4-62 



NATURE 



[April 1 6, 1874 



laws of motion, though the Reviewer asserts that it is. Further, 

 by the words I have italicised, Newton implicitly describes Galileo 

 as having asserted these laws of motion, if not as giatuitoiis 

 hypotheses (which he says they are not), then as a priori intui- 

 tions. For a proposition which is confirmed by experiment, and 

 which is said to agree with experience, must have been entertained 

 before the alleged verifications could be reached. And as before 

 he made his experiments on falling bodies and projectiles, Galileo 

 had no facts serving as an inductive basis for the Second Law of 

 Motion, the law could not have been arrived at by induction. 



Let me end what I have to say on this vexed question by add- 

 ing a further reason to those I have already given, for saying that 

 physical axioms cannot be established experimentally. The 

 belief in their experimental establishment rests on the licit 

 assumption that experiments can be made, and conclusioris 

 drawn from them, without any truths being postulated. It is 

 forgotten that there is a foundation of preconceptions without 

 which the perceptions and inferences of the physicist cannot 

 A3.xA—prcconceplions zuhich are the prodiicls of simpler expe- 

 riences than those yielded by consciously-made experiments. 

 Passing over the many which do not immediately con- 

 cern us, I will name only that which does, — the exact quan- 

 titative relation between cause and effect. It is taken by the 

 chemist as a truth needing no proof, that if two volumes of 

 hydrogen unite with one volume of oxygen to form a certain 

 quantity of water, four volumes of hydrogen uniting with two 

 volumes of oxygen will form double the quantity of water. If a 

 cubic foot of ice at 32° is liquefied by a specified quantity of heat, 

 it is taken to be unquestionable that three times the quantity of 

 heat will liquefy three cubic feet. And similarly with mechanical 

 forces, the unhesitating assumption is that if one unit of force 

 acting in a given direction produces a certain result, two units 

 will produce twice the result. Every process of measurement in 

 a physical experiment takes this for granted ; as we see in one of 

 the simplest of them — the process of weighing. If a measured 

 quantity of metal, gravitating towards the earth, counterbalances 

 a quantity of some other substance, the truth postulated in every 

 act of weighing is, that any multiple of such weight will counter- 

 balance an equi-multiple of such substance. That is to say, each 

 unit of force is assumed to work its equivalent of effect in the 

 direction in which it acts. Now this is nothing else than the 

 assumption which the Second Law of Motion expresses in respect 

 to effects of another kind. " If any force generates a motion, a 

 double force will generate a double motion," &c., &c. ; and when 

 carried on to the composition of motions, the law is, similarly, 

 the assertion that any other force, acting in any other direction, 

 will similarly produce in that direction a proportionate motion. 

 So that the law simply asserts the exact equivalence of causes 

 and effects of this particular class, while all physical experiments 

 assume this exact equivalence among causes and effects of all 

 classes. Hence, the proposal to prove the laws of motion expe- 

 rimentally, is the proposal to make a wider assumption for the 

 purpose of justifying one of the narrower assumptions included 

 in it. 



Reduced to its briefest form the argument is this : — If definite 

 quantitative relations between causes and effects be assumed 

 h priori, then, the Second Law of Motion is an immediate corol- 

 lary. If there are not definite quantitative relations between 

 causes and effects, all the conclusions drawn from physical expe- 

 riments are invalid. And further, in the absence of this h priori 

 assumption of equivalence, the quantified conclusion from any 

 experiment may be denied, and any other quantification of the 

 conclusion asserted. Herbert Spencer 



Mr. Spencer's letter in Nature, vol. ix. p. 420, is likely to give 

 to such of your readers as have not followed the controversy in 

 which he is engaged a false notion of the issues therein. Mr. 

 Spencer writes as though the views of the nature of physical 

 truth that were objected to by Prof. Tait and myself amounted 

 to the ascription of our knowledge of sundry physical laws to 

 organised ancestral instead ol individual experiences. In one 

 portion of his reply to me he intimates the same, as, for in- 

 stance, where he says of me ; — 



"His argument proceeds throughout on the assumptionth.it 

 I understand a priori truths after the ancient manner as truths 

 independent of experience ; and he shows this more than tacitly 

 where he ' trusts ' that he is attacking one of the last attempts 

 to deduce the laws of nature from our innei , consciousness. 

 Manifestly a leading thesis of one of the works he professes to 

 review is entirely unknown to him — the thesis that forms of 

 thought, and consequently those intuitions which those forms of 



thought involve, result entirely from the effects of experiences 

 organised and inherited " (" Replies to Criticisms," p. 332). 



But, in his "First Principles," Mr. Spencer expresses him- 

 self far too cleai-ly for him to be able to assign the above as his 

 views at that time on these so-called ii priori truths. Speaking 

 of the indestructibility of matter, one of the three truths in 

 question, he siys : — 



" The annihilation of matter is unthinkable for the same 

 reason that the creation of matter is unthinkable — and its inde- 

 structibility thus becomes an .( priori cognition of the highest 

 order — not one that results from a. long continued registry of experi- 

 ences gradually organised into an irret^ersible mode of thought; 

 but one that is given in the form of all experiences whatever." 



For the second of the truths he claims a similar authority ; 

 while for the third — the Persistence of Force — he claims a yet 

 higher warrant : — ■ 



" Deeper than demonstration — deeper even than definite 

 cognition — deep as the very nature of mind is the postulate at 

 which we have arrived {i.e. the Persistence of Force). Its 

 authority transcends all other tvhatever ; Jor not only is it given in 

 the constitution of our otun consciousness, but it is impossible to 

 imagine a consciousness so constituted as not to give it." (" First 

 Principles," p. 192). 



Had Mr. Spencer confined himself to defending such an 

 () priori origin of physical truths as he now seems inchned to put 

 forward, I should never have compared his theories to those of 

 the Ptolemaists. But I can leave it with confidence to the 

 readers of Nature to decide between us as to whether the above 

 passages do not show that at the time when they were written 

 Mr. Spencer understood a priori, as there applied, in a manner 

 very like the " ancient manner," and whether he did not main- 

 tain that these a priori truths were indeed "truths independent 

 of experience." 



The Author of the Article on Herbert Spencer 

 IN THE British Quarterly Review 



[The Editor, very properly wishing, I doubt not, to end the 

 controversy, has sent to me the foregoing letter in proof. My 

 comment on it is very brief. 



Had the reviewer read the " Principles of Psychology," placed 

 at the head of his article apparently for form's sake only, he 

 would, not, I think, have made the above rejoinder. 



That view of the d priori origin of physical truths which 

 the Reviewer now seems to think defensible is the view 

 implied in "First Principles" and the view set forth in the 

 "Principles of Psychology," published years before. Tacitly 

 throughout that work, and explicitly near the end, in a chapter 

 on "Reason," the doctrine is that the "forms of thought" 

 themselves are the products of experience. If the nervous system 

 as a whole and in all its structures has been evolved by converse 

 between the organism and the environment, the fundamental 

 principles of its action, the very " forms of all experiences " have 

 been evolved. Experience itself grew into definiteness gradually. 

 And if the very form of our thought, the very frame-work of our 

 consciousness, has been thus moulded, the inability to conceive 

 a mode of thinking fundamentally different, is simply the result 

 of inability to invert the fundamental action of the structures by 

 which we think. — H. S.] 



On the Word "Axiom" 



In reference to the controversy between Mr. Spencer and his 

 reviewer about Sir I. Newton's calling his laws of motion 

 " axioms," it is to be observed that there is a certain ambiguity 

 in the word. "Axiom "is from ajiiiw (I demand), and would 

 thus signify a first principle to be taken for granted. It does not, 

 of course, carry with it the meaning of a necessary judgment 

 which cannot be contradicted. Whatever may be considered the 

 ground of Euclid's " axioms" so called, Euclid himself did not 

 apjily that name to them ; Init the first nine he called " common 

 notions," and the last three (which are peculiar to geometry) he 

 placed among the postulates '^bixaKo'yi\)xa.ra), and heads them 

 with "let it be granted." Now it is clear, from Newton's own 

 words, that in calling his Leges motus "axioms, " he does not 

 imply that they are necessary judgments, but that he requires 

 them first of all to be granted (however established) in onlcr to 

 the following reasoning. In other words, they arepo^tulatcs, like 

 Euclid's last three "axioms." In our modern use of the words 

 " axiom," " axiomatic," there is always implied the ground why 

 a proposition is demanded as granted, viz., because its necessity 

 is self evident ; but this wider use is not required by etymology, 

 or (I think) in inteipreling all ancient writings. F.M.S. 



