Chapter VIII. How <i>A Priori</i> Knowledge is Possible

by Bertrand Russell

　　Immanuel Kant is generally regarded as the greatest of the modernphilosophers. Though he lived through the Seven Years War and the FrenchRevolution, he never interrupted his teaching of philosophy at Königsbergin East Prussia. His most distinctive contribution was the invention ofwhat he called the 'critical' philosophy, which, assuming as a datum thatthere is knowledge of various kinds, inquired how such knowledge comes tobe possible, and deduced, from the answer to this inquiry, manymetaphysical results as to the nature of the world. Whether these resultswere valid may well be doubted. But Kant undoubtedly deserves credit fortwo things: first, for having perceived that we have a prioriknowledge which is not purely 'analytic', i.e. such that the oppositewould be self-contradictory, and secondly, for having made evident thephilosophical importance of the theory of knowledge.

　　Before the time of Kant, it was generally held that whatever knowledge wasa priori must be 'analytic'. What this word means will be bestillustrated by examples. If I say, 'A bald man is a man', 'A plane figureis a figure', 'A bad poet is a poet', I make a purely analytic judgement:the subject spoken about is given as having at least two properties, ofwhich one is singled out to be asserted of it. Such propositions as theabove are trivial, and would never be enunciated in real life except by anorator preparing the way for a piece of sophistry. They are called'analytic' because the predicate is obtained by merely analysing thesubject. Before the time of Kant it was thought that all judgements ofwhich we could be certain a priori were of this kind: that in allof them there was a predicate which was only part of the subject of whichit was asserted. If this were so, we should be involved in a definitecontradiction if we attempted to deny anything that could be known apriori. 'A bald man is not bald' would assert and deny baldness of thesame man, and would therefore contradict itself. Thus according to thephilosophers before Kant, the law of contradiction, which asserts thatnothing can at the same time have and not have a certain property,sufficed to establish the truth of all a priori knowledge.

　　Hume (1711-76), who preceded Kant, accepting the usual view as to whatmakes knowledge a priori, discovered that, in many cases which hadpreviously been supposed analytic, and notably in the case of cause andeffect, the connexion was really synthetic. Before Hume, rationalists atleast had supposed that the effect could be logically deduced from thecause, if only we had sufficient knowledge. Hume argued—correctly,as would now be generally admitted—that this could not be done.Hence he inferred the far more doubtful proposition that nothing could beknown a priori about the connexion of cause and effect. Kant, whohad been educated in the rationalist tradition, was much perturbed byHume's scepticism, and endeavoured to find an answer to it. He perceivedthat not only the connexion of cause and effect, but all the propositionsof arithmetic and geometry, are 'synthetic', i.e. not analytic: in allthese propositions, no analysis of the subject will reveal the predicate.His stock instance was the proposition 7 + 5 = 12. He pointed out, quitetruly, that 7 and 5 have to be put together to give 12: the idea of 12 isnot contained in them, nor even in the idea of adding them together. Thushe was led to the conclusion that all pure mathematics, though a priori,is synthetic; and this conclusion raised a new problem of which heendeavoured to find the solution.

　　The question which Kant put at the beginning of his philosophy, namely'How is pure mathematics possible?' is an interesting and difficult one,to which every philosophy which is not purely sceptical must find someanswer. The answer of the pure empiricists, that our mathematicalknowledge is derived by induction from particular instances, we havealready seen to be inadequate, for two reasons: first, that the validityof the inductive principle itself cannot be proved by induction; secondly,that the general propositions of mathematics, such as 'two and two alwaysmake four', can obviously be known with certainty by consideration of asingle instance, and gain nothing by enumeration of other cases in whichthey have been found to be true. Thus our knowledge of the generalpropositions of mathematics (and the same applies to logic) must beaccounted for otherwise than our (merely probable) knowledge of empiricalgeneralizations such as 'all men are mortal'.

　　The problem arises through the fact that such knowledge is general,whereas all experience is particular. It seems strange that we shouldapparently be able to know some truths in advance about particular thingsof which we have as yet no experience; but it cannot easily be doubtedthat logic and arithmetic will apply to such things. We do not know whowill be the inhabitants of London a hundred years hence; but we know thatany two of them and any other two of them will make four of them. Thisapparent power of anticipating facts about things of which we have noexperience is certainly surprising. Kant's solution of the problem, thoughnot valid in my opinion, is interesting. It is, however, very difficult,and is differently understood by different philosophers. We can,therefore, only give the merest outline of it, and even that will bethought misleading by many exponents of Kant's system.

　　What Kant maintained was that in all our experience there are two elementsto be distinguished, the one due to the object (i.e. to what we havecalled the 'physical object'), the other due to our own nature. We saw, indiscussing matter and sense-data, that the physical object is differentfrom the associated sense-data, and that the sense-data are to be regardedas resulting from an interaction between the physical object andourselves. So far, we are in agreement with Kant. But what is distinctiveof Kant is the way in which he apportions the shares of ourselves and thephysical object respectively. He considers that the crude material givenin sensation—the colour, hardness, etc.—is due to the object,and that what we supply is the arrangement in space and time, and all therelations between sense-data which result from comparison or fromconsidering one as the cause of the other or in any other way. His chiefreason in favour of this view is that we seem to have a prioriknowledge as to space and time and causality and comparison, but not as tothe actual crude material of sensation. We can be sure, he says, thatanything we shall ever experience must show the characteristics affirmedof it in our a priori knowledge, because these characteristics aredue to our own nature, and therefore nothing can ever come into ourexperience without acquiring these characteristics.

　　The physical object, which he calls the 'thing in itself',(1) he regardsas essentially unknowable; what can be known is the object as we have itin experience, which he calls the 'phenomenon'. The phenomenon, being ajoint product of us and the thing in itself, is sure to have thosecharacteristics which are due to us, and is therefore sure to conform toour a priori knowledge. Hence this knowledge, though true of allactual and possible experience, must not be supposed to apply outsideexperience. Thus in spite of the existence of a priori knowledge,we cannot know anything about the thing in itself or about what is not anactual or possible object of experience. In this way he tries to reconcileand harmonize the contentions of the rationalists with the arguments ofthe empiricists.

　　(1) Kant's 'thing in itself' is identical in definition with thephysical object, namely, it is the cause of sensations. In the propertiesdeduced from the definition it is not identical, since Kant held (in spiteof some inconsistency as regards cause) that we can know that none of thecategories are applicable to the 'thing in itself'.

　　Apart from minor grounds on which Kant's philosophy may be criticized,there is one main objection which seems fatal to any attempt to deal withthe problem of a priori knowledge by his method. The thing to beaccounted for is our certainty that the facts must always conform to logicand arithmetic. To say that logic and arithmetic are contributed by usdoes not account for this. Our nature is as much a fact of the existingworld as anything, and there can be no certainty that it will remainconstant. It might happen, if Kant is right, that to-morrow our naturewould so change as to make two and two become five. This possibility seemsnever to have occurred to him, yet it is one which utterly destroys thecertainty and universality which he is anxious to vindicate forarithmetical propositions. It is true that this possibility, formally, isinconsistent with the Kantian view that time itself is a form imposed bythe subject upon phenomena, so that our real Self is not in time and hasno to-morrow. But he will still have to suppose that the time-order ofphenomena is determined by characteristics of what is behind phenomena,and this suffices for the substance of our argument.

　　Reflection, moreover, seems to make it clear that, if there is any truthin our arithmetical beliefs, they must apply to things equally whether wethink of them or not. Two physical objects and two other physical objectsmust make four physical objects, even if physical objects cannot beexperienced. To assert this is certainly within the scope of what we meanwhen we state that two and two are four. Its truth is just as indubitableas the truth of the assertion that two phenomena and two other phenomenamake four phenomena. Thus Kant's solution unduly limits the scope of apriori propositions, in addition to failing in the attempt atexplaining their certainty.

　　Apart from the special doctrines advocated by Kant, it is very commonamong philosophers to regard what is a priori as in some sensemental, as concerned rather with the way we must think than with any factof the outer world. We noted in the preceding chapter the three principlescommonly called 'laws of thought'. The view which led to their being sonamed is a natural one, but there are strong reasons for thinking that itis erroneous. Let us take as an illustration the law of contradiction.This is commonly stated in the form 'Nothing can both be and not be',which is intended to express the fact that nothing can at once have andnot have a given quality. Thus, for example, if a tree is a beech itcannot also be not a beech; if my table is rectangular it cannot also benot rectangular, and so on.

　　Now what makes it natural to call this principle a law of thoughtis that it is by thought rather than by outward observation that wepersuade ourselves of its necessary truth. When we have seen that a treeis a beech, we do not need to look again in order to ascertain whether itis also not a beech; thought alone makes us know that this is impossible.But the conclusion that the law of contradiction is a law of thoughtis nevertheless erroneous. What we believe, when we believe the law ofcontradiction, is not that the mind is so made that it must believe thelaw of contradiction. This belief is a subsequent result ofpsychological reflection, which presupposes the belief in the law ofcontradiction. The belief in the law of contradiction is a belief aboutthings, not only about thoughts. It is not, e.g., the belief that if we thinka certain tree is a beech, we cannot at the same time think that itis not a beech; it is the belief that if the tree is a beech, itcannot at the same time be not a beech. Thus the law ofcontradiction is about things, and not merely about thoughts; and althoughbelief in the law of contradiction is a thought, the law of contradictionitself is not a thought, but a fact concerning the things in the world. Ifthis, which we believe when we believe the law of contradiction, were nottrue of the things in the world, the fact that we were compelled to thinkit true would not save the law of contradiction from being false; and thisshows that the law is not a law of thought.

　　A similar argument applies to any other a priori judgement. When wejudge that two and two are four, we are not making a judgement about ourthoughts, but about all actual or possible couples. The fact that ourminds are so constituted as to believe that two and two are four, thoughit is true, is emphatically not what we assert when we assert that two andtwo are four. And no fact about the constitution of our minds could makeit true that two and two are four. Thus our a prioriknowledge, if it is not erroneous, is not merely knowledge about theconstitution of our minds, but is applicable to whatever the world maycontain, both what is mental and what is non-mental.

　　The fact seems to be that all our a priori knowledge is concernedwith entities which do not, properly speaking, exist, either in themental or in the physical world. These entities are such as can be namedby parts of speech which are not substantives; they are such entities asqualities and relations. Suppose, for instance, that I am in my room. Iexist, and my room exists; but does 'in' exist? Yet obviously the word'in' has a meaning; it denotes a relation which holds between me and myroom. This relation is something, although we cannot say that it exists inthe same sense in which I and my room exist. The relation 'in' issomething which we can think about and understand, for, if we could notunderstand it, we could not understand the sentence 'I am in my room'.Many philosophers, following Kant, have maintained that relations are thework of the mind, that things in themselves have no relations, but thatthe mind brings them together in one act of thought and thus produces therelations which it judges them to have.

　　This view, however, seems open to objections similar to those which weurged before against Kant. It seems plain that it is not thought whichproduces the truth of the proposition 'I am in my room'. It may be truethat an earwig is in my room, even if neither I nor the earwig nor any oneelse is aware of this truth; for this truth concerns only the earwig andthe room, and does not depend upon anything else. Thus relations, as weshall see more fully in the next chapter, must be placed in a world whichis neither mental nor physical. This world is of great importance tophilosophy, and in particular to the problems of a prioriknowledge. In the next chapter we shall proceed to develop its nature andits bearing upon the questions with which we have been dealing.