Engels' Dialectics of Nature

Appendix: Notes to Anti-Dühring

The following notes were written by Engels towards the end of 1877 and beginning of 1878, after the publication in separate form of the first section (Philosophy) of "Anti- Dühring," to the pages of which he refers at the beginning of each note. In view of their great intrinsic importance and their close connection with the subjects dealt with in Dialectics of Nature, they are included here as an appendix.

(a) On the Prototype of Mathematical "Infinity" in the Real World.

Re pp. 17-18: Concordance of thought and being - Mathematical infinity.

The fact that our subjective thought and the objective world are subject to the same laws, and that consequently too in the final analysis they cannot be in contradiction to one another in their results, but must coincide, governs absolutely our whole theoretical thought. It is the unconscious and unconditional premise for theoretical thought. Eighteenth century materialism, owing to its essentially metaphysical character, investigated this premise only as regards content. It restricted itself to the proof that the content of all thought and knowledge must derive from sensuous experience, and revived the principle: nihil est in intellectu, quod non fuerit in sensu. It was modern idealistic, but at the same time dialectical, philosophy, and especially Hegel, which for the first time investigated it also as regards form. In spite of all the innumerable arbitrary constructions and fantasies that we encounter here, in spite of the idealist, topsy-turvy, form of its result - the unity of thought and being - it is undeniable that this philosophy proved the analogy of the processes of thought to those of nature and history and vice versa, and the validity of similar laws for all these processes, in numerous cases and in the most diverse fields. On the other hand, modern natural science has extended the principle of the origin of all thought content from experience in a way that breaks down its old metaphysical limitation and formulation. By recognising the inheritance of acquired characters, it extends the subject of experience from the individual to the genus; the single individual that must have experienced is no longer necessary, its individual experience can be replaced to a certain extent by the results of the experiences of a number of its ancestors. If, for instance, among us the mathematical axioms seem self-evident to every eight-year-old child, and in no need of proof from experience, this is solely the result of "accumulated inheritance." It would be difficult to teach them by a proof to a bushman or Australian negro.

In the present work dialectics is conceived as the science of the most general laws of all motion. Therein is included that their laws must be equally valid for motion in nature and human history and for the motion of thought. Such a law can be recognised in two of these three spheres, indeed even in all three, without the metaphysical philistine being clearly aware that it is one and the same law that he has come to know.

Let us take an example. Of all theoretical advances there is surely none that ranks so high as a triumph of the human mind as the discovery of the infinitesimal calculus in the last half of the seventeenth century. If anywhere, it is here that we have a pure and exclusive feat of human intelligence. The mystery which even to-day surrounds the magnitudes employed in the infinitesimal calculus, the differentials and infinites of various degree, is the best proof that it is still imagined that what are dealt with here are pure "free creations and imaginings " of the human mind, to which there is nothing corresponding in the objective world. Yet the contrary is the case. Nature offers prototypes for all these imaginary magnitudes.

Our geometry has, as its starting point, space relations, and our arithmetic and algebra numerical magnitudes, which correspond to our terrestrial conditions, which therefore correspond to the magnitude of bodies that mechanics terms masses - masses such as occur on earth and are moved by men. In comparison to these masses, the mass of the earth seems infinitely large and indeed terrestrial mechanics treats it as infinitely large. The radius of the earth == ∞, this is the basic principle of all mechanics in the law of falling. But not merely the earth but the whole solar system and the distances occurring in the latter in their turn appear infinitely small as soon as we have to deal with the distances reckoned in light years in the stellar system visible to us through the telescope. We have here, therefore, already an infinity, not only of the first but of the second degree, and we can leave it to the imagination of our readers to construct further infinities of a higher degree in infinite space, if they feel inclined to do so.

According to the view prevailing in physics and chemistry today, however, the terrestrial masses, the bodies with which mechanics operates, consists of molecules, of smallest particles which cannot be further divided without abolishing the physical and chemical identity of the body concerned. According to W. Thomson's calculations, the diameter of the smallest of these molecules cannot be smaller than a fifty-millionth of a millimetre. But even if we assume that the largest molecule itself attains a diameter of a twentyfive- millionth of a millimetre, it still remains an infinitesimally small magnitude compared with the smallest mass dealt with by mechanics, physics, or even chemistry. Nevertheless, it is endowed with all the properties peculiar to the mass in question, it can represent the mass physically and chemically, and does actually represent it in all chemical equations. In short, it has the same properties in relation to the corresponding mass as the mathematical differential has in relation to its variable. The only difference is that what seems mysterious and inexplicable to us in the case of the differential, here seems a matter of course and as it were obvious.

Nature operates with these differentials, the molecules, in exactly the same way and according to the same laws as mathematics does with its abstract differentials. Thus, for instance, the differential of x3==3x2dx, where 3xdx2 and dx3 are neglected. If we put this in geometrical form, we have a cube with sides of length x, the length being increased by the infinitely small amount dx. Let us suppose that this cube consists of a sublimated element, say sulphur; and that three of the surfaces around one corner are protected, the other three being free. Let us now expose this sulphur cube to an atmosphere of sulphur vapour and lower the temperature sufficiently; sulphur will be deposited on the three free sides of the cube. We remain quite within the ordinary mode of procedure of physics and chemistry in supposing, in order to picture the process in its pure form, that in the first place a layer of thickness of a single molecule is deposited on each of these three sides. The length x of the sides of the cubes will have increased by the diameter of a molecule dx. The content of the cube x3 has increased by the difference between x3 and x3+3x2dx+3xdx2+dx3, where dx3, a single molecule and 3xdx2, three rows of length x+dx, consisting merely of lineally arranged molecules, can be neglected with the same justification as in mathematics. The result is the same, the increase in mass of the cube is 3x2dx.

Strictly speaking dx3 and 3xdx2 do not occur in the case of the sulphur molecule, because two or three molecules cannot occupy the same space, and the cube's increase of bulk is therefore exactly 3x2dx+3xdx+dx. This is explained by the fact that in mathematics dx is a linear magnitude, while it is well known that such lines, without thickness or breadth, do not occur independently in nature, hence also the mathematical abstractions have unrestricted validity only in pure mathematics. And since the latter neglects 3xdx2+dx3, it makes no difference.

Similarly in evaporation. When the uppermost molecular layer in a glass of water evaporates, the height of the water layer, x, is decreased by dx, and the continual flight of one molecular layer after another is actually a continued differentiation. And when the warm vapour is once more condensed to water in a vessel by pressure and cooling, and one molecular layer is deposited on another (it is permissible to leave out of account secondary circumstances that make the process an impure one) until the vessel is full, then literally an integration has been performed which differs from the mathematical one only in that the one is consciously carried out by the human brain, while the other is unconsciously carried out by nature. But it is not only in a transition from the liquid to the gaseous state and vice versa that processes occur which are completely analogous to those of the infinitesimal calculus.

When mass motion, as such, is abolished - by impact - becomes transformed into heat, molecular motion, what is it that happens but that the mass motion is differentiated? And when the movements of the molecules of steam in the cylinder of the steam engine become added together so that they lift the piston by a definite amount, so that they become transformed into mass motion, have they not been integrated? Chemistry dissociates the molecules into atoms, magnitudes of more minute mass and spatial extension, but magnitudes of the same order, so that the two stand in definite, finite relations to one another. Hence, all the chemical equations which express the molecular composition of bodies are in their form differential equations. But in reality they are already integrated in the atomic weights which figure in them. For chemistry calculates with differentials, the mutual proportions of their magnitudes being known.

Atoms, however, are in no wise regarded as simple, or in general as the smallest known particles of matter. Apart from chemistry itself, which is more and more inclining to the view that atoms are compound, the majority of physicists assert that the luminiferous ether, which transmits light and heat radiations, likewise consists of discrete particles, which, however, are so small that they have the same relation to chemical atoms and physical molecules as these have to mechanical masses, that is to say as d2x to dx. Here, therefore, in the now usual notion of the constitution of matter, we have likewise a differential of the second degree, and there is no reason at all why anyone, to whom it would give satisfaction, should not imagine that analogies of d3x, d4x, etc., also occur in nature.

Hence, whatever view one may hold of the constitution of matter, this much is certain, that it is divided up into a series of big, well-defined groups of a relatively massive character in such a way that the members of each separate group stand to one another in definite finite mass ratios, in contrast to which those of the next group stand to them in the ratio of the infinitely large or infinitely small in the mathematical sense. The visible system of stars, the solar system, terrestrial masses, molecules and atoms, and finally ether particles, each of them form such a group. It does not alter the case that intermediate links can be found between the separate groups. Thus, between the masses of the solar system and terrestrial masses come the asteroids (some of which have a diameter no greater than, for example, that of the Reuss principality, younger branch), meteors, etc. Thus, in the organic world the cell stands between terrestrial masses and molecules. These intermediate links prove only that there is no leap in nature, precisely because nature is composed entirely of leaps.

In so far as mathematics calculates with real magnitudes, it also employs this mode of outlook without hesitation. For terrestrial mechanics the mass of the earth is regarded as infinitely large, just as for astronomy terrestrial masses and the corresponding masses of meteors are regarded as infinitely small, and just as the distances and masses of the planets of the solar system are reduced to nothing as soon as astronomy investigates the constitution of our system of stars extending beyond the nearest fixed stars. As soon, however, as the mathematicians withdraw into their impregnable fortress of abstraction, so-called pure mathematics, all these analogies are forgotten, infinity becomes something totally mysterious, and the manner in which operations are carried out with it in analysis appears as something absolutely incomprehensible, contradicting all experience and all reason. The stupidities and absurdities by which mathematicians have rather excused than explained their mode of procedure, which remarkably enough always leads to correct results, exceed the most pronounced apparent and real fantasies, e.g. of the Hegelian philosophy of nature, about which mathematicians and natural scientists can never adequately express their horror. What they charge Hegel with doing, viz. pushing abstractions to the extreme limit, they do themselves on a far greater scale. They forget that the whole of so-called pure mathematics is concerned with abstractions, that all their magnitudes, taken in a strict sense, are imaginary, and that all abstractions when pushed to extremes are transformed into nonsense or into their opposite. Mathematical infinity is taken from reality although unconsciously, and consequently also can only be explained from reality and not from itself, from mathematical abstraction. And, as we have seen, if we investigate reality in this regard we come also upon the real relations from which the mathematical relation of infinity is taken, and even the natural analogies of the way in which this relation operates. And thereby the matter is explained. (Hæckel's bad reproduction of the identity of thinking and being.) But also the contradiction between continuous and discrete matter, see Hegel.

(b) On the "Mechanical Conception of Nature.

Note 2. Re page 46: The various forms of motion and the sciences dealing with them.

Since the above article appeared (Vorwärts, Feb. 9, 1877), Kekulé (Die wissenschaftlichen Ziele and Leistungen der Chemie [The Scientific Aims and Achievements of Chemistry] has defined mechanics, physics, and chemistry in a very similar way:

"If this idea of the nature of matter is made the basis, one could define chemistry as the science of atoms and physics as the science of molecules, and then it would be natural to separate that part of modern physics which deals with masses as a special science, reserving for it the name of mechanics. Thus mechanics appears as the basic science of physics and chemistry, in so far as in certain aspects and especially in certain calculations both of these have to treat their molecules or atoms as masses."

It will be seen that this formulation differs from that in the text and in the previous note only by being rather less definite. But when an English journal (Nature)[1] translated the above statement of Kekulé to the effect that mechanics is the statics and dynamics of masses, physics the statics and dynamics of molecules, and chemistry the statics and dynamics of atoms, then it seems to me that this unconditional reduction of even chemical processes to something merely mechanical unduly restricts the field, at least of chemistry. And yet it is so much the fashion that, for instance, Hæckel continually uses "mechanical" and "monistic" as having the same meaning, and in his opinion "modern physiology ... in its field allows only of the operation of physico-chemical - r in the wider sense, mechanical - forces." (Perigenesis.[2])

If I term physics the mechanics of molecules, chemistry the physics of atoms, and furthermore biology the chemistry of proteins, I wish thereby to express the transition of each of these sciences into the other, hence both the connection, the continuity, and the distinction, the discrete separation. To go further and to define chemistry as likewise a kind of mechanics seems to me inadmissible. Mechanics - in the broader or narrower sense - knows only quantities, it calculates with velocities and masses, and at most with volumes. When the quality of bodies comes across its path, as in hydrostatics and aerostatics, it cannot achieve anything without going into molecular states and molecular motion, it is itself only a mere auxiliary science, the prerequisite for physics. In physics, however, and still more in chemistry, not only does continual qualitative change take place in consequence of quantitative change, the transformation of quantity into quality, but there are also many qualitative changes to be taken into account whose dependence on quantitative change is by no means proven. That the present tendency of science goes in this direction can be readily granted, but does not prove that this direction is the exclusively correct one, that the pursuit of this tendency will exhaust the whole of physics and chemistry. All motion includes mechanical motion, change of place of the largest or smallest portions of matter, and the first task of science, but only the first, is to obtain knowledge of this motion. But this mechanical motion does not exhaust motion as a whole. Motion is not merely change of place, in fields higher than mechanics it is also change of quality. The discovery that heat is a molecular motion was epoch-making. But if I have nothing more to say of heat than that it is a certain displacement of molecules, I should best be silent. Chemistry seems to be well on the way to explaining a number of chemical and physical properties or elements from the ratio of the atomic volumes to the atomic weights. But no chemist would assert that all the properties of an element are exhaustively expressed by its position in the Lothar Meyer curve,[3] that it will ever be possible by this alone to explain, for instance, the peculiar constitution of carbon that makes it the essential bearer of organic life, or the necessity for phosphorus in the brain. Yet the "mechanical" conception amounts to nothing else. It explains all change from change of place, all qualitative differences from quantitative, and overlooks that the relation of quality and quantity is reciprocal, that quality can become transformed into quantity just as much as quantity into quality, that, in fact, reciprocal action takes place. If all differences and changes of quality are to be reduced to quantitative differences and changes, to mechanical displacement, then we inevitably arrive at the proposition that all matter consists of identical, smallest particles, and that all qualitative differences of the chemical elements of matter are caused by quantitative differences in number and by the spatial grouping of those smallest particles to form atoms. But we have not got so far yet.

It is our modern natural scientists' lack of acquaintance with any other philosophy than the most mediocre vulgar philosophy, like that now rampant in the German universities, which allows them to use expressions like "mechanical" in this way, without taking into account, or even suspecting, the consequences with which they thereby necessarily burden themselves. The theory of the absolute qualitative identity of matter has its supporters - empirically it is equally impossible to refute it or to prove it. But if one asks these people who want to explain everything "mechanically" whether they are conscious of this consequence and accept the identity of matter, what a variety of answers will be heard!

The most comical part about it is that to make "materialist" equivalent to "mechanical" derives from Hegel, who wanted to throw contempt on materialism by the addition "mechanical." Now the materialism criticised by Hegel - the French materialism of the eighteenth century - was in fact exclusively mechanical, and indeed for the very natural reason that at that time physics, chemistry, and biology were still in their infancy, and were very far from being able to offer the basis for a general outlook on nature. Similarly Hæckel takes from Hegel the translation: causae efficientes==mechanically acting causes, and causae finales==purposively acting causes; where Hegel, therefore, puts mechanical as equivalent to blindly acting, unconsciously acting, and not as equivalent to mechanical in Hæckel's sense of the word.[4] But this whole antithesis is for Hegel himself so much a superseded standpoint that he does not even mention it in either of his two accounts of causality in his Logic - but only in his History of Philosophy, in the place where it comes historically (hence a sheer misunderstanding on Hæckel's part due to superficiality!) and quite incidentally in dealing with teleology (Logic, III, II, 3) where he mentions it as the form in which the old metaphysics conceived the antagonism of mechanism and teleology, but otherwise treating it as a long superseded standpoint.[5] Hence Hæckel copied incorrectly in his joy at finding a confirmation of his "mechanical" conception and so arrives at the beautiful result that if a particular change is produced in an animal or plant by natural selection it has been effected by a causa efficiens, but if the same change arises by artificial selection then it has been effected by a causa finalis! The breeder as causa finalis! Of course a dialectician of Hegel's calibre could not be caught in the vicious circle of the narrow opposition of causa efficiens, and causa finalis. And for the modern standpoint the whole hopeless rubbish about this opposition is put an end to because we know from experience and from theory that both matter and its mode of existence, motion, are uncreatable and are, therefore, their own final cause; while to give the name effective causes to the individual causes which momentarily and locally become isolated in the mutual interaction of the motion of the universe, or which are isolated by our reflecting mind, adds absolutely no new determination but only a confusing element. A cause that is not effective is no cause.

N.B. Matter as such is a pure creation of thought and an abstraction. We leave out of account the qualitative difference of things in comprehending them as corporeally existing things under the concept matter. Hence matter as such, as distinct from definite existing pieces of matter, is not anything sensuously existing. If natural science directs its efforts to seeking out uniform matter as such, to reducing qualitative differences to merely quantitative differences in combining identical smallest particles, it would be doing the same thing as demanding to see fruit as such instead of cherries, pears, apples, or the mammal as such instead of cats, dogs, sheep, etc., gas as such, metal, stone, chemical compound as such, motion as such. The Darwinian theory demands such a primordial mammal, Hæckel's pro-mammal, but it, at the same time, has to admit that if this pro-mammal contains within itself in germ all future and existing mammals, it was in reality lower in rank than all existing mammals and exceedingly crude, hence more transitory than any of them. As Hegel has already shown, Encyclopædia I, p.199,[6] this view is therefore "a one-sided mathematical standpoint," according to which matter must be looked upon as having only quantitative determination, but, qualitatively, as identical originally, "no other standpoint than that" of the French materialism of the eighteenth century. It is even a retreat to Pythagoras, who regarded number, quantitative determination as the essence of things.

In the first place, Kekulé. Then: the systematising of natural science, which is now becoming more and more necessary, cannot be found in any other way than in the interconnections of phenomena themselves. Thus the mechanical motion of small masses on any heavenly body ends in the contact of two bodies, which has two forms, distinct from one another only in degree, viz. friction and impact. So we investigate first of all the mechanical effect of friction and impact. But we find that they are not thereby exhausted: friction produces heat, light, and electricity, impact produces heat and light if not electricity also - hence conversion of motion of masses into molecular motion. We enter the realm of molecular motion, physics, and investigate further. But here too we find that molecular motion does not represent the conclusion of the investigation. Electricity passes into and arises from chemical reaction. Heat and light, ditto. Molecular motion becomes transformed into motion of atoms - chemistry. The investigation of chemical processes is confronted by the organic world as a field for research, that is to say, a world in which chemical processes take place, although under different conditions, according to the same laws as in the inorganic world, for the explanation of which chemistry suffices. In the organic world, on the other hand, all chemical investigations lead back in the last resort to a body - protein - which, while being the result of ordinary chemical processes, is distinguished from all others by being a self-acting, permanent chemical process. If chemistry succeeds in preparing this protein, a so-called protoplasm, with the specific nature which it obviously had at its origin, a specificity, or rather absence of specificity, such that it contains potentially within itself all other forms of protein (though it is not necessary to assume that there is only one kind of protoplasm), then the dialectical transition has also been accomplished in reality, hence completely accomplished. Until then, it remains a matter of thought, alias of hypothesis. When chemistry produces protein, the chemical process will reach out beyond itself, as in the case of the mechanical process above, that is, it will come into a more comprehensive realm, that of the organism. Physiology is, of course, the chemistry and especially the physics of the living body, but with that it also ceases to be specially chemistry, on the one hand its domain becomes restricted but, on the other hand, inside this domain it becomes raised to a higher power.


(c) On Nageli's Incapacity to Know the Infinite.

Nägeli,[7] pp. 12, 13.

Nägeli first of all says that we cannot know real qualitative differences, and immediately afterwards says that such "absolute differences" do not occur in Nature! P.12.

In the first place, every qualitative infinity has many quantitative gradations, e.g. shades of colour, hardness and softness, length of life, etc., and these, although qualitatively distinct, are measurable and knowable.

In the second place, qualities do not exist but only things with qualities and indeed with infinitely many qualities. Two different things always have certain qualities (properties attaching to corporeality at least) in common, others differing in degree, while still others may be entirely absent in one of them. If we consider two such extremely different things - e.g. a meteorite and a man - together but in separation, we get very little out of it, at most that heaviness and other corporeal properties are common to both. But an infinite series of other natural objects and natural processes can be put between the two things, permitting us to complete the series from meteorite to man and to allocate to each its place in the interconnection of nature and thus to know them. Nägeli himself admits this.

Thirdly, our various senses might give us absolutely different impressions as regards quality. According to this, properties which we experience by means of sight, hearing, smell, taste, and touch would be absolutely different. But even here the differences disappear with the progress of investigation. Smell and taste have long ago been recognised as allied senses belonging together, which perceive conjoint if not identical properties; sight and hearing both perceive wave oscillations. The sense of touch and sight are mutually complementary to such an extent that from the appearance of an object we can often enough predict its tactile properties. And, finally, it is always the same "I" that receives and elaborates all these different sense impressions, that comprehends them into a unity, and likewise these various impressions are provided by the same thing, appearing as its common properties, and therefore helping us to know it. To explain these different properties, accessible only to different senses, to bring them into connection with one another, is therefore the task of science which so far has not complained because we have not a general sense in place of the five special senses, or because we are not able to see or hear tastes and smells.

Wherever we look, nowhere in nature are there to be found such "qualitatively or absolutely distinct fields," which are put forward as incomprehensible. The whole confusion springs from the confusion about quality and quantity. In accordance with the prevailing mechanical view, Nägeli regards all qualitative differences as explained only in so far as they can be reduced to quantitative differences (on which what is necessary to be said will be found elsewhere), or because quality and quantity are for him absolutely distinct categories. Metaphysics.

"We can know only the finite, etc." This is quite correct in so far as only finite objects enter the sphere of our knowledge. But the statement needs to be completed by this: "fundamentally we can know only the infinite." In fact all real, exhaustive knowledge consists solely in raising the single thing in thought from singularity into particularity and from this into universality in seeking and establishing the infinite in the finite, the eternal in the transitory. The form of universality, however, is the form of self-completeness, hence infinity; it is the comprehension of the many finites in the infinite. We know that chlorine and hydrogen within certain limits of temperature and pressure and under the influence of light, combine with an explosion to form hydrochloric acid gas, and as soon as we know this, we know also that this takes place everywhere and at all times where the above conditions are present, and it can be a matter of indifference, whether this occurs once or is repeated a million times, or on how many heavenly bodies. The form of universality in nature is law, and no one talks more of the eternal character of the laws of nature than the natural scientist. Hence if Nägeli says that the finite is made impossible to establish by not desiring to investigate merely this finite, adding instead something eternal to it, then he denies either the possibility of knowing the laws of nature or their eternal character. All true knowledge of nature is knowledge of the eternal, the infinite, and hence essentially absolute.

But this absolute knowledge has an important drawback. Just as the infinity of knowable matter is composed of the purely finite, so the infinity of thought which knows the absolute is composed of an infinite number of finite human minds, working side by side and successively at this infinite knowledge, committing practical and theoretical blunders, setting out from erroneous, one-sided, and false premises, pursuing false, tortuous, and uncertain paths, and often not even finding the right one when they run their noses against it (Priestley[8]).

The cognition of the infinite is therefore beset with double difficulty and from its very nature can only take place in an infinite asymptotic progress. And that fully suffices us in order to be able to say: the infinite is just as much knowable as unknowable, and that is all that we need.

Curiously enough, Nägeli says the same thing: "We can know only the finite, but also we can know all that is finite that comes into the sphere of our sensuous perception." The finite that comes into the sphere, etc., constitutes in sum precisely the infinite, for it is just from this that Nägeli has derived his idea of the infinite! Without this finite, etc., he would have indeed no idea of the infinite!

(Bad infinity, as such, to be dealt with elsewhere.)

(Before this investigation of infinity comes the following):

(1) The "insignificant sphere" in regard to space and time.

(2) The "probably defective elaboration of the sense organs."

(3) That we can only know the finite, transitory, changing and what differs in degree, the relative, etc. (as far as), "we do not know what time, space, force and matter, motion and rest, cause and effect are."

It is the old story. First of all one makes sensuous things into abstractions and then one wants to know them through the senses, to see time and smell space. The empiricist becomes so steeped in the habit of empirical experience, that he believes that he is still in the field of sensuous knowledge when he is operating with abstractions. We know what an hour is, or a metre, but not what time and space are! As if time was anything other than just hours, and space anything but just cubic metres! The two forms of existence of matter are naturally nothing without matter, empty concepts, abstractions which exist only in our minds. But, of course, we are also not supposed to know what matter and motion are! Of course not, for matter as such and motion as such have not yet been seen or otherwise experienced by anyone, but only the various, actually existing material things and forms of motion. Matter is nothing but the totality of material things from which this concept is abstracted, and motion as such nothing but the totality of all sensuously perceptible forms of motion; words like matter and motion are nothing but abbreviations in which we comprehend many different sensuously perceptible things according to their common properties. Hence matter and motion cannot be known in any other way than by investigation of the separate material things and forms of motion, and by knowing these, we also pro tanto know matter and motion as such. Consequently, in saying that we do not know what time, space, motion, cause, and effect are, Nägeli merely says that first of all we make abstractions of the real world through our minds, and then cannot know these self-made abstractions because they are creations of thought and not sensuous objects, while all knowing is sensuous measurement! This is just like the difficulty mentioned by Hegel, we can eat cherries and plums, but not fruit, because no one has so far eaten fruit as such.

When Nägeli asserts that there are probably a whole number of forms of motion in nature which we cannot perceive by our senses, that is a poor apology, equivalent to the suspension - at least for our knowledge - of the law of the uncreatability of motion. For they could certainly be transformed into motion perceptible to us! That would be an easy explanation, of, for instance, contact electricity.

Ad vocem Nägeli. Impossibility of conceiving the infinite. As soon as we say that matter and motion are not created and are indestructible, we are saying that the world exists as infinite progress, i.e. in the form of bad infinity, and thereby we have conceived all of this process that is to be conceived. At the most the question still arises whether this process is an eternal repetition - in a great cycle - or whether the cycles have upward and downward portions.


1. See quotation in Appendix II, p. 329.

2. See Appendix II, p. 330.

3. In which atomic volumes are plotted against atomic weights.

4., 5. See Appendix 11, p. 330.

6. See Appendix II, p. 331.

7. C. von Nägeli. Über die Schranken der naturwissenschaftlichen Erkenntnis [The Limits of Scientific Knowledge], September, 1877.

8. Priestley discovered oxygen without knowing it.

Transcribed in 2001 for MEIA by jjazz@hwcn.org