56o 



NA TURE 



[Oct. 25, 1877 



We shall probably never succeed in explaining definitely why 

 the origin of a chemical compound and of a crystal must be the 

 necessary result of known forces and motions of elementary 

 atoms and molecules. This will be the case still less with the 

 formation of cells, with the growth of organisms, with the propa- 

 gation and inheritance of peculiarities. And yet we may, even 

 in these ilomains, speak of causal knowledge with some show of 

 right, only the elements which constitute this knowledge are not 

 simple forces and motions, but very complicated combinations of 

 these, which are not analysed further. Our causal knowledge 

 will arrive at perfection when we succeed in predicting future 

 events with the same certainty and exactness as astronomers do. 

 Now we already find certain indications of this in the chemistry 

 of compoiinds and in organic morphology, since it is possible 

 to make deductions from certain stages of development of an 

 orqanism with regard to earlier or later stages of the same. And 

 a time will arrive when the organic laws of the still youthful 

 history of development of the individual and of the still younger 

 history of development of the species will have been more 

 investigated, and when we need no longer presuppose ontogenetic 

 and phylogenetic necessity as a matter of course, but when we 

 will also be able to understand the cause of this necessity. 



The objection will perhaps be raised that causal knowledge 

 certainly consists of our understanding the necessity, as in the 

 case of mechanics, but that this does not apply in domains where 

 we must start from uninvestigated compound objects. The 

 mechanics of tlie heavens is based upon general gravitation and 

 centrifugal force, and both are simple forces acting in a straight 

 line. But both are hypotheses, which rest upon our experience 

 and of the reason of which we are ignorant. Astronomy reveals 

 to us the necessity of astronomical phenomena only under the 

 supposition of facts we have experienced — not the necessity in 

 iltelf. If we were to demand that to our knowledge the "why?" 

 should be clear, there would not even be any astronomical nor 

 yet any physical knowledge. In the organic domains causal 

 knowledge is entitled to the same imporlance as physical know- 

 ledge is in the inorganic field. By experience we know a system 

 of forces and motions, for example, the cell. We ascertain 

 ceitain general facts relating to this system (in the same way as 

 with gravitation and centrifugal force in the heavens), and we 

 use these facts for further deductions. Our insight into the 

 necessity of some process of growth consists in our recognising 

 this process as a necessary consequence of those facts. 



Our knowledge of natural things therefore rests upon our being 

 able to measure them, either by themselves or by one another. 

 Another method of observation leads us to the same result. We 

 understand and master something perfectly, if vee create it our- 

 selves, because in this case we see its cause. The only thing in 

 the domain of knowledge, which, based upon our sensual per- 

 ceptions, we can accomplish, is mathematics. The tenor of this 

 foimal science is perfectly clear to us, because, indeed, it is the 

 product of our own mind. We can therefore also understand 

 real things with certainty, as far as we find mathematical ideas, 

 number, magnitude, and everything which mathematics deduces 

 from these, realised in them. Natural knowledge therefore 

 consists in our applying mathematical methods to natural pheno- 

 mena ; to understand a natural event means nothing else as it 

 were, than to repeat it in thought, to reproduce it in our mind. 



While designating natural knowledge as mathematical and at 

 the same time as relative, which judges things according to a 

 measure deduced from themselves, I depart considerably from 

 the views of my predecessor. Prof. Du Bois Reymond. He con- 

 siders it to be a condition of natural knowledge, that we should 

 succeed in reducing the changes in the material world to motions 

 of atoms caused by their central forces which are independent of 

 time, or in other words, in resolving natural phenomena into the 

 mechanics of atoms. 



While Du Bois Reymond 'thus starts from the undeniable 

 fact that a compound can only be known from its parts, yet 

 he stops not at the finite and reil parts, but continues the 

 division down to the real unitUs, which are unthinkable, and 

 thus he marks out the conditions for impossible absolute know- 

 ledge. But as we do not crave divine but only human know- 

 ledge, we may not ask more of the latter than that in each finite 

 sphere it should advance as far as mathematical understanding ; 

 and the saying of Kant, that in each special natural science we 

 can find only as much real science as we can find mathematics in 

 it, is after all still quite correct. 



If Uu Bois Reymond wishes to continue the analysis of matter 

 down to atoms with simple central forces, he carries a favourite 

 method of modem physics and physiology to extremes, and if he 



shows that this way of proceeding does not lead to understanding, 

 he destroys the claims of exclusive adherence to the domain of 

 science, which the employers of this method sometimes raise. 

 If physics and physical physiology go back to supposed atoms, 

 material points, elements of volume which we imagine to be 

 infinitely small, then this hypothesis is justified inasmuch as the 

 real chemical molecules are so small that we may, without error 

 of calculation, consider space to be continuously filled with matter. 

 For instance, for a molecule of albumen, consisting of numerous 

 atoms of carbon, hydrogen, oxygen, and nitrogen, we may sub- 

 stitute a mass differential of this compound. At all events it is 

 useful to make this hypothesis, as it must be seeniiow far a con- 

 ception of this kind can be treated mathematically, and as from 

 the result we may draw conclusions backwards witli regard to 

 the composition of matter. 



But we must beware of the opinion which is frequently asso- 

 ciated with this method, that it alone is natural science and that 

 knowledge can only be gained by employing it. In this case 

 we would have to confine our desire to understand nature to a 

 single domain, and we would lose others which are capable of 

 safe confirmation. Natural knowledge need not necessarily 

 begin with hypothetical and the smallest unknown things. It 

 begins wherever matter has shaped itself to unities of the same 

 order, which may be compared to and measured by one another, 

 and wherever such unities combine to form compound unities of 

 a higher order, and yield a measure for their comparison with 

 one another. Natural knowledge may begin at every age from 

 the organisation or composition of matter ; at the atom of che- 

 mical elements, which forms the chemical compounds; at the 

 molecule of the compounds, which composes the crystal ; at the 

 crystalline granule, which composes the cell and its parts ; at 

 the cell, which builds up the organism ; at the organism or 

 individual, which becomes the element of the formation of 

 species. Each natural scientific discipline has its justification 

 essentially in itself. 



Our knowledge of nature is therefore always a mathematical 

 one, and consists either in simple measurement, as in the mor- 

 phological and descriptive natural sciences, or in causal measure- 

 ment, as in the physical and physiological sciences. By means 

 of mathematics, however, by weight, measure, or number, we 

 can only understand relative or quantitative differences. Actual 

 qualities, absolutely different properties, escape our understand- 

 ing, since we possess no measure for them. We cannot conceive 

 really qualitative differences, because qualities cannot be com- 

 pared. This is an important fact for our attempts to under- 

 stand nature. Its consequences are, that if within nature 

 there are domains which are qualitively or absolutely dif- 

 ferent, scientific knowledge is only possible separately within 

 each single one of them, and that no connecting bridge leads 

 from one domain into another. But another consequence is 

 that, as far as we can investigate nature continuously, as far as 

 our measuring knowledge advances without gaps, and especially 

 as far as we understand one phenomenon through another, or 

 can prove it to have arisen from the other, that absolute differ- 

 ences, chasms which cannot be filled, do not exist at all in 

 nature. 



I have tried to determine the capacity of the Ego, the accessi- 

 bility of nature, and the essence of human understanding. It is 

 easy now to fix the limits of natural knowledge. 



We can know only what our senses acquaint us with, and this 

 is limited in time and space to an infinitesimal domain, and 

 perhaps only to a part of the natural phenomena occurring in 

 this domain, on account of a deficient development of our organs 

 of sense. Of that with which we are acquainted at all, we can 

 only know the finite, the changeable and perishable, only what 

 is relative and differs by degrees, because we can only apply 

 mathematical ideas to natural things, and can judge the latter 

 only by the measures we have gained from themselves. Of all 

 that is endless or eternal, of all that is stable or constant, of all 

 absolute differences we have no conception. We have a perfect 

 idea of an hour, a metre, a kilogramme, but we have no idea of 

 time, space, matter and force, motion and rest, cause and effect. 



The extent and limit of our possible natural knowledge we 

 may shortly and exactly state thus: — We can only knmv the 

 finite, but we can kiic,^' all the finite which comes within reach oj 

 our sensual perception. 



If we are clearly conscious of this limitation of our knowledge 

 we free natural observation from many difficulties and errors, 

 which consist, on the one hand, in the attempt to investigate not 

 only the really finite, but a mixture of the finite and the eternal, 

 which is uninvestigable ; and, on the other hand, in our not 



