Bertrand Russell · Public domain edition · 56 cards · 15 chapters
Bertrand Russell’s The Problems of Philosophy argues that our knowledge of the external world rests on inference from private sense-data rather than direct access to physical objects. The deck covers his distinctions between sense-data and sensation, his treatment of Berkeley and Descartes, and his account of matter, testimony, and simplicity.
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Chapter 1 · Question
What distinction does Russell draw between 'sense-data' and 'sensation'?
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Chapter 1 · Answer
Russell defines 'sense-data' as the things immediately known in sensation—colours, sounds, smells, hardnesses, roughnesses. 'Sensation' is the experience of being immediately aware of these things. So when we see a colour, the colour itself is the sense-datum, while the awareness of it is the sensation. Sense-data are what we are immediately aware of; sensation is the awareness itself.
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CHAPTER I. APPEARANCE AND REALITY4 cards
What distinction does Russell draw between 'sense-data' and 'sensation'?
Russell defines 'sense-data' as the things immediately known in sensation—colours, sounds, smells, hardnesses, roughnesses. 'Sensation' is the experience of being immediately aware of these things. So when we see a colour, the colour itself is the sense-datum, while the awareness of it is the sensation. Sense-data are what we are immediately aware of; sensation is the awareness itself.
Chapter 1
Why does Russell say the table has no one particular colour?
Colour depends on the table, the spectator, and the light falling on it. Different viewpoints, artificial light, colour-blindness, blue spectacles, or darkness all change the apparent colour. Since no viewpoint has a better claim to reveal the 'real' colour than another, Russell concludes we must deny that the table in itself has any single particular colour; 'the colour of the table' only means what a normal spectator sees under usual conditions.
Chapter 1
What does Berkeley argue about matter, and how does Russell assess him?
In Three Dialogues between Hylas and Philonous, Berkeley argues there is no such thing as matter; the world consists only of minds and their ideas, with the 'real' table being an idea in the mind of God. Russell says Berkeley's arguments vary in value—some sound, others confused or quibbling—but credits him with showing matter's existence can be denied without absurdity.
Chapter 1
What two questions does Russell restate about matter?
Russell asks: (1) Is there any such thing as matter—that is, is there a real table at all? (2) If so, what is its nature—what sort of object can it be? He notes that Berkeley and Leibniz both answer the first affirmatively, differing only on the second: Berkeley says ideas in God's mind, Leibniz says a colony of souls.
Chapter 1
CHAPTER II. THE EXISTENCE OF MATTER4 cards
What does Descartes' method of systematic doubt conclude is absolutely certain?
Descartes resolves to doubt whatever he can, imagining a deceitful demon presenting unreal things to his senses. Doubt about perceived things remains possible, but doubt about his own existence is not: if he did not exist, no demon could deceive him. Thus 'I think, therefore I am' is his absolute certainty, and on this basis he rebuilds knowledge. Russell credits this method as a great service to philosophy.
Chapter 2
Why does Russell say 'I think, therefore I am' claims more than is strictly certain?
Russell argues that immediate certainty belongs to particular experiences, not to a permanent self. When I see a brown colour, what is certain is 'a brown colour is being seen,' not 'I am seeing it.' Something must see it, but it need not be the same continuing person from moment to moment. The real Self is as hard to reach as the real table, so particular thoughts and feelings have primitive certainty.
Chapter 2
Why can't we appeal to other people's testimony to prove physical objects exist?
Russell notes that other people are represented to us only by sense-data, such as the sight of them or the sound of their voices. If we had no reason to believe in objects independent of our sense-data, we would have no reason to believe other people exist except as part of our dream. So appealing to their testimony begs the question, since that testimony itself consists of sense-data. We must find evidence within our own private experiences.
Chapter 2
What role does simplicity play in justifying belief in an external world?
Russell admits we can never strictly prove things exist other than ourselves and our experiences; the dream hypothesis is not logically impossible. But it is a less simple explanation of our life's facts than common sense. A cat seen in different places seems to move, not pop in and out of existence; it can grow hungry between meals only if it exists unperceived. Every principle of simplicity urges accepting independent objects.
Chapter 2
CHAPTER III. THE NATURE OF MATTER2 cards
According to Russell, what does physical science assign as the only properties of matter?
Russell says physical science has drifted into reducing all natural phenomena to motion, treating light, heat, and sound as wave-motions travelling through aether or gross matter. The only properties science assigns to this matter are position in space and the power of motion according to the laws of motion. Science does not deny other properties may exist, but such properties are not useful to the scientist explaining phenomena.
Chapter 3
Why does Russell say 'light is a form of wave-motion' is misleading?
Russell argues the light we immediately see through our senses is not a wave-motion but something quite different, known to sighted people yet indescribable to a blind man. A wave-motion, by contrast, could be described to a blind man, who can learn space by touch and experience waves at sea. What science really means is that waves are the physical cause of our sensations of light, not that light itself is waves.
Chapter 3
CHAPTER IV. IDEALISM4 cards
How does Russell define idealism in this chapter?
Russell defines idealism as the doctrine that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental. He notes the doctrine is widely held, takes several forms, and is advocated on several different grounds. He adds that common sense regards material objects as radically different from minds, but idealism should not be dismissed as obviously absurd.
Chapter 4
What did Berkeley mean by calling things 'ideas'?
Berkeley applied 'idea' to anything immediately known, such as sense-data like a colour seen or a voice heard. The term also covered things remembered or imagined, since we have immediate acquaintance with them at the moment of remembering or imagining. All such immediate data he called 'ideas', and he argued that to be known is to be 'in' a mind and therefore mental.
Chapter 4
What fallacy does Russell find in Berkeley's argument?
Russell argues Berkeley confuses the act of apprehension with the object apprehended, since either might be called an 'idea'. The mental act is undoubtedly mental, but that does not show the thing apprehended is mental. By an unconscious equivocation, the claim that ideas are in the mind gets transferred from acts to objects, yielding the conclusion that whatever we can apprehend must be in our minds.
Chapter 4
Why does Russell reject the claim that we cannot know what we are not acquainted with?
Russell says the statement trades on two senses of 'know': knowledge of truths (judgement) and knowledge by acquaintance. Restated, it claims we can never truly judge that something with which we are not acquainted exists, which Russell calls a palpable falsehood. He notes he is not acquainted with the Emperor of China yet truly judges that he exists, and things may be known by description.
Chapter 4
CHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY…4 cards
How does Russell distinguish knowledge by acquaintance from knowledge by description?
Russell defines acquaintance as direct awareness of something without inference or knowledge of truths, such as sense-data. Knowledge by description, by contrast, always involves some knowledge of truths as its source and ground. He argues that knowledge of a physical object like a table is description, since we know it only as 'the physical object which causes such-and-such sense-data.'
Chapter 5
What kinds of things does Russell say we have acquaintance with?
Russell lists sense-data in sensation, thoughts, feelings and desires in introspection, and remembered things in memory. He adds that it is probable, though not certain, that we are acquainted with the Self as that which is aware. He also holds that we are acquainted with universals, which he calls concepts, and that all knowledge rests on acquaintance as its foundation.
Chapter 5
What does Russell mean by a definite description?
A description is any phrase of the form 'a so-and-so' or 'the so-and-so.' Russell calls the first an ambiguous description and the second, in the singular, a definite description, like 'the man with the iron mask.' An object is known by description when we know it is 'the so-and-so'—that exactly one object has a certain property—without being acquainted with it.
Chapter 5
Why does Russell say proper names are usually really descriptions?
Russell argues that the thought behind a proper name can generally only be expressed explicitly by replacing the name with a description. That description varies between people and times, while the object named stays constant. So long as the object remains constant, the particular description involved usually makes no difference to the truth or falsehood of the proposition.
Chapter 5
CHAPTER VI. ON INDUCTION4 cards
What two parts make up the principle of induction as Russell states it?
Russell states it in two parts: (a) the greater the number of cases in which A has been found associated with B, with no known failures, the greater the probability of association in a fresh case; (b) a sufficient number of such cases makes the probability of a fresh association approach certainty without limit. He repeats both parts for the general law that A is always associated with B.
Chapter 6
Why does Russell say the argument from 'past futures' begs the question?
Some argue the future will resemble the past because former futures have become pasts and always resembled the past, giving us experience of 'past futures.' Russell replies this begs the question: we have experience of past futures, not of future futures, and whether future futures resemble past futures is exactly what is in dispute, so an argument from past futures alone cannot settle it.
Chapter 6
What does Russell conclude about proving or disproving induction by experience?
Russell argues the inductive principle cannot be disproved by experience, since things failing our expectations does not show they will not probably be fulfilled; apparent counterexamples like black swans merely add fresh data. Nor can it be proved by experience, since any experiential argument would itself rely on induction. Probability, relative to given data, is all we can seek, never certainty.
Chapter 6
What is the chicken example meant to illustrate?
A chicken fed daily expects food when the feeder appears, then has its neck wrung. Russell uses this to show that past uniformities cause expectations in animals and humans, but such crude expectations are liable to mislead. The mere fact that something has happened repeatedly does not by itself justify the expectation, so we may be no better off than the chicken.
Chapter 6
CHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES4 cards
What does Russell say about how we come to know general principles?
The author argues we first realize a particular application of a principle, then recognize that the particularity is irrelevant and that a generality may equally truly be affirmed. He illustrates with arithmetic: 'two and two are four' is first learned through particular pairs of couples until one sees it holds for any pair. The same happens with logical principles.
Chapter 7
What is the logical principle Russell says underlies all demonstrations?
The principle states: if this implies that, and this is true, then that is true; in other words, 'anything implied by a true proposition is true' or 'whatever follows from a true proposition is true.' Russell says concrete instances of it are involved in all demonstrations, and its truth is impossible to doubt, though its obviousness makes it seem almost trivial.
Chapter 7
How does Russell adjudicate the empiricist–rationalist controversy?
The author argues the rationalists were right on the most important point: logical principles are known to us and cannot be proved by experience, since all proof presupposes them. But the empiricists were right that nothing can be known to exist except by experience, and that a priori knowledge of existence is only hypothetical. He also rejects 'innate' as a description, preferring 'a priori.'
Chapter 7
Why does Russell hold that pure mathematics is a priori, not empirical?
The author argues mathematics is a priori like logic, rejecting the empiricist view that repeated experience of two things plus two things making four leads by induction to the general conclusion. A few instances only help us think of 'two' abstractly; once we drop irrelevant particularity, we see the general principle, and further instances add no certainty.
Chapter 7
CHAPTER VIII. HOW _A PRIORI_ KNOWLEDGE IS POSSIBLE4 cards
What did Kant contribute to philosophy, according to Russell?
Russell credits Kant with two achievements: perceiving that we have a priori knowledge which is not purely analytic (its opposite would not be self-contradictory), and making evident the philosophical importance of the theory of knowledge. Russell adds that whether Kant's metaphysical results are valid may well be doubted, but the credit for these two things is still deserved.
Chapter 8
What was Hume's argument about cause and effect?
Hume accepted the usual view of what makes knowledge a priori, but found that in many cases previously supposed analytic, notably cause and effect, the connexion was really synthetic. He argued, correctly as Russell says is now generally admitted, that the effect cannot be logically deduced from the cause even with sufficient knowledge. From this he inferred the more doubtful proposition that nothing can be known a priori about cause and effect.
Chapter 8
What is Russell's main objection to Kant's solution?
Russell argues that what must be explained is our certainty that facts always conform to logic and arithmetic. Saying logic and arithmetic are contributed by us does not explain this, since our nature is itself a fact of the existing world and might change; then two and two might become five. This possibility, Russell says, destroys the certainty and universality Kant wanted for arithmetical propositions.
Chapter 8
Why does Russell reject calling the law of contradiction a law of thought?
Russell argues that what we believe when we believe the law of contradiction is about things, not merely thoughts: if a tree is a beech it cannot at the same time not be a beech. The belief that our minds are so made is a subsequent psychological reflection presupposing the law. If the law were not true of things, being compelled to think it true would not save it from being false.
Chapter 8
CHAPTER IX. THE WORLD OF UNIVERSALS4 cards
Why does Russell prefer the term 'universal' to Plato's 'idea'?
Russell adopts 'universal' because the word 'idea' has acquired misleading associations, suggesting something that exists in minds. Plato's 'ideas' or 'forms' are not mental entities, though they may be apprehended by minds. A universal is anything shareable by many particulars, opposed to the particulars given in sensation, and is eternal, immutable, and indestructible.
Chapter 9
How does Russell argue that relations, not just qualities, must be universals?
Berkeley and Hume denied abstract ideas, saying we reason about particular images. Russell replies that to know a thing is white or triangular, we need resemblance to a chosen particular, and resemblance must hold between many pairs, making it a universal. Since resemblance is a relation, relations are proven universals, so denying whiteness becomes pointless.
Chapter 9
What does the proposition 'Edinburgh is north of London' show about universals?
Russell argues the relation 'north of' subsists independently of our knowledge. We do not create the truth by knowing it; we apprehend a fact that was already there. The relation would hold even with no minds in the universe. Since the fact involves this universal and nothing mental, the relation belongs to an independent world thought apprehends but does not create.
Chapter 9
Why did neglect of verbs and prepositions shape metaphysics, according to Russell?
Adjectives and nouns express qualities of single things, while verbs and prepositions express relations between things. Russell argues that overlooking relational universals led philosophers to treat every proposition as attributing a property to one thing, so relations seemed impossible. This produced monism (Spinoza, Bradley) and monadism (Leibniz), which the author sees as resulting from undue attention to one sort of universal.
Chapter 9
CHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS4 cards
According to Russell, what does all a priori knowledge deal exclusively with?
The author argues that all a priori knowledge deals exclusively with the relations of universals. He supports this by analyzing 'two and two are four,' which he says concerns the universals 'couple,' 'two,' and 'four,' not any actual particular couples. Understanding the proposition requires acquaintance only with these universals, not with all the couples in the world, which are infinitely numerous.
Chapter 10
How does Russell distinguish a priori general propositions from empirical generalizations?
The author argues the difference lies not in meaning but in the nature of the evidence. Both are understood once the universals involved are grasped. But an empirical generalization like 'all men are mortal' rests on particular instances—innumerable cases of men dying. An a priori proposition rests on a perceived connexion between universals, as in logic and arithmetic, not on inductive evidence from instances.
Chapter 10
What example does Russell give of a general proposition whose truth is undeniable but of which no instance can be given?
Russell offers: 'All products of two integers, which never have been and never will be thought of by any human being, are over 100.' Since integers are infinite and only finitely many pairs are ever thought of, such unthought pairs exist, and all deal with products over 100. No instance can be given, because any numbers we think of are excluded by the proposition's terms.
Chapter 10
Why does Russell say our knowledge of physical objects depends on general knowledge where no instance can be given?
The author argues physical objects are known only by inference, not by acquaintance; we are acquainted with sense-data, not the objects themselves. So no proposition of the form 'this is a physical object' can ever be known, since 'this' would have to be immediately known. Thus all our knowledge of physical objects, and of other minds, rests on the possibility of general knowledge without instances.
Chapter 10
CHAPTER XI. ON INTUITIVE KNOWLEDGE4 cards
According to the chapter, what happens when we demand a reason for every reason?
The author argues that if we keep demanding a reason for each reason, we are eventually driven back to a general principle or instance that seems luminously evident and cannot be deduced from anything more evident. In daily life this is often the inductive principle; beyond it there is no further regress, and the same holds for other logical principles.
Chapter 11
Why does the chapter say sense-data themselves are neither true nor false?
The chapter holds that a patch of colour we see simply exists; it is not the kind of thing that can be true or false. What is true is that there is such a patch, that it has a certain shape and brightness, and that it is surrounded by other colours. Self-evident truths from the senses must therefore differ from the sense-data they come from.
Chapter 11
What does the chapter say constitutes the essence of memory, as opposed to an image?
The author argues the essence of memory is not an image, since the image is present while what is remembered is known to be past. Memory consists in having immediately before the mind an object recognized as past. Without this, we could not know there was a past at all, and all knowledge of the past ultimately depends on intuitive judgements of memory.
Chapter 11
How does the chapter describe degrees of self-evidence, and how does memory illustrate them?
The author argues self-evidence comes in degrees, not simply present or absent. Perception and some logical principles have the highest degree; immediate memory has an almost equally high degree. Memory is trustworthy in proportion to vividness and nearness in time, and its self-evidence diminishes as memories become remoter and fainter. Where propositions conflict, the more self-evident is to be retained.
Chapter 11
CHAPTER XII. TRUTH AND FALSEHOOD4 cards
What preliminary question does Russell address in this chapter?
Russell asks what we mean by truth and falsehood, not which beliefs are true. He insists these questions must be kept separate, since confusing them produces an answer applicable to neither. A clear account of meaning may later help us determine which beliefs are true, but that is a distinct inquiry.
Chapter 12
What three requisites must any theory of truth satisfy?
Russell requires that a theory of truth (1) admit its opposite, falsehood, unlike acquaintance; (2) make truth and falsehood properties of beliefs, so a world of mere matter contains facts but no truths; and (3) make truth depend on relations between beliefs and outside things, not on any internal quality of the belief.
Chapter 12
Why does Russell reject coherence as the definition of truth?
He gives two objections. First, there is no proof only one coherent system exists: a novelist might invent a past fitting all known facts, and rival hypotheses may both explain the evidence. Second, coherence presupposes the laws of logic, such as contradiction, which cannot themselves be established by the coherence test. Coherence remains an important test of truth, not its meaning.
Chapter 12
How does Russell analyze belief to allow for falsehood?
Belief cannot be a relation to a single object, or it would always be true. Instead, judging is a multiple relation knitting together the subject and objects into one complex whole, with a sense or order. Othello's belief involves Othello, Desdemona, loving, and Cassio; truth depends on whether the corresponding complex exists.
Chapter 12
CHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION2 cards
Why is a true belief not knowledge when derived from a false belief?
Russell argues that a true belief cannot count as knowledge when it is deduced from a false belief. His example: a man who believes Mr. Balfour was the late Prime Minister still holds the true belief that the late Prime Minister's name began with a B, but this is not knowledge. Similarly, a newspaper's lucky guess about a battle result produces true belief without knowledge.
Chapter 13
What is the first, absolute kind of self-evidence?
A truth is self-evident in the absolute sense when we have acquaintance with the fact corresponding to it. Such facts are private: only Desdemona could have acquaintance with the fact of her loving Cassio, so that truth could be self-evident only to her. Facts about universals lack this privacy, since many minds can be acquainted with the same universals. This self-evidence absolutely guarantees truth.
Chapter 13
CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE4 cards
What does Russell conclude about metaphysics' ability to prove things about the universe as a whole?
The author argues that the hope of proving such theses as the fundamental dogmas of religion or the essential rationality of the universe by a priori metaphysical reasoning is vain. He holds that knowledge of the universe as a whole cannot be obtained by metaphysics, and that proposed proofs claiming things must or cannot exist do not survive critical scrutiny.
Chapter 14
What is Hegel's main thesis as Russell interprets it?
According to Russell's interpretation, Hegel holds that everything short of the Whole is fragmentary and cannot exist without the rest of the world. The metaphysician sees from any one piece of reality what the whole must be, since every piece has hooks grappling it to the next. Incomplete ideas generate contradictions, pass into opposites, and are resolved in syntheses until the Absolute Idea.
Chapter 14
How does Russell refute the argument that a thing's relations are logically necessary?
Russell says the view turns on 'nature' meaning 'all the truths about a thing.' But a truth about a thing is not part of the thing itself. Acquaintance with a thing does not involve knowledge of its relations, and knowledge of some relations does not involve knowledge of all. So from a thing being what it is, we cannot deduce that it must have the relations it in fact has.
Chapter 14
How did Cantor's work on infinite collections affect the case against the reality of space and time?
Kant deduced that space and time were merely subjective from the contradiction between their apparent infinity and the supposed impossibility of infinite collections. Russell says mathematicians, notably Georg Cantor, showed that infinite collections are not self-contradictory, only contrary to mental prejudices. Hence the reasons for regarding space and time as unreal became inoperative.
Chapter 14
CHAPTER XV. THE VALUE OF PHILOSOPHY4 cards
According to Russell, where must the value of philosophy primarily be sought?
The author argues that, unlike physical science, philosophy's utility does not extend to the ignorant masses through inventions. Its value must be sought primarily in its effects on the lives of those who study it, and exclusively among the goods of the mind, not the goods of the body.
Chapter 15
How does Russell explain philosophy's apparent lack of positive results?
The author argues this is partly more apparent than real: once definite knowledge on a subject becomes possible, it ceases to be called philosophy and becomes a separate science, as astronomy and psychology did. But he adds this is only part of the truth, since many profound questions must remain insoluble to the human intellect.
Chapter 15
What does Russell say philosophy does for the mind despite its uncertainty?
The author argues philosophy's value lies largely in its very uncertainty. Though unable to give certain answers, it suggests many possibilities that enlarge our thoughts and free them from the tyranny of custom. It diminishes certainty about what things are while increasing knowledge of what they may be, and keeps alive our sense of wonder.
Chapter 15
What is the chief value Russell finds in philosophic contemplation?
The author argues philosophy's chief value lies in the greatness of the objects it contemplates and the freedom from narrow personal aims this brings. Unalloyed contemplation starts from the not-Self, enlarging the Self through the infinity of the universe, and fosters greatness of soul, unlike philosophies that assimilate the universe to Man.
Chapter 15
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Text used: Project Gutenberg eBook #5827 (Public domain in the United States). Generated from the full text; cards paraphrase the source.
Version: Public domain edition. Retrieved 2026-10-18. Cards reviewed 2026-10-18.
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