I have dwelt upon these misconceptions to show why Mill was driven in defence of experience to assume the burthen of proving paradoxes which would be destructive to our very capacity for obtaining experience.Mill prided himself with some reason on his 'four methods.'Although they have been severely criticised,(93)they have,I take it,a genuine value;and,if we ask how they can be valuable in spite of his errors,a satisfactory answer may perhaps be given.In the first place,his assumptions represent one genuine 'moment'in all reasoning about facts.The primitive intellect may be supposed to regard facts as simply conjoined,and to be guided by 'association of ideas.'The early generalisations of which Mill speaks --'fire burns,''water drowns,'and so forth are really of this kind,and are apparently formed even by dogs and monkeys.Mill is quite right,moreover,in holding that a purely empirical element runs through the whole fabric of knowledge.The error,I think,is in his failure to allow for the way in which it is modified in scientific construction.The ultimate element out of which that construction is developed is always an observation of fact,but the fact means a definite relation of time and space.We start from a 'fact,'but it is not as a simple unanalysable unit,but as something which already is the base of a relation.The unit which corresponds to the final cell out of which tissue is composed is not properly a fact,but a 'truth.'We do not say simply 'this is,'but this is so and so,and has a certain order and configuration.This is gradually elaborated into physical science by the help of the geometrical and numerical relations already implied.Thus,causation,or the connection between phenomena,is not simple collocation,but supposes continuity.The unconditional sequence which Mill identifies with 'causation'does not,and cannot,give the 'cause,'though it does indicate 'causal connection.'So long as two things are entirely separate and distinguishable,we cannot say,in the full sense,that one is the cause of the other;but the connection,if proved,proves that there is a cause which may or may not be discoverable.Brown was right in thinking that something was still wanting,though his mode of filling the gap by an intuition was erroneous.Mill's answer that the 'intuition'was needless left the difficulty where Hume had put it.Two facts are supposed to be unrelated and yet always combined.That states a difficulty,and only pronounces it to be insoluble.It has,in fact,to be surmounted by scientific hypotheses.Thunder and lightning,for example,are causally connected,but not so that lightning can be properly called the cause of thunder.They are regarded as due to a common cause to the processes which we call electric disturbance,and so forth.We cannot give the 'law'or state the casual connection adequately,but we regard them as indicating some common element,which is continuous and capable of being described in terms of pure number and geometry.Hence any observation,as soon as we begin to reason,may be regarded as a particular case of some general law,or rather,as being conceivably a case of an indefinite number of laws.Not only so,but any law under which it may be arranged is 'necessary'if all the conditions be restored.The process by which we select one of the possible formula,therefore,comes to eliminating all the formula which are incorrect when various conditions are altered.We all along assume that some coherent system of 'laws'is possible,or that the rule is there if only we can discover it.If lightning goes once with thunder,we are entitled to say not only that it may go with thunder hereafter,but that it must go with thunder under the same conditions.Therefore the simple inference from an empirical conjunction is justified by the 'law of causation'or the 'uniformity of nature.'
Now,Mill's 'four methods'are applicable to the merely empirical conjunctions,which form a large part of our knowledge,and are implied in every stage.The methods do,in fact,I take it,form an approximately accurate mode of dealing with such knowledge.His cases are,for the most part,selected from the sciences,chemistry in particular,where in point of fact our knowledge is still purely empirical,and we can only assert a collocation,or sequence,without bringing it under a more general rule.He also observes,and the remark must be remembered,that he is trying to give a method of proof,rather than of discovery.(94)If the scientific theory be true,these purely empirical truths will hold good,although from them alone the theory might not have been discoverable.The phenomenon which we call the fall of a stone will be presented when an unsupported stone is near the earth,although the law of gravitation requires an application of methods not summed up by simple observation of conjoined phenomena.The most unsatisfactory part of the 'four methods'results from this view.(95)The process of discovery is not sufficiently represented by the case of A occurring with or without B.The sciences which have risen to be quantitative advance by showing how a variety of cases can be brought within some general and precise formula,and every approximation to,or deviation from,the law be exactly measured.Mill pays too little attention to this essential characteristic,partly,perhaps,because he considers mathematics as simply one part of the 'inductive'or empirical sciences.
