limits of empiricism

8/14/2019 Limits of Empiricism

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The Limits of Empiricism

Author(s): Bertrand RussellSource: Proceedings of the Aristotelian Society, New Series, Vol. 36 (1935 - 1936), pp. 131-150Published by: Blackwell Publishing on behalf of The Aristotelian SocietyStable URL: http://www.jstor.org/stable/4544270

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Meetingof the Aristotelianociety t 55, RussellSquare,London,W.C. , on 4pril 6th, 19364at 8 p.m.

VII.-THE LIMITS OF EMPIRICISM.By BERTRAND RUSSELL.

EMPIRICISM, says the Encyclopaedia Britannica, is " thetheory that all knowledgeis derivedfromsense experience."Accepting this definition, three questions arise before wecan discuss whether empiricismis true or false. We mustask what is meant by " knowledge," what by " derivedfrom," and what by " sense experience." The word " know-ledge" is one of which there is no accepted definition, andto all suggested definitionsthere are grave objections. Thewords " derived from" may be interpreted either logicallyor causally. The words " sense experience" are capableof either a wide or a narrow interpretation; for example,when I see a rainbow,and notice that the blue and green aremore similar than the blue and yellow, is this to be includedin " sense experience " or is it " derived from " sense experi-ence?Where so many questions are involved, it is not easy toknow where to begin. I think the best starting point is toinquire: What are sense-data, and what is the knowledgemost immediately dependent upon them ? This leads atonce to the question: How is this knowledge dependentupon these data ? When these questionshave been decided,we can go on to inquire whether there is any other know-ledge, and, if so, what reason there is for believing it.

Let us start with some every-day example of empiricalknowledge. Supposea number of people are playing cards,and one of them plays the ten of spades. The others seeit and know that it has been played. The proposition" theten of spades has been played " is known through sense, andis not (at least consciously)inferred, although it may be thebasis of inferences, such as that the player has not got thenine. R


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THE LIMITS OF EMPIRICISM. 133

observer's past history. Knowing is differentfrom seeing;it involves noticing, and it seemsto involve something thatmight be called classifying.At this point, however, we are faced with a logical diffi-culty. We are in search of the empirical premisses orourknowledge of the world, and we have seemed to find thatthe most immediate knowledgewe can expressdepends, notonly upon the sensible fact, but also upon previous occur-rences in our own lives. Obviously we cannot, when weare at the very beginning of empirical knowledge, alreadyknow about the effect of the past upon ourselves; this is alate discovery,made by assumingthat we could, in the past,know facts then present, and can now rememberthem. Wecan never discover that past experience-i.e. that involvedin learning to speak-has made us say " that is the ten ofspades," unless we have had reason to believe facts of thesame kind as that it is the ten of spades. You could notknow that you say " cat " when you see a cat, unless youknew that it is a cat independently of your saying so. Youmust also have a knowledge, not essentiallyverbal, that yousay " cat." ObviouslyI may-noticea featureof the environ-ment without using wordsabout it; and to say that I knowthe meaning of the word " cat " is to say that I can noticefeline featuresof the environment, and know that these arefeatures to which the word " cat " applies. Thus it cannotbe essential to sense-knowledge hat it should be verbal.The point may be illustrated by the following fact. Imay say: " Cat is the word I apply to cats," and when Isay this, I am not uttering a tautology. This is evident ifyou imagine a Frenchman trying to report my statement.He would have to say: " Cat est le mot que M. Russellapplique aux chats." This no longer has the remotestappearance of a tautology.Sense-knowledgewhich is not verbal must be knowledgeof that which words can express. E.g. when I say " thereis a cat" because I see a cat, I must notice the cat, and beaware of its feline character. But when I say " There is aweasel " because I see a stoat, it cannot be maintained thatI am knowing nothing: my sense-knowledgemay be justR2


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134 BERTRAND RUSSELL.as great as if I used the rightword. How, then, does sense-knowledge differ from sense ? Only, I think, by isolationof certain features. It is this isolation that makes the use ofwords possible. Sense knowledge, therefore, is merely aselectionfrom sensible facts.This raises a new logical puzzle: How do I know thatthere are sensible facts that I do not know ? I am con-vinced that my visual field, for example, contains manyfeaturesthat I do not notice. Do I know his ? And, if so,how have I discoveredit ?The natural answer would be: If I keep my eyes still,I can, at will, successively notice a number of differentthings; I can, for example, attend to things remote fromthe point on which I am focussing. I believe that thesethings were there all the time, partly because I have foundthat moving objects attract attention, and thereforeobjectswhich had not attracted my attention were probably notmoving; also because I can repeat the process of directingmy attention, and again notice successively he sameobjectsthat I noticed before. And, of course, as a common senseperson, not a philosopher,I feel sure that my books do notjump out of the shelvesas soon as I take my eyes off them.But all this assumesa great deal that ought not to be assumedin the searchfor first premisses.I think we must conclude that belief in sensible objectswhich we are not noticing should be put among inferentialbeliefs; only what is noticedcan be accepted as an empiricalpremiss in our knowledge of the world. Moreover know-ledge, like noticing, is a matter of degree; there is not asharpline, in sense,between what is known and what is notknown.This primitive non-verbal sense-knowledge, thoughlogically necessaryas a basis for other empirical knowledge,has not yet the characteristics hat make knowledgeservice-able. Before a datum can be used as a premiss in philo-sophy or science, it must be remembered, and expressedinwords; until then, it is too vague and fleeting to be impor-tant. We must, therefore, examine the transitionfrom thenon-verbal sensible fact of which I am aware while it exists,


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THE LIMITS OF EMPIRICISM. 135to the verbal fact of which the knowledge can survive, andwhich I can communicate to others.For our purposes, the process of learning to speak isnot what is essential. In its simplestform, it consistsin theestablishment of certain causal relations: the presence ofa cat causes the word " cat" to be spoken, and hearing theword " cat " may cause expectation of a cat. These causalrelationsareproducedby the usualprocessof learningwhichis common to men and animals. It is in virtue of theircauses and effects that words have " meaning." But allthis, though important in other connexions, has not muchbearing upon the problems with which we are concerned.For our purposes, we may assume that all mankind speakone language, and speak it perfectly. What, granting thisassumption, is the relation between a piece of non-verbalsense-knowledgeand the verbal expressionof it? And howdo we know the character of this relation?There is here a distinction to be made, which is impor-tant if " meaning " is to be understood. In a person whoknows a language, there are causal relationsbetween wordsand what they mean: a cat causesthe word " cat," and theword " cat" causes expectation of a cat, or perhaps theactual sight of one. But these causal relationswhich con-stitute the understanding of a language are themselvescaused: they are caused by the experiences which consti-tute the learning of the language. My contention is thatthe causal relations (or at least relations connected withthem) which exist after the language has been learnt cansometimes be perceived; but I make no such claim asregards the causal processeswhich constitute the learningofthe language.Supposethat I see a cat and say " thereis a cat." Fromwhat has alreadybeen said, we must believe that my words" express" a piece of knowledge which is not essentiallyverbal, though the word " express" remains to be defined.The verbal proposition " there is a cat " can form part ofthe official corpus of human knowledge, whereas the non-verbal knowledge, if not " expressed" in words, cannot bea public premiss for anything. Non-verbal knowledge,


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136 BERTRAND RUSSELL.therefore, is important to science solely as a source of verbalknowledge.I doubt whether any empiricist will deny, in the casesupposed, that I know (1) a sensible fact expressed, perhapsinaccurately, by the words " there is a cat " ; (2) that Isay " there is a cat "; (3) that I say " there is a cat "because a cat (or a sensible appearance resembling that of acat) is there. If any of these three pieces of knowledge iscalled in question, it is difficult to see how anyverbal know-ledge can be known to be " derived from sense experience."

We need not waste further time upon (1) and (2), whichare of the same sort; (1) must be interpreted as know-ledge of a visual fact and of how to classify it; (2) is know-ledge of an auditory fact, except in so far as it asserts that Iam speaking, which may be interpreted as asserting simul-taneous laryngeal and oral sensations. It is (3) that raisesdifficulties.What do we know when we know that our wordsexpress " something we see ? I see a cat and say " thereis a cat." Someone also says " why did you say ' there is acat ' ? " and I reply " because I saw a cat." I feel just assure of the second statement as of the first ; yet the word" because " seems to take me beyond what an empiricistought to know.The word " because " must be taken as expressing arelation which is, at least partly, that of cause and effect.But when I know that I said " cat " because there was acat, I am not knowing that, in large numbers of similarinstances, similar visual appearances have been followed bysimilar utterances. This may be true, but it is not what Iam asserting. I am asserting something which I can knowwithout going outside what is now happening. This isessential, since the knowledge in question is required for theconnexion of sensible occurrences with the verbal assertionof them. At least, wlhat is essential is the connexion of thecat with my intention to say " cat " ; I may, for variousbodily reasons, be unable actually to utter.the word eventhough I try to do so. The connexion of will with bodilymovements raises problems which need not concern us


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in this connexion; we may confine ourselves to the con-nexion of the sensible appearance with the will to utter theappropriate word or words.If I say: " I said ' cat' because I saw a cat," I amsaying more than is warranted. One should say: " Iwilled to say ' cat' because there was a visual occurrencewhich I classified as feline." This statement, at any rate,isolates the " because " as much as possible. What I ammaintaining is that we can know this statement in the sameway in which we know that there was the feline appearance,and that, if we could not, there would be no verbal empiricalknowledge. I think that the word "because" in thissentence must be understood as expressing a more or lesscausal relation, and that this relation must be perceived,notmerely inferred from frequent concomitance. " Cause,"accordingly, must mean something other than " invariableantecedent," and the relation of causation, or some relationintimately connected with it, must be one which can some-times be perceived.If this view is accepted, we can say that the verbal pre-misses of verbal empirical knowledge are sentences per-ceived to be caused by something perceived. If we refuseto admit " cause " in this sense, it seems impossible toexplain the connexion between what we perceive and thewords in which we describe it. And science, as organizedknowledge, requires words. The possibility of empiricalscience, therefore, if the above argument is correct, dependsupon the possibility of perceiving causal or quasi-causalrelations.

Problems connected with language are absent in someinstances in which the same relation can be perceived, e.g.if I am hurt and cry out. We seem, here, to perceiveindubitably a connexion between the pain and the cry.If I were to say, without qualification, that we must beable to perceive "causal " relations, I should be too definite.What I have a right to say is that, between a sensibleappearance and the will to utter words describing it, I canperceive some relation having an intimate connexion withthat of cause and effect. The relation which I perceive


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138 BERTRAND RUSSELL.may, however,be one which is only presentin someinstancesof causation, not in all. Moreover,it differsfromcausationas ordinarilyunderstood n sciencein one importantrespect,namely that certain conditions must be present if the ante-cedent is to give uiseto the consequent. The sight of a catwill not cause the word " cat " in a Frenchmanor in a mannot interestedin cats. The sensible appearance, therefore,is only part of the cause of the word. We shall have to saythat the relation which we perceive is one which may bepresent between an effect and part of its cause, but is notinvariably present where there is causation, and is neverpresent where causation is absent. To distinguish it fromcausation, we will call it " producing." It can only beperceived when it holds between two parts of a sensiblewhole, and is then perceived as we perceive (say) that onething is above another.

I come now to another difficulty in thorough-goingempiricism,and that is, the difficultyof justifying inferencesfromfacts to facts. The point is best explainedby referenceto Wittgenstein'sTractatus Logico-Philosophicus,where hesays:" Atomic facts are independent of one another. Fromthe existence or non-existenceof an atomic fact we cannotinfer the existence or non-existence of another" (2061'062). " The events of the future cannot be inferredfromthose of the present. Superstition s the belief in the causalnexus" (5-1361).The reference to atomic facts (the existence of which isquestionable) is not essential to the above doctrine. WhatWittgenstein is saying is that all valid inference proceedsaccording to the laws of deduction: the connexion betweenpremissand conclusion must be tautologous. Suppose, forexample, that, within one speciouspresent,we perceive thatA precedes B, and within another speciouspresentwe per-ceive that B precedes C, we cannot infer that A precedes C,unlesswe can show that this is logically implied.It is obviousthat this doctrinesweepsaway all inferencesthat have any practical utility. When we smell food, wecannot guess how it will taste; from a railway time-table


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we cannot tell how the trains will run; when we read abook, we have no reason to suppose that someone composedit; when we talk, we must regard it as a lucky accident ifwe hear a reply. No one in fact holds these views, and aphilosophy which professes hem cannot be wholly sincere.Let us, to begin with, concentrate on the inference " Aprecedes B, and B precedes C ; therefore A precedes C."This may be a purely verbal inference. We may say that"A sensibly precedesB " is to mean that A and B are partsof one specious present, and that we perceive a relation ofsequence in which A comes before B. We may then saythat " A precedesZ" means that there are a series of inter-mediates B, C. . . Y, such that A sensibly precedes B andso on. In that case, the transitiveness of " precedes" islogically necessary. Let us examine this theory.In the first place, it confines temporal order withinioneexperience. We cannot say " Casar's invasion of Britainpreceded William the Conqueror's,"because no one experi-enced both. If we are to extend the time-seriesbeyond ourown lives, we must have some means of knowing when anevent in A's life is simultaneouswith one in B's. This canbe made a matter of definition, adopting the principles ofphysics. We shall say that if A hears what he believes tobe B speaking, A's experience of hearing is almost exactlysimultaneous with B's experience of speaking, which Ahypothetically assumesto exist although, in doing so, he issinning against the principleof not inferringfactsfromfacts.In this somewhatdubious manner, we can extend the time-series as far as sentient experience extends.But difficulties remain. We certainly know that, if Asensibly precedes B, B does not sensibly precede A. And inorder that the above transition from " sensibly preceding"to " preceding " may be feasible, we must know that, if Asensibly precedes B, and B sensibly precedes C, and A andC are in one species present, then A sensibly precedes C.Perhaps we could construct the time-series with smalleraxioms than these, but something of the sort is necessaryfor temporal order. In any case, it seems undeniable thatthe relation " sensibly preceding" is transitive and


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140 BERTRAND RUSSELL.asymmetrical, and that our knowledge of this fact has not themerely probable character of a generalization from a numberof instances. It seems that, when we perceive that Aprecedes B, we can attend to the relation " preceding," andperceive that it has the characters of transitiveness andasymmetry. Wittgenstein and Carnap attempt to explainsuch propositions as merely grammatical, but I am notsatisfied that their attempt is successful.That it is possible to perceive facts about universalsappears also in many other ways. In looking at the rain-bow, we can perceive that blue and green are more similarthan blue and yellow; moreover, it is evident that this isnot merely a relation between three particular patches ofcolour, but between their shades, which are universals. Wecan perceive, again, that a semitone is a smaller intervalthan a tone, which is also a relation of universals.

These things are known empirically in one sense, butnot in another. Take the case of blue, green, and yellow.It is only through sense that we know green to be betweenblue and yellow: when we see all three colours simul-taneously, we can also see their resemblances and differences,and we can see that these are properties of the shades, notof the particulars. The sensible fact must be held toinclude not only particulars, but their predicates and rela-tions, with their predicates and relations. Our knowledgeof all this depends upon the occurrence of a suitable sensiblefact, and is in that sense empirical. But in so far as theknowledge concerns universals, it is knowledge which maybe exemplified in other sensible facts, and which gives ushypothetical knowledge concerning such facts. That is tosay, having carefully observed blue, green, and yellow inone sensible fact, we can say : Wherever these shades mayoccur, green will be intermediate in colour between blueand yellow. In this way attention to the facts of sense cangive rise to general knowledge. One perceived instanceof three events in a time-order can enable us to know thatpreceding is a transitive relation. Hence, from the twofacts " A precedes B " and " B precedes C " we can infer" A precedes C," which is contrary to what Wittgenstein


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144 BERTRAND RUSSELL.Deity ? And if there is such a Deity, may he not reveal theanswer to a mathematical Moses ? And would not thisbe a demonstration ? It seems to follow that, if a form ofwords p is syntactically correct, we always " know what ismeant by the statement that p is demonstrated." If revela-tion is rejected as demonstration, it will be found that wedo not know of the existence of Cape Horn unless we haveseen it.The opinion that the phrase " after an infinite numberof operations " is self-contradictory, seems scarcely correct.Might not a man's skill increase so fast that he performedeach operation in half the time required for its predecessor ?In that case, the whole infinite series would take only twiceas long as the first operation.A question arises as to what is a proper definition of aclass. Miss Ambrose, apparently, allows a finite class to bedefined by a property common and peculiar to its members,whereas an infiniteclass must be defined by a rule for con-structing its members, such as " start with 0 and go onadding 1 indefinitely; anything you reach is one of thenatural numbers." Another finitist writer (Mr. Good-stein), in an as yet unpublished paper, says: " The pro-perty ' sub-class of a class ' does not construct a class ; itis not a defining property. A sub-class of a class must bedefined by a rule for selecting its members." I do notunderstand this. The class of sub-classes of men, forinstance, is the class of those classes whose members are men.There is a perfectly satisfactory defining property of thisclass of classes, though not necessarily of its members Inthis it is in just the same position as the class of men, whichis defined as " rational animals " or " featherless bipeds "or what not, but has members of whose several definitionsnothing is known to the logician in the vast majority ofinstances. Shall we then say that men are. not really aclass ? Certainly the class of men is not so defined as togive us a " rule for selecting its members."I cannot undersand how Miss Ambrose can allowproperty-definitions of finite classes, but not of infinite ones.Outside mathematics, we do not know with any certainty


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whether classes are finite or infinite, except in a few cases.And even when we think we know, it is no great help.Consider such a proposition as " all men are mortal."If this is to be ascertained by examining instances, itrequires inspection of everything in the universe. It maybe that, in fact, the only men are A, B, C, . . . Y and Z;but in order to know this, we must have observed that allthe other things in the world are not men. Classes thatcan be provedto be finite (unless they are defined by enu-meration) are hardly to be found outside mathematics.We know that " integers less than 100 " is a finite class, butwe do not know that " man " is a finite class. And if any-one maintains that we do know this, he must believe thatwe have means of knowing something about all the thingsin the world, over and above what logic has to say. Ibelieve this to be the case, but the finitist position, if I havenot misunderstood it, results from assuming the opposite.Miss Ambrose, if we are to interpret her literally, musthold that the statement " all men are mortal " is neither truenor false, since we are not " certain of being able to verifyit or prove it false." To prove it false is obviously impos-sible, since, however long a man may have lived, we cannotknow that he will never die. To prove it true is theoreticallypossible, but only by one very drastic method: we mightmurder all -he rest of the human race and then commitsuicide. But no man can be " certain " of being able todo this, so that, on finitist principles, the form of words " allmen are mortal " is outside the scope of the Law of ExcludedMiddle.For my part, I hold that, as soon as I know what ismeant by "men " and what by " mortal," I know what ismeant by" all men are mortal," and I know quite certainlythat either this statement is true or some man is immortal.I am led to reject finitism because (1) it rests on whatseems to me an untenable general principle, that whatcannot be proved or disproved is neither true nor false,(2) it cannot enunciate mathematical induction or define thenatural numbers, (3) its advocates, if I am not mistaken, onlythink it feasible because they do not carry it out logically.


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146 BERTRAND RUSSELL.

I come now to another question, namely: In whatsense can physics be empirical ?The practice of physicists is by no means wholly empirical.Thus Dirac, in the preface to his " Quantum Mechanics,"after describing the aims of classical physics, says:" It has become increasingly evident in recent times,however, that nature works on a different plan. Herfundamental laws do not govern the world as it appearsin our mental picture in any very direct way, but insteadthey control a substratum of which we cannot form a mentalpicture without introducing irrelevancies. The formula-tion of these laws requires the use of the mathematics oftransformations. The important things in the world ajpearas the invariants (or more generally the nearly invariants,or quantities with simple transformation properties) of thesetransformations. The things we are immediately aware ofare the relations of these nearly invariants to a certain frameof reference, usually one chosen so as to introduce speciaisimplifying features which are unimportant from the pointof view of general theory."This statement of the position is one with which I am inentire agreement ; but it is a statement incompatible withthoroughgoing empiricism. " The things we are immedi-ately aware of " cannot be proved o be relations of invariantsto a frame of reference. This is an interpretation, recom-mended as the simplest way yet discovered of formulatinglaws compatible with all that has been observed. A greatdeal is assumed that cannot be observed, and cannot beinferred from what is observed, unless forms of inference areadmitted which pure empiricism must reject.Physics, as ordinarily understood, accepts as factualpremisses not only what I observe now, but also what Iobserved formerly and what others have observed; and itaccepts as legitimate inferences, not only unobserved pastoccurrences, but also future occurrences implied by itslaws. Thus we may distinguish the following stages:A. I observenow, andsee so-and-so. This may be regardedas mere matter of fact, although, as we saw in the first partof this paper, it involves much complication, and is not


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intelligible unless relations which are more or less causalcan be perceived. Since we have already discussed thismatter, no more need be said now.B. I observedormerly, and saw so-and-so. This involvesreliance on memory. Now it is obvious that the existenceof a memory does not logically prove the existence of thething remembered; we might have memories of a whollyfictitious past. It is obvious also that, since our memoriesreferto the past, no futureevidence can prove them accurate.We may, of course, obtain what looks like confirmation ofour memorics: we may, for example, remember writingsomething, and find it written in what is apparently ourhandwriting. But this only shows that the present is whatit would be if our memories were accurate; there is noway of proving that no other hypothesis will account forits being what it is. The empiricist,therefore, must includeamong his premisses the trustworthinessof memory (withthe limitationsdemanded by common sense), in spite of thefact that neither now nor hereaftercan we find any evidencefor the truth of this premiss.C. Othersobserved, nd saw so-and-so. This, prima acie,involves acceptance of testimony; that is to say, it involvesthe assumption that, when I hear noises or see shapeswhich I should use to expresscertain experiences, someoneis having or has had similar experiences. We cannot getvery far in any science without accepting testimony, yet theassumption involved is considerable. And owing to theexistence of different languages, a further complication isnecessary; we must know what we mean by saying thattwo different statements have the same meaning. When-ever an English physicist uses a French observation, heassumes that when he seesa body which emits Frenchnoises,the causes and effects of these noises can be assimilated tothose of his own noises by using the dictionary. All this ispresupposedin recordingwhat everyone would considertobe the data of physics.D. Future bservationsill showso-and-so. To make state-ments of this kind possible is the whole practicalpurpose ofscience. To say that science has utility is to say that its


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148 BERTRAND RUSSELL.enables us to foresee future occurrences ; if it does not dothis, it may still be delightful or elevating, but it cannothelp us to conduct matters so as to achieve desired ends.We are all firmly persuadedthat the laws of nature will notchange, and that scientificapparatuswill workin the futureas in the past. Nevertheless this assumptionthat the futurewill resemble the past is one for which it is logically impos-sible that we should have evidence deducible by logic alonefrom past events. We may argue as to the precise formwhich our axiom is to take, but some axiom we must haveif we are to be able to infer anything about the future.And if, in our capacity of professional philosophers, wepretend to complete agnosticism as to the future, we arenot sincere, for we still avoid arsenic unless we are tired oflife.It seems clear, therefore, that we all in fact are unshake-ably convinced that we know things which pure empiricismwould deny that we can know. We must accordingly seeka theory of knowledge other than pure empiricism.Collecting the resultsof our argument up to the present,we have found reason to believe:(1) That if any verbal knowledge can be known to bein any sense derived from sense experience, we must beable, sometimes, to " see " a relation, analogous to causa-tion, between two parts of one speciouspresent.(2) That facts about universals can sometimes beperceived when the universals are exemplified in sensibleoccurrences; for example, that " preceding " is transitive,and that blue is more like green than like yellow.(3) That we can understanda form of words, and knowthat it expresseseither a truth or a falsehood,even when weknow of no method of deciding the alternative.(4) That physics requires the possibility of inferring, atleast with probability, occurrences which have not beenobserved, and, more particularly,future occurrences.Without these principles, what is ordinarilyregarded asempirical knowledge becomes impossible.It is not necessary to maintain that we can arrive atknowledge in advance of experience, but rather that


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THE LIMITS OF EMPIRICISM. 149experience gives more information than pure empiricismsupposes. In perceiving a sensible fact, we can perceivethe universals which are qualities or relations of parts of thefact, and we can perceive relations and propertiesof theseuniversals. When I am hurt and cry out, I can perceivenot only the hurt and the cry, but the fact that the one" produces" the other. When I perceive three events ina time-order, I can perceive that preceding is transitive-ageneral truth of which an instance is contained in the pre-sent sense-datum. General propositions,such as " all menare mortal " or " every finite integer is increased by theaddition of I," can be understood s soon as we understandtheir terms. If we have understood the word "man ",and seen something die, we have had all the experiencerequired for understanding the proposition " all man aremortal " ; at least, this would be the case if " men"and "mortal" had definite meanings. Sometimes asingle sensible occurrence suffices, not only to enableus to understand a general proposition, but even toknow that it is true ; of this, the relations of yellow,green, and blue in the rainbow have given us aninstance. It is obvious, as a matter of logic, that generalpropositions cannot be deduced from propositions whichare not general; therefore, if we know any generalpropositions, there must be some among premisses. Imaintain that " yellow is more like green than like blue "is such a premiss, derivable by attention to one singleinstance of the sensible compresence of yellow, green, andblue.Knowledge concerning unobservedfacts, such as physicsrequires, becomes possible if we admit such sources ofknowledge as we have just been considering. If we cansometimes perceive elations which are analogous to causa-tion, we do not depend wholly upon enumerationof instancesin the proof of causal laws. If we perceive two events Aand B, and perceive that A precedes B, we know that what-ever follows B follows A. When we come to matters whichmust be at best probable, the apparatusof perceived generalpropositions may suffice to give an a priori probability,


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150 BERTRAND RUSSELL.which is necessary for the satisfactory working of probableinference. I do not profess to know, in detail, how this isto be done, but at any rate it is no longer, as in pure empiri-cism, an obvious logical impossibility.

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