Thus, whenever we see a colour, we have a sensation of the color, but the color itself is a sense-datum, not a sensation.

We cannot say that the table is the sense-data, or even that the sense-data are directly properties of the table.

Berkeley retains the merit of having shown that the existence of Matter is capable of being denied without absurdity, and that if there are any things that exist independently of us they cannot be the immediate objects of our sensations.

Although the table does not depend for its existence upon being seen by me, it does depend upon being seen (or otherwise apprehended in sensation) by some mind—not necessarily the mind of God, but more often the whole collective mind of the universe.

Very many philosophers, perhaps a majority, have held that there is nothing real except Minds and their Ideas.

They either say, like Berkeley, that matter is really nothing but a collection of ideas, or they say, like Leibniz (1646-1716), that what appears as matter is really a collection of more or less rudimentary Minds.

What the Senses immediately tell us is not the truth about the Object as it is apart from us, but only the truth about certain sense-data which, so far as we can see, depend upon the relations between us and the object.

When I look at my table and see a certain brown color, what is quite certain at once is not 'I am seeing a brown color', but rather, 'a brown color is being seen'.

One great reason why it is felt that we must secure a physical object in addition to the sense-data, is that we want the same object for different people.

Thus it is the fact that different people have similar sense-data, and that one person in a given place at different times has similar sense-data, which makes us suppose that over and above the sense-data there is a permanent public object which underlies or causes the sense-data of various people at various times.

In one sense it must be admitted that we can never prove the existence of things other than ourselves and our experiences. No logical absurdity results from the hypothesis that the world consists of myself and my thoughts and feelings and sensations, and that everything else is mere fancy.

Hence, by organizing our instinctive beliefs and their consequences, by considering which among them is most possible, if necessary, to modify or abandon, we can arrive, on the basis of accepting as our sole data what we instinctively believe, at an orderly systematic organization of our knowledge, in which, though the possibility of error remains, its likelihood is diminished by the interrelation of the parts and by the critical scrutiny which has preceded acquiescence.

Physical science, more or less unconsciously, has drifted into the view that all natural phenomena ought to be reduced to motions.

The only properties which science assigns to it are position in space, and the power of motion according to the laws of motion.

When it is said that light is waves, what is really meant is that waves are the physical cause of our sensations of light.

It is not only colors and sounds and so on that are absent from the scientific world of matter, but also space as we get it through sight or touch. It is essential to science that its matter should be in a space, but the space in which it is cannot be exactly the space we see or feel.

We agreed provisionally that physical objects cannot be quite like our sense-data, but may be regarded as causing our sensations.

It is mainly the relative positions of the object and our body that determine what sensations we shall derive from the object.

Assuming that there is physical space, and that it does thus correspond to private spaces, what can we know about it? We can know only what is required in order to secure the correspondence. That is to say, we can know nothing of what it is like in itself, but we can know the sort of arrangement of physical objects which results from their spatial relations.

Thus, in so far as time is constituted by duration, there is the same necessity for distinguishing a public and a private time as there was in the case of space. But in so far as time consists in an order of before and after, there is no need to make such a distinction; the time-order which events seem to have is, so far as we can see, the same as the time-order which they do have.

Hence we regard the order as true also in physical space, whereas the shape is only supposed to correspond to the physical space so far as is required for the preservation of the order.

Thus we find that, although the Relations of physical objects have all sorts of knowable properties, derived from their correspondence with the relations of sense-data, the physical objects themselves remain unknown in their intrinsic nature, so far at least as can be discovered by means of the senses.

Thus idealists deny the existence of Matter as something intrinsically different from mind, though they do not deny that our sense-data are signs of something which exists independently of our private sensations.

We have seen that, even if physical objects do have an independent existence, they must differ very widely from sense-data, and can only have a correspondence with sense-data,

The grounds on which idealism is advocated are generally grounds derived from the theory of knowledge, that is to say, from a discussion of the conditions which things must satisfy in order that we may be able to know them.

But he went on to argue that sense-data were the only things of whose existence our perceptions could assure us; and that to be known is to be 'in' a mind, and therefore to be mental.

Whatever is known without being in my mind must be in some other mind.

He gives the name 'idea' to anything which is immediately known, as, for example, sense-data are known.

The 'real' tree, which corresponds to what we called the physical object, consists of Ideas in the Mind of God, ideas more or less like those we have when we see the tree, but differing in the fact that they are permanent in God's mind so long as the tree continues to exist.

So when Berkeley says that the tree must be in our minds if we can know it, all that he really has a right to say is that a thought of the tree must be in our minds.

But this is an entirely different point from the one by which Berkeley seeks to prove that whatever can be immediately known must be in a mind.

Our previous arguments concerning the color did not prove it to be mental; they only proved that its existence depends upon the relation of our Sense organs to the physical Object—in our case, the table.

This question of the distinction between act and object in our apprehending of things is vitally important, since our whole power of acquiring Knowledge is bound up with it.

In its first use it is applicable to the sort of knowledge which is opposed to error, the sense in which what we know is true, the sense which applies to our beliefs and convictions, i.e. to what are called judgements.

In the second use of the word 'know' above, the word applies to our knowledge of things, which we may call acquaintance. This is the sense in which we know sense-data.

What happens, in cases where I have true Judgment without acquaintance, is that the thing is known to me by description, and that, in virtue of some general principle, the existence of a thing answering to this description can be inferred from the existence of something with which I am acquainted.

All knowledge of truths, as we shall show, demands acquaintance with things which are of an essentially different character from sense-data, the things which are sometimes called 'abstract ideas', but which we shall call 'universals'.

The question whether we are also acquainted with our bare selves, as opposed to particular thoughts and feelings, is a very difficult one, upon which it would be rash to speak positively.

Thus, when I am acquainted with my seeing the sun, the whole fact with which I am acquainted is 'Self-acquainted-with-sense-datum'. Further, we know the truth 'I am acquainted with this sense-datum'. It is hard to see how we could know this truth, or even understand what is meant by it, unless we were acquainted with something which we call 'I'.

In some sense it would seem we must be acquainted with our Selves as opposed to our particular experiences.

In addition to our acquaintance with particular existing things, we also have acquaintance with what we shall call universals, that is to say, general ideas, such as whiteness, diversity, brotherhood, and so on.

Awareness of universals is called conceiving, and a universal of which we are aware is called a concept.

Common words, even proper names, are usually really descriptions.

Here the proper name has the direct use which it always wishes to have, as simply standing for a certain object, and not for a description of the object.

I suspect that even the Universe, as considered by metaphysics, involves such a connection with particulars. In logic, on the contrary, where we are concerned not merely with what does exist, but with whatever might or could exist or be, no reference to actual particulars is involved.

Here, as in the case of particulars, knowledge concerning what is known by description is ultimately reducible to knowledge concerning what is known by acquaintance.

Thus when, for example, we make a statement about Julius Caesar, it is plain that Julius Caesar himself is not before our minds, since we are not acquainted with him.

Thus our statement does not mean quite what it seems to mean, but means something involving, instead of Julius Caesar, some Description of him which is composed wholly of particulars and universals with which we are acquainted.

The chief importance of knowledge by description is that it enables us to pass beyond the limits of our private Experience.

In view of the very narrow range of our immediate experience, this result is vital, and until it is understood, much of our knowledge must remain mysterious and therefore doubtful.

Thus our inductive principle is at any rate not capable of being disproved by an appeal to experience. The inductive principle, however, is equally incapable of being proved by an appeal to experience.

Hence we can never use experience to prove the inductive principle without begging the question.

All our conduct is based upon associations which have worked in the past, and which we therefore regard as likely to work in the future; and this likelihood is dependent for its validity upon the inductive principle.

The belief that every event must have a cause, are as completely dependent upon the inductive principle

This affords no evidence for their truth in the future, unless the inductive principle is assumed.

For no very good reason, three of these principles have been singled out by tradition under the name of 'Laws of Thought'. They are as follows: (1) The law of identity: 'Whatever is, is.' (2) The law of contradiction: 'Nothing can both be and not be.' (3) The law of excluded middle: 'Everything must either be or not be.'

It must be admitted, for the reasons already stated, that logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them. In this, therefore, which was the most important point of the controversy, the rationalists were in the right.

It would certainly be absurd to suppose that there are innate principles in the sense that babies are born with a knowledge of everything which men know and which cannot be deduced from what is Experienced.

The phrase 'a priori' is less objectionable, and is more usual in modern writers.

We shall nevertheless hold that some knowledge is a priori, in the sense that the experience which makes us think of it does not suffice to prove it, but merely so directs our attention that we see its truth without requiring any proof from experience.

Nothing can be known to exist except by the help of experience.

All the knowledge that we can acquire a priori concerning existence seems to be hypothetical: it tells us that if one thing exists, another must exist, or, more generally, that if one proposition is true, another must be true.

Thus the scope and power of a priori principles is strictly limited. All knowledge that something exists must be in part dependent on experience. When anything is known immediately, its existence is known by experience alone; when anything is proved to exist, without being known immediately, both experience and a priori principles must be required in the proof. Knowledge is called Empirical when it rests wholly or partly upon experience. Thus all knowledge which asserts existence is empirical, and the only a priori knowledge concerning existence is hypothetical, giving connections among things that exist or may exist, but not giving actual existence.

All pure mathematics is a priori, like logic. This was strenuously denied by the empirical philosophers, who maintained that experience was as much the source of our knowledge of arithmetic as of our knowledge of geography. They maintained that by the repeated experience of seeing two things and two other things, and finding that altogether they made four things, we were led by Induction to the conclusion that two things and two other things would always make four things altogether. If, however, this were the source of our knowledge that two and two are four, we should proceed differently, in persuading ourselves of its truth, from the way in which we do actually proceed. In fact, a certain number of instances are needed to make us think of two abstractly, rather than of two coins or two books or two people, or two of any other specified kind. But as soon as we are able to divest our thoughts of irrelevant particularity, we become able to see the general principle that two and two are four; any one instance is seen to be typical, and the examination of other instances becomes unnecessary.

We do not, in fact, feel our certainty that two and two are four increased by fresh instances, because, as soon as we have seen the truth of this proposition, our certainty becomes so great as to be incapable of growing greater. Moreover, we feel some quality of necessity about the proposition 'two and two are four', which is absent from even the best attested empirical generalizations.

In any possible world, on the contrary, we feel that two and two would be four: this is not a mere fact, but a necessity to which everything actual and possible must conform.

The fact is that, in simple mathematical judgements such as 'two and two are four', and also in many judgements of logic, we can know the general proposition without inferring it from instances, although some instance is usually necessary to make clear to us what the general proposition means. This is why there is real utility in the process of deduction, which goes from the general to the general, or from the general to the Particular, as well as in the process of induction, which goes from the particular to the particular, or from the particular to the general.

Hence we shall reach the conclusion that Socrates is mortal with a greater approach to certainty if we make our argument purely inductive than if we go by way of 'all men are mortal' and then use deduction.

In regard to the former, deduction is the right mode of argument, whereas in regard to the latter, induction is always theoretically preferable, and warrants a greater confidence in the truth of our conclusion, because all empirical generalizations are more uncertain than the instances of them.

Kant undoubtedly deserves credit for two things: first, for having perceived that we have a priori knowledge which is not purely 'analytic', i.e. such that the opposite would be self-contradictory, and secondly, for having made evident the philosophical importance of the theory of knowledge.

They are called 'analytic' because the predicate is obtained by merely analysing the subject.

Thus according to the philosophers before Kant, the law of contradiction, which asserts that nothing can at the same time have and not have a certain property, sufficed to establish the truth of all a priori knowledge.

In many cases which had previously been supposed analytic, and notably in the case of cause and effect, the connection was really synthetic.

Hence he inferred the far more doubtful proposition that nothing could be known a priori about the connection of cause and effect.

He perceived that not only the connection of cause and effect, but all the propositions of arithmetic and geometry, are 'synthetic', i.e. not analytic: in all these propositions, no analysis of the subject will reveal the predicate.

The idea of 12 is not contained in them, nor even in the idea of adding them together.

What Kant maintained was that in all our experience there are two elements to be distinguished, the one due to the object (i.e. to what we have called the 'physical object'), the other due to our own nature.

He considers that the crude material given in sensation—the color, hardness, etc.—is due to the object, and that what we supply is the arrangement in space and time, and all the relations between sense-data which result from comparison or from considering one as the cause of the other or in any other way. His chief reason in favour of this view is that we seem to have a priori knowledge as to space and time and causality and comparison, but not as to the actual crude material of sensation.

The physical object, which he calls the 'thing in itself',(1) he regards as essentially unknowable; what can be known is the object as we have it in experience, which he calls the 'phenomenon'.

Hence this knowledge, though true of all actual and possible experience, must not be supposed to apply outside experience.

In spite of the existence of a priori knowledge, we cannot know anything about the thing in itself or about what is not an actual or possible object of experience.

It is true that this possibility, formally, is inconsistent with the Kantian view that time itself is a form imposed by the subject upon phenomena, so that our real Self is not in time and has no to-morrow. But he will still have to suppose that the time-order of phenomena is determined by characteristics of what is behind phenomena, and this suffices for the substance of our argument.

Thus Kant's solution unduly limits the scope of a priori propositions, in addition to failing in the attempt at explaining their certainty.

What we believe, when we believe the law of contradiction, is not that the mind is so made that it must believe the law of contradiction. This belief is a subsequent result of psychological reflection, which presupposes the belief in the law of contradiction.

Thus the law of contradiction is about things, and not merely about thoughts; and although Belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world.

The fact seems to be that all our a priori knowledge is concerned with entities which do not, properly speaking, exist, either in the mental or in the physical world. They are such entities as qualities and Relations.

Many philosophers, following Kant, have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have.

At the end of the preceding chapter we saw that such entities as relations appear to have a being which is in some way different from that of physical objects, and also different from that of minds and from that of sense-data.

We shall therefore use the word 'universal' instead of the word 'idea', to describe what Plato meant.

We speak of whatever is given in sensation, or is of the same nature as things given in sensation, as a particular; by opposition to this, a universal will be anything which may be shared by many particulars,

When we examine common words, we find that, broadly speaking, proper names stand for Particulars, while other substantives, adjectives, prepositions, and verbs stand for universals.

All Truths involve universals, and all knowledge of truths involves acquaintance with universals.

Even among philosophers, we may say, broadly, that only those universals which are named by adjectives or substantives have been much or often recognized, while those named by verbs and prepositions have been usually overlooked. This omission has had a very great effect upon philosophy; it is hardly too much to say that most Metaphysics, since Spinoza, has been largely determined by it. The way this has occurred is, in outline, as follows: Speaking generally, adjectives and common nouns express qualities or properties of single things, whereas prepositions and verbs tend to express relations between two or more things. Thus the neglect of prepositions and verbs led to the belief that every proposition can be regarded as attributing a property to a single thing, rather than as expressing a relation between two or more things. Hence it was supposed that, ultimately, there can be no such entities as relations between things. Hence either there can be only one thing in the universe, or, if there are many things, they cannot possibly interact in any way, since any interaction would be a relation, and relations are impossible.

The second, advocated by Leibniz but not very common nowadays, is called monadism, because each of the isolated things is called a monad.

Result, in my opinion, from an undue attention to one sort of universals, namely the sort represented by adjectives and substantives rather than by verbs and prepositions.

We cannot strictly prove that there are such entities as qualities, i.e. the universals represented by adjectives and substantives, whereas we can prove that there must be relations, i.e. the sort of universals generally represented by verbs and prepositions.

The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worth while to invent difficult and unplausible theories to avoid the admission of such universals as whiteness and triangularity.

Like their adversaries, they only thought of qualities, and altogether ignored relations as universals.

We must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.

There is no place or time where we can find the relation 'north of'.

We shall find it convenient only to speak of things existing when they are in time, that is to say, when we can point to some time at which they exist (not excluding the possibility of their existing at all times). Thus thoughts and feelings, minds and physical objects exist. But Universals do not exist in this sense; we shall say that they subsist or have being, where 'being' is opposed to 'existence' as being timeless.

All a priori knowledge deals exclusively with the Relations of universals. The only case in which it might seem, at first sight, as if our proposition were untrue, is the case in which an a priori proposition states that all of one class of particulars belong to some other class, or (what comes to the same thing) that all particulars having some one property also have some other. In this case it might seem as though we were dealing with the particulars that have the property rather than with the property. The proposition 'two and two are four' is really a case in point, for this may be stated in the form 'any two and any other two are four', or 'any collection formed of two twos is a collection of four'. If we can show that such statements as this really deal only with universals, our proposition may be regarded as proved.

The thing that seemed mysterious, when we formerly considered such knowledge, was that it seemed to anticipate and control experience. This, however, we can now see to have been an error. No fact concerning anything capable of being experienced can be known independently of experience. We know a priori that two things and two other things together make four things, but we do not know a priori that if Brown and Jones are two, and Robinson and Smith are two, then Brown and Jones and Robinson and Smith are four. The reason is that this proposition cannot be understood at all unless we know that there are such people as Brown and Jones and Robinson and Smith, and this we can only know by experience. Hence, although our general proposition is a priori, all its applications to actual particulars involve experience and therefore contain an Empirical element.

Thus the difference between an a priori general Proposition and an empirical generalization does not come in the meaning of the proposition; it comes in the nature of the evidence for it.

But that only means that our generalization has been subsumed under a wider generalization, for which the evidence is still of the same kind, though more extensive. The progress of science is constantly producing such subsumptions, and therefore giving a constantly wider inductive basis for scientific generalizations. But although this gives a greater degree of certainty, it does not give a different kind: the ultimate ground remains inductive, i.e. derived from instances, and not an a priori connection of universals such as we have in logic and arithmetic.

Hence we arrive at the proposition: 'All products of two integers, which never have been and never will be thought of by any human being, are over 100.' Here is a general proposition of which the truth is undeniable, and yet, from the very nature of the case, we can never give an instance; because any two numbers we may think of are excluded by the terms of the proposition. This possibility, of knowledge of general propositions of which no instance can be given, is often denied, because it is not perceived that the knowledge of such propositions only requires a knowledge of the relations of universals, and does not require any knowledge of instances of the universals in question.

Hence our knowledge as to physical objects depends throughout upon this possibility of general knowledge where no instance can be given.

Among universals, there seems to be no principle by which we can decide which can be known by acquaintance,

Our derivative knowledge of things, which we call knowledge by description, always involves both acquaintance with something and knowledge of truths.

But knowledge of truths raises a further problem, which does not arise in regard to knowledge of things, namely the problem of error.

Error can only arise when we regard the immediate object, i.e. the sense-datum, as the mark of some physical object.

All arithmetic, moreover, can be deduced from the general principles of Logic,

It would seem that cases of fallacious memory can probably all be dealt with in this way, i.e. they can be shown to be not cases of memory in the strict sense at all.

This is a question of the very greatest difficulty, to which no completely satisfactory answer is possible. There is, however, a preliminary question which is rather less difficult, and that is: What do we mean by truth and falsehood?

(1) Our theory of truth must be such as to admit of its opposite, falsehood. A good many philosophers have failed adequately to satisfy this condition: they have constructed theories according to which all our thinking ought to have been true, and have then had the greatest difficulty in finding a place for falsehood. In this respect our theory of belief must differ from our theory of acquaintance, since in the case of acquaintance it was not necessary to take account of any opposite.

In fact, truth and falsehood are properties of beliefs and statements:

Truth or falsehood of a belief always depends upon something which lies outside the belief itself.

Although truth and falsehood are properties of beliefs, they are properties dependent upon the Relations of the beliefs to other things, not upon any internal quality of the beliefs.

Truth consists in some form of correspondence between belief and fact.

The most important attempt at a definition of this sort is the theory that truth consists in coherence. It is said that the mark of falsehood is failure to cohere in the body of our beliefs, and that it is the essence of a truth to form part of the completely rounded system which is The Truth.

It assumes the meaning of 'coherence' known, whereas, in fact, 'coherence' presupposes the truth of the laws of logic.

For the above two reasons, coherence cannot be accepted as giving the meaning of truth, though it is often a most important test of truth after a certain amount of truth has become known.

The necessity of allowing for falsehood makes it impossible to regard belief as a Relation of the mind to a single object, which could be said to be what is believed. If belief were so regarded, we should find that, like acquaintance, it would not admit of the opposition of truth and falsehood, but would have to be always true.

Some relations demand three terms, some four, and so on. Take, for instance, the relation 'between'. So long as only two terms come in, the relation 'between' is impossible: three terms are the smallest number that render it possible.

Believing, plainly, is not a Relation which Othello has to each of the three Terms concerned, but to all of them together:

What is called belief or Judgment is nothing but this relation of believing or judging, which relates a Mind to several things other than itself.

This property of having a 'sense' or 'direction' is one which the relation of judging shares with all other relations. The 'sense' of relations is the ultimate source of order and series and a host of mathematical concepts;

Thus a Belief is true when it corresponds to a certain associated complex, and false when it does not.

Hence we account simultaneously for the two facts that beliefs (a) depend on minds for their existence, (b) do not depend on minds for their truth.

Thus a belief is true when there is a corresponding Fact, and is false when there is no corresponding fact.

At first sight we might imagine that knowledge could be defined as 'true belief'.

This belief, though true, would not be thought to constitute knowledge.

Thus it is clear that a true belief is not knowledge when it is deduced from a false belief.

But are we to say that nothing is knowledge except what is validly deduced from true premisses? Obviously we cannot say this. Such a definition is at once too wide and too narrow. In the first place, it is too wide, because it is not enough that our premisses should be true, they must also be known.

Knowledge is what is validly deduced from known premisses. This, however, is a circular definition: it assumes that we already know what is meant by 'known premisses'. It can, therefore, at best define one sort of knowledge, the sort we call derivative, as opposed to intuitive knowledge.

The chief objection to it is that it unduly limits knowledge.

There are in fact many ways, besides logical Inference, by which we pass from one belief to another:

But in fact 'knowledge' is not a precise conception: it merges into 'probable opinion',

Any such definition must be more or less misleading.

Does not arise over derivative knowledge, but over intuitive knowledge.

All our knowledge of truths is infected with some degree of doubt, and a theory which ignored this fact would be plainly wrong.

What we firmly believe, if it is true, is called knowledge, provided it is either intuitive or inferred (logically or psychologically) from intuitive knowledge from which it follows logically. What we firmly believe, if it is not true, is called Error. What we firmly believe, if it is neither knowledge nor error, and also what we believe hesitatingly, because it is, or is derived from, something which has not the highest degree of self-evidence, may be called probable Opinion. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion.

A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually.

But this test, though it increases probability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system. Thus the mere organization of probable opinion will never, by itself, transform it into indubitable knowledge.

Just as a comparative anatomist, from a single bone, sees what kind of animal the whole must have been, so the metaphysician, according to Hegel, sees, from any one piece of reality, what the whole of reality must be—at least in its large outlines.

This essential incompleteness appears, according to Hegel, equally in the world of thought and in the world of things. In the world of thought, if we take any idea which is abstract or incomplete, we find, on examination, that if we forget its incompleteness, we become involved in contradictions; these contradictions turn the idea in question into its opposite, 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 its antithesis.

In this way Hegel advances until he reaches the 'Absolute Idea', which, according to him, has no incompleteness, no opposite, and no need of further development.

Hence, (1) acquaintance with a thing does not logically involve a knowledge of its Relations, and (2) a knowledge of some of its relations does not involve a knowledge of all of its relations nor a knowledge of its 'nature' in the above sense.

Thus the fact that a thing has relations does not prove that its relations are logically necessary.

It follows that we cannot prove that the universe as a whole forms a single harmonious system such as Hegel believes that it forms.

Most of the great ambitious attempts of metaphysicians have proceeded by the attempt to prove that such and such apparent features of the actual world were self-contradictory, and therefore could not be real. The whole tendency of modern thought, however, is more and more in the direction of showing that the supposed contradictions were illusory, and that very little can be proved a priori from considerations of what must be.

Kant, who first emphasized this contradiction, deduced the impossibility of space and time, which he declared to be merely subjective; and since his time very many philosophers have believed that space and time are mere appearance, not characteristic of the world as it really is. Now, however, owing to the labours of the mathematicians, notably Georg Cantor, it has appeared that the impossibility of infinite collections was a mistake.

Hence the reasons for regarding space and time as unreal have become inoperative, and one of the great sources of metaphysical constructions is dried up.

Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge;

The essential characteristic of philosophy, which makes it a study distinct from science, is criticism.

Rene Descartes' 'methodical doubt', with which modern philosophy began, is not of this kind, but is rather the kind of criticism which we are asserting to be the essence of philosophy.