Chapter XIV. The Limits of Philosophical Knowledge

by Bertrand Russell

　　In all that we have said hitherto concerning philosophy, we have scarcelytouched on many matters that occupy a great space in the writings of mostphilosophers. Most philosophers—or, at any rate, very many—professto be able to prove, by a priori metaphysical reasoning, suchthings as the fundamental dogmas of religion, the essential rationality ofthe universe, the illusoriness of matter, the unreality of all evil, andso on. There can be no doubt that the hope of finding reason to believesuch theses as these has been the chief inspiration of many life-longstudents of philosophy. This hope, I believe, is vain. It would seem thatknowledge concerning the universe as a whole is not to be obtained bymetaphysics, and that the proposed proofs that, in virtue of the laws oflogic such and such things must exist and such and such otherscannot, are not capable of surviving a critical scrutiny. In this chapterwe shall briefly consider the kind of way in which such reasoning isattempted, with a view to discovering whether we can hope that it may bevalid.

　　The great representative, in modern times, of the kind of view which wewish to examine, was Hegel (1770-1831). Hegel's philosophy is verydifficult, and commentators differ as to the true interpretation of it.According to the interpretation I shall adopt, which is that of many, ifnot most, of the commentators and has the merit of giving an interestingand important type of philosophy, his main thesis is that everything shortof the Whole is obviously fragmentary, and obviously incapable of existingwithout the complement supplied by the rest of the world. Just as acomparative anatomist, from a single bone, sees what kind of animal thewhole must have been, so the metaphysician, according to Hegel, sees, fromany one piece of reality, what the whole of reality must be—at leastin its large outlines. Every apparently separate piece of reality has, asit were, hooks which grapple it to the next piece; the next piece, inturn, has fresh hooks, and so on, until the whole universe isreconstructed. This essential incompleteness appears, according to Hegel,equally in the world of thought and in the world of things. In the worldof thought, if we take any idea which is abstract or incomplete, we find,on examination, that if we forget its incompleteness, we become involvedin contradictions; these contradictions turn the idea in question into itsopposite, or antithesis; and in order to escape, we have to find a new,less incomplete idea, which is the synthesis of our original idea and itsantithesis. This new idea, though less incomplete than the idea we startedwith, will be found, nevertheless, to be still not wholly complete, but topass into its antithesis, with which it must be combined in a newsynthesis. In this way Hegel advances until he reaches the 'AbsoluteIdea', which, according to him, has no incompleteness, no opposite, and noneed of further development. The Absolute Idea, therefore, is adequate todescribe Absolute Reality; but all lower ideas only describe reality as itappears to a partial view, not as it is to one who simultaneously surveysthe Whole. Thus Hegel reaches the conclusion that Absolute Reality formsone single harmonious system, not in space or time, not in any degreeevil, wholly rational, and wholly spiritual. Any appearance to thecontrary, in the world we know, can be proved logically—so hebelieves—to be entirely due to our fragmentary piecemeal view of theuniverse. If we saw the universe whole, as we may suppose God sees it,space and time and matter and evil and all striving and struggling woulddisappear, and we should see instead an eternal perfect unchangingspiritual unity.

　　In this conception, there is undeniably something sublime, something towhich we could wish to yield assent. Nevertheless, when the arguments insupport of it are carefully examined, they appear to involve muchconfusion and many unwarrantable assumptions. The fundamental tenet uponwhich the system is built up is that what is incomplete must be notself-subsistent, but must need the support of other things before it canexist. It is held that whatever has relations to things outside itselfmust contain some reference to those outside things in its own nature, andcould not, therefore, be what it is if those outside things did not exist.A man's nature, for example, is constituted by his memories and the restof his knowledge, by his loves and hatreds, and so on; thus, but for theobjects which he knows or loves or hates, he could not be what he is. Heis essentially and obviously a fragment: taken as the sum-total of realityhe would be self-contradictory.

　　This whole point of view, however, turns upon the notion of the 'nature'of a thing, which seems to mean 'all the truths about the thing'. It is ofcourse the case that a truth which connects one thing with another thingcould not subsist if the other thing did not subsist. But a truth about athing is not part of the thing itself, although it must, according to theabove usage, be part of the 'nature' of the thing. If we mean by a thing's'nature' all the truths about the thing, then plainly we cannot know athing's 'nature' unless we know all the thing's relations to all the otherthings in the universe. But if the word 'nature' is used in this sense, weshall have to hold that the thing may be known when its 'nature' is notknown, or at any rate is not known completely. There is a confusion, whenthis use of the word 'nature' is employed, between knowledge of things andknowledge of truths. We may have knowledge of a thing by acquaintance evenif we know very few propositions about it—theoretically we need notknow any propositions about it. Thus, acquaintance with a thing does notinvolve knowledge of its 'nature' in the above sense. And althoughacquaintance with a thing is involved in our knowing any one propositionabout a thing, knowledge of its 'nature', in the above sense, is notinvolved. Hence, (1) acquaintance with a thing does not logically involvea knowledge of its relations, and (2) a knowledge of some of its relationsdoes not involve a knowledge of all of its relations nor a knowledge ofits 'nature' in the above sense. I may be acquainted, for example, with mytoothache, and this knowledge may be as complete as knowledge byacquaintance ever can be, without knowing all that the dentist (who is notacquainted with it) can tell me about its cause, and without thereforeknowing its 'nature' in the above sense. Thus the fact that a thing hasrelations does not prove that its relations are logically necessary. Thatis to say, from the mere fact that it is the thing it is we cannot deducethat it must have the various relations which in fact it has. This only seemsto follow because we know it already.

　　It follows that we cannot prove that the universe as a whole forms asingle harmonious system such as Hegel believes that it forms. And if wecannot prove this, we also cannot prove the unreality of space and timeand matter and evil, for this is deduced by Hegel from the fragmentary andrelational character of these things. Thus we are left to the piecemealinvestigation of the world, and are unable to know the characters of thoseparts of the universe that are remote from our experience. This result,disappointing as it is to those whose hopes have been raised by thesystems of philosophers, is in harmony with the inductive and scientifictemper of our age, and is borne out by the whole examination of humanknowledge which has occupied our previous chapters.

　　Most of the great ambitious attempts of metaphysicians have proceeded bythe attempt to prove that such and such apparent features of the actualworld were self-contradictory, and therefore could not be real. The wholetendency of modern thought, however, is more and more in the direction ofshowing that the supposed contradictions were illusory, and that verylittle can be proved a priori from considerations of what mustbe. A good illustration of this is afforded by space and time. Space andtime appear to be infinite in extent, and infinitely divisible. If wetravel along a straight line in either direction, it is difficult tobelieve that we shall finally reach a last point, beyond which there isnothing, not even empty space. Similarly, if in imagination we travelbackwards or forwards in time, it is difficult to believe that we shallreach a first or last time, with not even empty time beyond it. Thus spaceand time appear to be infinite in extent.

　　Again, if we take any two points on a line, it seems evident that theremust be other points between them however small the distance between themmay be: every distance can be halved, and the halves can be halved again,and so on ad infinitum. In time, similarly, however little time mayelapse between two moments, it seems evident that there will be othermoments between them. Thus space and time appear to be infinitelydivisible. But as against these apparent facts—infinite extent andinfinite divisibility—philosophers have advanced arguments tendingto show that there could be no infinite collections of things, and thattherefore the number of points in space, or of instants in time, must befinite. Thus a contradiction emerged between the apparent nature of spaceand time and the supposed impossibility of infinite collections.

　　Kant, who first emphasized this contradiction, deduced the impossibilityof space and time, which he declared to be merely subjective; and sincehis time very many philosophers have believed that space and time are mereappearance, not characteristic of the world as it really is. Now, however,owing to the labours of the mathematicians, notably Georg Cantor, it hasappeared that the impossibility of infinite collections was a mistake.They are not in fact self-contradictory, but only contradictory of certainrather obstinate mental prejudices. Hence the reasons for regarding spaceand time as unreal have become inoperative, and one of the great sourcesof metaphysical constructions is dried up.

　　The mathematicians, however, have not been content with showing that spaceas it is commonly supposed to be is possible; they have shown also thatmany other forms of space are equally possible, so far as logic can show.Some of Euclid's axioms, which appear to common sense to be necessary, andwere formerly supposed to be necessary by philosophers, are now known toderive their appearance of necessity from our mere familiarity with actualspace, and not from any a priori logical foundation. By imaginingworlds in which these axioms are false, the mathematicians have used logicto loosen the prejudices of common sense, and to show the possibility ofspaces differing—some more, some less—from that in which welive. And some of these spaces differ so little from Euclidean space,where distances such as we can measure are concerned, that it isimpossible to discover by observation whether our actual space is strictlyEuclidean or of one of these other kinds. Thus the position is completelyreversed. Formerly it appeared that experience left only one kind of spaceto logic, and logic showed this one kind to be impossible. Now, logicpresents many kinds of space as possible apart from experience, andexperience only partially decides between them. Thus, while our knowledgeof what is has become less than it was formerly supposed to be, ourknowledge of what may be is enormously increased. Instead of being shut inwithin narrow walls, of which every nook and cranny could be explored, wefind ourselves in an open world of free possibilities, where much remainsunknown because there is so much to know.

　　What has happened in the case of space and time has happened, to someextent, in other directions as well. The attempt to prescribe to theuniverse by means of a priori principles has broken down; logic,instead of being, as formerly, the bar to possibilities, has become thegreat liberator of the imagination, presenting innumerable alternativeswhich are closed to unreflective common sense, and leaving to experiencethe task of deciding, where decision is possible, between the many worldswhich logic offers for our choice. Thus knowledge as to what existsbecomes limited to what we can learn from experience—not to what wecan actually experience, for, as we have seen, there is much knowledge bydescription concerning things of which we have no direct experience. Butin all cases of knowledge by description, we need some connexion ofuniversals, enabling us, from such and such a datum, to infer an object ofa certain sort as implied by our datum. Thus in regard to physicalobjects, for example, the principle that sense-data are signs of physicalobjects is itself a connexion of universals; and it is only in virtue ofthis principle that experience enables us to acquire knowledge concerningphysical objects. The same applies to the law of causality, or, to descendto what is less general, to such principles as the law of gravitation.

　　Principles such as the law of gravitation are proved, or rather arerendered highly probable, by a combination of experience with some whollya priori principle, such as the principle of induction. Thus ourintuitive knowledge, which is the source of all our other knowledge oftruths, is of two sorts: pure empirical knowledge, which tells us of theexistence and some of the properties of particular things with which weare acquainted, and pure a priori knowledge, which gives usconnexions between universals, and enables us to draw inferences from theparticular facts given in empirical knowledge. Our derivative knowledgealways depends upon some pure a priori knowledge and usually alsodepends upon some pure empirical knowledge.

　　Philosophical knowledge, if what has been said above is true, does notdiffer essentially from scientific knowledge; there is no special sourceof wisdom which is open to philosophy but not to science, and the resultsobtained by philosophy are not radically different from those obtainedfrom science. The essential characteristic of philosophy, which makes it astudy distinct from science, is criticism. It examines critically theprinciples employed in science and in daily life; it searches out anyinconsistencies there may be in these principles, and it only accepts themwhen, as the result of a critical inquiry, no reason for rejecting themhas appeared. If, as many philosophers have believed, the principlesunderlying the sciences were capable, when disengaged from irrelevantdetail, of giving us knowledge concerning the universe as a whole, suchknowledge would have the same claim on our belief as scientific knowledgehas; but our inquiry has not revealed any such knowledge, and therefore,as regards the special doctrines of the bolder metaphysicians, has had amainly negative result. But as regards what would be commonly accepted asknowledge, our result is in the main positive: we have seldom found reasonto reject such knowledge as the result of our criticism, and we have seenno reason to suppose man incapable of the kind of knowledge which he isgenerally believed to possess.

　　When, however, we speak of philosophy as a criticism of knowledge,it is necessary to impose a certain limitation. If we adopt the attitudeof the complete sceptic, placing ourselves wholly outside all knowledge,and asking, from this outside position, to be compelled to return withinthe circle of knowledge, we are demanding what is impossible, and ourscepticism can never be refuted. For all refutation must begin with somepiece of knowledge which the disputants share; from blank doubt, noargument can begin. Hence the criticism of knowledge which philosophyemploys must not be of this destructive kind, if any result is to beachieved. Against this absolute scepticism, no logical argument canbe advanced. But it is not difficult to see that scepticism of this kindis unreasonable. Descartes' 'methodical doubt', with which modernphilosophy began, is not of this kind, but is rather the kind of criticismwhich we are asserting to be the essence of philosophy. His 'methodicaldoubt' consisted in doubting whatever seemed doubtful; in pausing, witheach apparent piece of knowledge, to ask himself whether, on reflection,he could feel certain that he really knew it. This is the kind ofcriticism which constitutes philosophy. Some knowledge, such as knowledgeof the existence of our sense-data, appears quite indubitable, howevercalmly and thoroughly we reflect upon it. In regard to such knowledge,philosophical criticism does not require that we should abstain frombelief. But there are beliefs—such, for example, as the belief thatphysical objects exactly resemble our sense-data—which areentertained until we begin to reflect, but are found to melt away whensubjected to a close inquiry. Such beliefs philosophy will bid us reject,unless some new line of argument is found to support them. But to rejectthe beliefs which do not appear open to any objections, however closely weexamine them, is not reasonable, and is not what philosophy advocates.

　　The criticism aimed at, in a word, is not that which, without reason,determines to reject, but that which considers each piece of apparentknowledge on its merits, and retains whatever still appears to beknowledge when this consideration is completed. That some risk of errorremains must be admitted, since human beings are fallible. Philosophy mayclaim justly that it diminishes the risk of error, and that in some casesit renders the risk so small as to be practically negligible. To do morethan this is not possible in a world where mistakes must occur; and morethan this no prudent advocate of philosophy would claim to have performed.