screen with two small holes in it. The diameter of the holes may be not much bigger than the wave length of the light, but their distance will be very much bigger. At some distance behind the screen a photographic plate registers the incident light. If one describes this experiment in terms of the wave picture, one says that the primary wave penetrates through the two holes, there will be secondary spherical waves starting from the holes that interfere with one another, and the interference will produce a pattern of varying intensity on the photographic plate.
The blackening of the photographic plate is a quantum process, a chemical reaction produced by single light quanta. Therefore, it must also be possible to describe the experiment in terms of light quanta. If it would be permissible to say what happens to the single light quantum between its emission from the light source and its absorption in the photographic plate, one could argue as follows: The single light quantum can come through the first hole or through the second one. If it goes through the first hole and is scattered there, its probability for being absorbed at a certain point of the photographic plate cannot depend upon whether the second hole is closed or open. The probability distribution on the plate will be the same as if only the first hole was open. If the experiment is repeated many times and one takes together all cases in which the light quantum has gone through the first hole, the blackening of the plate due to these cases will correspond to this probability distribution. If one considers only those light quanta that go through the second hole, the blackening should correspond to a probability distribution derived from the assumption that only the second hole is open. The total blackening, therefore, should just be the sum of the blackenings in the two cases; in other words, there should be no interference pattern. But we know this is not correct, and the experiment will show the interference pattern. Therefore, the statement that any light quantum must have gone either through the first or through the second hole is problematic and leads to contradictions. This example shows clearly that the concept of the probability function does not allow a description of what happens between two observations. Any attempt to find such a description would lead to contradictions; this must mean that the term 'happens' is restricted to the observation.
Now, this is a very strange result, since it seems to indicate that the observation plays a decisive role in the event and that the reality varies, depending upon whether we observe it or not. To make this point clearer we have to analyse the process of observation more closely.
To begin with, it is important to remember that in natural science we are not interested in the universe as a whole, including ourselves, but we direct our attention to some part of the universe and make that the object of our studies. In atomic physics this part is usually a very small object, an atomic particle or a group of such particles, sometimes much larger - the size does not matter; but it is important that a large part of the universe, including ourselves, does not belong to the object.
Now, the theoretical interpretation of an experiment starts with the two steps that have been discussed. In the first step we have to describe the arrangement of the experiment, eventually combined with a first observation, in terms of classical physics and translate this description into a probability function. This probability function follows the laws of quantum theory, and its change in the course of time, which is continuous, can be calculated from the initial conditions; this is the second step. The probability function combines objective and subjective elements. It contains statements about possibilities or better tendencies ('potentia' in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer; and it contains statements about our knowledge of the system, which of course are subjective in so far as they may be different for different observers. In ideal cases the subjective element in the probability function may be practically negligible as compared with the objective one. The physicists then speak of a 'pure case'.
When we now come to 'the next observation. the result of which should be predicted from the theory, it is very important to realize that our object has to be in contact with the other part of-the world, namely, the experimental arrangement, the measuring rod, etc., before or at least at the moment of observation. This means that the equation of motion for the probability function does now contain the influence of the interaction with the measuring device. This influence introduces a new element of uncertainty, since the measuring device is necessarily described in the terms of classical physics; such a description contains all the uncertainties concerning the microscopic structure of the device which we know from thermodynamics, and since the device is connected with the rest of the world, it contains in fact the uncertainties of the microscopic structure of the whole world. These uncertainties may be called objective in so far as they are simply a consequence of the description in the terms of classical physics and do not depend on any observer. They may be called subjective in so far as they refer to our incomplete knowledge of the world.
After this interaction has taken place, the probability function contains the objective element of tendency and the subjective element of incomplete knowledge, even if it has been a 'pure case' before. It is for this reason that the result of the observation cannot generally be predicted with certainty; what can be predicted is the probability of a certain result of the observation, and this statement about the probability can be checked by repeating the experiment many times. The probability function does - unlike the common procedure in Newtonian mechanics - not describe a certain event but, at least during the process of observation, a whole ensemble of possible events.
The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place. Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation also has undergone the discontinuous change and we speak of a 'quantum jump'. When the old adage 'Natura non facit saltus' is used as a basis for criticism of quantum theory, we can reply that certainly our knowledge can change suddenly and that this fact justifies the use of the term 'quantum jump'.
Therefore, the transition from the 'possible' to the 'actual' takes place during the act of observation. If we want to describe what happens in an atomic event, we have to realize that the word 'happens' can apply only to the observation, not to the state of affairs between two observations. It applies to the physical, not the psychical act of observation, and we may say that the transition from the 'possible' to the 'actual' takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.
To what extent, then, have we finally come to an objective description of the world, especially of the atomic world? In classical physics science started from the belief - or should one say from the illusion? - that we could describe the world or at least parts of the world without any reference to ourselves. This is actually possible to a large extent. We know that the city of London exists whether we see it or not. It may be said that classical physics is just that idealisation in which we can speak about parts of the world without any reference to ourselves. Its success has led to the general ideal of an objective description of the world. Objectivity has become the first criterion for the value of any scientific result. Does the Copenhagen interpretation of quantum theory still comply with this ideal? One may perhaps say that quantum theory corresponds to this ideal as far as possible. Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event. But it starts from the division of the world into the 'object' and the rest of the world, and from the fact that at least for the rest of the world we use the classical concepts in our description. This division is arbitrary and historically a direct consequence of our scientific method; the use of the classical concepts is finally a consequence of the general human way of thinking. But this is already a reference to ourselves and in so far our description is not completely objective.
It has been stated in the beginning that the Copenhagen interpretation of quantum theory starts with a paradox. It starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately. The tension between these two starting points is the root of the statistical character of quantum theory. Therefore, it has sometimes been suggested that one should depart from the classical concepts altogether and that a radical change in the concepts used for describing the experiments might possibly lead back to a non-statical, completely objective description of nature.
This suggestion, however, rests upon a misunderstanding. The concepts of classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of all natural science. Our actual situation in science is such that we do use the classical concepts for the description of the experiments, and it was the problem of quantum theory to find theoretical interpretation of the experiments on this basis. There is no use in discussing what could be done if we were other beings than we are. At this point we have to realize, as von Weizsäcker has put it, that 'Nature is earlier than man, but man is earlier than natural science.' The first part of the sentence justifies classical physics, with its ideal of complete objectivity. The second part tells us why we cannot escape the paradox of quantum theory, namely, the necessity of using the classical concepts.
We have to add some comments on the actual procedure in the quantum-theoretical interpretation of atomic events. It has been said that we always start with a division of the world into an object, which we are going to study, and the rest of the world, and that this division is to some extent arbitrary. It should indeed not make any difference in the final result if we, e.g., add some part of the measuring device or the whole device to the object and apply the laws of quantum theory to this more complicated object. It can be shown that such an alteration of the theoretical treatment would not alter the predictions concerning a given experiment. This follows mathematically from the-fact that the laws of quantum theory are for the phenomena in which Planck's constant can be considered as a very small quantity, approximately identical with the classical laws. But it would be a mistake to believe that this application of the quantum-theoretical laws to the measuring device could help to avoid the fundamental paradox of quantum theory.
The measuring device deserves this name only if it is in close contact with the rest of the world, if there is an interaction between the device and the observer. Therefore, the uncertainty with respect to the microscopic behaviour of the world will enter into the quantum-theoretical system here just as well as in the first interpretation. If the measuring device would be isolated from the rest of the world, it would be neither a measuring device nor could it be described in the terms of classical physics at all.
With regard to this situation Bohr has emphasised that it is more realistic to state that the division into the object and the l rest of the world is not arbitrary. Our actual situation in research work in atomic physics is usually this: we wish to understand a l certain phenomenon, we wish to recognise how this phenomenon follows from the general laws of nature. Therefore that part of matter or radiation which takes part in the phenomenon is the natural 'object' in the theoretical treatment and should be separated in this respect from the tools used to study the phenomenon. This again emphasises a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning. Our scientific work in physics consists in asking questions about nature in the language that we possess and trying to get an answer from experiment by the means that are at our disposal. In this way quantum theory reminds us, as Bohr has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence we are ourselves both players and spectators. It is understandable that in our scientific relation to nature our own activity becomes very important when we have to deal with parts of nature into which we can penetrate only by using the most elaborate tools.
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MIA Philosophy Resource from Andy Blunden Galilei Galileo (1615)
Galileo’s Considerations on the Copernican Opinion
Source: Galileo’s Considerations on the Copernican System, 1615, from The Galileo Affair, edited by Maurice Finocchiaro. Complete letter.
In order to remove (as much as the blessed God allows me) the occasion to deviate from the most correct judgment about the resolution of the pending controversy, I shall try to do away with two ideas. These are notions which I believe some are attempting to impress on the minds of those persons who are charged with the deliberations, and, if I am not mistaken, they are concepts far from the truth.
The first is that no one has any reason to fear that the outcome might be scandalous; for the earth’s stability and sun’s motion are so well demonstrated in philosophy that we can be sure and indubitably certain about them; on the other hand, the contrary position is such an immense paradox and obvious foolishness so that no one can doubt in any way that it cannot be demonstrated now or ever, or indeed that it can never find a place in the mind of sensible persons. The other idea which they try to spread is the following: although that contrary assumption has been used by Copernicus and other astronomers, they did this in a suppositional manner, and insofar as it can account more conveniently for the appearances of celestial motions and facilitate astronomical calculations and computations, and it is not the case that the same persons who assumed it believed it to be true de facto and in nature; so the conclusion is that one can safely proceed to condemn it. However, if I am not mistaken, these ideas are fallacious and far from the truth, as I can show with the following considerations. These will only be general and suitable to be understood without much effort and labor even by someone who is not well versed in the natural and astronomical sciences. For, if there were the opportunity to treat these points with those who are very experienced in these studies, or at least who have the time to do the work required by the difficulty of the subject, then I should propose nothing but the reading of Copernicus’s own book; from it and from the strength of his demonstrations one could clearly see how true or false are the two ideas we are discussing.
That it is not to be disparaged as ridiculous is, therefore, clearly shown by the quality of the men, both ancient and modern, who have held and do hold it. No one can regard it as ridiculous unless he considers ridiculous and foolish Pythagoras with all his school, Philolaus (teacher of Plato), Plato himself (as Aristotle testifies in his book On the Heavens), Heraclides of Pontus, Ecphantus, Aristarchus of Samos, Hicetas and Seleucus the mathematician. Seneca himself not only does not ridicule it, hut he makes fun of those who do, writing in his book On Comets: “It is also important to study these questions in order to learn whether the universe goes around the motionless earth, or the earth rotates but the universe does not. For some have said that we are naturally unaware of motion, that sunrise and sunset are not due to the motion of the heavens, but that it is we ourselves who rise and set. The matter deserves consideration, so that we may know the conditions of our existence, whether we stand still or move very fast, whether God drives everything around us or drives us.” Regarding the moderns, Nicolaus Copernicus first accepted it and amply confirmed it in his whole book. Then there were others: William Gilbert, a distinguished physician and philosopher, who treats it at length and confirms it in his book On the Loadstone; Johannes Kepler, a living illustrious philosopher and mathematician in the service of the former and the current Emperor, follows the same opinion; Origanus (David Tost) at the beginning of his Ephemerides supports the earth’s motion with a very long discussion; and there is no lack of other authors who have published their reasons on the matter. Furthermore, though they have not published anything, I could name very many followers of this doctrine living in Rome, Florence, Venice, Padua, Naples, Pisa, Parma, and other places. This doctrine is not, therefore, ridiculous, having been accepted by great men; and, though their number is small compared to the followers of the common position, this is an indication of its being difficult to understand, rather than of its absurdity. Moreover, that it is grounded on very powerful and effective reasons may be shown from the fact that all its followers were previously of the contrary opinion, and indeed that for a long time they laughed at it and considered it foolish. Copernicus and I, and all others who are alive, are witnesses to this. Now, who will not believe that an opinion which is considered silly and indeed foolish, which has hardly one out of a thousand philosophers following it, and which is disapproved by the Prince of the prevailing philosophy, can become acceptable through anything but very firm demonstrations, very clear experiences, and very subtle observations? Certainly no one will be dissuaded of an opinion imbibed with mother’s milk from his earliest training, accepted by almost the whole world and supported by the authority of very serious writers, unless the contrary reasons are more than effective. If we reflect carefully, we find that there is more value in the authority of a single person who follows the Copernican opinion than in that of one hundred others who hold the contrary, since those who are persuaded of the truth of the Copernican system were in the beginning all very opposed. So I argue as follows.
Either those who are to be persuaded are capable of understanding the reasons of Copernicus and others who follow him, or they are not; moreover, either these reasons are true and demonstrative, or they are fallacious. If those who are to be persuaded are incapable, then they will never be persuaded by the true or by the false reasons; those who are capable of understanding the strength of the demonstrations will likewise never be persuaded if these demonstrations are fallacious; so neither those who do nor those who do not understand will be persuaded by fallacious reasons. Therefore, given that absolutely no one can be dissuaded from the first idea by fallacious reasons, it follows as a necessary consequence that, if anyone is persuaded of the contrary of what he previously believed, the reasons arc persuasive and true. But as a matter of fact there are many who are already persuaded by Copernican reasons. Therefore, it is true both that these reasons are effective and that the opinion does not deserve the label of ridiculous but the label of worthy of being very carefully considered and pondered.
Furthermore, how futile it is to argue for the plausibility of this or that opinion simply from the large number of followers may be easily inferred from this: no one follows this opinion who did not previously believe the contrary; but instead you will not find even a single person who, after holding this opinion, will pass to the other one, regardless of any discussion he hears; consequently, one may judge, even if he does not understand the reasons for one side or for the other, that probably the demonstrations for the earth’s motion are stronger than those for the other side. But I shall say more, namely that if the probability of the two positions were something to be won by ballot, I would be willing to concede defeat when the opposite side had one more vote than I out of one hundred; not only that, but I would be willing to agree that every individual vote of the opponents was worth ten of mine, as long as the decision was made by persons who had perfectly heard, intimately penetrated, and subtly examined all the reasons and evidence of the two sides; indeed it is reasonable to expect that such would be those who cast the votes. Hence this opinion is not ridiculous and contemptible, but somewhat shaky is the position of whoever wanted to capitalise on the common opinion of the many who have not accurately studied these authors. What then should we say of the noises and the idle chatter of someone who has not understood even the first and simplest principles of these doctrines, and who is not qualified to understand them ever? What importance should we give him?
Consider now those who persist in wanting to say that as an astronomer Copernicus considered the earth’s motion and the sun’s stability only a hypothesis which is more adequate to save celestial appearances and to calculate the motions of planets, but that he did not believe it to be true in reality and in nature. With all due respect, these people show that they have been too prone to believe the word of someone who speaks more out of whim than out of experience with Copernicus’s book or understanding the nature of this business. For this reason they talk about it in a way that is not altogether right.
First, limiting ourselves to general considerations, let us see his preface to Pope Paul III, to whom he dedicates the work. We shall find, to begin with, as if to comply with what they call the astronomer’s task, that he had done and completed the work in accordance with the hypothesis of the prevailing philosophy and of Ptolemy himself, so that there was in it nothing lacking. But then, taking off the clothes of a pure astronomer and putting on those of a contemplator of nature, he undertook to examine whether this astronomical assumption already introduced, which was completely satisfactory regarding the calculations and the appearances of the motions of all planets, could also truly happen in the world and in nature. He found that in no way could such an arrangement of parts exist: although each by itself was well proportioned, when they were put together the result was a very monstrous chimera.
And so he began to investigate what the system of the world could really be in nature, no longer for the sole convenience of the pure astronomer, whose calculations he had complied with, but in order to come to an understanding of such a noble physical problem; he was confident that, if one had been able to account for mere appearances by means of hypotheses which are not true, this could be done much better by means of the true and physical constitution of the world. Having at his disposal a very large number of physically true and real observations of the motions of the stars (and without this knowledge it is wholly impossible to solve the problem), he worked tirelessly in search of such a constitution. Encouraged by the authority of so many great men, he examined the motion of the earth and the stability of the sun. Without their encouragement and authority, by himself either he would not have conceived the idea, or he would have considered it a very great absurdity and paradox, as he confesses to have considered it at first. But then, through long sense observations, favourable results, and very firm demonstrations, he found it so consonant with the harmony of the world that he became completely certain of its truth. Hence this position is not introduced to satisfy the pure astronomer, but to satisfy the necessity of nature.
Furthermore, Copernicus knew and wrote in the same place that publishing this opinion would have made him look insane to the numberless followers of current philosophy, and especially to each and every layman. Nevertheless, urged by the requests of the Cardinal of Capua and the Bishop of Kulm, he published it. Now, would he not have been truly mad if, considering this opinion physically false, he had published that he believed it to be true, with the certain consequence that he would be regarded as a fool by the whole world? And why would he not have declared that he was using it only as an astronomer, but that he denied it as a philosopher, thus escaping the universal label of foolishness, to the advantage of his common sense?
Moreover, Copernicus states in great detail the grounds and reasons why the ancients believed the earth to be motionless, and then, examining the value of each in turn, he shows them to be ineffective. Now, who ever saw a sensible author engaged in confuting the demonstrations that confirm a proposition he considers true and real? And what kind of judgment would it be to criticise and to condemn a conclusion while in reality he wanted the reader to believe that he accepted it? This sort of incoherence cannot be attributed to such a man. Furthermore, note carefully that, since we are dealing with the motion or stability of the earth or of the sun, we are in a dilemma of contradictory propositions (one of which has to be true), and we cannot in any way resort to saying that perhaps it is neither this way nor that way. Now, if the earth’s stability and sun’s motion are de facto physically true and the contrary position is absurd, how can one reasonably say that the false view agrees better than the true one with the phenomena clearly visible and sensed in the movements and arrangement of the stars? Who does not know that there is a most agreeable harmony among all truths of nature, and a most sharp dissonance between false positions and true effects? Will it happen, then, that the earth’s motion and sun’s stability agree in every way with the arrangement of all other bodies in the universe and with all the phenomena, a thousand of them, which we and our predecessors have observed in great detail, and that this position is false? And can the earth’s stability and sun’s motion be considered true and not agree in any way with the other truths? If one could say that neither this nor that position is true, it might happen that one would be more convenient than the other in accounting for the appearances. But, given two positions, one of which must be true and the other false, to say that the false one agrees better with the effects of nature is really something that surprises my imagination. I add: if Copernicus confesses to having fully satisfied astronomers by means of the hypothesis commonly accepted as true, how can one say that by means of the false and foolish one he could or would want to satisfy again the same astronomers?
However, I now go on to consider the nature of the business from an internal viewpoint, and to show with how much care one must discuss it.
Astronomers have so far made two sorts of suppositions: some are primary and pertain to the absolute truth of nature; others are secondary and are imagined in order to account for the appearances of stellar motions, which appearances seem not to agree with the primary and true assumptions. For example, before trying to account for the appearances, acting not as a pure astronomer but as a pure philosopher, Ptolemy supposes, indeed he takes from philosophers, that celestial movements are all circular and regular, namely uniform; that heaven has a spherical shape; that the earth is at the center of the celestial sphere, is spherical, motionless, etc. Turning then to the inequalities we see in planetary movements and distances, which seem to clash with the primary physical suppositions already established, he goes on to another sort of supposition; these aim to identify the reasons why, without changing the primary ones, there is such a clear and sensible inequality in the movements of planets and in their approaching and their moving away from the earth. To do this he introduces some motions that are still circular, but around centers other than the earth’s, tracing eccentric and epicyclic circles. This secondary supposition is the one of which it could be said that the astronomer supposes it to facilitate his computations, without committing himself to maintaining that it is true in reality and in nature.
Let us now see in what kind of hypothesis Copernicus places the earth’s motion and sun’s stability. There is no doubt whatever, if we reflect carefully, that he places them among the primary and necessary suppositions about nature. For, as I have already stated, it seems that he had already given satisfaction to astronomers by the other road, and that he takes this one only to try to solve the greatest problem of nature. In fact, to say that he makes this supposition to facilitate astronomical calculations is so false that instead we can see him, when he comes to these calculations, leaving this supposition and returning to the old one, the latter being more readily and easily understood and still very quick even in computations. This may be seen as follows. Intrinsically, particular calculations can be made by taking one position as well as the other, that is, by making the earth or the heavens rotate; nevertheless, many geometers and astronomers in many books have already demonstrated the properties of orthogonal and oblique displacements of parts of the zodiac in relation to the equator, the declinations of the parts of the ecliptic, the variety of angles between it and both meridians and oblique horizons, and a thousand other specific details necessary to complete astronomical science. This ensures that, when he comes to examining these details of the primary motions, Copernicus himself examines them in the old manner, namely as occurring along circles traced in the heavens and around the motionless earth, even though stillness and stability should belong to the highest heaven, called the Prime Mobile, and motion to the earth. Thus in the introduction to Book Two he concludes: “People should not be surprised if we still use the ordinary terms for the rising and setting of the Sun and stars and similar occurrences, but should recognise that we are speaking in customary language, which is acceptable to everyone, yet always bearing in mind that ‘For us who ride the Earth, the Sun and Moon are passing; patterns of stars return, and then again recede’.” We should therefore understand clearly that Copernicus takes the earth’s motion and sun’s stability for no other reason and in no other way than to establish it, in the manner of the natural philosopher, as a hypothesis of the primary sort; on the contrary, when he comes to astronomical computations, he goes back to the old hypothesis, which takes the circles of the basic motions with their details to be located in the highest heaven around the motionless earth, being easier for everyone to understand on account of ingrained habit. But what am I saving? Such is the strength of truth and the weakness of falsehood, that those who speak this way reveal themselves not completely capable of understanding these subjects and not well versed in them; this happens when they let themselves be persuaded that the secondary kind of hypothesis is considered chimerical and fictional by Ptolemy and by other serious astronomers, and that they really regard them as physically false and introduced only for the sake of astronomical computations. The only support they give for this very fanciful opinion is a passage in Ptolemy where, unable to observe more than one simple anomaly in the sun, he wrote that to account for it one could take the hypothesis of a simple eccentric as well as that of an epicycle on a concentric, and he added he preferred the first for being simpler than the second; from these words some very superficially argue that Ptolemy did not consider necessary, but rather wholly fictional, both this and that supposition, since he said they are both equally convenient, while one and only one can be attributed to the sun’s behaviour. But what kind of superficiality is this? Who can do both of the following? First, to suppose as true the primary suppositions that planetary motions are circular and regular, and to admit (as the senses themselves necessarily force us) that in running through the zodiac all planets are now slow and now fast, indeed that most of them can be not only slow but also stationary and retrograde, and that we see them now very large and very near the earth and now very small and very far; and then, having understood these former points, to deny that eccentrics and epicycles can really exist in nature? This is wholly excusable for men who are not specialists in these sciences, but for others who would claim to be experts in them it would be an indication that they do not even understand the meaning of the terms eccentric and epicycle. One might just as well first admit that there are three letters, the first of which is G, the second O, and the third D, and then at the end deny that their combination yields GOD and claim that the result is SHADOW. But if rational arguments were not sufficient to make one understand the necessity of having to place eccentrics and epicycles really in nature, at least the senses themselves would have to persuade him: for we see the four Medicean planets’ trace four small circles around Jupiter which are very far from enclosing the earth, in short, four epicycles; Venus, which is seen now full of light and now very thinly crescent, provides conclusive evidence that its revolution is around the sun and not around the earth, and consequently that its orbit is an epicycle; and the same may be argued for the case of Mercury. Moreover, the three outer planets are very near the earth when they are in opposition to the sun, and very far when in conjunction; for example, Mars at its closest appears to the senses more than fifty times larger than at its farthest, so that some have occasionally feared that it had gotten lost or had vanished, being really invisible because of its great distance; now, what else can one conclude but that their revolution is made in eccentric circles, or in epicycles, or in a combination of the two, if we take the second anomaly into consideration? So, to deny eccentrics and epicycles in the motions of planets is like denying the light of the sun, or else it is to contradict oneself. Let us apply what I am saying more directly to our purpose: some say that modern astronomers introduce the earth’s motion and sun’s stability suppositionally in order to account for the phenomena and to facilitate calculations, just as epicycles and eccentrics are assumed in the same manner, though the same astronomers consider them physically chimerical and repugnant; I answer that I shall gladly agree with all this talk, as long as they limit themselves to staying within their own conceptions, namely that the earth’s motion and sun’s stability are as false or true in nature as epicycles and eccentrics. Let them, then, make every effort to do away with the true and real existence of these circles, for if they succeed in demonstrating their non-existence in nature, I shall immediately surrender and admit the earth’s motion to be a great absurdity. But if, on the contrary, they are forced to accept them, let them also accept the earth’s motion, and let them admit to have been convinced by their own contradictions.
I could present many other things for this same purpose. However, since I think that whoever is not persuaded by what I have said would not be persuaded by many more reasons either, I want these to suffice. I shall only add something about what could have been the motive why some have concluded with any plausibility that Copernicus himself did not really believe his own hypothesis.
There is on the reverse side of the title page of Copernicus’s book a certain preface to the reader, which is not by the author since it mentions him in the third person and is without signature. It clearly states that no one should believe in the least that Copernicus regarded his position as true, but only that he feigned and introduced it for the calculation of celestial motions; it ends its discussion by concluding that to hold it as true and real would be foolish. This conclusion is so explicit that whoever reads no further, and believes it to have been placed at least with the author’s consent, deserves to be somewhat excused for his error. But what weight to give to the opinion of those who would judge a book without reading anything but a brief preface by the printer or publisher, I let each one decide for himself. I say that this preface can only have originated from the publisher to facilitate the sale of a book which common people would have regarded as a fanciful chimera if a similar preface had not been added; for most of the time buyers are in the habit of reading such prefaces before buying the work. Not only was this preface not written by the author, but it was included without his consent, and also without his knowledge; this is shown by the errors it contains, which the author would never have committed.
This preface says no one can consider it verisimilar, unless he is completely ignorant of geometry and optics, that Venus has such a large epicycle enabling it now to precede and now to follow the sun by 40 degrees or more; for it would have to happen that when it is highest its diameter should appear only one-fourth of what it appears when it is lowest, and that in the latter location its body should be seen as sixteen times bigger than in the former; but these things, he says, are repugnant to the observations made throughout the centuries. In these assertions we see, first, that the writer does not know that Venus departs on one side and on the other of the sun by about 48 degrees, and not 40 as he says. Moreover, he asserts that its diameter should appear four times, and its body sixteen times, larger in one position than in the other. Here, first, due to a geometrical oversight he does not understand that when one globe has a diameter four times larger than another, its body is sixty-four times bigger, and not sixteen, as he stated. Hence, if he considered such an epicycle absurd and wanted to declare it to be physically impossible, if he had understood this subject, he could have made the absurdity much greater; for, according to the position he wants to refute (well known to astronomers), Venus digresses from the sun almost 48 degrees, and when farthest from the earth its distance must be six times greater than when closest, and consequently its apparent diameter in the latter position is more than six times larger than in the former (not four times), and its body more than two hundred and sixteen times greater (and not just sixteen). These errors are so gross that it is impossible to believe they were committed by Copernicus, or by anyone else but the most unqualified persons. Moreover, why label such a large epicycle most absurd, so that because of such an absurdity we would conclude that Copernicus did not regard his assumptions as true, and that neither should others so regard them? He should have remembered that in chapter 10 of the first hook Copernicus is speaking ad hominem and is attacking other astronomers who allege that it is a great absurdity to give Venus such an epicycle, which is so large as to exceed the whole lunar orbit by more than two hundred times, and which does not contain anything inside; he then removes the absurdity when he shows that inside Venus’s orbit is contained the orbit of Mercury and, placed at the centre, the body of the sun itself. What frivolity is this, then, to want to show a position mistaken and false on account of a difficulty which that position not only does not introduce in nature, but completely removes? Similarly it removes the immense epicycles which out of necessity other astronomers assumed in the other system. This only touches the writer of Copernicus’s preface; so we may argue that, if he had included something else professionally relevant, he would have committed other errors.
But finally, to remove any shadow of a doubt, if the failure to observe such great variations in the apparent sizes of the body of Venus should cast doubt on its circular revolution around the sun (from the viewpoint of the Copernican system), then let us make careful observations with a suitable instrument, namely with a good telescope, and we shall find all effects and experiences exactly agreeing; that is, we shall see Venus crescent when it is nearest to the earth, and with a diameter six times larger than when it is at its maximum distance, namely above the sun, where it is seen round and very small. I have discussed elsewhere the reasons for not detecting these variations with our simple eyesight, but just as from this failure we could reasonably deny that supposition, so now, from seeing the very exact correspondence in this and every other detail, we should abandon any doubt and consider the supposition true and real. As for the rest of this admirable system, whoever desires to ascertain the opinion of Copernicus himself should not read the fanciful preface of the printer, but the whole work of the author himself; without a doubt he will grasp first-hand that Copernicus held as very true the stability of the sun and the motion of the earth.
II
The motion of the earth and stability of the sun could never be against Faith or Holy Scripture, if this proposition were correctly proved to be physically true by philosophers, astronomers, and mathematicians, with the help of sense experiences, accurate observations, and necessary demonstrations. However, in this case, if some passages of Scripture were to sound contrary, we would have to say that this is due to the weakness of our mind, which is unable to grasp the true meaning of Scripture in this particular case. This is the common doctrine, and it is entirely right, since one truth cannot contradict another truth. On the other hand, whoever wants to condemn it judicially must first demonstrate it to be physically false by collecting the reasons against it.
Now, one wants to know where to begin in order to ascertain its falsity, that is, whether from the authority of Scripture or from the refutation of the demonstrations and observations of philosophers and astronomers. I answer that one must start from the place which is safest and least likely to bring about a scandal; this means beginning with physical and mathematical arguments. For if the reasons proving the earth’s motion arc found fallacious, and the contrary ones conclusive, then we have already become certain of the falsity of this proposition and the truth of the opposite, which we now say corresponds to the meaning of Scripture; so one would be free to condemn the false proposition and there would be no danger. But if those reasons arc found true and necessary, this will not bring any harm to the authority of Scripture; instead we shall have been cautioned that due to our ignorance we had not grasped the true sense of Scripture, and that we can learn this meaning with the help of the newly acquired physical truth. Therefore, beginning with the arguments is safe in any case. On the other hand, if we were to fix only on what seemed to us the true and certain meaning of Scripture, and we were to go on to condemn such a proposition without examining the strength of the arguments, what a scandal would follow if sense experiences and reasons were to show the opposite? And who would have brought confusion to the Holy Church ? Those who had suggested the greatest consideration of the arguments, or those who had disparaged them? One can see, then, which road is safer.
Moreover, we admit that a physical proposition which has been proved true by physical and mathematical demonstrations can never contradict Scripture, but that in such a case it is the weakness of our mind which prevents us from grasping its true meaning. On the other hand, whoever wants to use the authority of the same passages of Scripture to confute and prove false the same proposition would commit the error called “begging the question.” For, the true meaning of Scripture being in doubt in the light of the arguments, one cannot take it as clear and certain in order to refute the same proposition; instead one must cripple the arguments and find the fallacies with the help of other reasons and experiences and morc certain observations. When thc factual and physical truth has been found in this manner, then, and not before, can one be assured of the true meaning of Scripture and safely use it. Thus the safe road is to begin with the arguments, confirming the true and refuting the fallacious ones.
If the earth de facto moves, we cannot change nature and arrange for it not to move. But we can rather easily remove the opposition of Scripture with the mere admission that we do not grasp its true meaning. Therefore, the way to be sure not to err is to begin with astronomical and physical investigations, and not with scriptural ones.
I am always told that, in interpreting the passages of Scripture relevant to this point, all Fathers agree to the meaning which is simplest and corresponds to the literal meaning; hence, presumably, it is improper to give them another meaning or to change the common interpretation, because this would amount to accusing the Fathers of carelessness or negligence. I answer by admitting that the Fathers indeed deserve reasonable and proper respect, hut I add that we have an excuse for them very readily: it is that on this subject they never interpreted Scripture differently from the literal meaning, because at their time the opinion of the earth’s motion was totally buried and no one even talked about it, let alone wrote about it or maintained it. But there is no trace of negligence by the Fathers for not thinking about what was completely hidden. That they did not think about it is clear from the fact that in their writings one cannot find even a word about this opinion. And if anyone were to say that they considered it, this would make its condemnation more dangerous; for after considering it, not only did they not condemn it, but they did not express any doubt about it.
Thus the defence of the Fathers is readily available and very easy. On the contrary, it would be very difficult or impossible to excuse or exonerate from a similar charge of carelessness the Popes, Councils, and Congregations of the Index of the last eighty years, if this doctrine were erroneous and deserving of condemnation; for they have let this opinion circulate in a book which was first written on orders from a Pope, and then printed on orders from a cardinal and a bishop, dedicated to another Pope, and, most important, received by the Holy Church, so that one cannot say that it had remained unknown. If, then, the inappropriateness of charging our highest authorities with negligence is to be taken into account, as it should, Let us make sure that in trying to escape one absurdity we do not fall into a greater one.
But assume now that someone regards it as inappropriate to abandon the unanimous interpretation of the Fathers, even in the case of physical propositions not discussed by them and whose opposite they did not even consider; I then ask what one should do if necessary demonstrations showed the facts of nature to be the opposite. Which of the two decrees should be changed? The one which stipulates that no proposition can be both true and erroneous, or the other one which obliges us to regard as articles of faith physical propositions supported by the unanimous interpretation of the Fathers? It seems to me, if I am not mistaken, that it would be safer to modify this second decree than to be forced to hold as an article of faith a physical proposition which had been demonstrated with conclusive reasons to be factually false in nature. It also seems to me that one could say that the unanimous interpretation of the Fathers should have absolute authority in the case of propositions which they aired, and for which no contrary demonstrations exist and it is certain that none could ever exist. I do not bring in the fact that it is very clear that the Council requires only that one agree with the unanimous interpretation of the Fathers “in matters of faith and morals, etc.”
III
1. Copernicus uses eccentrics and epicycles, but these were not the reason for rejecting the Ptolemaic system, since they undoubtedly exist in the heavens; it was other difficulties.
2. In regard to philosophers, if they were true philosophers, namely lovers of truth, they should not get irritated, but, learning that they were wrong, they should thank whoever shows them the truth; and if their opinion were to stand up, they would have reason to take pride in it, rather than being irritated. Theologians should not get irritated because, if this opinion were found false then they could freely prohibit it, and if it were discovered true then they should rejoice that others have found the way to understand the true meaning of Scripture and have restrained them from perpetrating a serious scandal by condemning a true proposition.
In regard to falsifying Scripture, this is not and will never be the intention of Catholic astronomers such as ourselves; rather our view is that Scripture corresponds very well to truths demonstrated about nature. Moreover, certain theologians who are not astronomers should be careful about falsifying Scripture by wanting to interpret it as opposed to propositions which may be true and demonstrable.
3. It might happen that we could have difficulties in interpreting Scripture, but this would occur because of our ignorance and not be cause there really are or can be insuperable difficulties in reconciling Scripture with demonstrated truths.
4. The Council speaks “about matters of faith and morals, etc.” So there is an answer to the claim that such a proposition is “an article of faith by reason of the speaker,” though not “by reason of the topic,” and that therefore it is among those covered by the Council. The answer is that everything in Scripture is “an article of faith by reason of the speaker,” so that in this regard it should be included in the rule of the Council; but this clearly has not been done because in that case it would have said that “the interpretation of the Fathers is to be followed for every word of Scripture, etc.,” and not “for matters of faith and morals”; having thus said “for matters of faith,” we see that its intention was to mean “for matters of faith by reason of the topic.”
Then consider that it is much more a matter of faith to hold that Abraham had some children and that Tobias had a dog, because Scripture says it, than it would be to hold that the earth moves, even if this were found in the same Scripture, and further that to deny the former is a heresy, but not to deny the latter. It seems to me that this depends on the following reason. There have always been in the world men who had two, four, six children, etc., or none, and similarly people who have dogs and who do not, so that it is equally credible that some have children or dogs and others do not; hence there appears to be no reason why in such propositions the Holy Spirit should speak differently from the truth, the negative and the affirmative sides being equally credible to all men. But it is not so with the motion of the earth and the stability of the sun; these propositions are very far removed from the understanding of the masses, for on these matters not relevant to their eternal life the Holy Spirit chose to conform its pronouncements with their abilities, even when facts are otherwise from the point of view of the thing in itself.
5. In regard to placing the sun in heaven and the earth outside it, as Scripture seems to affirm, etc., this truly seems to me to be a simple perception of ours and a manner of speaking only for our convenience. For, in reality all that is surrounded by heaven is in heaven, just as all that is surrounded by the city walls is in the city; indeed, if one were to express a preference, what is in the middle is more in heaven and in the city, being, as it were, at the heart of the city and of heaven. That difference exists because one takes the elemental region surrounding the earth as being very different from the celestial region. But such a difference will always exist regardless of where these elements are placed; and it will always be true that from the viewpoint of our convenience the earth is below us and heaven above, since all the inhabitants of the earth have heaven above our heads, which is our upwards, and the center of the earth under our feet, which is our downwards; so, in relation to us the center of the earth and the surface of heaven are the farthest places, that is, the endpoints of our up and down, which are diametrically opposite points.
6. Not to believe that there is a demonstration of the earth’s mobility until it is shown is very prudent, nor do we ask that anyone believe such a thing without a demonstration. On the contrary, we only seek that, for the advantage of the Holy Church, one examine with the utmost severity what the followers of this doctrine know and can advance, and that nothing be granted them unless the strength of their arguments greatly exceeds that of the reasons for the opposite side. Now, if they are not more than ninety percent right, they may be dismissed; but if all that is produced by philosophers and astronomers on the opposite side is shown to be mostly false and wholly inconsequential, then the other side should not he disparaged, nor deemed paradoxical, so as to think that it could never he clearly proved. It is proper to make such a generous offer since it is clear that those who hold the false side cannot have in their favour any valid reason or experiment, whereas it is necessary that all things agree and correspond with the true side.
7. It is true that it is not the same to show that one can save the appearances with the earth’s motion and the sun’s stability, and to demonstrate that these hypotheses are really true in nature. But it is equally true, or even more so, that one cannot account for such appearances with the other commonly accepted system. The latter is undoubtedly false, while it is clear that the former, which can account for them, may be true. Nor can one or should one seek any greater truth in a position than that it corresponds with all particular appearances.
8. One is not asking that in case of doubt the interpretation of the Fathers should be abandoned, but only that an attempt be made to gain certainty regarding what is in doubt, and that therefore no one disparage what attracts and has attracted very great philosophers and astronomers. Then, after all necessary care has been taken, the decision may be made.
9. We believe that Solomon, Moses, and all other sacred writers knew perfectly the constitution of the world, as they also knew that God has no hands, no feet, and no experience of anger, forgetfulness, or regret; nor will we ever doubt this. But we say what the Holy Fathers and in particular St. Augustine say about these matters, namely that the Holy Spirit inspired them to write what they wrote for various reasons, etc.
10. The error of the apparent movement of the shore and stability of the ship is known by us after having many times observed the motion of boats from the shore, and many other times observed the shore from a boat; and so, if we could now stay on earth and now go to the sun or other star, perhaps we would acquire sensible and certain knowledge of which one of them moves. To be sure, if we looked only at these two bodies, it would always seem to us that the one we were on was standing still, just as looking only at the water and the boat always gives the appearance that the water is flowing and the boat is standing still. Moreover, the two situations are very different: there is great disparity between a small boat, separable from its environment, and the immense shore, known by us through thousands of experiences to be motionless, that is, motionless in relation to the water and the boat; but the other comparison is between two bodies both of which are substantial and equally inclined toward motion and toward rest. Thus it would be more relevant to compare between themselves two boats, in which case it is absolutely certain that the one we were on would always appear to us as motionless, as long as we could not consider any other relationship but that which holds between these two ships.
There is, therefore, a very great need to correct the error about observing whether the earth or else the sun moves, for it is clear that to someone on the moon or any other planet it would always appear that it was standing still and the other stars were moving. But these and many other more plausible reasons of the followers of the common opinion are the ones that must be untied very openly, before one can pretend even to be heard, let alone approved; unfortunately we have not done a very detailed examination of what is produced against us. Moreover, neither Copernicus nor his followers will ever use this phenomenon of the shore and the boat to prove that the earth is in motion and the sun at rest. They only adduce it as an example that serves to show, not the truth of their position, but the absence of contradiction between the appearance of a stable earth and moving sun to our simple sense experience, and the reality of the contrary. For if this were one of Copernicus’s demonstrations, or if his others did not argue more effectively, I really think that no one would agree with him. powered by performancing firefox
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January 2007 |
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