Chapter 3 2. Rules to guide the mind

introduction Men have long been bound by the false belief that objects of experience determine science, that knowledge depends on experience.But the author emphasizes that the acquisition of knowledge depends on the use of the mind.The mind, the "power of knowledge," is unitary, and therefore no matter what object it is applied to, the knowledge it acquires is of the same kind.The correct use of human cognitive ability can lead to truth and certainty, otherwise it will fall into error.All sane people have a natural ability to distinguish truth from falsehood, a "natural light of reason."Of course, we don't think anyone can discover new truths just by using this set of rules.In addition to the innate psychic abilities that people have within themselves, there is a long probationary period of self-discipline.How to train yourself?This manuscript illustrates an alternative approach to the traditional one.In particular, it highlights man's innate rationality, takes back the right to know the world from the church and theologians, and gives readers a strong feeling.

Principle one The purpose of investigation should be to direct our minds to form firm and true judgments about all that presents itself.It is the custom of men, whenever they see some resemblance between two things, to apply to them in their inner judgment the same true understanding of the one, even though the difference between the two things may be the same. Regardless, in this way, people mistakenly equate science and technology.Little do they know that science is all that the mind knows, while art requires specific uses and habits of the body.At the same time, people have also noticed that it is impossible for a single person to learn all the skills. Only those who practice a single skill can easily become outstanding craftsmen, because it is very convenient for the same hands to do a single job.It is not so convenient to be suitable for field work, but also good at playing sitar, or adapting to various other tasks.So it was thought that the sciences were like this, and they distinguished each science according to its object, and once thought it necessary to pursue each of them, while the other sciences were ignored.Thus their hopes were utterly defeated, for all science is nothing but the intellect of man, and the intellect of man is always one and only like itself, however different objects it may be applied to; it recognizes no object There is no difference between us, just as the sun does not admit that all things under the sun are different from each other; so there is no need to confine our minds within any boundaries.Since, as is the case with a single art, knowledge of one truth does not divert us from the revelation of another, but rather assists us in it.I am, of course, amazed that most people examine with the utmost care the properties of the various plants, the motions of the planets, the magic touch, and such subdivisions, but hardly any one thinks that conscience, or Wisdom, it is said, is in all men, and all others are worthy of attention not so much for their own sake as for their contribution to this conscience or wisdom.

Therefore, it is not unreasonable for us to propose this principle and make it the first principle.Since nothing distracts us more from the right path of the search for truth than to direct our investigations not to this general end, but to other ends.And I'm not even talking about those evil reprehensible ends.For example, false glory and shameful self-interest are very obvious, and artificial reasoning and illusions that cater to the mediocre mind open a much more convenient path than a sure knowledge of the truth.I speak of certain honestly admirable ends, for they often deceive us more cunningly, as if we study science for the convenience of life, or the pleasure of contemplating truth, which is almost a part of life. The only happiness that is unadulterated, the only happiness that is not disturbed by any pain.For, although we may reasonably expect these fruits from science, in fact, if we think about them a little while we study them, we find that they often lead us to abandon many things that are needed in order to know several other things. , the latter being less useful and less noteworthy, we must therefore believe that all sciences are so closely connected with one another that it is much more convenient to learn them all in their entirety than to separate them from each other; Determined to seriously seek the truth of things, he must not choose a particular science: because things are interconnected and interdependent; he must only focus on how to develop the natural light of reason,-not to solve this or That school dispute, but for the purpose of letting the understanding guide the will in various situations in life.Then, before long, he will be amazed to find that he has advanced far beyond those who study particular things, and that he has not only achieved what they hoped to achieve, but has achieved more than they could possibly achieve.

Principle Two We should consider only those objects which our minds seem to suffice for definite knowledge.Any science is a definite and obvious knowledge; and those who doubt many things are no more knowledgeable than those who have never thought of them, or rather, the former are probably less knowledgeable than the latter, if they are aware of the Some form of wrong opinion.Therefore, rather than examining difficult subjects--which are so difficult that we have no way of distinguishing the truth from the false, and have to take the doubtful for certainty--it is better not to study them at all, because there is little hope of increasing knowledge and there is a danger of knowledge diminishing. Not small.Therefore, through this proposition, we reject all knowledge that is only probable, and advocate only believing in things that are already fully known and beyond doubt.The learned, however, may be convinced that such knowledge hardly exists, because they have never bothered to think about it, but have concluded, from a vice common to all mankind, that it is the easiest thing to acquire, that it is common to all. but I would advise them that there are far more of them than they can imagine, and that they are sufficient to confirm an innumerable number of propositions, of which they could only take it for granted; Feeling that, being so learned, it would be too embarrassing to admit utter ignorance on a subject, it is their usual habit to embellish their false arguments in such a way that they themselves believe them, and publish them as they are. real arguments.

But if we really follow this principle, we will find that there is very little we can devote ourselves to.Because there may not be a problem in science, and wise people don't always have different opinions.However, whenever two of them make opposite judgments about the same thing, at least one of them must be wrong, and it may even be considered that neither of them has a real knowledge of it: because if his reason If it is certain and obvious, he can raise it to the other party, so that he can finally comprehend it.It therefore appears impossible for us to acquire adequate knowledge of subjects that are subject to conjecture, since it would be rash for us to pretend that we can go further than those who have preceded us.It appears, then, that, if we consider carefully, of the sciences which have been revealed, the only two which apply this principle without error are arithmetic and geometry.

This does not mean, however, that we should condemn the method of philosophical reasoning which is still being revealed;The structure of the syllogism is so ingenious that it is doubtful whether school education is necessary, because the use of the syllogism can train and inspire the talents of young people through some kind of competition.It is best for young people to be nurtured with such insights, even if they show uncertainty, and scholars are still discussing with each other.For young people, we can't let it be and let it go; otherwise, since they don't get guidance, they may end up on the cliff and the abyss.But if they always follow the teacher's lead, they may, at least where the more prudent ones have tried, take a more sure course, though they may sometimes stray from the truth.Besides, we were educated in this way in school in the past, and we are very satisfied with it.But, now that the oath which bound us to the Word of the Master is broken, and we grow older, and our hands escape the ruler, if we wish ourselves to formulate the principles by which the highest human understanding may be followed, then , perhaps one of the first principles should be the following, namely, never to waste our time like so many people who despise all easy things, concentrate on hard problems, and conceive with great ingenuity all kinds of real problems. Very ingenious conjectures and all kinds of arguments that may be extremely true.However, after a lot of hard work, they finally regretted it and realized that they had only added to the vast amount of doubts they already had in their minds, and had not learned any real knowledge.

Now, therefore, we have said before, that, of the known sciences, arithmetic and geometry alone are exempt from the fault of falsehood or inaccuracy.In order, then, to speculate more carefully why this is the case, it must be noted that we arrive at the truth of things by two means: first, through experience, and second, through deduction.However, we must also pay attention to this aspect. Regarding things, even if you have experience, you are often deceived.If this is not seen, there is no need for any deduction or pure inference from one thing to another; and with an understanding, even an irrational one, no deduction or deduction can ever be false.Those logical series which the dialecticians hold to govern human reason do not seem to me of much use for this purpose, though I do not deny that they are quite suitable for other uses.Any error that may occur to man (only man), and not to animals, is by no means derived from absurd inferences, but merely from a misbelief of something which he does not understand well, or from hasty judgments without any grounds. .

It can be seen from this that the reason why arithmetic and geometry are far more reliable than all other sciences is that only arithmetic and geometry study objects that are pure and simple, and they will never mistake things that have been proved to be untrue by experience. Only arithmetic and geometry It is a conclusion drawn entirely from rational deduction.That is to say, arithmetic and geometry are extremely clear, extremely easy to grasp, and the objects of study are exactly what we want, unless we take them lightly.It seems impossible for man to err in these two disciplines.But do not be surprised if there are some who themselves prefer to employ their intellect in other arts, or in philosophy.The reason for this is that everyone is willing to make random guesses about obscure questions, and feel that they are more sure than grasping obvious questions. It is much more convenient to make a guess about any question than to have a firm grasp of the truth about any very easy question.

It is time to draw conclusions from all the above.The conclusion is not, of course, that there is no need to study anything but arithmetic and geometry; but only that the seeker of truth should not think about anything unless he can acquire the same certainty as arithmetic and geometry. Principle three It is not some other's opinion, nor our own conjecture, that should be required of the object to be examined, but what we can clearly and distinctly intuit it, or deduce it with certainty; for, There is no other way to gain true knowledge. It is necessary to read the works of the ancients, for it is a great advantage to us to be able to draw upon the labors of so many men: both to know what has been rightly discovered in the past, and to know that we still have to use the best of our minds to Ask for something to be resolved.At the same time, however, there is a worry that too much attention to reading those works may introduce certain errors which, after we have acquired them, we cannot help but imprint upon them, however careful we are to avoid them.Such is the state of mind of writers, in fact, that whenever they make up their minds to defend an opinion which is objected to, they make up their minds to defend an opinion which is objected to, using all sorts of very insidious arguments. We also agree with that opinion; on the contrary, whenever they have discovered by a very lucky chance a definite and obvious truth, they never bring it up without covering it up with some obscure phrases: probably because they Lest the truth be simple and clear, their revelations would be undignified, that is to say, they would do everything possible to deny us the truth as it is laid bare.

At the same time, however, even if they are all sincere and frank, never imposing doubts on us as truth, but stating them in full sincerity, there is hardly a truth that is not said by one, and it is true of the other. One person puts forward a contrary opinion, and we still cannot decide whose statement to believe.And counting votes is useless in order to follow what is presumably the most authoritative opinion, because, if a difficult question is involved, it is more plausible that a few have discovered the truth than many.Even if the opinions of the majority are all in agreement, it is not enough for us to present their reasons, because in a word, even if we can recite all the proofs of others, we are not mathematicians; if we We are not wise enough to solve all the problems that may arise, nor to be called philosophers; if we are familiar with all the arguments of Plato and Aristotle, we cannot make firm judgments of things that arise, because, then, It seems that we have not gained true knowledge, but just remembered some anecdotes.

In addition, we all know very well that judgments about the truth of things must never be mixed with speculation.It is not trivial to make this point.There can never be any assertion in general philosophy sufficiently obvious and definite not to be open to any controversy.The main reason for this is that scholars are not satisfied with trying to discern the obvious and certain things, but insist on affirming the obscure and unknown things, so they have to take it for granted. Later, they themselves gradually believe in it. Indiscriminately, they are all confused with the real and obvious things, and finally, any conclusion they draw seems to depend on such propositions, so the conclusion is not certain. In order, therefore, that we should avoid repeating this mistake, we shall examine each of those faculties of understanding by which we know things without the slightest fear of being disappointed, and we should employ only two of them, namely, intuition and deduction.I use the word intuition not to mean the variable representations of the senses, nor the false judgments of the imagination in false combinations, but the conceptions of the pure and attentive mind, which are easy and unique, and which keep us from thinking of our own in other words, the meaning is the same, namely, the unquestionable conception of the pure and concentrated mind arising from the only light--the light of reason, which is more simple than the deduction itself. For sure, although we said earlier that it is impossible for people to make false deductions.Thus everyone can intuit with the mind (the following propositions): he exists, he thinks, a triangle is bounded by only three straight lines, a circle lies in only one plane, etc., far more than most people usually Watch what you can, for these people disdain to turn their hearts to so easy a thing. However, lest anyone should be surprised by the new use of the word intuition (there are also uses of words for which I will have to deviate from the usual meaning below), I will say here in general: I do not consider How all these terms are used these days in our school, because it's a very embarrassing thing if the terms are the same but the views are fundamentally different.Therefore, on my part, I only pay attention to the original Latin meaning of each word, so that whenever I can't find a suitable word, I transplant the word that I think is most suitable according to the meaning I have given. However, the reason why intuition is so obvious and certain is not because it simply states, but because it can comprehensively observe.For example, if there is such a conclusion: the sum of 2+2 is equal to the sum of 3+1; this not only needs to intuit that 2+2 gets 4, and 3+1 also gets 4, but also needs to intuit that The third proposition (ie the conclusion). From this it may perhaps be doubted why, in addition to intuition, we have proposed above a method of knowing, that is, using the method of deduction: we mean everything that must be deduced from something already known.It is quite necessary for us to mention this, because there are many things which, though not evident in themselves, are known with certainty to us, if they are such a continuous and uninterrupted movement that the mind perceives each thing clearly and separately, Deduced from known true principles.This is like we know that the next link of a long chain is closely linked to the previous link. I have seen all the links all the time, and I still remember that every link is tightly linked from beginning to end (you can know it by deduction).Thus the intuition of the mind differs from definite deduction in that we suppose that in deduction there is movement or some kind of succession, whereas in intuition it is not.Moreover, apparent visibility is not as necessary in deduction as it is in intuition, rather, it is somehow assured from memory.From this it follows that, with regard to propositions which are directly derived from initial principles, we may say with certainty that some of them are known by intuition and others by deduction, according to the manner in which they are examined; It is known only by intuition, whereas further inferences are obtained only by deduction. These two paths are the surest paths to true knowledge, and in matters of the heart we should take no other, and reject all others which are dubious and false; Consider divine things more certain than any knowledge, since belief in them--belief itself always involves obscure matters--is not an operation of the mind, but of the will; if the basis of belief In the understanding, then these grounds must and can be found chiefly by one of the two paths mentioned above.We may have to speak more fully on this point in the future. Principle Four Methods are (absolutely) necessary to seek the truth of things.Man is often driven by blind curiosity, leading his soul into unknown paths, with no basis for hope, but with the intention of trying: simply to see if what he desires is not there.This is like a person who, because of a stupid desire to seek treasure, searches around non-stop, hoping that some passer-by will leave some gold and silver treasure.This is how nearly all chemists, most geometers, and many philosophers conduct their research.Of course, I am not saying that they must not have good luck and find some truth after wandering around; but I do not agree that this means that they are more diligent, they just have better luck.To seek the truth without a method, it is better not to seek the truth of anything at all, for, surely, such haphazard studies and ambiguous meditations only dim the light of nature and blind our minds: what has been People who are used to walking in the dark like this will have their eyesight greatly weakened, and they will no longer be able to bear it when they see the light.This point is also proved by experience, because we often see some people, although they never pay attention to academic research, when they encounter something, their judgments are much more solid and clear than those who have been in school all their lives.What I mean by method is definite and easy-to-grasp principles. Those who follow these principles accurately will never again take falsehoods as truths in the future, and will never waste their minds in vain and foolish work. Make its learning grow endlessly, so as to truly know everything that the mind can know. Therefore, we should pay attention to two points here: It is certain that we will not take falsehoods as truth to achieve the knowledge of everything: if there is anything we can know that we do not know, it is only because we do not have the awareness to make us understand. The road to this realization, or because we fall into the opposite error.But if the method can correctly show how we should use the mind to intuit, so that we don't fall into the opposite error, if it can show how to find the deduction, so that we can come to the knowledge of all things, then, in my opinion, such a The method is already perfect, and there is no need to add anything.Since it has been said above, no knowledge can be grasped except by intuition of the mind or by deduction.For the method cannot be perfected to such a degree; even to teach you how to use intuition and deduction, since these are the simplest and most fundamental things, if our understanding has not mastered them long before using them , however easy a rule our method may furnish, the understanding will not understand it in the slightest.As for the other operations of the mind, those which the dialectician tries to guide by means of these two primary operations (intuition and deduction) are of no use here at all; for, if anything is added to the pure brilliance of reason, it must be eclipsed in one way or another. The method which we speak of is so useful that any endeavor to scholarly study which does not depend on it would probably do more harm than good.So, it was easy for me to believe it.With the wisdom of the ancients, even if they were only guided by pure nature, they had already been more or less aware of this method, because the human mind is endowed with something sacred, and the original seeds of beneficial thoughts have long been sown in it. How they have been neglected and smothered by the obstacles of the world, yet they often bear fruit of their own accord.As we have tried in the two easiest sciences, arithmetic and geometry, we have in fact found that the ancient geometers also used a certain analytical method, and extended it to solve all problems, although they took care not to disclose it to posterity. The mystery of this method.Now a certain kind of arithmetic is flourishing, called algebra, which uses numbers to achieve what the ancients did with graphics.In fact, these two sciences are nothing but fruits that ripen by themselves from our method, from our natural inherent principles.Where these fruits have grown more abundantly has hitherto been in the simple objects of the two arts, and not in those respects where greater obstacles have often suffocated them, but which, if carefully cultivated, can doubtless also reach full maturity— -I'm not surprised by this. For me, this is the main goal I am trying to achieve in this paper.In fact, I would not give much importance to the principles I am about to reveal if they could only solve those vain problems with which calculators and geometers are accustomed to while away their time, because then I would feel that nothing would be gained, It's just doing some boring things, and it's not necessarily better than others.Although it is my intention to speak at length of figures and numbers, since it is impossible to obtain such clear and definite illustrations from other sciences, it is not difficult for anyone who is willing to examine my views to perceive that what I have in mind here is not Not mathematics in general, but some other discipline, not so much of which they are a part, but of a kind which is clothed in them.For this science is supposed to contain the first attempts of human reason, and it is supposed to be extended to the possibility of finding truth from any subject; source of discipline.When I use the word coat, I do not mean that I wish to conceal this doctrine, to wrap it up so that common people cannot see it, but to coat it, adorn it, and make it more accessible to the human mind. accepted.When I formerly began to devote my intellect to the various subjects of mathematics, I first read most of the authoritative authors that are commonly read, and I was particularly fond of arithmetic and geometry, since these two sciences are said to be very simple, and are generally Pathways to other sciences. In neither, however, have I met writers with whom I am completely satisfied: in mathematics, though I have read a good deal which, after calculations, proved to be true; Many, and they draw those conclusions from certain (rational) results; but they do not seem to indicate to our minds why, nor how to know it; so I do not find it surprising that among them Most of the wisest and most learned people, when they first try these arts, they immediately dismiss them as childish and useless; As if intending to stop at such foolish cognitions, bent on superficial proofs of this kind, proofs that are often discovered by fluke rather than by skill, have nothing to do with the understanding, but involve only visual and imaginative proofs, and the result is that We lose to some extent the use of reason; in short, nothing is more complicated than by this mode of proof, and new difficulties are found to be entangled with the confusion of figures. So, later I thought of reason, so I thought: Those sages who first revealed philosophy were only willing to take people who were familiar with Matthies as disciples to study human wisdom. They probably felt that in order to ponder people's intelligence, This discipline is the most convenient and most necessary to make it suitable for other and more important sciences.When I think of it this way, I feel a little speculative: the Matthias they know is probably very different from what is popular in our century.Not that I presume they are well versed in it, since the ecstasy of even the slightest revelation makes them willing to make sacrifices, which openly shows how ignorant they are.It was not the devices of these men which the historians boasted of to change my mind, for, however primitive they were, they could easily be said to Miraculous. Nevertheless, I still believe that the seeds of truth that nature first sowed in the human mind, the seeds of truth that were buried in our hearts because of too many falsehoods we read or hear every day, in the simple and pure ancient times, among them Some still retain their original power, so that the ancients were enlightened by the light of the soul. Although they don't know why, they saw that virtue should be preferred to pleasure, and integrity should be preferred to utility. and Matthies, though they fall short of the heights of the two sciences themselves.I even think that traces of this true Matthis can be found in the writings of Papus and Diophantus, two scholars who did not live as far back as the primordial age, but who, after all, were The ancients who preceded us by many centuries.I simply suspect that both of these writers, out of disgusting cunning, themselves later deleted it from their works, as many artisans do with their own inventions, because the real Matthis is very simple. Easily, lest they should lose their value by disclosure, they would rather show us something else, namely, certain empty and useless facts which, as the fruit of their art, are proved by the conclusions drawn in a most ingenious way. Truth, for the sake of our admiration, refuses to impart to us virtuosity itself, because then others would have no chance of admiration.There are also men, of great intellect, who have tried in this century to restore the true Matthis: the art which they call algebra in Arabic terms seems to me to be nothing else—if only we could bring those Stripped of the countless numbers and incomprehensible symbols that spoil it, the art no longer lacks that wonderful ease and clarity that we suppose should exist in a real Matthies.These ideas diverted my attention from the particular studies of arithmetic and geometry to the quest for some kind of general Matthias. So, I first pondered: What is the connotation of this name, what is it that everyone understands; also, why do people refer to various parts of mathematics, not only the above two, but also astronomy, music, optics, mechanics and others, etc. .It is not enough to examine the origin of the term here, because the meaning of the word Matthis is "discipline".All other sciences, then, may also be called "mathematics," in a right not inferior to geometry itself.Still, hardly anyone, even just walking through the school gates, can easily discern, among the assortment of things that come up, which concerns Matthies and which simply concerns other disciplines.Nevertheless, whoever studies more carefully will find that Matthias is involved only in those things in which some order and measure can be perceived, and this measure, whether in numbers, figures, stars, It should make no difference whether you are looking for it in the sound or in any object. So there should be some kind of general science that can explain everything there is to know about order and measure.It has no reference to any particular subject matter, and may adopt, instead of a borrowed name, the already old conventional name, Mathesis Universalis, because it contains in itself everything that makes the other sciences also called mathematics.It is both useful and easy, and far surpasses all the sciences subordinate to it.How far it goes beyond, will be seen from these two points; it goes as far as the other sciences go, and only goes beyond it; the other sciences have the same difficulties (if they have any), but, It does not have all the other difficulties which other sciences encounter due to their particular objects.In this way, since everyone is familiar with its name and what it focuses on, even if they don't study it exclusively, then why do most people take pains to study other disciplines that belong to it instead of studying it? itself? Perhaps I would have been astonished, too, if I hadn't known that everyone thought it easy; if I hadn't noticed that the human mind is constantly giving up what it thinks it can get easily, in favor of the mysterious. Novelties are sought after. As for myself, I know my weakness, and when I seek to know things, I make up my mind to follow a certain order.That is, always start with the simplest and easiest things, and never think of others until there is no hope left for these things.Therefore, until now, as long as Mathesis Universalis is still in my heart, I have continued to cultivate it. After that, I think that I can engage in other higher scientific research without being impatient.But before I turn to further investigations, I shall endeavor to collect and put into order all that I have found to be quite noteworthy in my previous studies.This is done, both so that, when my memory fails in old age, it may be easily found again in this pamphlet, if custom requires, and so that my memory may be relieved of this burden, so that I may The mind is free to transfer to the research of other subjects. Principle five The whole method is but this: to arrange into order those things which the mind's eye should observe, in order to discover some truth.If you want to strictly follow this principle, you must reduce the confused and ambiguous propositions step by step to other simpler propositions, and then start from the simplest of all propositions by intuition, and try to rise up to know all other propositions step by step.Only in this is contained the sum of the endeavors of the whole human race.Therefore, if anyone wants to solve the problem of knowing things, he must abide by this principle, just as Tesseus must follow the ball of thread rolling in front of him if he wants to go deep into the maze.But there are many who do not take into account the indications of this principle, or are ignorant of it, or profess to have no need of it, and who deal with very difficult problems with great disorder.Thus, it seemed to me that they were eager to jump on the roof of the building with their feet.这或者是由于他们根本不管用于此目的的楼梯是一级一级的，或者是由于他们没有发现还有这样的一级一级的楼梯。一切星相学家正是这样，他们根本不懂得天的本性，甚至没有充分观察其运动，就希望能够指明其运动的后果。脱离物理学而研究力学，胡乱制造各种产生运动的新机器的人，大抵也是这样。忽视经验，认为真理可以从他们自己的头脑里蹦出来，就像米纳娃从朱庇特头脑里蹦出来一样。这类哲学家也是这样。 固然，上述这些人显然违反本原则。但是，这里所要求的秩序，也与一般秩序一样，有些暧昧含混，以至于不是所有的人都能认识其究竟的，所以他们犯错误也许是在所难免，如果他们不小心翼翼遵守下一命题所述。 原则六 要从错综复杂的事物中区别出最简单的事物，然后予以有秩序的研究，就必须在我们已经用它们互相直接演绎出某些真理的每一系列事物中，观察哪一个是最简单项，其余各项又是怎样同它的关系或远或近，或者同等距离的。 虽然这一命题看起来并没有教给我们什么非常新鲜的东西，其实它却包含着这一技艺的主要奥秘，整个这篇论文中其它命题都没有它这样有用：它实际上告诉我们，一切事物都可以排列为某种系列，依据的当然不是它们与某一存在物类属有何关系，即不是像往昔哲学家那样依据各类事物的范畴加以划分，而是依据各事物是怎样从他事物中获知的；这样，每逢出现困难，我们就可以立刻发现：是否宜于首先通观某些其它事物、它们是哪些以及应该依据怎样的秩序。 要正确做到这一点，首先必须注意：一切事物，按照它们能否对于我们有用来看待，即，不是一个个分别考察它们的性质，而是把它们互相比较，以便由此及彼予以认识。那么，对一切事物都可以说它们或者是相对的，或者是绝对的。我所称的绝对，是指自身含有所需纯粹而简单性质的一切，例如，被认为独立、原因、简单、普遍、单一、相等、相似、正直等等的事物；这个第一项，我也把它称作最简单、最容易项，便于运用它来解决各项问题。 相反，相对是指源出于同一性质，或者至少源出于得之于同一性质之物的，因而得与绝对相对应，得以通过某种顺序而演绎得到的一切。但是，相对之为概念，还包含我称为相互关系的某些其它项。例如，被称为依附、结果、复合、特殊、繁多、不等、不相似、歪斜等等之物。这些相对项包含的互相从属的这类相互关系越多，它们与绝对的距离就越远。本原则告诉我们，必须把它们互相区别，考察它们互相之间的联系和它们之间的天然秩序，使我们可以从最低项开始，逐一通过其它各项而达到最绝对项。 这一技艺的奥秘全在于：从一切项中细心发现最绝对项。因为，某些项，从某种角度考虑，固然比其它项较为绝对，但是换个角度来看，则较为相对。例如，普遍虽然比特殊较为绝对，因为它具有较简单的性质，但是，也可以说它较为相对，因为它的存在取决于个别，如此等等。同样，某些项确实比其它项较为绝对，却还不是一切项中最绝对的。比方说，我们拿个体来看，种是一个绝对项；但要是我们拿属来看，种则是一个相对项。在可度量项中，广延是一个绝对项，但是，在广延中则以长度为绝对项，如此等等。最后，为了更清楚地指出：我们在这里考察的是我们要认识的事物的顺序，而不是每一事物的性质，(我们要说，)我们得识别各绝对物之间的因果关系和相对关系，尽管它们的性质确实是相对的，依靠的仍然是奋勉努力，因为，在哲学家看来，原因和结果是对应项，但是，如果我们在这里要寻求结果是什么，就必须找出原因是什么，而不是相反。相等项也是互相对应的，但是我们认识不相等，只是通过与相等项比较，而不是相反，如此等等。 其次，应该注意，少有这样的事物性质：纯粹而简单，可以依其自身直观而不必取决于任何他物，只需通过我们的经验，或者凭借我们内心中某种光芒来加以直观。我们说，必须细心考察这类事物性质，因为不管我们把怎样的系列称为最简单系列，在该系列中这类事物都保持着同样性质。相反，我们得以知觉其它一切性质，都只是从上述性质中演绎而得的；或者是依据邻近命题直接演绎，或者是通过两、三个或更多个不同的推论来演绎。我们还必须注意这样的推论数量多寡，这样才可以看出他们距离起始的最简单命题远近程度如何。环环相扣，互为因果的事物发展，在一切地方，都正是如此。这就产生了要研究的事物的顺序，任何问题都必须归结于这种事物顺序，才能够以确定无疑的方法加以研究。但是，因为把一切事物都归成类别是不容易做到的，也因为用不着把一切事物都记忆在脑里来集中运用心灵之力把它们加以区别。所以，必须设法训练我们的心灵，使它每遇必需之时，就能够立即分辨事物之不同。照我自己的体会，最合适的方法，就是使我们养成习惯，惯于思考事物中最细微者，我们原已相当灵巧地知觉了的那些事物中最细微者。 再次，还必须注意，我们的研究不应该从探究困难事物开始：我们应该在从事研究某些特定问题之前，首先不经任何选择，接受自行显现的那些真理，然后再看看还有没有其它可以从中演绎出来，然后再看看从其他中还可以演绎出什么，这样逐一进行下去。这样做了以后，还要仔细思考已经发现的这些真理，细心考虑为什么其中的一些比其它一些发现得快速而容易，以及它们是哪些。这样，日后如果我们着手解决某一特定问题，我们就可以判断首先致力于什么对于我们最为有利。例如，如果呈现的是：6为3的两倍；我求6的两倍，则为12；如果我愿意，我再求12的两倍，为24；然后，我很容易就演绎得知：3与6之间、6与12之间有一比例，12与24之间……也是如此；这样，3、6、12、24、48……各数成连比。也许正因为如此，虽然这些演算都是一目了然的，甚至好像有点幼稚，但是，仔细推敲起来，就可以明白：凡属涉及比例或对比关系的问题，是按照怎样的条理性而掩盖着的，我们应该依据怎样的秩序去把它们找出来。只有这里面才包含着整个纯数学科学的总和。 首先，我注意到，求得6的倍数并不比求得3之倍数困难；还注意到，其它也都一样，任二量之比一旦求得，同一比例的无数其它量也都可以得出；困难的性质也没有改变，如果要求的是三个、四个或更多个此种量，因为需要的是逐一分别得出，而不是依据其它量得出。随后，我注意到，设已知量为3和6，虽然我可以很容易得出连比的第三项为12，但是，如果已知为首尾两项3和12，求中项6就不那么容易了。在直观其中条理性的人看来，这里的困难是另一种性质的，完全不同于前者的，因为，如要求得比例中项，必须既注意首尾两项，也注意此两项之比，才可以用除法得到新的一项；这就完全不同于已知两个量而求连比的第三项。我进一步探讨，看一看已知两个量为3和24，求两比例中项6和12之一是否可能也一样容易。这里出现的困难又是另一种性质的，比前两种较为复杂：实际上这里应该注意的不仅仅是一项或两项，而是三个不同项同时注意，以求得第四项。还可以更进一步，看一看：如果仅仅已知3和48，三中项6、12和24之一是否更难得出。乍看起来，似乎肯定无疑，但是，立刻就可以看出：这个困难是可以分割而减少的，即，如果首先只求3和48之间的一个中项，即12，然后求3和12之间的另一中项6，再求12和48之间的中项24；这样，困难也就缩小为上述第二种了。 从上述种种，我注意到，对同一事物的认识是怎样可以通过不同的途径而获得，其中有些途径比别的途径长而艰难。例如，如要求得连比四项3、6、12、24，假设已知连续两项为3和6，或6和12，或12和24，由此求得其它各项是很容易做到的。于是，我们说，要求得的比例是直接考虑的。但是，假设已知为相间两项：3和12，或6和24，由此求其它各项，我们则说，其困难是按照头一种方式间接考虑的。同样，假设已知为首尾两项3和24，由此求中项6和12，则要按照第二种方式间接考虑。我还可以照此进一步进行，由这个单一例子演绎出其它许多推论。这些推论足以使读者知道：要是我说某一命题是直接或间接演绎而得的，是个什么意思；也足以使读者理解：专心思考、精细分辨的人们，从某些浅易可知的起始事物，还可以在其它若干学科中发现许许多多这类命题。 原则七 要完成真知，必须以毫无间断的连续的思维运动，逐一全部审视他们所要探求的一切事物，把它们包括在有秩序的充足列举之中。上面说过的那些不能从起始的自明之理中直接演绎出来的真理，如要归入确定无疑之列，就必须遵守在这里提出的(准则)。因为，推论的连续发展如果历时长久，有时就会有这样的情况：当我们达到这些真理的时候，已经不易记起经历过的全部路程了。因此，我们说，必须用某种思维运动来弥补我们记忆之残缺。例如，如果最初我通过若干演算已经得知：甲量和乙量之间有何种比例关系，然后乙和丙之间，再后丙和丁，最后丁和戊，即使如此，我还是不知道甲和戊之间的比例关系如何，要是我记不得一切项，我就不能从已知各项中得知此一比例关系的究竟。所以，我要用某种连续的思维运动，多次予以全部通观，逐一直观每一事物，而且统统及于其它，直至已经学会如何迅速地由此及彼，差不多任何部分都不必委之于记忆，而是似乎可以一眼望去就看见整个事物的全貌；这样，事实上，既可以减轻记忆的负担，又可以纠正思想之缓慢，而且由于某种原因，还增长了心智的能力。 但是，还得指出，在任何一点上都不要中断这一运动，因为常有这样的情况：想从较远原理中过于急促演绎出什么结论的人，并不通观整个系列的中间环节，他们不够细心，往往轻率地跳过了若干中间环节。然而，只要忽略了这一项，哪怕是微小的一项，串链就会在那里断裂，结论就会完全丧失其确切性。 此外，我们说，要完成真知，列举是必需的，因为，其它准则固然有助于解决许多问题，但是，只有借助于列举，才能够在运用心智的任何问题上，始终作出真实而确定无疑的判断，丝毫也不遗漏任何东西，而是看来对于整体多少有些认识。因此，这里所说的列举，或者归纳，只不过是对于所提问题的一切相关部分进行仔细而准确的调查，使我们得以得出明显而确定的结论，不至于由于粗心大意而忽略了什么，这样，每逢我们运用列举之后，即使所要求的事物我们仍然看不清楚，至少有一点我们比较有知识了，那就是，我们将肯定看出：通过我们已知的任何途径，都是无法掌握这一事物的；而且，假如--也许常常确实如此，--我们确实历经了人类为了认识它而可以遵循的一切途径，我们就可以十分肯定地断言：认识它，非人类心灵所能及。 此外，应该指出，我们所说的充足列举或归纳，仅仅指比不属于单纯直观范围之内的任何其它种类的证明，更能确定无疑地达到真理的那一种；每逢我们不能够把某一认识归结为单纯直观，例如在放弃了三段论式的一切联系的时候，那么，可以完全信赖的就只剩下这一条道路了。因为，当我们从此一命题直接演绎出彼一命题的时候，只要推论是明显的，在这一点上就已经确实是直观了。但是，假如我们从许多互不关联的命题出发推论出某个单一项，我们的悟性能力往往不足以用单纯一次直观把那所有的命题统统概括净尽；在这种情况下，使悟性具有概括所有命题的能力的，是把列举运用得确定无误。这就正如：虽然我们不能一眼看尽并区别稍长一些的串链上每一环节，但是，只要我们已经看清每环与下一环的联结，就足以断言我们也已经发现最后一环与最前一环是怎样联结的。我说这一运用应该是充足的，是因为它往往可能有缺陷，从而可能有很多失误。事实上，有时候，虽然我们可以用一次列举通观许许多多十分明显的事物。但是，只要我们哪怕只是略去最微小的部分，串链就会断裂，结论的确定性也就完全丧失。有时候，我们也能用一次列举包括一切事物，但是，分辨不清每一事物，所以对全部事物的认识也就只是模模糊糊的。