The two connections may interfere,and we have to consider how they can be disentangled.This leads to a distinction to which he attaches,very rightly,I think,the highest importance.In some cases,the correct version of the facts can be obtained by simply superposing the laws of simpler cases.A body moves to the north under certain conditions;but other conditions force it to move also east or south.We then have only to combine the two 'laws,'and to say that it is moving both north and east,that is,north-east,or perhaps to interpret rest as an equal movement to both north and south.This,as he remarks,represents the general case in regard to mechanical phenomena.We have simply to combine two rules to get what is called in dynamics 'the composition of forces';and,in accordance with this phase,he uses the general phrase,'the composition of causes.'(64)But,as he observes,this principle is in many cases not applicable.In chemical combinations,in particular,we cannot infer the properties of the compound from the properties of the components.The laws of simple substances will not give us the laws of the product,and we can only learn these derivative laws by experiment.This holds,still more conspicuously,of organised bodies.From considering the properties of its chemical constituents separately you cannot deduce the properties of the human body.We thus come to a kind of knot in the web;we are at a deadlock,because the laws from which we start are superseded by an entirely different set of laws.Mill marks this by speaking of 'heteropathic laws.'(65)Such laws are not analysable into simple laws.He thinks,indeed,that 'heteropathic laws'are --at least 'in some cases may be derived from the separate laws,according to a fixed principle.'The fact to which he calls attention is undeniable.We discover countless laws as to the properties of bodies which it is impossible at present either to resolve into simpler laws,or to deduce from the laws of the constituent elements.Such laws are properly 'empirical.'The observation of the facts asserted is the sole guarantee for our belief in their truth;and they can he reduced under no more general formula.Is this,however,simply a challenge to the man of science to inquire further,or does it oppose an insuperable obstacle to further scientific researches?Mill avowedly limits himself to 'our present state of knowledge.'He recognised that Grove,in his Correlation of Forces,(66)made out a strong,though still only a probable,case for believing that a 'heteropathic law'may represent a complete transformation of one set of forces into another.Heat,light,and magnetism may be all different manifestations of a single force --not so much causes of one another as 'convertible into one another.'(67)Grove,as Mill adds,is not,as might be supposed,deviating into ontology,but giving a strictly philosophical statement.Mill is here speaking of a great principle,imperfectly known at the time,which has been accepted by modern science,and he is quite ready to welcome it.It is,however,noticeable that he still guards himself against admitting any intrusion of 'necessity.'He will not allow that the dependence of the properties of compounds upon these elements must result in all cases 'according to a fixed principle.'The meaning of this may appear from his later assault upon the doctrine that 'like produces like.'This he reckons among the fallacies which he discovers in all manner of pestilent a priori philosophising.Descartes,Spinoza,Leibniz,and Coleridge have all been guilty of it in various forms.(68)We are therefore under no obligation to go further when we come to totally disparate phenomena in our series.We have unravelled our web sufficiently when we find laws disappearing and being superseded by a totally different set of laws,not describable even in the same language.That we may be forced to be content with such a result is undeniable.But it is equally true that one main end of scientific theorists is to get round this difficulty.
Without inquiring in what sense the axiom that 'like produces like'may be fallacious,we must at least admit that to give a scientific law --that is,a rule by which one set of events is deducible from another --we must be able to express it in terms of some single measure.Til I we can get such a statement,we have not the complete formula.There is a breach of continuity in our theories,which we try to remove by reducing all the forces to measures assignable in terms of space and number.The hypothesis of an ether and vibrating atoms enables us to regard phenomena as corresponding in some way to the laws which,as Mill says,can be compounded by simple superposition,without introducing heterogeneous terms.Though he does not condemn this hypothesis,Mill regards it with a certain suspicion as an attempt to wander into ontology,and the search for what is in its nature inaccessible.(69)At any rate,it does not appear to him that further inquiry is necessary when we come to an irreducible breach of continuity.to a case in which one set of phenomena is simply superseded by another,instead of being transformable into it.If a compound is made of certain elements exclusively,a physicist would clearly infer that its properties must be a result of the properties of the elements according to 'some fixed principle.'Mill is only prepared to admit that this may be the case.The physicist,again,seeks for a mode of stating the principle in theorems capable of being combined and superposed,whereas Mill holds that our knowledge may have come to an ultimate insuperable end.
V.PLURALITY OF CAUSES
