In other words,because our logic requires a basis in fact,and the fact must be given by experience,the logic is itself dependent upon experience.If 'inconceivable'be limited,as Ithink it should be limited in logic,to the contradictory,an inconceivable proposition is incredible because it is really no proposition at all.We may,no doubt,believe statements which are implicitly contradictory.but when the contradiction is made explicit,the belief becomes impossible.Similarly we may disbelieve statements which appear to be contradictory;and when the error is exposed,we may believe what was once 'inconceivable.'That only shows that our thoughts are often in a great muddle,and in great need of logical unification.It does not prove any incoherence in the logical process itself.
IV.CAUSATION
We can now proceed to what may be called the constructive part of the logic.We have got rid of proofs from intuitions,from definitions,and from inconceivabilities,and the question remains how we can prove anything.All knowledge is inductive.It is all derived from facts;it proceeds from particulars to particulars;the previous coexistence of sequences which have been observed constitute our whole raw material.What,then,serves to bind facts together?or how are we to know that facts are bound together,or that any two given facts have this relation?The fundamental postulate of science is the so-called 'uniformity of nature.'But Nature,as it is seen by the unscientific mind,is anything but uniform.There are,it is true,certain simple uniformities which frequently recur.Fire burns,water drowns,stones thrown up fall down;and such observations are the germs of what we afterwards call scientific 'laws.'But things are constantly happening of which we can give no account.Catastrophes occur without any assignable 'antecedent';storm and sunshine seem to come at random;and the same combination of events never recurs in all its details.
Variety is as manifest as uniformity.How can cosmos be made out of chaos?How do we come to trace regularity in this bewildering world of irregularities?From any fact taken by itself,as Hume had fully shown,we can deduce no necessity for any other fact.
The question is,whether we are to account for the belief in uniformity by an 'intuition'or by James Mill's universal solvent of 'association of ideas.'J.S.Mill was fully convinced of the efficacy of this panacea,but he sees difficulties over which his father had passed.If association explains everything,the tie between ideas ought to be stronger,it might be supposed,in proportion to the frequency of their association.The oftener two facts have been joined,the more confidently we should expect a junction hereafter.But this does not hold true universally.Achemist,as Mill observes,analyses a substance;and assuming the accuracy of his results,we at once infer a general law of nature from 'a single instance.'But if any one from the beginning of the world has seen that crows are black,and a single credible witness says that he has seen a grey crow,we abandon at once a conjunction which seemed to rest upon invariable and superabundant evidence.Why is a 'single instance'sufficient in one case,and any number of instances insufficient in the other?
'Whoever can answer this question,'says Mill,'knows more of the philosophy of logic than the wisest of the ancients,and has solved the problem of induction.'(57)Here Mill again professes to set metaphysics aside.He has nothing to do with 'ontology.'He deals with 'physical,'not 'efficient,'causes.He does not ask whether there be or be not a 'mysterious'tie lying behind the phenomena and actually producing them.(58)He is content to lay down as his statement of the 'law of causation'that there is an invariable succession between 'every fact in nature'and 'some other fact which has preceded it.'This,he assumes,is a truth,whatever be the nature of things in themselves.The true account is rather that he will show that 'ontology'is a set of meaningless phrases.He can answer his problem without it.Causation is,in fact,conceived by him as it was conceived by all the psychologists,including Brown;and he has simply to show that Brown's supposed 'intuition'is a superfluity.His treatment of the question gives the really critical part of his philosophy.It leads to some of the results which have been most highly and,as I think,most deservedly praised.It also leads to some of his greatest errors,and shows the weak point of his method.
Mathematical knowledge,as Mill remarks,has nothing to do with causation.Every geometrical or arithmetical formula is true without supposing change.One theorem does not 'cause'the others;it 'implies'them.The most complex and the most simple are mutually involved in the single perception,though our knowledge of one may be the cause of our knowing the others.
