From Essential Selections in 19th and 20th Century Philosophy, by James Fieser


Copyright 2014, updated 5/1/2015


A FREE MAN’S WORSHIP (from “A Free Man’s Worship”, 1902)


Humans as a Product of Nature’s Blind Power

. . . That Man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labors of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man’s achievement must inevitably be buried beneath the debris of a universe in ruins—all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built.

            How, in such an alien and inhuman world, can so powerless a creature as Man preserve his aspirations untarnished? A strange mystery it is that Nature, omnipotent but blind, in the revolutions of her secular hurryings through the abysses of space, has brought forth at last a child, subject still to her power, but gifted with sight, with knowledge of good and evil, with the capacity of judging all the works of his unthinking Mother. In spite of Death, the mark and seal of the parental control, Man is yet free, during his brief years, to examine, to criticize, to know, and in imagination to create. To him alone, in the world with which he is acquainted, this freedom belongs; and in this lies his superiority to the resistless forces that control his outward life.


Religious Worship of Nature’s Blind Power

The savage, like ourselves, feels the oppression of his impotence before the powers of Nature; but having in himself nothing that he respects more than Power, he is willing to prostrate himself before his gods, without inquiring whether they are worthy of his worship. Pathetic and very terrible is the long history of cruelty and torture, of degradation and human sacrifice, endured in the hope of placating the jealous gods: surely, the trembling believer thinks, when what is most precious has been freely given, their lust for blood must be appeased, and more will not be required. The religion of Moloch—as such creeds may be generically called—is in essence the cringing submission of the slave, who dare not, even in his heart, allow the thought that his master deserves no adulation. Since the independence of ideals is not yet acknowledged, Power may be freely worshiped, and receive an unlimited respect, despite its wanton infliction of pain.

            But gradually, as morality grows bolder, the claim of the ideal world begins to be felt; and worship, if it is not to cease, must be given to gods of another kind than those created by the savage. Some, though they feel the demands of the ideal, will still consciously reject them, still urging that naked Power is worthy of worship. Such is the attitude inculcated in God’s answer to Job out of the whirlwind: the divine power and knowledge are paraded, but of the divine goodness there is no hint. Such also is the attitude of those who, in our own day, base their morality upon the struggle for survival, maintaining that the survivors are necessarily the fittest. But others, not content with an answer so repugnant to the moral sense, will adopt the position which we have become accustomed to regard as specially religious, maintaining that, in some hidden manner, the world of fact is really harmonious with the world of ideals. Thus Man creates God, all-powerful and all-good, the mystic unity of what is and what should be.


Freeing Oneself from the Tyranny of Nature’s Power

But the world of fact, after all, is not good; and, in submitting our judgment to it, there is an element of slavishness from which our thoughts must be purged. For in all things it is well to exalt the dignity of Man, by freeing him as far as possible from the tyranny of non-human Power. When we have realized that Power is largely bad, that man, with his knowledge of good and evil, is but a helpless atom in a world which has no such knowledge, the choice is again presented to us: Shall we worship Force, or shall we worship Goodness? Shall our God exist and be evil, or shall he be recognized as the creation of our own conscience?

            The answer to this question is very momentous, and affects profoundly our whole morality. The worship of Force, to which Carlyle and Nietzsche and the creed of Militarism have accustomed us, is the result of failure to maintain our own ideals against a hostile universe: it is itself a prostrate submission to evil, a sacrifice of our best to Moloch. . . .


Humans United by the Tie of Common Doom

The life of Man, viewed outwardly, is but a small thing in comparison with the forces of Nature. The slave is doomed to worship Time and Fate and Death, because they are greater than anything he finds in himself, and because all his thoughts are of things which they devour. But, great as they are, to think of them greatly, to feel their passionless splendor, is greater still. And such thought makes us free men; we no longer bow before the inevitable in Oriental subjection, but we absorb it, and make it a part of ourselves. To abandon the struggle for private happiness, to expel all eagerness of temporary desire, to burn with passion for eternal things—this is emancipation, and this is the free man’s worship. And this liberation is effected by a contemplation of Fate; for Fate itself is subdued by the mind which leaves nothing to be purged by the purifying fire of Time.

            United with his fellow-men by the strongest of all ties, the tie of a common doom, the free man finds that a new vision is with him always, shedding over every daily task the light of love. The life of Man is a long march through the night, surrounded by invisible foes, tortured by weariness and pain, towards a goal that few can hope to reach, and where none may tarry long. One by one, as they march, our comrades vanish from our sight, seized by the silent orders of omnipotent Death. Very brief is the time in which we can help them, in which their happiness or misery is decided. Be it ours to shed sunshine on their path, to lighten their sorrows by the balm of sympathy, to give them the pure joy of a never-tiring affection, to strengthen failing courage, to instill faith in hours of despair. Let us not weigh in grudging scales their merits and demerits, but let us think only of their need—of the sorrows, the difficulties, perhaps the blindnesses, that make the misery of their lives; let us remember that they are fellow-sufferers in the same darkness, actors in the same tragedy with ourselves. And so, when their day is over, when their good and their evil have become eternal by the immortality of the past, be it ours to feel that, where they suffered, where they failed, no deed of ours was the cause; but wherever a spark of the divine fire kindled in their hearts, we were ready with encouragement, with sympathy, with brave words in which high courage glowed.




Unsatisfactory Explanations about the Nature of Mathematics

Preface. The present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles, is undertaken in Parts 2.7 of this Volume, and will be established by strict symbolic reasoning in Volume 2. The demonstration of this thesis has, if I am not mistaken, all the certainty and precision of which mathematical demonstrations are capable. As the thesis is very recent among mathematicians, and is almost universally denied by philosophers, I have undertaken, in this volume, to defend its various parts, as occasion arose, against such adverse theories as appeared most widely held or most difficult to disprove. . . .

1.3. The Philosophy of Mathematics has been hitherto as controversial, obscure and unprogressive as the other branches of philosophy. Although it was generally agreed that mathematics is in some sense true, philosophers disputed as to what mathematical propositions really meant: although something was true, no two people were agreed as to what it was that was true, and if something was known, no one knew what it was that was known. So long, however, as this was doubtful, it could hardly be said that any certain and exact knowledge was to be obtained in mathematics. We find, accordingly, that idealists have tended more and more to regard all mathematics as dealing with mere appearance, while empiricists have held everything mathematical to be approximation to some exact truth about which they had nothing to tell us. This state of things, it must be confessed, was thoroughly imsatisfactory. Philosophy asks of Mathematics: What does it mean? Mathematics in the past was unable to answer, and Philosophy answered by introducing the totally irrelevant notion of mind. But now Mathematics is able to answer, so far at least as to reduce the whole of its propositions to certain fundamental notions of logic. At this point, the discussion must be resumed by Philosophy. I shall endeavour to indicate what are the fundamental notions involved, to prove at length that no others occur in mathematics, and to point out briefly the philosophical difficulties involved in the analysis of these notions. A complete treatment of these difficulties would involve a treatise on Logic, which will not be found in the following pages.


Logic as the Premises of Mathematics

1.10. The connection of mathematics with logic, according to the above account, is exceedingly close. The fact that all mathematical constants are logical constants, and that all the premisses of mathematics are concerned with these, gives, I believe, the precise statement of what philosophers have meant in asserting that mathematics is à priori. The fact is that, when once the apparatus of logic has been accepted, all mathematics necessarily follows. The logical constants themselves are to be defined only by enumeration, for they are so fundamental that all the properties by which the class of them might be defined presuppose some terms of the class. But practically, the method of discovering the logical constants is the analysis of symbolic logic, which will be the business of the following chapters. The distinction of mathematics from logic is very arbitrary, but if a distinction is desired, it may be made as follows. Logic consists of the premisses of mathematics, together with all other propositions which are concerned exclusively with logical constants and with variables but do not fulfil the above definition of mathematics (§1). Mathematics consists of all the consequences of the above premisses which assert formal implications containing variables, together with such of the premisses themselves as have these marks. Thus some of the premises of mathematics, e.g. the principle of the syllogism, if p implies q and q implies r, then p implies r, will belong to mathematics, while others, such as implication is a relation, will belong to logic but not to mathematics. But for the desire to adhere to usage, we might identify mathematics and logic, and define either as the class of propositions containing only variables and logical constants; but respect for tradition leads me rather to adhere to the above distinction, while recognizing that certain propositions belong to both sciences.

            From what has now been said, the reader will perceive that the present work has to fulfil two objects, first, to show that all mathematics follows from symbolic logic, and secondly to discover, as far as possible, what are the principles of symbolic logic itself.




The Paradox Explained (Introduction to Mathematical Philosophy, 1919, 8)

When I first came upon this contradiction, in the year 1901, I attempted to discover some flaw in Cantor's proof that there is no greatest cardinal, which we gave in Chapter VIII. Applying this proof to the supposed class of all imaginable objects, I was led to a new and simpler contradiction, namely, the following:

            The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. In other words, if there is such a thing as “everything,” then, “everything” is something, and is a member of the class “everything.” But normally a class is not a member of itself. Mankind, for example, is not a man. Form now the assemblage of all classes which are not members of themselves. This is a class: is it a member of itself or not? If it is, it is one of those classes that are not members of themselves, i.e., it is not a member of itself. If it is not, it is not one of those classes that are not members of themselves, i.e. it is a member of itself. Thus of the two hypotheses – that it is, and that it is not, a member of itself – each implies its contradictory. This is a contradiction.

            There is no difficulty in manufacturing similar contradictions ad lib. The solution of such contradictions by the theory of types is set forth fully in Principia Mathematica . . . . For the present an outline of the solution must suffice.

            The fallacy consists in the formation of what we may call "impure" classes, i.e. classes which are not pure as to [hierarchical] "type." As we shall see in a later chapter, classes are logical fictions, and a statement which appears to be about a class will only be significant if it is capable of translation into a form in which no mention is made of the class. This places a limitation upon the ways in which what are nominally, though not really, names for classes can occur significantly: a sentence or set of symbols in which such pseudo-names occur in wrong ways is not false, but strictly devoid of meaning. The supposition that a class is, or that it is not, a member of itself is meaningless in just this way. And more generally, to suppose that one class of individuals is a member, or is not a member, of another class of individuals will be to suppose nonsense; and to construct symbolically any class whose members are not all of the same grade in the logical hierarchy is to use symbols in a way which makes them no longer symbolise anything.


Barber Example: Does he Shave Himself? (“The Philosophy of Logical Atomism” 1918, 5)

That contradiction is extremely interesting. You can modify its form; some forms of modification are valid and some are not. I once had a form suggested to me which was not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, and those only, who do not shave themselves" [i.e., every man in town either shaves himself or is shaved by the barber.] The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. But in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i. e., that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just a noise without meaning.


Theory of Types Solution: Higher-Tier Types include only Lower-Tier Types (Principles of Mathematics, Appendix B)

The doctrine of types is here put forward tentatively, as affording a possible solution of the contradiction; but it requires, in all probability, to be transformed into some subtler shape before it can answer all difficulties. In case, however, it should be found to be a first step towards the truth, I shall endeavour in this Appendix to set forth its main outlines, as well as some problems which it fails to solve.

            [Tier 1 Type:] A term or individual is any object which is not a range. This is the lowest type of object  . . . say a certain point in space . . . .

            [Tier 2 Type:] The next type consists of ranges or classes of individuals [i.e., sets of Tier 1 objects]. . . . Thus "Brown and Jones" is an object of this type. . . .

            [Tier 3 Type:] The next type after classes of individuals consists of classes of classes of individuals [i.e., sets of Tier 2 objects]. Such are, for example, associations of clubs; the members of such associations, the clubs, are themselves classes of individuals.  It will be convenient to speak of classes only where we have classes of individuals, of classes of classes only where we have classes of classes of individuals, and so on. . . .

            To sum up: it appears that the special contradiction of Chapter X is solved by the doctrine of types [i.e., a type cannot be a member of itself], but that there is at least one closely analogous contradiction which is probably not soluble by this doctrine.


LOGICAL ATOMISM (“The Philosophy of Logical Atomism” 1918)


Logical Atomism Explained

The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the sort of last residue in analysis are logical atoms and not physical atoms. Some of them will be what I call “particulars,” — such things as little patches of color or sounds, momentary things — and some of them will be predicates or relations and so on. The point is that the atom I wish to arrive at is the atom of logical analysis, not the atom of physical analysis.

            It is a rather curious fact in philosophy that the data which are undeniable to start with are always rather vague and ambiguous. You can, for instance, say: “There are a number of people in this room at this moment.” That is obviously in some sense undeniable. But when you come to try and define what this room is, and what it is for a person to be in a room, and how you are going to distinguish one person from another, and so forth, you find that what you have said is most fearfully vague and that you really do not know what you meant. That is a rather singular fact, that everything you are really sure of, right off is something that you do not know the meaning of, and the moment you get a precise statement you will not be sure whether it is true or false, at least right off. The process of sound philosophizing, to my mind, consists mainly in passing from those obvious, vague, ambiguous things, that we feel quite sure of, to something precise, clear, definite, which by reflection and analysis we find is involved in the vague thing that we started from, and is, so to speak, the real truth of which that vague thing is a sort of shadow. . . .

            I propose now to consider what sort of language a logically perfect language would be. In a logically perfect language the words in a proposition would correspond one by one with the components of the corresponding fact, with the exception of such words as “or,” “not,” “if,” “then,” which have a different function. In a logically perfect language, there will be one word and no more for every simple object, and everything that is not simple will be expressed by a combination of words, by a combination derived, of course, from the words for the simple things that enter in, one word for each simple component. A language of that sort will be completely analytic, and will show at a glance the logical structure of the facts asserted or denied. The language which is set forth in Principia Mathematica is intended to be a language of that sort. It is a language which has only syntax and no vocabulary whatsoever. Barring the omission of a vocabulary I maintain that it is quite a nice language. It aims at being that sort of a language that, if you add a vocabulary, would be a logically perfect language. . . .


Atomic Facts

The first truism to which I wish to draw your attention — and I hope you will agree with me that these things that I call truisms are so obvious that it is almost laughable to mention them — is that the world contains facts, which are what they are whatever we may choose to think about them, and that there are also beliefs, which have reference to facts, and by reference to facts are either true or false. I will try first of all to give you a preliminary explanation of what I mean by a “fact.” When I speak of a fact — I do not propose to attempt an exact definition, but an explanation, so that you will know what I am talking about — I mean the kind of thing that makes a proposition true or false. If I say “It is raining,” what I say is true in a certain condition of weather and is false in other conditions of weather. The condition of weather that makes my statement true (or false as the case may be), is what I should call a “fact.” If I say “Socrates is dead,” my statement will be true owing to a certain physiological occurrence which happened in Athens long ago. If I say, “Gravitation varies inversely as the square of the distance,” my statement is rendered true by astronomical fact. If I say, “Two and two are four,” it is arithmetical fact that makes my statement true. On the other hand, if I say “Socrates is alive,” or “Gravitation varies directly as the distance,” or “Two and two are five,” the very same facts which made my previous statements true show that these new statements are false. . . .

            The simplest imaginable facts are those which consist in the possession of a quality by some particular thing. Such facts, say, as “This is white.” They have to be taken in a very sophisticated sense. I do not want you to think about the piece of chalk I am holding, but of what you see when you look at the chalk. If one says, “This is white” it will do for about as simple a fact as you can get hold of. The next simplest would be those in which you have a relation between two facts, such as: “This is to the left of that.” Next you come to those where you have a triadic relation between three particulars. (An instance which Royce gives is “A gives B to C”). So you get relations which require as their minimum three terms, those we call triadic relations; and those which require four terms, which we call tetradic, and so on. There you have a whole infinite hierarchy of facts, — facts in which you have a thing and a quality, two things and a relation, three things and a relation, four things and a relation, and so on. That whole hierarchy constitutes what I call atomic facts, and they are the simplest sort of fact. You can distinguish among them some simpler than others, because the ones containing a quality are simpler than those in which you have, say, a pentadic relation, and so on. The whole lot of them, taken together, are as facts go very simple, and are what I call atomic facts. The propositions expressing them are what I call atomic propositions [i.e., propositions that contain a single verb].

            Atomic facts contain, besides the relation, the terms of the relation — one term if it is a monadic relation, two if it is dyadic, and so on. These “terms” which come into atomic facts I define as “particulars.”


Particulars = terms of relations in atomic facts. Definition.


            That is the definition of particulars, and I want to emphasize it because the definition of a particular is something purely logical. The question whether this or that is a particular, is a question to be decided in terms of that logical definition. In order to understand the definition it is not necessary to know beforehand “This is a particular” or “That is a particular”. It remains to be investigated what particulars you can find in the world, if any. The whole question of what particulars you actually find in the real world is a purely empirical one which does not interest the logician as such. The logician as such never gives instances, because it is one of the tests of a logical proposition that you need not know anything whatsoever about the real world in order to understand it.


Atomic Propositions: Particulars

Passing from atomic facts to atomic propositions, the word expressing a monadic relation or quality is called a “predicate,” and the word expressing a relation of any higher order would generally be a verb, sometimes a single verb, sometimes a whole phrase. At any rate the verb gives the essential nerve, as it were, of the relation. The other words that occur in the atomic propositions, the words that are not the predicate or verb, may be called the subjects of the proposition. There will be one subject in a monadic proposition, two in a dyadic one, and so on. The subjects in a proposition will be the words expressing the terms of the relation which is expressed by the proposition.

            The only kind of word that is theoretically capable of standing for a particular is a proper name, and the whole matter of proper names is rather curious.


Proper Names = words for particulars. Definition.


I have put that down although, as far as common language goes, it is obviously false. It is true that if you try to think how you are to talk about particulars, you will see that you cannot ever talk about a particular particular except by means of a proper name. . . .


Atomic Propositions: Predicates

I pass on from particulars to predicates and relations and what we mean by understanding the words that we use for predicates and relations. . . . Understanding a predicate is quite a different thing from understanding a name. By a predicate, as you know, I mean the word that is used to designate a quality such as red, white, square, round, and the understanding of a word like that involves a different kind of act of mind from that which is involved in understanding a name. To understand a name you must be acquainted with the particular of which it is a name, and you must know that it is the name of that particular. You do not, that is to say, have any suggestion of the form of a proposition, whereas in understanding a predicate you do. To understand “red,” for instance, is to understand what is meant by saying that a thing is red. You have to bring in the form of a proposition. . . .


Molecular Propositions

. . . I come on now to the proper topic of to-day’s lecture, that is molecular propositions. I call them molecular propositions because they contain other propositions which you may call their atoms, and by molecular propositions I mean propositions having such words as “or,” “if,” “and,” and so forth. If I say, “Either to-day is Tuesday, or we have all made a mistake in being here,” that is the sort of proposition that I mean that is molecular. Or if I say, “If it rains, I shall bring my umbrella,” that again is a molecular proposition because it contains the two parts “It rains” and “I shall bring my umbrella.” If I say, “It did rain and I did bring my umbrella,” that again is a molecular proposition. Or if I say, “The supposition of its raining is incompatible with the supposition of my not bringing my umbrella,” that again is a molecular proposition. There are various propositions of that sort, which you can complicate ad infinitum


Propositions with Two Verbs: Belief

You will remember that after speaking about atomic propositions I pointed out two more complicated forms of propositions which arise immediately on proceeding further than that: the first, which I call molecular propositions, which I dealt with last time, involving such words as “or,” “and,” “if,” and the second involving two or more verbs such as believing, wishing, willing, and so forth. In the case of molecular propositions it was not clear that we had to deal with any new form of fact, but only with a new form of proposition, i.e., if you have a disjunctive proposition such as “p or q” it does not seem very plausible to say that there is in the world a disjunctive fact corresponding to “p or q” but merely that there is a fact corresponding to p and a fact corresponding to q, and the disjunctive proposition derives its truth or falsehood from those two separate facts. Therefore in that case one was dealing only with a new form of proposition and not with a new form of fact. Today we have to deal with a new form of fact. . . .

            Take any sort of proposition, say “I believe Socrates is mortal.” Suppose that that belief does actually occur. The statement that it occurs is a statement of fact. You have there two verbs. You may have more than two verbs, you may have any number greater than one. I may believe that Jones is of opinion that Socrates is mortal. There you have more than two verbs. You may have any number, but you cannot have less than two. You will perceive that it is not only the proposition that has the two verbs, but also the fact, which is expressed by the proposition, has two constituents corresponding to verbs. I shall call those constituents verbs for the sake of shortness, as it is very difficult to find any word to describe all those objects which one denotes by verbs. Of course, that is strictly using the word “verb” in two different senses, but I do not think it can lead to any confusion if you understand that it is being so used. This fact (the belief) is one fact. It is not like what you had in molecular propositions where you had (say) “p or q.” It is just one single fact that you have a belief. That is obvious from the fact that you can believe a falsehood. It is obvious from the fact of false belief that you cannot cut off one part: you cannot have


I believe/Socrates is mortal.


Definite Descriptions

There are two sorts of descriptions, what one may call “ambiguous descriptions,” when we speak of “a so-and-so,” .and what one may call “definite descriptions,” when we speak of “the so-and-so” (in the singular). Instances are:



A man, a dog, a pig, a Cabinet Minister.


The man with the iron mask.

The last person who came into this room.

The only Englishman who ever occupied the Papal See.

The number of the inhabitants of London.

The sum of 43 and 34.


(It is not necessary for a description that it should describe an individual: it may describe a predicate or a relation or anything else.)

            It is phrases of that sort, definite descriptions, that I want to talk about today. I do not want to talk about ambiguous descriptions, as what there was to say about them was said last time.

            I want you to realize that the question whether a phrase is a definite description turns only upon its form, not upon the question whether there is a definite individual so described. For instance, I should call “The inhabitant of London” a definite description, although it does not in fact describe any definite individual.

            The first thing to realize about a definite description is that it is not a name. We will take “The author of Waverley.” That is a definite description, and it is easy to see that it is not a name. . . . You sometimes find people speaking as if descriptive phrases were names, and you will find it suggested, e. g., that such a proposition as “Scott is the author of Waverley” really asserts that “Scott” and “the author of Waverley” are two names for the same person. That is an entire delusion; first of all, because “the author of Waverley” is not a name, and, secondly, because, as you can perfectly well see, if that were what is meant, the proposition would be one like “Scott is Sir Walter,” and would not depend upon any fact except that the person in question was so called, because a name is what a man is called. . . .

            There are a great many other sorts of incomplete symbols besides descriptions. These are classes, which I shall speak of next time, and relations taken in extension, and so on. Such aggregations of symbols are really the same thing as what I call “logical fictions,” and they embrace practically all the familiar objects of daily life: tables, chairs, Piccadilly, Socrates, and so on. Most of them are either classes, or series, or series of classes. In any case they are all incomplete symbols, i. e, they are aggregations that only have a meaning in use and do not have any meaning in themselves.




Acquaintance and Description Explained

In the preceding chapter we saw that there are two sorts of knowledge: knowledge of things, and knowledge of truths. In this chapter we shall be concerned exclusively with knowledge of things, of which in turn we shall have to distinguish two kinds. Knowledge of things, when it is of the kind we call knowledge by acquaintance, is essentially simpler than any knowledge of truths, and logically independent of knowledge of truths, though it would be rash to assume that human beings ever, in fact, have acquaintance with things without at the same time knowing some truth about them. Knowledge of things by description, on the contrary, always involves, as we shall find in the course of the present chapter, some knowledge of truths as its source and ground. But first of all we must make clear what we mean by ‘acquaintance’ and what we mean by ‘description’.

            We shall say that we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths. Thus in the presence of my table I am acquainted with the sense-data that make up the appearance of my table—its colour, shape, hardness, smoothness, etc.; all these are things of which I am immediately conscious when I am seeing and touching my table. The particular shade of colour that I am seeing may have many things said about it—I may say that it is brown, that it is rather dark, and so on. But such statements, though they make me know truths about the colour, do not make me know the colour itself any better than I did before so far as concerns knowledge of the colour itself, as opposed to knowledge of truths about it, I know the colour perfectly and completely when I see it, and no further knowledge of it itself is even theoretically possible. Thus the sense-data which make up the appearance of my table are things with which I have acquaintance, things immediately known to me just as they are.

            My knowledge of the table as a physical object, on the contrary, is not direct knowledge. Such as it is, it is obtained through acquaintance with the sense-data that make up the appearance of the table. We have seen that it is possible, without absurdity, to doubt whether there is a table at all, whereas it is not possible to doubt the sense-data. My knowledge of the table is of the kind which we shall call ‘knowledge by description’. The table is ‘the physical object which causes such-and-such sense-data’. This describes the table by means of the sense-data. In order to know anything at all about the table, we must know truths connecting it with things with which we have acquaintance: we must know that ‘such-and-such sense-data are caused by a physical object’. There is no state of mind in which we are directly aware of the table; all our knowledge of the table is really knowledge of truths, and the actual thing which is the table is not, strictly speaking, known to us at all. We know a description, and we know that there is just one object to which this description applies, though the object itself is not directly known to us. In such a case, we say that our knowledge of the object is knowledge by description.


Knowledge by Acquaintance: Sense Data, Memory, Introspection

All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundation. It is therefore important to consider what kinds of things there are with which we have acquaintance.

            Sense-data, as we have already seen, are among the things with which we are acquainted; in fact, they supply the most obvious and striking example of knowledge by acquaintance. But if they were the sole example, our knowledge would be very much more restricted than it is. We should only know what is now present to our senses: we could not know anything about the past—not even that there was a past—nor could we know any truths about our sense-data, for 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’. We have therefore to consider acquaintance with other things besides sense-data if we are to obtain any tolerably adequate analysis of our knowledge.

            The first extension beyond sense-data to be considered is acquaintance by memory. It is obvious that we often remember what we have seen or heard or had otherwise present to our senses, and that in such cases we are still immediately aware of what we remember, in spite of the fact that it appears as past and not as present. This immediate knowledge by memory is the source of all our knowledge concerning the past: without it, there could be no knowledge of the past by inference, since we should never know that there was anything past to be inferred.

            The next extension to be considered is acquaintance by introspection. We are not only aware of things, but we are often aware of being aware of them. When I see the sun, I am often aware of my seeing the sun; thus ‘my seeing the sun’ is an object with which I have acquaintance. When I desire food, I may be aware of my desire for food; thus ‘my desiring food’ is an object with which I am acquainted. Similarly we may be aware of our feeling pleasure or pain, and generally of the events which happen in our minds. This kind of acquaintance, which may be called self-consciousness, is the source of all our knowledge of mental things. It is obvious that it is only what goes on in our own minds that can be thus known immediately. What goes on in the minds of others is known to us through our perception of their bodies, that is, through the sense-data in us which are associated with their bodies. But for our acquaintance with the contents of our own minds, we should be unable to imagine the minds of others, and therefore we could never arrive at the knowledge that they have minds. It seems natural to suppose that self-consciousness is one of the things that distinguish men from animals: animals, we may suppose, though they have acquaintance with sense-data, never become aware of this acquaintance. I do not mean that they doubt whether they exist, but that they have never become conscious of the fact that they have sensations and feelings, nor therefore of the fact that they, the subjects of their sensations and feelings, exist.

            We have spoken of acquaintance with the contents of our minds as self-consciousness, but it is not, of course, consciousness of our self: it is consciousness of particular thoughts and feelings. 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. When we try to look into ourselves we always seem to come upon some particular thought or feeling, and not upon the ‘I’ which has the thought or feeling. Nevertheless there are some reasons for thinking that we are acquainted with the ‘I’, though the acquaintance is hard to disentangle from other things. . . .

            We may therefore sum up as follows what has been said concerning acquaintance with things that exist. We have acquaintance in sensation with the data of the outer senses, and in introspection with the data of what may be called the inner sense—thoughts, feelings, desires, etc.; we have acquaintance in memory with things which have been data either of the outer senses or of the inner sense. Further, it is probable, though not certain, that we have acquaintance with Self, as that which is aware of things or has desires towards things.

            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. Every complete sentence must contain at least one word which stands for a universal, since all verbs have a meaning which is universal. We shall return to universals later on, in Chapter IX; for the present, it is only necessary to guard against the supposition that whatever we can be acquainted with must be something particular and existent. Awareness of universals is called conceiving, and a universal of which we are aware is called a concept.


Knowledge by Description: Derived from Acquaintance

It will be seen that among the objects with which we are acquainted are not included physical objects (as opposed to sense-data), nor other people’s minds. These things are known to us by what I call ‘knowledge by description’, which we must now consider.

            By a ‘description’ I mean any phrase of the form ‘a so-and-so’ or ‘the so-and-so’. A phrase of the form ‘a so-and-so’ I shall call an ‘ambiguous’ description; a phrase of the form ‘the so-and-so’ (in the singular) I shall call a ‘definite’ description. Thus ‘a man’ is an ambiguous description, and ‘the man with the iron mask’ is a definite description. . . . I shall therefore, in the sequel, speak simply of ‘descriptions’ when I mean ‘definite descriptions’. Thus a description will mean any phrase of the form ‘the so-and-so’ in the singular.

            All names of places—London, England, Europe, the Earth, the Solar System—similarly involve, when used, descriptions which start from some one or more particulars with which we are acquainted. 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. . . .

            It will be seen that there are various stages in the removal from acquaintance with particulars: there is Bismarck to people who knew him; Bismarck to those who only know of him through history; the man with the iron mask; the longest-lived of men. These are progressively further removed from acquaintance with particulars; the first comes as near to acquaintance as is possible in regard to another person; in the second, we shall still be said to know ‘who Bismarck was’; in the third, we do not know who was the man with the iron mask, though we can know many propositions about him which are not logically deducible from the fact that he wore an iron mask; in the fourth, finally, we know nothing beyond what is logically deducible from the definition of the man. There is a similar hierarchy in the region of universals. Many universals, like many particulars, are only known to us by description. But 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.

            The fundamental principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.

            We shall not at this stage attempt to answer all the objections which may be urged against this fundamental principle. For the present, we shall merely point out that, in some way or other, it must be possible to meet these objections, for it is scarcely conceivable that we can make a judgement or entertain a supposition without knowing what it is that we are judging or supposing about. We must attach some meaning to the words we use, if we are to speak significantly and not utter mere noise; and the meaning we attach to our words must be something with which we are acquainted. 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. We have in mind some description of Julius Caesar: ‘the man who was assassinated on the Ides of March’, ‘the founder of the Roman Empire’, or, perhaps, merely ‘the man whose name was Julius Caesar. (In this last description, Julius Caesar is a noise or shape with which we are acquainted.) 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 spite of the fact that we can only know truths which are wholly composed of terms which we have experienced in acquaintance, we can yet have knowledge by description of things which we have never experienced. 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.




Neutral Monism Explained (“On the Nature of Acquaintance” 1914)

“Neutral monism” — as opposed to idealistic monism and materialistic monism — is the theory that the things commonly regarded as mental and the things commonly regarded as physical do not differ in respect of any intrinsic property possessed by the one set and not by the other, but differ only in respect of arrangement and context. The theory may be illustrated by comparison with a postal directory, in which the same names come twice over, once in alphabetical and once in geographical order; we may compare the alphabetical order to the mental, and the geographical order to the physical. The affinities of a given thing are quite different in the two orders, and its causes and effects obey different laws. Two objects may be connected in the mental world by the association of ideas, and in the physical world by the law of gravitation. The whole context of an object is so different in the mental order from what it is in the physical order that the object itself is thought to be duplicated, and in the mental order it is called an “idea,” namely the idea of the same object in the physical order. But this duplication is a mistake: “ideas” of chairs and tables are identical with chairs and tables, but are considered in their mental context, not in the context of physics.

            Just as every man in the directory has two kinds of neighbors, namely alphabetical neighbors and geographical neighbors, so every object will lie at the intersection of two causal series with different laws, namely the mental series and the physical series. “Thoughts” are not different in substance from “things”; the stream of my thoughts is a stream of things, namely of the things which I should commonly be said to be thinking of; what leads to its being called a stream of thoughts is merely that the laws of succession are different from the physical laws. In my mind, Caesar may call up Charlemagne, whereas in the physical world the two were widely sundered. The whole duality of mind and matter, according to this theory, is a mistake; there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other. . . .

            In favor of the theory, we may admit that what is experienced may itself be part of the physical world, and often is so; that the same thing may be experienced by different minds; that the old distinction of “mind” and “matter,” besides ignoring the abstract facts that are neither mental nor physical, errs in regarding “matter,” and the “space” in which matter is, as something obvious, given, and unambiguous, and is in hopeless doubt as to whether the facts of sensation are to be called physical or mental. . . .


Neutral Monism and Ockham’s Razor (“Philosophy of Logical Atomism” 1918)

I have naturally a bias in favor of the theory of neutral monism because it exemplifies Occam’s razor. I always wish to get on in philosophy with the smallest possible apparatus, partly because it diminishes the risk of error, because it is not necessary to deny the entities you do not assert, and therefore you run less risk of error the fewer entities you assume. The other reason — perhaps a somewhat frivolous one — is that every diminution in the number of entities increases the amount of work for mathematical logic to do in building up things that look like the entities you used to assume.


Different Causal Laws for Psychology and Physics (The Analysis of Mind, 1921)

My own belief—for which the reasons will appear in subsequent lectures—is that [William] James is right in rejecting consciousness as an entity, and that the American realists are partly right, though not wholly, in considering that both mind and matter are composed of a neutral-stuff which, in isolation, is neither mental nor material. I should admit this view as regards sensations: what is heard or seen belongs equally to psychology and to physics. But I should say that images belong only to the mental world, while those occurrences (if any) which do not form part of any “experience” belong only to the physical world. There are, it seems to me, prima facie different kinds of causal laws, one belonging to physics and the other to psychology. The law of gravitation, for example, is a physical law, while the law of association is a psychological law. Sensations are subject to both kinds of laws, and are therefore truly “neutral” in Holt’s sense. But entities subject only to physical laws, or only to psychological laws, are not neutral, and may be called respectively purely material and purely mental. Even those, however, which are purely mental will not have that intrinsic reference to objects which Brentano assigns to them and which constitutes the essence of “consciousness” as ordinarily understood. . . .

            The question whether it is possible to obtain precise causal laws in which the causes are psychological, not material, is one of detailed investigation. I have done what I could to make clear the nature of the question, but I do not believe that it is possible as yet to answer it with any confidence. It seems to be by no means an insoluble question, and we may hope that science will be able to produce sufficient grounds for regarding one answer as much more probable than the other. But for the moment I do not see how we can come to a decision.  . . .

            The conclusions at which we have arrived may be summed up as follows:

            I. Physics and psychology are not distinguished by their material. Mind and matter alike are logical constructions; the particulars out of which they are constructed, or from which they are inferred, have various relations, some of which are studied by physics, others by psychology. Broadly speaking, physics group particulars by their active places, psychology by their passive places. . . .

            VI. All our data, both in physics and psychology, are subject to psychological causal laws; but physical causal laws, at least in traditional physics, can only be stated in terms of matter, which is both inferred and constructed, never a datum. In this respect psychology is nearer to what actually exists.


Source: Bertrand Russell, “A Free Man’s Worship” (1902); Principles of Mathematics (1903); The Problems of Philosophy (1912); “On the Nature of Acquaintance” (1914); “The Philosophy of Logical Atomism” (1918); Introduction to Mathematical Philosophy (1919), The Analysis of Mind (1921).


Questions for Review








Questions for Analysis





5. Russell draws a sharp like between knowledge by acquaintance and knowledge by description. Explain the difference between the two and discuss whether the two notions blur together more than Russell assumes.

6. Peirce argues that Ockham’s Razor refutes the theory of neutral monism, but Russell argues that Ockham’s Razor supports it. Explain their respective reasoning and discuss which view seems best.