The Problems of Philosophy — Chapter-by-Chapter Outline

Author: Bertrand Russell First published: 1912 Edition covered: The standard text of the first edition (Home University Library of Modern Knowledge, Williams & Norgate, London, 1912; American printing Henry Holt & Co., New York), as reproduced in Project Gutenberg #5827 and the Standard Ebooks edition, and matching the Oxford World's Classics edition (Oxford University Press, 1997, introduction by John Skorupski). The 15-chapter structure is identical across editions; Russell called the book his "shilling shocker," written for a general audience.

Central thesis

The Problems of Philosophy is an introduction to philosophy written not as a survey of doctrines but as an exercise in critical thinking about knowledge. Russell opens by asking whether anything is so certain that no reasonable person could doubt it, and answers that our knowledge is built on two foundations: acquaintance with the immediate data of sense, memory, and introspection, and self-evident principles — logic, arithmetic, the principle of induction — that experience cannot prove but cannot do without. Everything else, including the physical world, other minds, and the future, is known only by description and probable inference.

Along the way Russell defends a series of positions: that the table he sits at is not what it appears to be; that the existence of matter is rationally credible though not demonstrable; that idealism rests on a confusion between the act of apprehension and its object; that universals form a timeless world of being that makes a priori knowledge possible; that truth consists in correspondence between belief and fact, not coherence; and that philosophy's value lies not in definite answers but in the enlargement of the mind through the contemplation of possibilities.

The book's deepest claim is that philosophy is possible at all: we can have genuine knowledge — including knowledge of things we have never experienced — because our knowledge of truths rests on acquaintance with universals and on principles whose truth we can see directly.

Is there any knowledge in the world which is so certain that no reasonable man could doubt it?

Chapter 1 — Appearance and Reality

Central question

Can we know anything with absolute certainty, and is the world as our senses present it to us?

Main argument

The table as the test case

Russell begins with the question "Is there any knowledge in the world which is so certain that no reasonable man could doubt it?" and immediately complicates the obvious answer. In daily life we assume a great deal: that the sun is ninety-three million miles away, that other people see the same chairs and tables we see, that the table we see is the table we feel. To show how fragile these assumptions are, Russell concentrates on a single object: the table in his room.

Colour, texture, shape, and touch all fail

• Colour. To the eye the table is oblong, brown, and shiny — but the parts that reflect light look brighter, some look white, and no two spectators ever see exactly the same distribution of colours. It changes with artificial light, with a colour-blind observer, with blue spectacles, and vanishes entirely in the dark. "We are compelled to deny that, in itself, the table has any one particular colour."
• Texture. The naked eye sees smoothness; a microscope reveals "roughnesses and hills and valleys." A stronger microscope changes the picture again, so there is no privileged level at which the "real" table is seen.
• Shape. A "really" rectangular table looks, from almost every point of view, as if it had two acute and two obtuse angles; parallel sides look as if they converge. "The 'real' shape is not what we see; it is something inferred from what we see."
• Touch and sound. Sensations of hardness depend on how hard we press and with what part of the body; the sound of rapping varies likewise. These can be at most signs of some property of the table, not the property itself.

Sense-data, sensations, physical objects

Russell introduces the book's foundational vocabulary. Sense-data are "the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on." A sensation is the experience of being immediately aware of a sense-datum — the colour is the datum, the awareness is the sensation. The real table, if it exists, is called a physical object, and the collection of all physical objects is matter. Two questions follow: Is there a real table at all? If so, what sort of object can it be?

The philosophers' answers so far

Berkeley (1685–1753), whose Three Dialogues between Hylas and Philonous Russell presents as the classic statement of the difficulty, argued that the immediate objects of the senses cannot exist independently of us. Berkeley's conclusion — that the "real" table is an idea in the mind of God — Russell treats as one of several "surprising possibilities." Leibniz says the table is a community of souls; "sober science" says it is "a vast collection of electric charges in violent motion." Almost all philosophers agree on one point: whatever our sense-data depend upon, their occurrence is a sign of something existing independently of us.

The modest result

The chapter's positive finding is deliberately small: what the senses immediately tell us is not the truth about the object apart from us, but only the truth about sense-data. "The one thing we know about it is that it is not what it seems." That is enough to launch philosophy, which is "merely the attempt to answer such ultimate questions, not carelessly and dogmatically... but critically."

Key ideas

• The distinction between appearance and reality — between what things seem to be and what they are — is one of the distinctions that cause most trouble in philosophy.
• No colour, shape, or texture of the table pre-eminently appears to be its colour, shape, or texture; the senses deliver perspective-relative appearances.
• The painter must unlearn the habit of seeing things as they "really" are; the philosopher wants what the practical man wants — the truth about the table — but is more troubled by the difficulty of getting it.
• Sense-data are the things immediately known in sensation; sensations are the awareness of them.
• The real table, if there is one, "is not immediately known to us at all, but must be an inference from what is immediately known."
• The central question divides into two: whether matter exists, and what its nature is.
• Even the strangest hypotheses about the table may be true; the one certain result is that the table is not what it seems.

Key takeaway

Appearance and reality diverge even for the most ordinary object: the senses give us sense-data, never the thing itself, so the real table must be inferred rather than perceived.

Chapter 2 — The Existence of Matter

Central question

Granted that we are certain of our own sense-data, have we any reason to regard them as signs of the existence of something else — a physical object that persists when we are not looking?

Main argument

The stakes: solipsism

If we cannot be sure of the independent existence of objects, we cannot be sure of other people's bodies, and therefore not of their minds either — "we shall be left alone in a desert." Russell concedes at once that no logical contradiction follows from the hypothesis that the whole of life is a dream; but there is no reason to suppose it true, and it is a less simple hypothesis than the common-sense one.

Descartes' method of doubt

Russell recruits Descartes (1596–1650) as the founder of the method: doubt everything that can be doubted, including the deliverances of the senses (the deceitful demon), until reaching what cannot be doubted — one's own existence: cogito, ergo sum. Russell then corrects Descartes. What has primitive certainty is not the permanent "I" but particular experiences: when I see a brown colour, what is certain is not "I am seeing a brown colour" but "a brown colour is being seen." This applies to dreams and hallucinations too: we really do have the sensations we think we have, even when no physical object corresponds to them. So "some at least of our immediate experiences seem absolutely certain," and this is the fixed point from which the chapter starts.

Why common sense wants physical objects

• Buying and selling. A table "can be bought and sold and pushed about"; if it were merely sense-data it would cease to exist when covered by a cloth, and the cloth would "rest, by a miracle, in the place where the table formerly was."
• Shared experience. When ten people sit round a dinner-table they want to be seeing the same tablecloth, knives, and forks; but each person's sense-data are private. "If there are to be public neutral objects... there must be something over and above the private and particular sense-data."

The argument must not beg the question

Other people's testimony cannot ground the inference, since other people are themselves presented to us only as sense-data — "if I had no reason to believe that there were physical objects independent of my sense-data, I should have no reason to believe that other people exist except as part of my dream." The reason must come from our own private experience.

The cat

Russell's central example: if the cat appears in one part of the room and then in another, the natural supposition is that it moved through intermediate positions. But if the cat is "merely a set of sense-data," it cannot have been anywhere we did not see it — it "suddenly sprang into being in a new place," and its hunger between meals becomes inexplicable, since "no hunger but my own can be a sense-datum to me." The behaviour of the sense-data representing the cat "becomes utterly inexplicable when regarded as mere movements and changes of patches of colour, which are as incapable of hunger as a triangle is of playing football." The same simplicity argument applies with even more force to human speech and thought.

The hierarchy of instinctive beliefs

The belief in an independent external world is not reached by argument at all; it is an instinctive belief, present in us "as soon as we begin to reflect." Russell generalizes into a method: philosophy should show us "the hierarchy of our instinctive beliefs," beginning with the strongest, isolating each from irrelevant additions, and keeping them all if they form a harmonious system. "There can never be any reason for rejecting one instinctive belief except that it clashes with others."

Key ideas

• The existence of the external world cannot be proved; no logical absurdity results from the dream hypothesis. But probability and simplicity favour the common-sense view.
• Our particular thoughts and feelings have primitive certainty; the permanent self and the physical object are both inferred.
• The appeal to other people's agreement begs the question, because other people are themselves given only as sense-data.
• The cat example shows that the physical-object hypothesis explains the behaviour of sense-data (hunger, continuous motion) that the sense-data-only hypothesis leaves miraculous.
• All knowledge must be built on instinctive beliefs; philosophy's task is to organize them into a harmonious, self-consistent system.
• The argument for matter is "typical of many philosophical arguments": not demonstrative, but weightier than any alternative.

Key takeaway

We can never prove that matter exists, but the belief that our sense-data are signs of independent objects is the simplest, most systematic explanation of our experience, and there is no reason to reject an instinctive belief that clashes with nothing.

Chapter 3 — The Nature of Matter

Central question

If the real table persists independently of perception, what can we know about its nature?

Main argument

What science says matter is

Physical science reduces natural phenomena to motions: light, heat, and sound are wave-motions travelling from body to perceiver, and what has the wave-motion is matter. Science assigns to matter "position in space, and the power of motion according to the laws of motion" — and nothing else; any further properties it may have are useless to science. Russell warns against the slogan "light is a form of wave-motion": the light we see is not a wave-motion. A blind man can understand wave-motion perfectly well (he knows space by touch and can ride a wave), but he can never understand light; so "light itself... is not supposed by science to form any part of the world that is independent of us and our senses."

The space of science is not the space we see or touch

• Visual space differs from tactile space; infants must learn to coordinate them.
• Different people see the same object as different shapes: "A circular coin, for example, though we should always judge it to be circular, will look oval unless we are straight in front of it." The coin's real shape belongs to a public physical space, different from anyone's private apparent space.
• The physical space of geometry and astronomy is known only through its relations — "we can know all those things about physical space which a man born blind might know through other people about the space of sight" — but never through immediate acquaintance with its intrinsic nature.

Public and private time

Our feeling of duration is unreliable — boredom makes time crawl, sleep erases it — so duration must be private too. But the order of before and after is public: "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." Yet this does not mean physical events are simultaneous with our perceptions of them: the thunder and the lightning are simultaneous as physical events, but the sense-datum of hearing the thunder comes later; and "when we see the sun we are seeing the sun of eight minutes ago."

The correspondence view

We may presume that differences in sense-data correspond to differences in physical objects, but we cannot be acquainted with the quality in the object that makes it look blue or red; science's "wave-motion" is itself in physical space, with which we have no direct acquaintance. The naive hypothesis that physical objects are more or less like sense-data (the "real" colour as a medium shade) is "groundless": the colour we see depends on the light-waves reaching the eye, so "it is quite gratuitous to suppose that physical objects have colours."

The result

"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." Whether any other method can discover that intrinsic nature — whether idealism is right that matter is mental — is the question of the next chapter.

Key ideas

• Science knows matter only as position in space and motion according to laws; it says nothing of its intrinsic nature.
• The experienced light, colour, and sound are not part of the scientific world of matter; they are effects of waves on our sense-organs.
• Physical space is public and neutral between the senses; the spaces of sight and touch are private and perceptual.
• The penny-shaped example — a circular coin that looks oval from most angles — shows that "real" shape belongs to physical space, not to any apparent space.
• Time's order (before/after) is public and reliable; time's duration is private and unreliable; perception lags physical events (the sun of eight minutes ago).
• Physical objects have knowable relations but unknown intrinsic nature; colour is not "really" in the object.

Key takeaway

The nature of matter is unknowable in itself: science tells us the structure of physical objects through their relations to sense-data, but never what those objects intrinsically are.

Chapter 4 — Idealism

Central question

Is the idealist doctrine — that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental — sound?

Main argument

What idealism claims

Idealism, as Russell defines it, holds that "whatever exists, or at any rate whatever can be known to exist, must be in some sense mental." It is not obviously absurd: we already saw that physical objects must differ widely from sense-data, so "the truth about physical objects must be strange." The idealist's grounds are epistemological, and the first serious attempt was Berkeley's.

Berkeley's argument

Berkeley proved, largely validly, that sense-data cannot exist independently of perceiving minds. But he then argued: sense-data are the only things our perceptions assure us of; to be known is to be "in" a mind; therefore nothing is known except what is in some mind. For the tree, esse est percipi: its being consists in being perceived. Berkeley fully admits the tree continues to exist unperceived — because God perceives it; the real tree is "ideas in the mind of God," and our perceptions are a partial participation in God's.

The fallacy: the ambiguity of "in the mind"

We speak of "bearing a person in mind" without meaning the person is literally in our minds — only that a thought of him is. Similarly, when Berkeley says the tree must be in the mind to be known, all he is entitled to say is that a thought of the tree must be in the mind. "To argue that the tree itself must be in our minds is like arguing that a person whom we bear in mind is himself in our minds."

The deeper diagnosis: act and object

Whenever an idea is before the mind, two distinct things are involved: the object we are aware of (the colour of the table) and the act of awareness. The act is undoubtedly mental; the object's being mental does not follow. Berkeley's plausibility depends on "an unconscious equivocation": taking "ideas are in the mind" as true of the act of apprehension, then transferring it to the object apprehended. Russell states the positive moral: "Acquaintance with objects essentially consists in a relation between the mind and something other than the mind; it is this that constitutes the mind's power of knowing things." If we say the known must be "in the mind," we either unduly limit the mind's power of knowing or utter a mere tautology.

The second argument: "we cannot know that anything exists which we do not know"

This alleged truism is false, and its falsity is exposed by distinguishing two senses of "know": knowledge of truths (judgement, savoir, wissen) and knowledge of things (acquaintance, connaître, kennen). Restated, the truism becomes: "We can never truly judge that something with which we are not acquainted exists" — "a palpable falsehood. I have not the honour to be acquainted with the Emperor of China, but I truly judge that he exists." Such knowledge is knowledge by description: from general principles plus acquaintance with something else, we infer the existence of things with which we are not acquainted. Whether there are such general principles is the subject of the following chapters.

Key ideas

• Idealism is not obviously absurd; the truth about physical objects must be strange whatever it is.
• Berkeley was right that sense-data depend on perceivers; wrong that only minds and their contents can exist or be known.
• The tree's esse is not percipi: existence is not being perceived, and being known does not make a thing mental.
• The fallacy is equivocation on "in the mind" and on "idea" — conflating the act of apprehension with the object apprehended.
• Acquaintance is a relation between the mind and something other than the mind; this is what makes knowledge possible at all.
• "We cannot know that anything exists which we do not know" is false — the Emperor of China exists, and I know it without acquaintance.

Key takeaway

Idealism fails because it slides from the trivial fact that awareness is mental to the false conclusion that what we are aware of is mental; the same distinction between act and object will later ground the whole theory of knowledge.

Chapter 5 — Knowledge by Acquaintance and Knowledge by Description

Central question

What are the two kinds of knowledge of things — acquaintance and description — and how does each relate to the limits of our experience?

Main argument

Acquaintance defined

We have acquaintance with anything of which we are directly aware, "without the intermediary of any process of inference or any knowledge of truths." I am acquainted with the sense-data that make up the appearance of my table: its colour, shape, hardness, smoothness. About the colour I can learn truths, but "no further knowledge of it itself is even theoretically possible." Knowledge of the table as a physical object, by contrast, is knowledge by description: the table is "the physical object which causes such-and-such sense-data."

The kinds of acquaintance

• Sensation — acquaintance with the data of the outer senses.
• Memory — immediate awareness of what was previously present to the senses, appearing as past; "the source of all our knowledge concerning the past."
• Introspection — acquaintance with our own mental events: "my seeing the sun," "my desiring food"; the source of all knowledge of mental things, and what distinguishes men from animals, who have sensations but never become aware of their sensations.
• The Self — probably, though not certainly: to know the truth "I am acquainted with this sense-datum" we seem to need acquaintance with something called "I," though when we look inward we find only particular thoughts and feelings.
• Universals — general ideas such as whiteness, diversity, brotherhood; awareness of a universal is called conceiving, and the universal is then called a concept. "Every complete sentence must contain at least one word which stands for a universal, since all verbs have a meaning which is universal."

Descriptions

A description is any phrase of the form "a so-and-so" (an ambiguous description) or "the so-and-so" (a definite description). An object is known by description when we know that it is "the so-and-so" — that exactly one object has the property — without being acquainted with it. The man with the iron mask existed and many propositions are known about him, but we do not know who he was.

The hierarchy of remoteness from acquaintance

Russell ranks cases by distance from acquaintance: Bismarck to his contemporaries (who knew his body's sense-data); Bismarck to us through history ("the first Chancellor of the German Empire"); the man with the iron mask; "the most long-lived of men" — where we know nothing beyond what follows logically from the description. Any description we know to be applicable must ultimately "involve some reference to a particular with which we are acquainted"; even place-names like London or England start from particulars we have experienced. In logic alone no reference to actual particulars is involved.

The fundamental principle

"Every proposition which we can understand must be composed wholly of constituents with which we are acquainted." When we speak of Julius Caesar, Caesar himself is not before our minds; we have in mind some description — "the man who was assassinated on the Ides of March" — composed wholly of particulars and universals with which we are acquainted. This is how knowledge by description escapes the prison of 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."

Key ideas

• Acquaintance is direct awareness without inference; description always involves knowledge of truths as its ground.
• The physical object is never given: all our knowledge of the table is knowledge of truths about sense-data, plus the description "the physical object which causes such-and-such sense-data."
• Memory, introspection, and (probably) self-acquaintance extend acquaintance beyond the present moment of sensation.
• We are acquainted with universals as well as particulars; conceiving is the awareness of a universal.
• A definite description asserts uniqueness: "the so-and-so exists" means one object, and no more, has the property.
• Knowledge by description is what lets us know Bismarck, Julius Caesar, and the physical world — things no one we know has ever encountered.

Key takeaway

All knowledge rests on acquaintance as its foundation, but description lets us pass beyond the limits of our private experience to know things we have never experienced.

Chapter 6 — On Induction

Central question

Do any number of past cases of association give us reason to expect the same association in the future?

Main argument

The question raised

To know of the existence of matter, other people, the unremembered past, and the future, we must know general principles linking one sort of thing with another — as thunder is a sign of the earlier existence of lightning. Russell takes the least doubted case: we are convinced the sun will rise tomorrow. Asked why, we answer "Because it always has risen every day." Pushed further, we appeal to the laws of motion; but the interesting doubt is whether the laws of motion will remain in operation until tomorrow — and the only reason to believe they will is that they have operated so far.

The chicken

Past uniformities cause expectations in animals and men alike — a horse resists a new road, domestic animals expect food from the feeder — but "the man who has fed the chicken every day throughout its life at last wrings its neck instead." Such crude expectations are unreliable; the question is whether any reasonable ground supports them.

The principle of induction

The belief in the uniformity of nature — that everything that happens is an instance of an exceptionless general law — is what science works with; balloons and aeroplanes are exceptions to "unsupported bodies in air fall," but the laws of motion and gravitation account for them too. The principle of induction has two parts:

• (a) The greater the number of cases in which things of sort A have been found associated with things of sort B, the greater the probability that they will be associated in a fresh case.
• (b) A sufficient number of cases makes the probability of a fresh association nearly a certainty, and approach certainty without limit.

The same two parts apply to the general law that A is always associated with B, with a correspondingly lower probability.

The swans

Probability is always relative to given data. A man who has seen many white swans may validly infer, on those data, that it is probable all swans are white; the existence of black swans does not disprove his argument, since a thing "may very well happen in spite of the fact that some data render it improbable." The principle cannot be disproved by experience.

The circle

Nor can it be proved by experience: any argument from experience to unexamined cases assumes the principle, so "we can never use experience to prove the inductive principle without begging the question." We must either accept it on its own intrinsic evidence or "forgo all justification of our expectations about the future." Without it: no expectation that bread will nourish rather than poison, that leaping from a roof will hurt, that our best friend's body is not inhabited by our worst enemy's mind. Even the reign of law and the principle that every event has a cause depend on it.

Key ideas

• All extension of knowledge beyond private experience requires general principles of inference; the inductive principle is the chief one.
• The uniformity of nature is a working hypothesis of science: exception-ridden rules are replaced by rules without exceptions (balloons fall under the laws of motion).
• The argument from "past futures" to "future futures" begs the question.
• The principle of induction has two parts: probability increases with repeated association, and approaches certainty without limit.
• Induction cannot be proved by experience (it would be circular) nor disproved by experience (probability is relative to data) — as the white/black swan case shows.
• All our conduct and all scientific generalization rest on it; if it is unsound, no expectation about the future has any justification.

Key takeaway

The principle of induction is incapable of proof and incapable of disproof, yet every inference from experience to the unexperienced — the sunrise, the next meal, the laws of motion — presupposes it.

Chapter 7 — On Our Knowledge of General Principles

Central question

What general principles, beyond induction, must we accept without proof, and how do we know them?

Main argument

Self-evident logical principles

The inductive principle is not alone: a number of principles can be neither proved nor disproved by experience yet are "used in arguments which start from what is experienced." The most fundamental is the principle that "anything implied by a true proposition is true" — illustrated by the dialogue: if yesterday was the 15th, today must be the 16th; yesterday was the 15th; therefore today is the 16th. Such principles of inference are apt to be overlooked "because of their very obviousness." How we know them is instructive: we first realize a particular application, then see that the particularity is irrelevant — as with learning that "two and two are four" from particular pairs of things.

The "laws of thought"

Tradition singles out three logical principles under this name:

• The law of identity: "Whatever is, is."
• The law of contradiction: "Nothing can both be and not be."
• The law of excluded middle: "Everything must either be or not be."

The name is misleading: what matters "is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them."

Empiricists and rationalists

The historic controversy between empiricists (Locke, Berkeley, Hume) and rationalists (Descartes, Leibniz) can now be decided. The rationalists were right that logical principles cannot be proved by experience — all proof presupposes them. But two things limit that victory. First, the word "innate" is wrong: such knowledge is "elicited and caused by experience," which "merely so directs our attention that we see its truth." Russell adopts the term a priori for knowledge that experience cannot prove. Second, the empiricists were right that nothing can be known to exist except by the help of experience: the Emperor of China exists for us by testimony, and testimony reduces to sense-data. "All knowledge which asserts existence is empirical, and the only a priori knowledge concerning existence is hypothetical."

Ethics and mathematics are a priori

• Ethics. Judgements of intrinsic value — happiness more desirable than misery, knowledge than ignorance — cannot be proved by experience: "the fact that a thing exists or does not exist cannot prove either that it is good that it should exist or that it is bad."
• Pure mathematics. "Two and two are four" is seen to be true from any single typical instance; fresh instances add nothing. It carries "some quality of necessity" absent from empirical generalizations. We can imagine a world with immortal men (Swift's Struldbrugs) but not a world where two and two make five. "All men are mortal" is a mere fact that might have been otherwise; "two and two are four" "is not a mere fact, but a necessity to which everything actual and possible must conform."

Deduction gives new knowledge

From "two and two always make four" plus "Brown and Jones are two, and so are Robinson and Smith," we deduce that the four men make four — new knowledge contained in neither premiss alone. The stock example "All men are mortal; Socrates is a man; therefore Socrates is mortal" is, by contrast, better run as a direct induction from the observed deaths of A, B, C to Socrates: an empirical generalization is more doubtful than its instances, so the inductive route warrants greater confidence.

Key ideas

• Some principles of inference must be granted before any argument or proof is possible; they are self-evident and indubitable.
• The "laws of thought" are really laws about things, not about thinking; the truth of inference principles is presupposed by all demonstration.
• Rationalists were right that there is a priori knowledge; empiricists were right that existence claims always need experience.
• "A priori" does not mean innate: experience elicits the knowledge while being unable to prove it.
• Judgements of intrinsic value and all pure mathematics are a priori; empirical generalizations like "all men are mortal" are never more than probable.
• Deduction from general a priori principles can yield genuinely new knowledge, as the Brown–Jones–Robinson–Smith example shows.

Key takeaway

Beyond induction there is a whole class of self-evident principles — logical, mathematical, ethical — known a priori, which are the skeleton of all inference, while every claim that something exists still rests on experience.

Chapter 8 — How A Priori Knowledge Is Possible

Central question

How can we know general propositions a priori — in advance of, and about, things we have never experienced?

Main argument

Kant's problem

Kant (1724–1804) deserves credit for two things: seeing that some a priori knowledge is not analytic (such that denying it would be self-contradictory), and making the theory of knowledge central to philosophy. "A bald man is a man" is analytic — the predicate is obtained by analysing the subject. Before Kant, philosophers thought all a priori knowledge was of this kind, guaranteed by the law of contradiction alone.

Hume's scepticism and Kant's answer

Hume (1711–76) showed that cause and effect is a synthetic connexion — the effect cannot be logically deduced from the cause. Kant agreed about arithmetic too: in 7 + 5 = 12, "the idea of 12 is not contained in them, nor even in the idea of adding them together." Hence pure mathematics is synthetic and a priori, and the question arises: how is it possible? The problem is that "such knowledge is general, whereas all experience is particular": we know that any two of London's inhabitants a hundred years hence, and any other two, will make four, without knowing who they are.

Kant's solution

Kant splits every experience into what is due to the object and what is due to our own nature: the crude material of sensation is given by the object, but space, time, causality, and comparison are supplied by the mind. The thing in itself is unknowable; the phenomenon is the joint product. Since we supply the forms, everything we can experience must conform to our a priori knowledge — but that knowledge applies only to phenomena, never to things in themselves.

Russell's two objections

• The certainty fails. "Our nature is as much a fact of the existing world as anything, and there can be no certainty that it will remain constant. It might happen, if Kant is right, that to-morrow our nature would so change as to make two and two become five."
• The scope is unduly limited. Two physical objects and two other physical objects must make four physical objects, even if physical objects cannot be experienced; a priori truths apply to things whether or not we think of them.

Laws of thought are about things, not thoughts

The law of contradiction is "a belief about things, not only about thoughts": if a tree is a beech, it cannot also be not a beech, whatever the mind does. "No fact about the constitution of our minds could make it true that two and two are four."

Relations and the world beyond mind

A priori knowledge concerns entities that do not properly exist — qualities and relations. "I am in my room": I exist, my room exists, but does "in" exist? It denotes a relation that holds between me and the room; "an earwig is in my room, even if neither I nor the earwig nor any one else is aware of this truth." Relations must therefore be placed in "a world which is neither mental nor physical" — the world of universals, to be explored next.

Key ideas

• Analytic judgements (a bald man is a man) are trivial; the interesting a priori truths are synthetic.
• Kant saw that all pure mathematics is synthetic a priori; Hume had shown cause and effect is synthetic.
• Kant's transcendental story — the mind supplies space, time, and categories — cannot explain the necessity of a priori truths: our nature might change, and a priori truths apply beyond experience anyway.
• "Two and two are four" is about all actual or possible couples, not about how our minds are made.
• The law of contradiction and other logical laws are facts about things in the world, not laws of thought.
• Relations such as "in" belong to a world neither mental nor physical — the world of being, which alone can ground a priori knowledge.

Key takeaway

A priori knowledge is possible neither as analytic truth nor as a contribution of the mind: its subject matter is the timeless world of universals and their relations, to which experience merely directs our attention.

Chapter 9 — The World of Universals

Central question

What is the nature of the entities — universals — that relations and qualities name, and what kind of being do they have?

Main argument

Plato's theory of ideas

The problem is as old as Plato, whose theory of ideas Russell calls "one of the most successful attempts hitherto made"; his own theory is "largely Plato's, with merely such modifications as time has shown to be necessary." Justice, like whiteness, is the common nature in virtue of which just acts and white things are just and white — an "idea" or "form" that is not in minds, is not particular, does not exist in the world of sense, and is "eternally itself, immutable and indestructible." Russell will use the word universal for what Plato meant, to avoid the misleading associations of "idea": a particular is what is given in sensation; a universal is what many particulars can share.

Universals are everywhere in language

Broadly speaking, proper names stand for particulars; other substantives, adjectives, prepositions, and verbs stand for universals. "No sentence can be made up without at least one word which denotes a universal": even "I like this" contains "like," which I may feel toward other things and other people may feel toward things. "Thus all truths involve universals, and all knowledge of truths involves acquaintance with universals."

Neglect of relations: monism and monadism

Philosophers have recognized the universals named by adjectives and substantives — qualities — while overlooking those named by verbs and prepositions — relations. This omission "is hardly too much to say... most metaphysics, since Spinoza, has been largely determined by it": if only qualities exist, every proposition attributes a property to a single thing, and relations are impossible — leading either to monism (Spinoza, Bradley: only one thing can exist) or to monadism (Leibniz: many isolated things that cannot interact).

The refutation of the denial of universals

Berkeley and Hume denied "abstract ideas": to think of whiteness, they said, is to reason about a particular white thing while being careful to use only what holds of all white things. The reply: how do we know a thing is white? By resemblance to a chosen particular — but "the resemblance required will have to be a universal," since it holds between many pairs. And if each pair had its own resemblance, those resemblances would themselves resemble each other. "Thus at last we shall be forced to admit resemblance as a universal" — and then there is no point denying whiteness and triangularity.

Subsistence versus existence

The relation "north of" in "Edinburgh is north of London" holds whether or not anyone thinks of it; but ask "Where and when does this relation exist?" and the answer is "Nowhere and nowhen." It is "neither in space nor in time, neither material nor mental; yet it is something." Universals do not exist but subsist: they have being, timelessly. "The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems... The world of existence is fleeting, vague, without sharp boundaries." Both worlds are real; both matter to the metaphysician. And universals are not thoughts: "One man's act of thought is necessarily a different thing from another man's," yet both may think of the same whiteness.

Key ideas

• Universals are Plato's ideas stripped of mysticism: what many particulars can share, apprehended by minds but not constituted by them.
• Every sentence contains at least one universal-term; all truths and all knowledge of truths involve universals.
• The neglect of relations (verbs and prepositions) generated monism and monadism, both mistaken.
• Berkeley and Hume's denial of abstract ideas collapses: resemblance is itself a universal, forced upon us by their own analysis.
• Relations like "north of" subsist independently of minds — Edinburgh would be north of London if no minds existed.
• Universals subsist (timeless being); particulars and minds exist (in time); both worlds are real.

Key takeaway

There is a world of being as real as the world of existence — the world of universals, whose relations are the subject matter of a priori knowledge and whose independence refutes both idealism and the denial of abstract ideas.

Chapter 10 — On Our Knowledge of Universals

Central question

How are we acquainted with universals, and what does that acquaintance explain about a priori knowledge?

Main argument

Acquaintance with universals

• Sensible qualities. We are acquainted with white, red, black, sweet, sour, loud, hard — universals exemplified in sense-data. Seeing many white patches, we "easily learn to abstract the whiteness which they all have in common."
• Relations of space and time. From a single complex sense-datum (the page before me) I perceive that some parts are to the left of others, and abstract the relation "being to the left of"; from a chime of bells retained in memory, I abstract "before and after."
• Resemblance. Seeing two shades of green together, I can see that they resemble each other more than either resembles a red; I am thus acquainted with the universal resemblance — and even with relations between relations ("greater than" holding between two resemblances).

The solution to a priori knowledge

"All a priori knowledge deals exclusively with the relations of universals." The test: to understand a proposition, we must be acquainted with what it deals with. We understand "two and two are four" — even read as "any collection formed of two twos is a collection of four" — as soon as we know "collection," "two," and "four," without knowing any particular couples (there are infinitely many). So the proposition is about the universal "couple," not about this or that couple. What seemed mysterious — that a priori knowledge "anticipated and controlled experience" — dissolves: no fact about what can be experienced is known independently of experience. We know a priori that any two things and any other two make four, but we need experience to know that Brown and Jones are two.

A priori versus empirical generality

"All men are mortal" and "two and two are four" do not differ in meaning — both are understood through universals — but in evidence: the empirical claim rests on instances (innumerable deaths), the a priori one on a perceived connexion between universals. Physiology can subsume "men are mortal" under a wider generalization, but the ultimate ground remains inductive.

General truths without instances

We can know general propositions of which no instance can be given: "All products of two integers, which never have been and never will be thought of by any human being, are over 100." This is vital: "we can never know any proposition of the form 'this is a physical object'" — no instance of a physical object is ever given in acquaintance — so all our knowledge of physical objects and of other people's minds "depends throughout upon this possibility of general knowledge where no instance can be given."

A survey of knowledge

The chapter closes with a map of the sources of knowledge: immediate knowledge of things (acquaintance — particulars such as sense-data and the self, and universals such as sensible qualities, space-time relations, similarity); derivative knowledge of things (description — involving acquaintance plus truths); immediate knowledge of truths (intuitive knowledge of self-evident truths); and derivative knowledge of truths (deduction from self-evident truths by self-evident principles). Since error is possible in knowledge of truths but not in acquaintance, the problem of error now moves to the centre.

Key ideas

• We are acquainted with sensible qualities, spatial and temporal relations, resemblance, and some relations between relations.
• All a priori knowledge deals exclusively with relations of universals; this dissolves the mystery of its "anticipating" experience.
• "Two and two are four" is about the universal couple; applying it to Brown and Jones requires experience.
• The difference between a priori truths and empirical generalizations lies in the evidence, not the meaning.
• We can know general truths with no given instances — a power on which all knowledge of physical objects and other minds depends.
• Knowledge divides into four kinds: acquaintance (things), description (things), intuitive knowledge (truths), derivative knowledge (truths).

Key takeaway

Acquaintance with universals makes a priori knowledge possible and explains our ability to know truths about classes of things — physical objects, other minds — of which we can never produce an instance.

Chapter 11 — On Intuitive Knowledge

Central question

What truths are self-evident, in what degrees, and can they bear the weight of all our other knowledge?

Main argument

The insistent Socrates

We believe most things for reasons, but "let us imagine some insistent Socrates, who, whatever reason we give him, continues to demand a reason for the reason." We are driven back, point by point, until we reach "some general principle, or some instance of a general principle, which seems luminously evident, and is not itself capable of being deduced from anything more evident." The inductive principle and the logical principles are the terminus: their truth is evident to us, and they themselves are incapable of demonstration.

Degrees of self-evidence

Self-evidence is not all-or-nothing; it "has degrees: it is not a quality which is simply present or absent." Truths of perception and the simplest logical principles have the highest degree; truths of immediate memory almost as high; the inductive principle less than the principle that what follows from a true premiss must be true; remote memories still less; judgements of intrinsic ethical or aesthetic value "apt to have some self-evidence, but not much." Where self-evident propositions conflict, "the more self-evident proposition is to be retained and the less self-evident rejected."

Truths of perception

Sense-data themselves are neither true nor false — a patch of colour simply exists. But two kinds of judgement based on them are self-evident: (1) bare assertions of existence — "there is that"; (2) analytical judgements — seeing a round patch of red, I judge "that patch of red is round," or "this is to the right of that," where the judgement analyses the datum into constituents and recombines them.

Judgements of memory

Memory is not constituted by images — the image is in the present, what is remembered is known to be past — but by "having immediately before the mind an object which is recognized as past." Without intuitive memory "we should not know that there ever was a past at all." Memory has graded trustworthiness: I am absolutely certain that half a minute ago I was sitting in this chair; less certain of this morning's breakfast; doubtful about the conversation at breakfast; and some alleged memories are wholly false — George IV came to believe he was at the battle of Waterloo "because he had so often said that he was": what he genuinely remembered was his repeated assertion, not the battle. Fallacious memory is thus "not a genuine case of memory in the strict sense."

The suggestion about two kinds of self-evidence

It is "highly probable that two different notions are combined in 'self-evidence'": one, corresponding to the highest degree, is "really an infallible guarantee of truth," while the others give only "a greater or less presumption." The chapter ends by deferring the question until the nature of truth has been settled.

Key ideas

• The regress of reasons must terminate in self-evident principles that are incapable of demonstration.
• Self-evidence comes in degrees, from absolute certainty to an almost imperceptible faintness.
• Truths of perception are of two kinds: assertions of the existence of sense-data, and judgements that analyse a complex datum.
• The essence of memory is having an object before the mind as past; images are not memory.
• Memory's trustworthiness tracks its self-evidence — recent and vivid events are certain, remote ones doubtful; George IV's Waterloo "memory" was no memory at all.
• All knowledge of truths rests ultimately on intuitive knowledge; error therefore enters only with judgement.

Key takeaway

All our knowledge of truths rests on self-evident intuitive judgements — perceptions, memories, and first principles — whose self-evidence admits of degrees and whose trustworthiness varies with them.

Chapter 12 — Truth and Falsehood

Central question

What do we mean by truth and falsehood — not which beliefs are true, but what truth itself consists in?

Main argument

Three requisites for a theory of truth

1. It must admit of its opposite, falsehood — unlike acquaintance, where "there is no dualism."
2. Truth and falsehood are properties of beliefs and statements: "a world of mere matter... would not contain any truths, in the sense in which truths are things of the same kind as falsehoods."
3. Yet truth depends on what is outside the belief: "If I believe that Charles I died on the scaffold, I believe truly, not because of any intrinsic quality of my belief... but because of an historical event which happened two and a half centuries ago."

Coherence fails as a definition

The rival theory — truth as coherence with the whole system of beliefs — fails twice. First, there is no proof that only one coherent system is possible: "a novelist might invent a past for the world that would perfectly fit on to what we know," and the hypothesis that life is one long dream is coherent with all known facts. Second, coherence presupposes the truth of the laws of logic — "this tree is a beech" and "this tree is not a beech" are incoherent because of the law of contradiction, which coherence cannot establish. Coherence remains valuable as a test of truth, but not as its definition.

Correspondence, and why belief is not a relation to a single object

We are "driven back to correspondence with fact." But to make room for falsehood, belief cannot be a two-term relation of mind to an object: "Othello believes falsely that Desdemona loves Cassio" — if there were an object "Desdemona's love for Cassio," the belief would be true; since there is no such object, Othello cannot be related to it. Relations can have more than two terms: "between" needs three (York is between London and Edinburgh), jealousy needs three people, "A wishes B to promote C's marriage with D" needs four.

The multiple-relation theory

Judging, therefore, is a relation with several terms — in Othello's case, four: Othello, Desdemona, loving, Cassio — "knitting together into one complex whole" the subject and objects. The objects are placed in an order by the "sense" or direction of the relation (Desdemona-loves-Cassio differs from Cassio-loves-Desdemona). One of the objects is itself a relation — "loving... is a brick in the structure, not the cement"; the cement is the relation of believing.

Truth defined

A belief is true when the objects, taken in the order they have in the belief, form a complex unity — when there is a corresponding fact ("Desdemona's love for Cassio," composed exclusively of the objects of the belief); false when no such complex exists. Minds create beliefs but not their truth: "What makes a belief true is a fact, and this fact does not (except in exceptional cases) in any way involve the mind of the person who has the belief." This satisfies all three requisites at once.

Key ideas

• Truth and falsehood are properties of beliefs; acquaintance admits of no falsehood.
• A belief's truth depends on something outside the belief — the Charles I example — so no internal quality of a belief can make it true.
• Coherence cannot define truth: many coherent systems are possible, and coherence presupposes the laws of logic.
• Belief cannot be a two-term relation to a single object, on pain of making falsehood impossible; relations may have any number of terms.
• Judging is a multiple-term relation whose "sense" orders its constituents; a belief's truth is the existence of the corresponding complex.
• Minds create beliefs but not their truth; the corresponding fact involves only the objects of the belief.

Key takeaway

Truth is correspondence between belief and fact: a belief is true when its objects, in the order the belief places them, form a complex whole in the world, and false when no such whole exists.

Chapter 13 — Knowledge, Error, and Probable Opinion

Central question

When we believe something, how can we tell whether the belief is knowledge, error, or merely probable opinion?

Main argument

Knowledge is not true belief

A man who believes "the late Prime Minister's last name began with a B" believes truly but does not know it if his premiss is false (he thinks Mr. Balfour was the late Prime Minister; it was Sir Henry Campbell Bannerman). A newspaper that "by an intelligent anticipation, announces the result of a battle before any telegram" may publish the truth, yet its readers do not know it. Nor does valid deduction from true premisses suffice, for the premisses must also be known; and a conclusion drawn by a fallacious process ("all Greeks are men; Socrates was a man; therefore Socrates was a Greek") is not knowledge even when true. "Derivative knowledge" is what is validly deduced from premisses known intuitively — but psychological inference (reading print and passing straight to its meaning: "the newspaper announces the King's death") also yields derivative knowledge, provided a discoverable logical inference runs parallel. "Knowledge" is not a precise conception: "it merges into 'probable opinion'."

Two ways of knowing a fact

Any complex fact may be known (1) by judgement — the parts are judged to be related as they are — or (2) by acquaintance with the complex fact itself, "which may (in a large sense) be called perception": you can know that the sun is setting by knowing the hour, or by looking west and seeing it. Judgement is liable to error; acquaintance with a fact is not.

The two kinds of self-evidence, now distinguished

• First kind (absolute): acquaintance with the fact corresponding to the truth. This guarantees truth — "the judgement that the terms are so related must be true" — but is private: facts about sense-data and mental things can be self-evident only to the one person acquainted with them, whereas relations between universals can be self-evident to many minds. Even so, passing from perception to judgement requires analysis, "in this process it is possible to commit an error."
• Second kind (degrees): self-evidence of judgements not derived from direct perception of the fact — the horse trotting away whose hoofbeats fade into doubt; comparing two shades of colour as one is gradually changed toward the other; tuning a musical instrument. Here self-evidence is a matter of degree, and "the higher degrees are more to be trusted than the lower."

Knowledge, error, probable opinion

What we firmly believe, if true and either intuitive or properly inferred, is knowledge; if not true, error; and "what we firmly believe, if it is neither knowledge nor error, and also what we believe hesitatingly... may be called probable opinion. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion." Coherence, rejected as the definition of truth, returns as a criterion: a body of individually probable opinions, mutually coherent, becomes more probable — "the test of coherence condemns the dreams and confirms the waking life" — though it "never gives absolute certainty, unless there is certainty already at some point in the coherent system."

Key ideas

• True belief is not knowledge when derived from false premisses or fallacious reasoning — the Campbell Bannerman and newspaper examples.
• Derivative knowledge requires known premisses plus a valid (or at least discoverable) logical connexion; psychological inference qualifies.
• A complex fact can be known by judgement or by acquaintance with the fact itself; only the first is liable to error.
• First-kind self-evidence (acquaintance with the fact) is infallible but private; second-kind self-evidence has degrees of trustworthiness.
• Knowledge, error, and probable opinion are distinguished by truth, firmness, and the degree of self-evidence behind the belief.
• Coherence is a legitimate test of probable opinion, not a definition of truth.

Key takeaway

Knowledge shades into probable opinion by degrees of self-evidence: only acquaintance with the corresponding fact is infallible, and most of what passes for knowledge is at best highly probable, though coherence can raise the probability of our beliefs.

Chapter 14 — The Limits of Philosophical Knowledge

Central question

Can metaphysics prove, a priori, the great theses — the rationality of the universe, the illusoriness of matter and evil — that philosophers have promised?

Main argument

Hegel's system as the great representative

The ambition to prove by a priori reasoning "the fundamental dogmas of religion, the essential rationality of the universe, the illusoriness of matter, the unreality of all evil" is vain, and the great modern representative of the attempt is Hegel (1770–1831). On the standard interpretation, every fragment of reality has "hooks which grapple it to the next piece," so anything short of the Whole is incomplete and self-contradictory; thought moves by thesis, antithesis, synthesis up to the Absolute Idea, and Absolute Reality is "one single harmonious system, not in space or time, not in any degree evil, wholly rational, and wholly spiritual."

The fatal flaw: the "nature" of a thing

The system turns on the notion of a thing's "nature" as all the truths about it. But "a truth about a thing is not part of the thing itself": I may be acquainted with my toothache "as complete as knowledge by acquaintance ever can be" without knowing all the dentist can tell me about its cause. Acquaintance with a thing does not involve knowing its relations; knowledge of some relations does not involve knowledge of all. "Thus the fact that a thing has relations does not prove that its relations are logically necessary." From this, "we cannot prove that the universe as a whole forms a single harmonious system" — and the unreality of space, time, matter, and evil falls with it.

Space and time: the antinomy dissolved

Kant found a contradiction between the apparent infinite extent and infinite divisibility of space and time and the supposed impossibility of infinite collections, and concluded they are merely subjective. "Now, however, owing to the labours of the mathematicians, notably Georg Cantor, it has appeared that the impossibility of infinite collections was a mistake. They are not in fact self-contradictory, but only contradictory of certain rather obstinate mental prejudices." And the mathematicians went further: non-Euclidean geometries show that "some of Euclid's axioms, which appear to common sense to be necessary... are now known to derive their appearance of necessity from our mere familiarity with actual space." The position is reversed: "logic... has become the great liberator of the imagination, presenting innumerable alternatives," while experience decides, where it can, between them. "Our knowledge of what is has become less than it was formerly supposed to be, our knowledge of what may be is enormously increased."

Philosophy as criticism, not a super-science

"Philosophical knowledge... does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science." Philosophy's essence is criticism — examining the principles of science and daily life. But not the criticism of absolute scepticism: "from blank doubt, no argument can begin." Descartes' methodical doubt — doubting whatever seems doubtful, retaining what survives reflection — is the model. Philosophy "diminishes the risk of error, and... in some cases renders the risk so small as to be practically negligible."

Key ideas

• The great metaphysical proofs — of religion, of the rationality of the universe, of the unreality of matter and evil — do not survive critical scrutiny.
• Hegel's dialectic rests on confusing truths about a thing with the thing itself; the toothache and the dentist refute the doctrine of necessary relations.
• Cantor's work on infinite collections dissolved Kant's antinomy of space and time.
• Non-Euclidean geometry showed Euclid's axioms are habits, not necessities; logic multiplies possible worlds rather than narrowing them.
• Knowledge of what exists is limited to experience (broadened by description); knowledge of what may exist is vastly enlarged.
• Philosophy is criticism of knowledge, not a source of esoteric wisdom; absolute scepticism is unreasonable because argument must start from some shared knowledge.

Key takeaway

Metaphysics cannot prove grand conclusions about the universe as a whole; philosophy's real power is critical — testing the principles of science and common sense and freeing the imagination from the illusion of necessity.

Chapter 15 — The Value of Philosophy

Central question

Why ought philosophy to be studied, if it cannot deliver definite answers?

Main argument

The charge of uselessness

Many people, "under the influence of science or of practical affairs," regard philosophy as "innocent but useless trifling." The view rests on a wrong conception of the ends of life and of the kind of goods philosophy pursues. Physical science is useful to those who never study it, through inventions; "utility does not belong to philosophy" in that way. Its value, if any, "must be primarily sought" in its effects on those who study it — among "the goods of the mind," which matter as much as the goods of the body.

The uncertainty is the point

Philosophy aims at knowledge — the knowledge "which gives unity and system to the body of the sciences, and the kind which results from a critical examination of the grounds of our convictions, prejudices, and beliefs." But it has no agreed body of results; as soon as definite knowledge becomes possible, the subject "ceases to be called philosophy, and becomes a separate science" — astronomy was once "natural philosophy," and psychology has just split off. The deepest questions — Has the universe unity of plan or purpose? Is consciousness a permanent part of the universe? Are good and evil of importance to the universe or only to man? — remain, "so far as we can see," insoluble. "The value of philosophy is, in fact, to be sought largely in its very uncertainty": philosophy suggests "many possibilities which enlarge our thoughts and free them from the tyranny of custom," diminishing dogmatism and "keeping alive our sense of wonder by showing familiar things in an unfamiliar aspect."

Philosophic contemplation and the enlargement of the Self

Philosophy's chief value lies in "the greatness of the objects which it contemplates, and the freedom from narrow and personal aims resulting from this contemplation." The instinctive man lives shut up in private interests — "like a garrison in a beleaguered fortress." Philosophic contemplation, unalloyed, "does not divide the universe into two hostile camps... it views the whole impartially"; it does not aim to prove the universe akin to man. "All acquisition of knowledge is an enlargement of the Self, but this enlargement is best attained when it is not directly sought." The philosophies that make Man the measure of all things — "that truth is man-made, that space and time and the world of universals are properties of the mind" — are not only untrue, on the book's earlier arguments; they "rob philosophic contemplation of all that gives it value," fettering it to Self. The free intellect "will see as God might see, without a here and now, without hopes and fears."

The closing claim

The impartiality of contemplation "is the very same quality of mind which, in action, is justice, and in emotion is that universal love which can be given to all." Contemplation makes us "citizens of the universe, not only of one walled city at war with all the rest." In this citizenship "consists man's true freedom." Philosophy is to be studied "not for the sake of any definite answers to its questions... but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great."

Key ideas

• Philosophy is not instrumentally useful to non-philosophers; its value lies in its effects on those who study it, among the goods of the mind.
• The uncertainty of philosophy is largely apparent: solved questions leave philosophy to become sciences (astronomy, psychology).
• The deepest questions remain genuinely unsettled, and philosophy's value resides in its uncertainty.
• Philosophy frees thought "from the tyranny of custom" and keeps alive the sense of wonder.
• Contemplation enlarges the Self by starting from the not-Self; self-assertive philosophies shrink it.
• The rejection of "Man is the measure" is not only a theoretical conclusion but the condition of philosophy's value.
• The impartiality of contemplation is justice in action and universal love in emotion — citizenship of the universe.

Key takeaway

Philosophy is to be studied for the questions themselves: they enlarge our sense of possibility, free the mind from dogma, and through the greatness of what it contemplates, the mind itself becomes great.

The book's overall argument

1. Chapter 1 (Appearance and Reality) — The senses deliver only perspective-relative sense-data, never the object itself, so the real table — if it exists — is inferred, not perceived; appearance and reality diverge even in the most ordinary case.
2. Chapter 2 (The Existence of Matter) — Matter's existence cannot be proved, but the belief in physical objects is the simplest, most systematic explanation of our experience (the cat, the shared dinner-table) and is one of our most basic instinctive beliefs, which philosophy should organize rather than reject.
3. Chapter 3 (The Nature of Matter) — Science reveals the relations of physical objects (through space, time, and correspondence with sense-data) but never their intrinsic nature; physical objects remain unknown in themselves.
4. Chapter 4 (Idealism) — Idealism fails because it conflates the act of apprehension (mental) with its object (not thereby mental); acquaintance is a relation to something other than the mind, and "we cannot know that anything exists which we do not know" is simply false.
5. Chapter 5 (Knowledge by Acquaintance and Knowledge by Description) — All knowledge rests on acquaintance (sense-data, memory, introspection, probably the Self, universals), while description — built on acquaintance plus truths — carries us beyond private experience to the physical world, other minds, and history.
6. Chapter 6 (On Induction) — Every inference from the experienced to the unexperienced presupposes the principle of induction, which experience can neither prove nor disprove, yet which all our expectations about the future — sunrise, bread, the laws of motion — require.
7. Chapter 7 (On Our Knowledge of General Principles) — Beyond induction, a family of self-evident logical, mathematical, and ethical principles is known a priori; the rationalists were right that such knowledge exists, the empiricists that existence claims still need experience.
8. Chapter 8 (How A Priori Knowledge Is Possible) — Kant's answer — the mind supplies the forms — fails because our nature might change and because a priori truths apply beyond experience; a priori knowledge concerns qualities and relations, whose home is a world neither mental nor physical.
9. Chapter 9 (The World of Universals) — That world is Plato's world of forms, defended and de-mystified: universals (including relations) subsist timelessly, are unavoidable in every sentence, and refute both the denial of abstract ideas and the monism/monadism that followed from neglecting relations.
10. Chapter 10 (On Our Knowledge of Universals) — We are acquainted with universals — sensible qualities, relations of space and time, resemblance — and this solves the standing problem: all a priori knowledge deals exclusively with relations of universals, and general truths without instances are possible.
11. Chapter 11 (On Intuitive Knowledge) — The regress of reasons terminates in self-evident truths — perceptions, memories, first principles — whose self-evidence has degrees; all knowledge of truths rests on this intuitive foundation.
12. Chapter 12 (Truth and Falsehood) — Truth and falsehood are properties of beliefs, yet depend on something outside them: a belief is true when its objects form a corresponding complex fact (the Othello case), false when not — coherence is at best a test, never a definition.
13. Chapter 13 (Knowledge, Error, and Probable Opinion) — Knowledge is not true belief; self-evidence comes in two kinds — infallible acquaintance with a fact, and graded judgemental self-evidence — so knowledge shades into probable opinion, whose probability coherence can raise but never perfect.
14. Chapter 14 (The Limits of Philosophical Knowledge) — The metaphysical systems (Hegel above all) fail: relations are not logically necessary, Cantor dissolved the antinomy of space and time, and non-Euclidean geometry freed logic from necessity; philosophy is criticism, not a super-science.
15. Chapter 15 (The Value of Philosophy) — With definite answers unavailable, philosophy's value lies in its questions: they enlarge the imagination, break the tyranny of custom, and through impartial contemplation of the universe enlarge the mind itself into citizenship of the universe.

Common misunderstandings

Misunderstanding: Russell is a skeptic who denies that the table (or the external world) exists. The book argues the opposite. Russell concedes the external world cannot be demonstrated, but he endorses the common-sense belief in physical objects as the simplest hypothesis, and in Chapter 2 he explicitly rejects the dream hypothesis as having "not the slightest reason" in its favour. His conclusion is that matter exists, probably, and that its nature is largely unknown — not that nothing exists.

Misunderstanding: "Sense-data" means "ideas in the mind," so Russell is a closet idealist. Chapter 4 is devoted to denying exactly this. The sensation — the awareness — is mental; the sense-datum — the colour seen — is the object of awareness, and nothing shows it to be mental. Berkeley's idealism is presented as a fallacy resting on the ambiguity of "in the mind."

Misunderstanding: A priori knowledge means knowledge we are born with, or knowledge independent of all experience. Russell rejects "innate ideas": a priori knowledge is "elicited and caused by experience," which directs our attention so that we see the truth without experience proving it. And a priori knowledge never tells us that anything exists — only hypothetical connexions ("if this, then that").

Misunderstanding: "All men are mortal" is known the way "two and two are four" is known. The difference is in evidence, not in meaning: "all men are mortal" rests on instances and is never more than probable; "two and two are four" rests on a perceived relation between universals and is necessary. Induction is preferable to deduction from the former; deduction is right for the latter.

Misunderstanding: Russell's famous example is "the king of France." It is not. The king of France belongs to Russell's 1905 paper "On Denoting" and his theory of descriptions, not to this book. The Problems of Philosophy's iconic examples are the table (Chapter 1), the penny — "a circular coin... will look oval" (Chapter 3) — and the cat (Chapter 2), along with the man with the iron mask, Bismarck, Julius Caesar, Othello, and the chicken whose neck is wrung.

Misunderstanding: Truth as coherence is the book's theory of truth. The opposite. Coherence is examined and rejected as a definition of truth (many coherent systems are possible; coherence presupposes the laws of logic), and retained only as a test that raises the probability of a body of beliefs.

Misunderstanding: The book proves philosophy has no value, since it cannot answer its questions. Chapter 15 argues the value of philosophy lies precisely in its questions and its uncertainty: they enlarge the mind, break the tyranny of custom, and issue in impartiality — justice in action and universal love in emotion.

Misunderstanding: Russell rejects metaphysics wholesale and endorses empiricism. He rejects the a priori proofs of the grand systems (Hegel's especially) but defends the reality of universals and a priori knowledge against the empiricists (Berkeley and Hume on abstract ideas, for instance), concluding in Chapter 7 that "in this... the rationalists were in the right" and in Chapter 9 that resemblance forces us to admit universals.

Central paradox / key insight

The book's most counterintuitive idea is that we know a priori — necessarily and in advance — truths about things we have never experienced, and even truths of which no instance can be given, while the objects of our most intimate acquaintance (sense-data) are exactly the things we cannot claim to know "as they are in themselves." The physical world, which common sense thinks it knows best, is known only by description, with no instance ever given in acquaintance; the world of universals, which common sense never notices, is what we know most certainly.

The apparent paradox dissolves in Chapter 10: a priori knowledge deals exclusively with the relations of universals, so it does not "anticipate experience" at all — it states connexions among universals, while experience supplies the existence of particulars to which those connexions apply. What remains genuinely paradoxical is the claim that any general proposition we can understand must be composed wholly of constituents with which we are acquainted, even when no instance of it can ever be exhibited.

The one thing we know about [the table] is that it is not what it seems... The world of being is unchangeable, rigid, exact, delightful to the mathematician... The world of existence is fleeting, vague, without sharp boundaries.

Important concepts

Sense-data. "The things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on." The brown colour I see is a sense-datum; it is not the table and not in the table, and it is not a mental act.

Sensation. The experience of being immediately aware of a sense-datum — the awareness itself, as opposed to the datum of which we are aware.

Physical object. The real table, if it exists: the cause of our sense-data, continuing to exist unperceived, differing in nature from all sense-data, known only by description. Kant's "thing in itself" is its definitional twin.

Matter. "The collection of all physical objects."

Appearance and reality. The distinction between what things seem to be (as delivered by the senses) and what they are; the senses give only appearances, which we take as signs of a reality behind them.

Acquaintance. Direct awareness of a thing "without the intermediary of any process of inference or any knowledge of truths." Its objects: sense-data, memory, introspection, probably the Self, and universals. It cannot be mistaken, but it is confined to what is before the mind.

Knowledge by description. Knowledge of an object as "the so-and-so" — the unique possessor of a property — without acquaintance with it. The table, Bismarck, Julius Caesar, other people's minds, and all physical objects are known by description. The fundamental principle: every proposition we can understand is composed wholly of constituents with which we are acquainted.

Definite / ambiguous description. "The so-and-so" (definite — asserts uniqueness of the object) versus "a so-and-so" (ambiguous). "The man with the iron mask" is a definite description.

Universal / particular. A particular is what is given in sensation (this patch, this moment); a universal is what many particulars can share (whiteness, brotherhood, "north of," "before"). Proper names stand for particulars; adjectives, verbs, and prepositions stand for universals. Universals subsist; they do not exist in time.

Subsistence / existence. To exist is to be in time; universals "subsist or have being," timelessly. The world of being (universals) and the world of existence (particulars, minds) are both real.

Concept / conceiving. The awareness of a universal is conceiving; a universal of which we are aware is a concept.

A priori / empirical. A priori knowledge is knowledge experience cannot prove, though experience may elicit it: logic, pure mathematics, and judgements of intrinsic value. All knowledge asserting existence is empirical; the only a priori knowledge concerning existence is hypothetical.

Analytic / synthetic. An analytic judgement's predicate is obtained by analysing the subject ("a bald man is a man"); a synthetic judgement's predicate adds something not contained in the subject (7 + 5 = 12). Kant showed pure mathematics is synthetic and a priori.

Uniformity of nature. The belief that everything that happens is an instance of an exceptionless general law; the working hypothesis of science, dependent on the principle of induction.

Principle of induction. The principle that repeated association of A and B (with no known dissociation) raises the probability of fresh association, approaching certainty without limit. It cannot be proved or disproved by experience; all arguments from experience to the unexperienced assume it.

Laws of thought. The law of identity, the law of contradiction, and the law of excluded middle. The name is misleading: they are laws about things, not about thinking.

Self-evidence. The property of truths that are immediately known (intuitive knowledge). It has degrees; the highest degree — acquaintance with the corresponding fact — is an infallible guarantee of truth, the others only presumption.

Truth (correspondence theory). A belief is true when its objects, taken in the order the belief places them, form a corresponding complex fact; false when no such fact exists. Truth depends on facts outside the mind, not on internal qualities of the belief.

Coherence. The rejected definition of truth (many coherent systems are possible; coherence presupposes the laws of logic), retained as a test that raises the probability of a body of probable opinions.

Judgement of perception. A self-evident judgement based on sense: either asserting the existence of a sense-datum ("there is that") or analysing a complex datum ("that patch of red is round").

Intuitive knowledge. Immediate knowledge of truths — the self-evident truths of perception, memory, logic, arithmetic, and (weakly) ethics — on which all derivative knowledge rests.

Probable opinion. What we believe firmly but without the highest self-evidence, or hesitatingly; most of what passes for knowledge is probable opinion.

Thing in itself / phenomenon. Kant's terms: the thing in itself is the unknowable cause of sensations; the phenomenon is the object as it appears in experience, a joint product of thing and mind.

Monism / monadism. The doctrines that there is only one thing (Spinoza, Bradley) or that there are many isolated things that cannot interact (Leibniz's monads) — both traced in Chapter 9 to the neglect of relations.

References and Web Links

Primary texts and editions

• Project Gutenberg — The Problems of Philosophy, full text (eBook #5827), based on the 1912 Home University Library edition: https://gutenberg.org/ebooks/5827
• Plain-text full text of the same edition: https://www.gutenberg.org/cache/epub/5827/pg5827.txt
• Wikisource — The Problems of Philosophy (transcription): https://en.wikisource.org/wiki/The_Problems_of_Philosophy
• Standard Ebooks — The Problems of Philosophy (modernized e-text, based on the Gutenberg transcription): https://standardebooks.org/ebooks/bertrand-russell/the-problems-of-philosophy
• Internet Archive — page scan of the 1912 first edition (Holt, New York printing, University of Toronto copy): https://archive.org/details/problemsofphilo00russuoft
• Oxford World's Classics edition page (Oxford University Press; ISBN 9780195115529, introduction by John Skorupski): https://global.oup.com/academic/product/the-problems-of-philosophy-9780195115529

Authoritative background and reference

• Wikipedia — "The Problems of Philosophy" (book history, preface, reception): https://en.wikipedia.org/wiki/The_Problems_of_Philosophy
• Stanford Encyclopedia of Philosophy — "Bertrand Russell" (the framework for acquaintance, description, and universals, with full bibliography): https://plato.stanford.edu/entries/russell/
• University College Oxford — reading-list page for The Problems of Philosophy: https://www.univ.ox.ac.uk/book/the-problems-of-philosophy/

Audio

• LibriVox — free public-domain audiobook recording of The Problems of Philosophy: https://librivox.org/the-problems-of-philosophy-by-bertrand-russell/

A note on study guides. The SEP entry and the Wikipedia article are the recommended supplements for orientation; chapter-by-chapter summaries by third parties (study-guide sites) are not listed here because they are secondary condensations of a text that is itself a popularization — Russell's own words remain the clearest exposition.