Chapter 5 Chapter Four Temporarily Into Spiritualism

Until I went to Cambridge in October 1890, I had no contact with professional philosophers, either in their books or in person, except Mill.Although I had to devote most of my time to mathematics in the first three years, I did read a lot of philosophy books and did a lot of philosophical debate.A Professor of Philosophy at Merdon, and a disciple of Bradley's, named Harold Jockin, our neighbor at Hetzelmere, and later my uncle's brother-in-law.I told him I was interested in philosophy.Thanks to his kindness, he gave me a list of must-read books.I only remember two items on the list now: one is Bradley's Logic, which he says is good but hard to read; the other is Bosanquet's Logic, which he says is This book is better, but harder.Perhaps against his expectation, I started reading the books on his list.But my reading of philosophy books was interrupted for a period by an accident.In early 1892 I had a mild bout of influenza.

This cold left me with absolutely no energy or interest in doing anything for months. At this time, my work is not doing well.Since I never told anyone about my cold and its aftermath, it was assumed that I messed up my mathematics because I was studying philosophy.I had asked James Ward what I should read.He called me over and told me that a "passed math test" is a "passed math test". From this example of the law of identity, he reasoned that it would be best not to study philosophy until I had passed the Mathematics Honors Examination. It turned out that my grades in mathematics were not as bad as he thought when he advised me.

When I was an undergraduate, the teaching of Mathematics at Cambridge was definitely bad.It was bad, partly because of the prioritization of grades in the honors exam, which was abolished shortly thereafter.Because it is necessary to carefully distinguish the abilities of different candidates, it pays attention to "problems" and does not pay attention to "study of books".Proving a mathematical principle is an insult to the logical understanding.Seriously, the whole subject of mathematics looks like a clever trick to pile up honors marks.The effect of all this on me is to make me think mathematics is disgusting.When I finished my honors exam, I sold all my math books and vowed never to read a math book again.And so, in my fourth year, I plunged into that strange and eccentric world of philosophy with utter joy.

The influence I received was all in the direction of German idealism, either Kant's idealism or Hegel's idealism.There was only one exception, and that exception was Henry Sidgwick.He was the last of the Benthamists alive.At that time, like other young people, I did not pay him due respect.We called him "Old West Season" and thought he was totally out of date.The two men closest to me were James Ward and G.  E．Stoute, the former is a Kantian, the latter a Hegelian.Bradley's Appearance and Reality was published at this time.Stott said that the achievement of this book is ontology to the best of human ability.But neither of these men had more influence on me than MacTarger.MacTague's answer to crude empiricism is Hegelian.Until then, crude empiricism has satisfied me.He said he could use logic to prove that the world is good and the soul is immortal.

He admitted that the proof was lengthy and difficult to understand.No one who studies philosophy can hope to understand this proof unless he has studied a period.I refuse to accept his influence.Gradually the resistance became weaker and weaker, until in 1894, just before I passed the Honors Examination in Moral Sciences, I turned entirely over to a half-Kantian, half-Hegelian metaphysics. After passing the magna cum laude, the next step in your studies is to write a University Researcher's thesis.I chose "Foundations of Geometry" as my title, paying special attention to the influence of "non-Euclidean geometry" on Kant's transcendental feeling.While I was doing this thesis, I was sometimes working on economics and German Social Democracy.Social Democracy in Germany was the title of my first book, based on the work of two winters in Berlin.These two winters and my trip to the United States with my wife in the second year (1896) did a great deal to free me from the intolerance of Cambridge, and made me aware of the German research in pure mathematics, which I had previously learned. Never heard of it.Although I made an oath in the past, I still read a lot of mathematics books, many of which I later found to be irrelevant to my main purpose.I read Darbault's "On Surfaces", Dein's "Theory of Functions of Real Variables", several French books on analysis, Gauss's "General Theory of Surfaces" and Grassmann's "Theory of Extension".It was Whitehead who inspired me to read this book.His book, Universal Algebra, which delighted me, was published not long after this time.This book is mainly concerned with Grassmann's system.But I believe that applied mathematics is more worthy of study than pure mathematics, because applied mathematics is more likely to promote human happiness (I assume this with Victorian optimism).I carefully read Clark Maxwell's "Electricity and Magnetism", and I studied Halts' "Principles of Mechanics".When Hertz succeeded in making electromagnetic waves, I was very happy.I for J. j.Thomson's experimental work was of great interest.I also read books that were more related to my interests, such as De Dikind and Kantor.Frege could have been more helpful to me, but I only found out about him later.

My first philosophy book, On the Foundations of Geometry, was an adaptation of my university researcher's thesis, which now appears to be somewhat muddled.I asked Kant's question "How can geometry be true?" I thought that the only condition for geometry to be true was if space was one of three recognized forms, one of which was Euclidean and the other two This is non-Euclidean (but has the property of maintaining a constant curvature measure.) Einstein's revolution wiped out everything like this idea.The geometry in Einstein's general theory of relativity I said was impossible.The tensor theory on which Einstein was based could have been useful to me.But I never heard of it before he used it.Details aside, I think there is absolutely nothing solid in this early book of mine.

But worse was yet to come.My theory of geometry mainly belongs to the school of Kant.But after that, I dealt with Hegel's dialectic with all my might.I wrote the article "On the Relationship between Number and Quantity", which is purely Hegelian.The gist of the essay is in the first two paragraphs.These two paragraphs are as follows: In this article I want to discuss one of the most fundamental problems in mathematical philosophy.Our interpretation of calculus and its results, and in general all higher mathematics, depends on the point of view we take with regard to this relation. The idea of ​​"continuity," (which has gradually become more pronounced in philosophy as well as in mathematics, and which, especially of late, sweeps away the atomistic view shared by Hume and Kant,) I think holds water. Whether or not it depends on which one is more reliable, quantity or number in mathematics.But there is no need to speak of mathematical considerations here, it is sufficient to consider numbers and quantities in purely logical terms.

The amount I use is always equal to the continuous amount.In this article I have tried to clarify the meaning of the word "continuous". My argument is as follows: first I shall discuss "Numbers"; and show that its extension beyond the positive integers is due to the nature of the gradual assimilation of cardinal numbers, and say less and less about integers, and then I shall discuss the use of numbers for succession, And try to explain that the number itself cannot explain the quantity, but can only be used for comparison with a base number that already has quantity.Visible quantities can only be obtained by analyzing the base.Assuming that quantity is an intrinsic property of quantities, I will discuss two assumptions.The first assumption regards quantity as an irreducible category, and the second assumes quantity as a kind of direct sense data.On the first postulate, we shall see, that an extensive quantity, if divisible, is contradictory, and must therefore be regarded as indeed indivisible, and therefore intensional.But if the quantity of intension is an internal property of several quantities of intension, it is obviously only a relation between them.Therefore, the assumption that "quantity is such a category given a quality" has to be denied.

The assumption that quantity is a sense-data also leads to contradictions, and we are therefore compelled to reject the view that quantity is an intrinsic property of quantities.We should consider it as a category of comparison.We hold that among the things that can be treated quantitatively, there are no common properties, except that contained in the external properties, there are other qualitatively similar things, which can be compared with these things quantitatively.This turns quantity into measure in a broad sense.In my opinion, our former difficulties disappear because of this.However, all relations with numbers are severed at the same time—we say that "quantity" or "measurement" is a completely independent comparative concept.But the discussion of the comparison involved in measure brings back our former difficulties in a new form; and we shall find that although we no longer regard the items compared as quantitative, they are There are quite a few contradictions, similar to those which belong to the quantity itself in the first part of this essay.

Although Gudullah described the article as "an exquisite dialectical masterpiece", I now consider it worthless. When I was younger I had (and probably still have) an almost unbelievable optimism about the conclusions of some of my theories.In 1896 I finished my book on the foundations of geometry, and immediately afterwards worked on my book on the foundations of physics, which was intended to be similarly written.The impression at that time was that the problem of geometry was solved. On the basis of physics, I worked for two years.But the only thing published to express my opinion at that time was the already mentioned article on number and quantity.I was a full-fledged Hegelian then.My purpose is to construct a complete dialectic about science, and finally to prove that all reality belongs to the mind.I accept the Hegelian view that no science is ever right, because all sciences depend on some kind of abstraction.Any abstraction sooner or later leads to contradictions.Wherever Kant and Hegel conflict, I always side with Hegel.Kant's "Principles of Natural Science in Metaphysics" impressed me deeply, and I took detailed notes on it, but I said: "This book is divided into four sections, corresponding to his category list. In each section There are three laws, corresponding to the three categories. But these three laws are often forced, and two are natural."

In the philosophy of physics, two questions particularly interest me.The first is the question of absolute versus relative motion. Newton had an argument showing that rotation must be absolute, not relative.But although this argument disturbs people, they cannot find an answer to it, and the argument to the contrary (that is, that all motion is relative) seems at least as convincing.This mystery has not been solved until Einstein put forward the "Theory of Relativity".From the point of view of Hegel's dialectics, this is a suitable source of self-contradiction: it is not necessary (as I thought then) to find a solution in physics, but it must be admitted that matter is an unreal abstraction effect. No science of matter is logically satisfactory. Another question that concerns me is whether matter consists of atoms separated by empty spaces, or of a plenitude that fills all space?Initially I leaned towards the former view.The most logical explanator of this view is Perskovitch.According to him, an atom occupies only one point in space.All interactions are actions at a distance, just like Newton's law of gravitation. But Farad's experiments produced a different view, and this view is reflected in Clark Maxwell's great book on electricity and magnetism.Whitehead's University Researcher's thesis was on the book.Whitehead urges me to adopt the book's insights and abandon Perskovitch's.In addition to the fact that the empirical argument is biased towards this view, it also has the advantage that it abandons the "interval effect".Interval action has always been implausible, even for Newton.When I took this more modern view, I put a Hegelian costume on it, presenting it as a dialectical transition from Leibniz to Spinoza.This allows me to let what I consider to be logical order prevail over chronological order. A re-reading of what I wrote on the philosophy of physics from 1896 to 1898 now appears to me to be utter nonsense.It's hard for me to imagine not thinking that way.Fortunately, as soon as any such research got to the point where I thought it could be published, I changed my whole philosophy and forgot everything I had done in those two years.But the notes I made at that time may still have historical value.While these notes now seem misguided, I don't think any more so than Hegel's writings.The following are some important passages from the notes I made during those years: On the concept of the dialectic of science (January 1, 1898) Including space and time first, and thereby obtaining an understanding of "phenomena" A dialectic more closely related than to pure logic seems possible.It differs from pure logic perhaps not only by the systematic arrangement of the categories, for there may be what we may call a chemical association between the categories and the senses, leading to new ideas which are formed only by It cannot be obtained by systematic arrangement of pure categories in the future.In this dialectic I should start from the result that quantity is a concept which can only be applied to immediate materials, which, by virtue of its application, become indirect.Therefore, all things dialectically derived from quantity are essentially different from logical categories.None of the logical categories can be applied to purely immediate material.The success of mathematics both supports this view and is explained by it. In the ideas of "continuity" and "fullness," an immediacy that logic cannot find is still there, and it seems possible.In this way, we may have found a way to turn phenomena into "reality", instead of first forming "reality" and then encountering a dualism that does not work. But it must be said that in this dialectic, in all stages except the final stage, we must avoid being too strict in demanding self-justification.Because a sensual component is always there.We cannot regard every contradiction as detrimental to our conception.Some contradictions must be seen as inevitably arising from the sensory element.Before such a dialectic can be constituted, therefore, a principle must be discovered by which to separate the avoidable from the unavoidable contradictions. I believe that the only unavoidable contradictions will be those of quantity, i.e., that two things may be different, even if they are conceptually identical, and that the difference may be a concept.It seems that the inevitability of this paradox derives from the fact that differences can exist in sensations. On the transition from geometry to dynamics it is generally assumed that matter can be defined by one of two properties: extension, or force.But if, as the discussion of geometry suggests, space is purely relative, extension cannot be a property of matter.Extension can only be the function of substance. Thus there remains only force, that is to say, the atom can only be regarded as the inextensible center of force, not spatial by nature, but having a place only by virtue of its interaction.Force can then express itself only by producing motion. The static idea of ​​the balance of forces is deduced from the dynamic idea.Geometry thus involves consideration of matter.Basically matter must be regarded as that which produces motion on other matter.Here we have a mostly relative view of matter, which is desirable.Moreover, if matter is regarded as the last category, the relativity of this view contains contradictions.We must first discuss the laws of motion, and then show that these laws and what they say about matter contain something more, and lead us to some other science. Note: For a dialectical transition from geometry to mechanics, geometry includes the opposition of different parts or shapes in space, which includes motion, and motion includes a matter that not only takes up space, because a A spatial position that can be delimited by its position cannot be moved.Therefore, geometry is impossible without matter in motion. This leads us to kinematics, and from kinematics to mechanics, because motion involves a moving matter, and the motion of this moving matter is relative only to other matter.There must be a reason for movement, since movement is a mutual relationship between bits and pieces of matter, the interaction between these bits and pieces of matter must be the reason.This already contains the laws of motion. Several definitions of matter generally define that matter is that kind of thing in the external sensory data that can be regarded as the logical subject or noumenon because it has less contradiction than any other sensory data. Ⅰ.Definition of Kinematics Matter is such a thing, and spatial relationship is its adjective. We know that in geometry the attempt to make space a logical subject is a total failure; the axioms which make the knowledge of space possible are true only on the condition that space is only an adjective.Therefore, it must be an adjective of something.Even geometry, though otherwise indifferent to matter, generally counts this something as a condition of its possibility.For geometry compares different parts of space; therefore its possibility involves the possibility of movement, that is to say of change of position.As far as geometry is concerned, this does not yet involve time, because how the change of position is caused is irrelevant.Nor does it implicate any property of matter, (the only property involved is that there may be different spatial adjectives without losing their identity.) But these are necessary, since motion is necessary, And motion involves something else besides space, since pure position is immobility.In short, space is immobile, so geometry is impossible without motion, and we need something that can move in space.And the space required by geometry is not just an adjective, but a relational adjective.The final constituents of this kinematic matter must therefore not contain space, but are positioned as points by virtue of their spatial relations.According to the axiom of free movement, these point-formed atoms must (for example) actually move, that is, transform their spatial relations. —but how they move is irrelevant here.Atoms can only be positioned in relation to each other.Only these relations, in their multiple possible values, generate space.So, for example, if there are only two atoms, space is just the line connecting them; if there are three, space is just the plane they lie on. Ⅱ.Definition of motion of matter.Matter is not only something that can move, but it can also cause other things to move; two pieces of matter can affect each other causally, thereby changing their spatial relationship. In the above definitions we have seen that matter must actually move, that is, change its spatial relation to other matter; this change is then one thing, and, according to the law of causality, this change There must be a reason.Nay, if we are to be able to form a dynamics, that is to say, a science of matter in motion, without regard to anything else in the universe, we must be able to find this cause in the concepts we already have, That is to say, find this cause in matter and space relationship.We cannot really form such a science apart from the higher categories.This is proved by the self-contradiction of absolute motion.Therefore, the cause of what appears to be a motion of matter must in fact be something more complex than mere matter or force.So we say that the cause of the motion of matter comes from matter: any two pieces of matter have a mutual causal relationship.This relationship has a tendency to change their spatial relationship (that is, their distance), which is the force. Forces must be reciprocal (third law), since their effect is a change in distance.The change of distance is a reciprocal relation: not only that, unless we think that it can produce finite results in infinitesimal time (which is absurd), its result must be, in a finite time, to the spatial relation Produces a finite change and, therefore, a finite speed.This produces its immediate consequence, which is acceleration (false!) (This is equal to the first law.) Also, for a science of force to hold, the force between two atoms must be their spatial relationship an effect of , since that alone is measurable. (This necessity can also be deduced from the opposite of the law of covariation, because the spatial relationship and force are causally connected.) Therefore, force = f (distance), which is the general form of the law of gravitation.Because experience does not directly confirm this, we have invented a new concept, that is, mass, which has the formula F=mm'f(π)(r). (This includes the second law of motion.) This is the idea that mass (equal to the amount of motion) is constant for the same particle no matter where or when it is.This stems from seeing matter as being (no!).The foregoing makes gravity the final law of mechanics, and the astronomical measurement of mass the fundamental measurement.Matter, therefore, as far as mechanics is concerned, is made up of related things.The relations that constitute these things are: (1) spatial relations (2) causal relations (forces).These causal relationships tend to alter spatial relationships.These relations are themselves measured by their effect on changing spatial relations and are functionally linked to these spatial relations.So their measurement and the auxiliary measurement of quality depend on the measurement of space and time, and therefore finally depend on the measurement of space. Dynamics and Absolute Motion The only way to determine a position and motion (and thus a motion) is with respect to an axis.In order to be perceivable, and in order to be able to give relation to spatial relations, the axis must be material, or rather must be produced by the relation of material points.Therefore motion can only be defined by the relation to matter.But as far as the laws of motion are concerned, what matters is that this matter should have no force (i.e. causal) relation to that matter whose motion is being considered, or indeed to any matter.If it had such a relation, the laws of motion would become inapplicable, and our equations would become untrue.But the laws of motion implicate gravity.If this were universal, there would be no relation of matter which had no power over any other matter.Hence the contradiction.In terms of mechanics, in geometry, our axes should be physical.In mechanics, the axis must be immaterial. How to resolve this contradiction?Obviously, this paradox is so fundamental that it renders a universe of pure forces absurd.In short, apart from space and force, real things must have other adjectives.The relativity of space and force destroys these real things.In practical use, this paradox does not harm the usefulness of mechanics.For, in order for our equations to be practically true, we can always find matter which has no relation at all to any matter whose motion we are studying.But theoretically, we cannot substitute relations for space and force, and the relativity of these relations does not make them incomprehensible.Perhaps there is hope to restore the salience of "here" as the source of absolute position; perhaps we can replace force with "conception" and go to psychology. Theory Matter and Motion Ordinary mechanistic theories (such as those proposed by Styro) start entirely from the dualistic idea of ​​noumenon and attributes (ie, matter and motion).It regards both as real, independent, quantum, and motion is transmitted from matter to matter, but cannot be annihilated.Not only that, this theory holds that there is an absolute space, and the movement of matter takes place in this absolute space.And according to this doctrine of absolute space, it would have to be affirmed (1) that the elements of matter must have extension, (2) that all communication of motion must be due to contact, (things cannot move where there is no contact.) With space The relativity of the two axioms disappear. Instead (1') the elements of things do not contain space, but are positioned as points by their geometrical relations. (2') All activity is activity at a distance, and distance itself is a relation.The replacement of the above two formulations by these two formulations eliminates many paradoxes, for example: (a) the inelastic paradox, because it cannot be deformed, but elastic, because it does not vary due to Collision and loss of energy. (b) Contradiction: The elements of mass must be equal quantitatively, but not chemically.For, if the elements are points, any necessary number of atoms can be packed together in any volume, however small.The last atom cannot be obtained empirically. (c) Contradiction: What is powerless moves at a distance: for according to this definition of matter its most important property is to move at a distance.The fact that it actuates and produces motion, it is totally incomplete.The above view shows that the gravitational force is immediate, and the intermediary object is not opaque to it.Does this view solve the self-contradiction of kinetic energy and potential energy?I do not know yet.It does not resolve the fundamental paradox of absolute motion, namely, that the motion of a system must be considered relative to matter itself, which is not affected by forces.But this concept of matter precludes the existence of any such matter.This is due to the excessive relativity of the definition of matter: matter both moves and is moved by other matter.This definition always makes it impossible to treat matter as a logical subject, a substance, or an absolute. Briefly describe the paradox of absolute motion (1) matter is both active and moved by other matter. (2) The motion of matter is the change in the spatial relation of some other matter. (3) The change of the spatial relationship between matter and matter can only be measured by the constant spatial relation between matter and matter. (4) It is impossible to know that two substances have a constant spatial relation unless they have no dynamic relation to each other and to other substances. (5) But this relation (within 1) constitutes the definition of matter.So (a) changes in the spatial relationship cannot be measured. (b) All motion, and therefore all matter and force, cannot be measured. (c) Mechanics becomes dialectically untenable because of the contradictions arising from the necessary relativity of matter. (d) Matter and motion cannot form a self-existing world and cannot constitute "reality". Notice.The relativity of motion leads to infinite regression in space, and this regression has a corresponding infinite regression in time, and this regression in time caused by cause and effect is also fatal.Movement has a double relativity in space and time, leading to two infinite regressions.It is important to note that, strictly speaking, the paradox does not arise for kinematic reasons, but only when matter is considered to be the cause of motion. pay attention to.The necessity of absolute motion is inseparable from trying to think of mass as inherent.The relativity of mass eliminates this necessity.Regarding "fullness", maybe this will help. Can we form a dialectical transition from the matter of the point to the "fullness"? The self-contradiction of absolute motion occurs only in dynamics, not in kinematics.So it turns out that the error lies in our thinking about forces, that is, about how atoms are connected to each other.The definition we give to the elements of matter is: to move other substances, and to be moved by other substances.But in this definition, elements are not self-existing at all.On the contrary, all adjectives of any element, except mass, are formed entirely by relation to all other elements.Quality is revealed only in these relationships.The inevitable path, therefore, seems to be to regard our atoms as mere adjectives of a single entity, or, if we prefer, as the same entity appearing in different places with the same result.For, in either case, what makes them characteristic is only of the adjectival nature.The correct view seems to be that of Lotze: if M (matter) is the whole, and A, B, become A'B', then M=A(A,B,...)=A(A',B', ...), it is this equation that connects A and B, not any immediate transient causal action.Since we still firmly regard matter as self-subsisting, we shall now say that M (matter) is a whole whose space and motion are only adjectives; Although in a sense there may be centers of cohesion, as in the spiritual world.That is to say, there may be certain adjectives, assigned to points in space, that give specific properties to each separate point.But since all space is an adjective of matter, in a sense matter exists everywhere.In this way, the distinction between ether and coarse matter may be preserved, and the laws of matter must come to some extent from the invariance of the whole, just like the above-mentioned M = A (A, B, ...) that as in the formula.How this principle is applied is perhaps a purely empirical matter to be investigated.It is likely that this view will resolve the paradox of absolute motion.For, apart from this whole, there is now no matter, and this is permanently free from force.But matter unaffected by forces is exactly what we need to resolve this paradox.Our dialectic principle seems to consist in gradually making the whole more apparent.Our separated particles first appear to be related to other particles, then they appear to be related to all other particles, and finally they appear to be completely separated particles, which is a mistake.Speaking of this, let's talk about "enrichment".With regard to the fullness, there is a rough idea that, in different places, there are really different parts of matter, but there is no distinction between parts.This view of enrichment is clearly hopeless.The correct view is that the same substance (necessarily a whole) exists at every point in space, and it is not extended as it is commonly said, but contains all extensions. ("Light is in the soul, her whole is in each part", The Judges' Game.) Our principle of motion, then, is in the permanence of the whole, not in the habit of the monad.So, from the beginning to the end, the overall obviousness is gradually increased. However, I don't know how to extend this process beyond mechanics. Notice.With regard to the kinematics of a motion in full, and to the question of absolute motion (or the first law), it is important to consider that it may not be possible to have a motion which is not a change.If change occurs only as a result of a change in motion, this accounts for the first law and allows motion in a uniform fullness.Note that our wholeness is not really expanded, the space is in it, not it in space.Space must be seen as only one aspect of its differentiation.The same goes for time.This results in qualitatively different adjectives, attached to each point of space and time.But actually space and time are abstracted from these qualitative adjectives, not the other way around.Like this, there will be differences due to changes in time or place.For the emergence of the movement, this is exactly what we need.Interestingly, in a sense, the entire universe exists at every point in space and time. （这是来自我们以前对物质所下的定义。一件东西存在于它所活动的地方，物质处处都活动。）论科学的逻辑每种科学都用有限的一些基本观念来进行研究，这些基本观念的数目比所有基本观念的数目要小些。那么，每种科学可以看做是企图全用它自己的观念来构成一个宇宙。 因此，在科学的逻辑里，我们所应做的是，用适当的一套观念来构成一个不包含矛盾的世界。（只包含由于这些观念不完全而有的不可避免的矛盾。在任何科学里，凡不是这种不可避免的矛盾，在逻辑上都是应该受到非难的。）从广泛的知识论的观点来讲，整个科学如果看成是形而上学，也就是说，独立自存的知识，就是应该受到非难的。因此，我们首先必须把科学的假设安排一下，这样才能留下最低限度的矛盾；然后对这些假定或观念加以补充，这种补充可以去掉该科学的特殊矛盾。然后进而走到另一科学，也可以用同样的方法来对待。 举例来说，数（算术的基本观念）包含某种可以数的东西。于是就有了几何学，因为空间是感觉上唯一可以直接测量的元素。而且，几何学包含某种可以定位的东西，和某种能动的东西，因为一个位置是不能动的。于是就有了物质和物理学。 但是，我认为两个类型的辩证的过渡是必须加以区别的：一个类型的过渡（象自数目到可加上数的东西的过渡、自空间到物质的过渡）只是对一个抽象的观念提供其必要和真实存在的补充，而对这个抽象的科学留给它本身的充分的确实性。在这件事上，几乎没有矛盾，只是不完全而已。另一种过渡（象自连续过渡到分离，自物质过渡到力，到（？））是真正黑格尔意义的辩证。这说明，该科学的观念基本上是自我矛盾的。若在形而上学上构成真实，非彻底代之以另一个观念不可。