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Study Guide: Mysticism and Logic and Other Essays

Bertrand Russell

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Mysticism and Logic and Other Essays — Chapter-by-Chapter Outline

Author: Bertrand Russell

First published: 1918

Edition covered: The standard ten-essay edition: first issued as Mysticism and Logic and Other Essays in December 1917 (second edition, George Allen & Unwin, London; the first edition of the collection, under the title Philosophical Essays, appeared in October 1910 with a different table of contents), and in the United States by Longmans, Green & Co. in 1918. This outline follows the 1917/1918 table of contents as verified against the Wikisource transcription of the 1917 Allen & Unwin edition, Project Gutenberg eBook #25447 (from an Internet Archive scan of the same edition), and a Drew University contents page for the Longmans 1918 edition (1919 third impression pagination). Modern reprints such as the Routledge Classics editions reproduce the same ten essays; the essays were written and first published between 1901 and 1917.

Central thesis

The collection argues for a philosophy built from two impulses that metaphysics has always united and conflicted: the mystical impulse, which seeks a sudden, comprehensive insight into the whole of reality, and the scientific impulse, which submits belief to observation, analysis, and impartial logic. Russell reads the history of philosophy as a series of attempts to blend the two — Heraclitus and Plato are his exemplary blends — and he finds most traditional metaphysics vitiated by letting ethical wishes and mystical certainties legislate for the facts.

Across the ten essays, the same move repeats in different registers: take the grandiose claims of religion, evolutionism, and idealist metaphysics, and submit them to the discipline of logic and science. The mystic's insight is commended as an attitude toward life — the source of reverence, resignation, and the love of truth — but rejected as a creed about the world. What remains is a philosophy that is piecemeal, analytic, ethically neutral, and confident that its problems can be solved by treating matter, space, time, and cause as logical constructions out of the immediate data of sense rather than as inferred metaphysical substances.

The collection's ambition is stated in its first sentence: metaphysics "has been developed, from the first, by the union and conflict of two very different human impulses, the one urging men towards mysticism, the other urging them towards science."

Can a philosophy combine the mystic's vision of the whole with the scientist's discipline of analysis, so that insight is disciplined by logic and logic is inspired by reverence?

Chapter 1 — Mysticism and Logic

Central question

Can the mystical vision of reality be reconciled with, and disciplined by, scientific logic — or must philosophy choose between them?

Main argument

The two impulses. Russell opens with the claim that metaphysics is the product of two human impulses, the mystical and the scientific. In Hume the scientific impulse reigns unchecked; in Blake "a profound mystic insight" coexists with hostility to science; the greatest philosophers — Heraclitus and Plato — achieved an intimate blending. Heraclitus is read as a scientist turned mystic: his flux doctrine ("You cannot step twice into the same rivers") is grounded in observation, but his sayings on the identity of opposites ("We step and do not step into the same rivers; we are and are not") express a mystical sense of unity. Plato's allegory of the cave is quoted at length as the classical statement of a reality truer than the senses — but Russell faults Plato (and Parmenides before him) for identifying the good with the truly real, "a divorce between philosophy and science, from which, in my opinion, both have suffered ever since."

The four beliefs of mysticism. Russell distils the mystical philosophy into four doctrines, each of which he then examines separately:

  • Insight against analysis — belief in a way of knowledge (revelation, intuition) superior to the slow, fallible study of appearance.
  • Unity and the denial of plurality — "good and ill are one"; reality is one indivisible whole.
  • The unreality of time — past and future are illusions; the ultimately real is immutable.
  • Good and evil as mere appearance — evil belongs to the world of phantoms from which insight liberates us.

Reason and intuition. Against Bergson's elevation of intuition to "sole arbiter of metaphysical truth," Russell argues that the opposition of instinct and reason is "mainly illusory": instinct supplies beliefs, reason tests their mutual compatibility. Intuition is an aspect of instinct — admirable in familiar surroundings, but "totally incompetent" when surroundings change, as the hen with a brood of ducklings discovers when they take to the water. Self-knowledge, Bergson's best example of intuition, is "proverbially rare and difficult"; the knowledge lovers believe they have of one another is constantly deceptive. Since philosophy deals with objects "strange, unusual, and remote," intellect, not intuition, is its instrument — and this restraint is itself "the outcome of" the mystical spirit, not its enemy.

Unity and plurality. The monism of Parmenides and Hegel rests on a logic that is "not quite disinterested or candid," a "malicious" logic inspired by hatred of the daily world — philosophers read "the book of Nature with a conviction that it is all illusion." The logic of mysticism is generated after the mood fades, to justify a belief already held.

Time. The denial of time's reality is a cardinal mystical doctrine (Russell quotes a Persian Sufi poet: "Past and future are what veil God from our sight"). He will not deny time's reality, but insists on "the unimportance of time" as the gate of wisdom: the felt difference between past and future is only a difference in relation to our wishes. The essay's chief target here is evolutionism — the philosophy of progress exemplified by Nietzsche, pragmatism, and Bergson — which lets time become "its tyrant rather than its servant" and makes the future better than the past an article of faith.

Good and evil. Ethical notions must be kept out of the investigation of facts: "It is a commonplace that happiness is not best achieved by those who seek it directly; and it would seem that the same is true of the good." Science's ethically neutral study of astronomy replaced astrology; philosophy must make the same transition. The seeming paradox is stated plainly: a philosophy that does not impose its own good and evil on the world "is not only more likely to achieve truth, but is also the outcome of a higher ethical standpoint" — the submission religion teaches in action is the submission science teaches in thought.

Key ideas

  • Metaphysics is the product of two impulses, mysticism and science, and the greatest philosophy blends them.
  • The four mystical beliefs are insight over analysis, unity over plurality, the unreality of time, and evil as appearance.
  • Bergson's intuition is instinct, which is admirable in customary surroundings but unreliable in the "strange, unusual, and remote" objects of philosophy.
  • "Insight, untested and unsupported, is an insufficient guarantee of truth" — even though much of the most important truth is first suggested by it.
  • Mysticism is "to be commended as an attitude towards life, not as a creed about the world."
  • Evolutionism is a hasty generalisation of biology that lets progress become the tyrant of thought.
  • Ethical neutrality is not amorality: it is the higher ethical standpoint, the submission of wishes to facts.
  • "To realise the unimportance of time is the gate of wisdom."

Key takeaway

The mystic's vision is the fuel of philosophy, but only the scientist's impartial analysis can make it knowledge — mysticism is commended as an attitude toward life, not as a creed about the world.

Chapter 2 — The Place of Science in a Liberal Education

Central question

What does the study of science contribute to a liberal education, over and above its practical uses?

Main argument

Two merits of science. Russell distinguishes science as a string of sensational triumphs — wireless telegraphy, aeroplanes, radio-activity — from science as "systems of patiently constructed knowledge," exemplified by the electromagnetic theory built by Faraday, Maxwell, and Hertz. Science possesses two merits as against literature and art: first, hopefulness — science is cumulative, so that "in science the successors stand upon the shoulders of their predecessors," and "where one man of supreme genius has invented a method, a thousand lesser men can apply it," whereas art stagnates before the past and needs ever-new genius; second, the irrelevance of human passions — "The kernel of the scientific outlook is a thing so simple, so obvious, so seemingly trivial, that the mention of it may almost excite derision. The kernel of the scientific outlook is the refusal to regard our own desires, tastes, and interests as affording a key to the understanding of the world."

Education as formation of outlook. Education, in Russell's defined sense, is "the formation, by means of instruction, of certain mental habits and a certain outlook on life and the world." Its moral end is to enlarge the scope of primary impulses through knowledge — making the student "a citizen of the universe" — and its intellectual end is the objective view of the world "as far as possible as it is in itself, and not merely through the distorting medium of personal desire."

Illustrations of the scientific temper. Aristotle decided that the stars must move in circles because the circle is the most perfect curve — an appeal to aesthetico-moral considerations that science now rejects. Malthus's doctrine of population is valuable not for its conclusions but for its temper: he treated man "as a part of nature," neither praising nor blaming. The objections that his doctrine was "horrible and depressing" were unscientific. Darwinism has made the scientific attitude toward man fairly common — "There is, however, one study which is as yet almost wholly untouched by the scientific spirit—I mean the study of philosophy." Philosophers quote science as the devil quotes Scripture; the scientific spirit, instead, "involves a sweeping away of all other desires in the interests of the desire to know."

The positive value. The scientific life is happy because disinterested curiosity finds that "science can unveil secrets which might well have seemed for ever undiscoverable," and the impersonal cosmic outlook fulfils "the desire for a larger life and wider interests, for an escape from private circumstances."

Key ideas

  • Science is cumulative and method-driven; art is not — hence science's hopefulness for ordinary students.
  • The kernel of the scientific outlook is the refusal to take our desires and tastes as a key to the world.
  • Education is the formation of mental habits and an outlook, judged by its approach to objectivity.
  • Malthus's value is his temper, not his conclusions: man treated as part of nature.
  • Philosophy remains the last stronghold of the unscientific spirit.
  • A classical education's defect is its "too exclusive emphasis on the past."
  • A life devoted to science is a happy life, drawing on the best sources available.

Key takeaway

Science earns its place in a liberal education not through its inventions but through a mental habit — the refusal to let wishes and tastes dictate beliefs about the world — and philosophy has not yet acquired it.

Chapter 3 — A Free Man's Worship

Central question

Given a universe that is indifferent or hostile to human ideals, what attitude can a free person adopt without self-deception?

Main argument

The world as science presents it. Russell opens with Mephistopheles' account of the creation — a god who builds a world of struggle and worship, lets another sun crash into Man's sun, and commands the play to be performed again. This, he says, is "even more purposeless, more void of meaning" than the world science presents: "Man is the product of causes which had no prevision of the end they were achieving"; all human achievement "is destined to extinction in the vast death of the solar system." Only "on the firm foundation of unyielding despair, can the soul's habitation henceforth be safely built."

The choice: Force or Goodness. The savage worships power, without inquiring whether the gods deserve worship — the religion of Moloch, "the cringing submission of the slave." God's answer to Job parades power and knowledge without goodness; the morality of the struggle for survival does the same. The alternative is the religious position that the world of fact is secretly harmonious with the world of ideals — "Thus Man creates God, all-powerful and all-good." Russell rejects both: the world of fact is not good, and to submit judgment to it is slavish. The choice is posed: "Shall we worship Force, or shall we worship Goodness?" The worship of Force — Carlyle, Nietzsche, the creed of militarism — is "a prostrate submission to evil, a sacrifice of our best to Moloch."

Freedom in thought. "In action, in desire, we must submit perpetually to the tyranny of outside forces; but in thought, in aspiration, we are free." Promethean rebellion is still a bondage, because indignation "compels our thoughts to be occupied with an evil world"; the Stoic freedom of wisdom lies in submitting desires, not thoughts. Resignation is "the very gate of wisdom," and Christianity's insistence on renunciation shows a wisdom beyond the Promethean creed — though Russell's ground is the austere truth that the world was not made for us, not a doctrine of providence.

The temple and the past. Passive renunciation is not the whole of wisdom: in imagination we build "a temple for the worship of our own ideals," and tragedy is "the proudest, the most triumphant" of the arts because it builds its citadel in the centre of the enemy's country. The past has a magical power — "what was eager and grasping, what was petty and transitory, has faded away; the things that were beautiful and eternal shine out of it like stars in the night." The essay ends with the famous definition: "To abandon the struggle for private happiness, to expel all eagerness of temporary desire, to burn with passion for eternal things—this is emancipation, and this is the free man's worship." The free man's last duty is to his fellow-sufferers on the march through the night.

Key ideas

  • Science gives us a world without purpose; the free man's task is to build ideals within it, not to pretend the facts are kind.
  • Worship of naked Power — Moloch religion, Job's God, Nietzsche, militarism — is slavery.
  • Rebellion (Prometheus) is still bondage; renunciation frees the desires, and only then can thought be free.
  • The free man's worship: abandon the struggle for private happiness, burn with passion for eternal things.
  • The past, being unalterable, is the kingdom of beauty and of the "immortality of the past."
  • Tragedy is the proudest art: it transmutes the evil material of the world into beauty.
  • The free man is united with others by "the tie of a common doom" and helps them in their need.

Key takeaway

Since power is not worthy of worship, freedom consists in resigning our desires to fate while keeping our thoughts and ideals independent of it — building, from the ruins of hope, a temple for the good.

Chapter 4 — The Study of Mathematics

Central question

What is the purpose and ideal of the study of mathematics — the value that entitles it to a place in every liberal education?

Main argument

Mathematics as an end in itself. Russell begins by asking what purpose every human activity serves, and complains that mathematics has been buried "beneath a great rubbish-heap of pedantries and trivialities": it is defended for making machines, for travel, for war, for training the reasoning faculties — all ends "of doubtful value." Plato's judgment in the Laws is quoted: mathematical knowledge is of "divine necessity," needed to become "a God to the world, nor a spirit, nor yet a hero." Russell's own statement follows: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture," without appeal to our weaker nature, "yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." The world of pure reason "knows no compromise, no practical limitations."

How it should be taught. The learner should be awakened to belief in reason: geometry should begin with startling theorems "easily verifiable by actual drawing," and the fallacious methods of the old textbooks should be excluded; algebra should be taught as the passage from arithmetic to "general truths"; and the notion of infinity, whose difficulties were solved by Cantor and Dedekind, should be taught in its logical purity rather than through the old confusions. The learner should be led backward from self-evident propositions to more fundamental principles, learning that "many propositions seem self-evident to the untrained mind which, nevertheless, a nearer scrutiny shows to be false."

The unifying science. Symbolic logic is "the fundamental science which unifies and systematises the whole of deductive reasoning"; "the discovery that all mathematics follows inevitably from a small collection of fundamental laws" is the intellectual beauty of the whole. Its principles are "few in number, and ... the sole source of everything in pure mathematics." Against the philosophers who held the laws of logic to be laws of thought, Russell insists they are not: "By this opinion the true dignity of reason is very greatly lowered"; mathematics is "an investigation into the very heart and immutable essence of all things actual and possible," and its beauty "belongs to the outer world as to the inner." At the same time, pure mathematics "can never pronounce upon questions of actual existence": reason cannot dictate to the world of fact.

Mathematics against scepticism. To the claim that there is no absolute truth, only opinion and private judgment, "mathematics is a perpetual reproof; for its edifice of truths stands unshakable and inexpungable to all the weapons of doubting cynicism." Utility is only "a consolation in moments of discouragement, not a guide in directing our studies" — the history of science shows that abstract propositions, like conic sections waiting two thousand years, may revolutionise daily life at any moment.

Key ideas

  • Mathematics possesses "supreme beauty — a beauty cold and austere, like that of sculpture."
  • The purpose of teaching mathematics is to awaken "belief in reason" and confidence in demonstration.
  • Cantor and Dedekind's solution of the problems of infinity is "probably the greatest achievement of which our own age has to boast."
  • All pure mathematics follows from a small number of logical principles; symbolic logic is the science that unifies it.
  • The laws of logic are not laws of thought: mathematics deals with a non-human world independent of us.
  • Pure mathematics never pronounces on questions of actual existence.
  • Mathematics is a "perpetual reproof" to the scepticism that denies absolute truth.
  • The love of truth, fostered by mathematics, is the chief of the "austerer virtues."

Key takeaway

Mathematics deserves study as the supreme example of pure, non-human truth — coldly beautiful, logically rigorous, and the strongest available proof that the mind can dwell in a realm of absolute necessity.

Chapter 5 — Mathematics and the Metaphysicians

Central question

How does the discovery that pure mathematics is formal logic dissolve the ancient metaphysical puzzles of infinity, continuity, space, time, and motion?

Main argument

What mathematics is. Russell announces that "pure mathematics was discovered by Boole," in the Laws of Thought (1854) — though Boole himself mistook his subject: "if his book had really contained the laws of thought, it was curious that no one should ever have thought in such a way before." The celebrated definition follows: "Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing" — hence "mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." All pure mathematics is built from the primitive ideas of logic; the deduction has already been accomplished over the greater part of the domain.

The instruments. Symbolism is useful "because it makes things difficult": obviousness is the enemy of correctness. Peano has reduced arithmetic, algebra, and the calculus to a dictionary of three words — zero, number, next after. Leibniz foresaw this "Universal Characteristic," hoping that philosophers would settle disputes by saying "Let us calculate."

Zeno vindicated. Zeno's four arguments against motion were "immeasurably subtle and profound" and were refuted by every philosopher down to our own day — until Weierstrass, Dedekind, and Cantor "completely solved" the three problems of the infinitesimal, the infinite, and continuity. Weierstrass banished the infinitesimal: "there is no such thing as the next moment," and "a body in motion is just as truly where it is as a body at rest." The infinite, far from being self-contradictory, is the source of the exact science of the infinite: "A collection of terms is infinite when it contains as parts other collections which have just as many terms as it has" — there are just as many even numbers as numbers. The axiom that the whole has more terms than the part, accepted by every philosopher for two thousand years, is "the specious maxim" that generated the contradictions; Zeno's Achilles is "strictly correct, if we allow the axiom," and "as the conclusion is absurd, the axiom must be rejected." The paradox of Tristram Shandy shows the tortoise, given infinite time, writes his whole biography because "the number of days in all time is no greater than the number of years."

Geometry and Kant. Geometry is "a whole collection of deductive sciences based on a corresponding collection of sets of axioms"; non-Euclidean systems show it "throws no more light upon the nature of space than Arithmetic throws upon the population of the United States." Euclid is deposed: "Countless errors are involved in his first eight propositions"; even his first proposition assumes circles intersect. The proof that all pure mathematics is formal logic is "a fatal blow to the Kantian philosophy," which invented a priori intuitions to explain why Euclid's proofs needed the figures — a defect in Euclid, not a feature of geometrical reasoning. The hope is a new philosophical logic built on the "exactitude and certainty" of mathematics.

Key ideas

  • "Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing."
  • Boole discovered that formal logic is the same thing as mathematics.
  • Weierstrass banished the infinitesimal; Zeno's paradoxes were strict arguments from a false axiom.
  • An infinite collection is one that has as many terms as some part of itself — "formerly thought to be a contradiction, is now transformed into a harmless definition of infinity."
  • The maxim that the whole has more terms than the part holds only for finite collections.
  • Geometry is the study of order, not of the space we live in; Euclid's propositions do not follow from his axioms.
  • The logicism of mathematics is "a fatal blow to the Kantian philosophy" of synthetic a priori intuition.

Key takeaway

The paradoxes of infinity, continuity, and motion that metaphysics had agonised over for two thousand years were generated by a single false axiom, and the modern reduction of mathematics to logic dissolves them.

Chapter 6 — On Scientific Method in Philosophy

Central question

What method should philosophy adopt if it is to make solid, progressive advances like the sciences?

Main argument

Motives: religious or scientific. Russell opens the Herbert Spencer Lecture by dividing the motives of philosophers into two groups: those derived from religion and ethics (Plato, Spinoza, Hegel) and those derived from science (Leibniz, Locke, Hume). His belief: "the ethical and religious motives ... have been on the whole a hindrance to the progress of philosophy." But philosophy must borrow not the most general results of science, which are "the least certain and the most liable to be upset by subsequent research," but its methods.

Two notions to extrude. The philosopher is expected to speak of "the universe" and of good and evil. Russell denies both: "I believe the conception of 'the universe' to be, as its etymology indicates, a mere relic of pre-Copernican astronomy." The apparent oneness of the world is "merely the oneness of what is seen by a single spectator." Following William James, the unity of the experienced world is either epistemological — an artifact of selection by one experiencer — or the tentative, partial unity of scientific laws; generalising either is fallacious. The second extrusion is ethical: "Human ethical notions ... are essentially anthropocentric"; the Grand Augur's speech to the pigs (from Chuang Tzǔ) shows how "the evolutionists too often resemble the Grand Augur and the pigs." Ethics is "in origin the art of recommending to others the sacrifices required for co-operation with oneself" — the product of the gregarious instinct, hence never impartial.

Two case studies in hasty generalisation. (1) The conservation of energy: Spencer's "persistence of force" is an empirical generalisation inflated into an a priori necessity, conflating a constant quantity with a persistent entity. (2) The philosophy of evolution: the history of biological development is "a very small selection of facts confined to an infinitesimal fragment of space and time"; an extra-terrestrial philosopher who watched one youth until twenty-one would infer an indefinite progress toward perfection — "this generalisation would be just as well founded."

The province of philosophy. A philosophical proposition must be general — applicable to everything that exists or may exist — and a priori — "such as can be neither proved nor disproved by empirical evidence." Philosophy thus becomes "the science of the possible," indistinguishable from logic, which provides "an inventory of possibilities." The view advocated "may be called logical atomism or absolute pluralism, because, while maintaining that there are many things, it denies that there is a whole composed of those things." The essence of philosophy "is analysis, not synthesis": "Divide and conquer" is the maxim of success.

The problem of space as illustration. Kant's single problem of space is really three: a logical problem (non-Euclidean geometry shows many possible spaces, exactly solvable), a physical problem (finding in the physical world a space of one of the kinds enumerated — points must be "constructed" as classes of physical entities, the solution due to Whitehead), and an epistemological problem ("How do we come to have knowledge of geometry a priori?") — which collapses: our knowledge of geometry is "partly from logic, partly from sense," and the Kantian problem "collapses" once the distinction is drawn. On realism, Russell argues that "real" and "independent" are so ambiguous that the controversy has been prolonged by confusion; his own view is that objects of perception do not persist unchanged unperceived, but are "the only empirically knowable part of the actual subject-matter of physics."

Key ideas

  • Philosophy should study scientific methods, not generalise scientific results.
  • "The universe" is a relic of pre-Copernican astronomy; there are no propositions of which the universe is the subject.
  • Ethical notions are anthropocentric and must be extruded from metaphysics; even vegetarians kill microbes to save a man.
  • The conservation of energy and the philosophy of evolution are hasty generalisations dressed as necessities.
  • Philosophical propositions are general and a priori: "philosophy is the science of the possible."
  • Logical atomism or absolute pluralism: many things, but no whole composed of them.
  • Philosophy's essence is analysis, not synthesis — piecemeal, tentative, progressive.
  • The Kantian problem of geometry collapses once the logical, physical, and epistemological problems are separated.

Key takeaway

Philosophy will progress like a science only by abandoning system-building and ethical legislation for the piecemeal analysis of logical forms — "philosophy is the science of the possible."

Chapter 7 — The Ultimate Constituents of Matter

Central question

What are the ultimate constituents of the physical world — and can the immediate objects of sense be among them?

Main argument

The problem of matter. Russell takes up "no less a question than the ancient metaphysical query, 'What is matter?'" Common sense divides the world into mind and matter; physics cuts matter into molecules, atoms, and corpuscles, until a unit of matter "tends more and more to be something like an electromagnetic field filling all space"; physiology shows what we see depends on eye and brain. These lines of argument are "a reductio ad absurdum of naïve realism" — but Russell identifies "two errors which support each other": that what we perceive is subjective, and that "what is physical must be persistent."

The cinematograph. Against the prejudice in favour of permanence, Russell borrows Bergson's illustration: the cinema shows "a succession of films, each with a different momentary man," and "the cinema is a better metaphysician than common sense, physics, or philosophy." A man, a table, the sun are not persistent entities but "a series of entities succeeding each other in time"; "A true theory of matter requires a division of things into time-corpuscles as well as into space-corpuscles." The world is a pattern of particulars; the things we speak of are logical constructions or symbolic fictions — classes or series of particulars, "not on the analogy of bricks in a building, but rather on the analogy of notes in a symphony."

Sense-data are physical. Russell defends the realism of Alexander and Nunn: when I see a flash of lightning, my seeing is mental, but what I see is not. Berkeley's argument from heat passing into pain rests on an ambiguity: the sensation is painful, not the object experienced. The causal dependence of what we see is on the body, not the mind: alterations by squinting are "of exactly the same kind as the alterations effected by spectacles or a microscope."

The sun problem. Physics says electromagnetic waves travel from the sun for eight minutes, reach the eye, disturb rods and cones, optic nerve, brain — "By some odd miracle, comes the experience which we call 'seeing the sun.'" Yet "such experiences form the whole and sole reason for our belief in" the entire chain. This "curious oppositeness of direction between the order of causation as affirmed by physics, and the order of evidence as revealed by theory of knowledge" is answered by radical reconstruction: the sun of eight minutes ago is "a class of particulars," and "what I see when I now look at the sun is one member of this class." The notion of the cause is rejected: "Any set of antecedents from which the event can theoretically be inferred by means of correlations might be called a cause."

Six-dimensional space. The prima facie objection that this packs the world too full is answered: the space of the real world has six dimensions — each perspective (the totality of particulars simultaneous with a given particular) has its own private three-dimensional space, and the perspectives themselves are arranged in a three-dimensional order. "Things" and "perspectives" are "merely two different ways of classifying particulars": the physicist classifies into things, the psychologist into perspectives and biographies. Dreams and hallucinations may be composed of "wild" particulars.

Key ideas

  • The question "What is matter?" can be split into an essentially soluble and an essentially insoluble part.
  • Two errors obscure the problem: that sense-objects are subjective, and that the physical must be persistent.
  • Things are series of momentary particulars — the cinema is a better metaphysician than common sense.
  • The immediate data of sense are "extra-mental, purely physical, and among the ultimate constituents of matter."
  • Berkeley's pain argument fails: painfulness is a quality of the sensation, not of the object sensed.
  • "The persistent particles of mathematical physics I regard as logical constructions, symbolic fictions."
  • The sun of eight minutes ago is a class of particulars spreading out from a centre with the velocity of light.
  • Perspectives and things are two classifications of the same particulars in a six-dimensional space.

Key takeaway

Matter is not a persistent substance behind appearance but a logical construction from evanescent particulars, and the immediate objects of sense — physical, extra-mental, causally dependent on the body — are among the ultimate constituents of the physical world.

Chapter 8 — The Relation of Sense-Data to Physics

Central question

How can physics be verified by observation if its supposed objects — molecules, atoms, electrons — never appear among the data of sense?

Main argument

The problem stated. Physics is an empirical science; observation yields "nothing ... except immediate data of sense: certain patches of colour, sounds, tastes, smells, etc." But "molecules have no colour, atoms make no noise, electrons have no taste." If physical objects are to be verified, it must be through correlation with sense-data — yet the correlation itself seems unverifiable, since only one term is ever found. Two ways out exist: an a priori principle of causation (to be avoided, as it makes physics non-empirical), or defining the objects of physics as functions of sense-data. The problem is posed with characteristic precision: "Physics exhibits sense-data as functions of physical objects, but verification is only possible if physical objects can be exhibited as functions of sense-data. We have therefore to solve the equations."

Sensibilia. A sense-datum is a particular singled out by attention; a sensibile is an object with the same status as a sense-datum "without necessarily being data to any mind" — the relation of a sensibile to a sense-datum "is like that of a man to a husband." The word is needed to ask whether sense-data can exist unperceived: "We cannot ask 'Can sense-data exist without being given?' ... We must ask 'Can sensibilia exist without being given?'" Russell's view: sense-data are not mental; their subjectivity is physiological, not psychical — "What the mind adds to sensibilia, in fact, is merely awareness."

Sense-data are physical. A particular is mental when it is aware of something; a sense-datum "does not contain the subject as a part." The distinction between a sensation (the subject's awareness, which is mental) and the sense-datum (the object of which the subject is aware, which is physical) removes the chief obstacle.

Constructions versus inferences. The essay's methodological centrepiece is the maxim: "The supreme maxim in scientific philosophising is this: Wherever possible, logical constructions are to be substituted for inferred entities." Irrational numbers are now defined as classes of ratios instead of being inferred as limits; cardinal numbers as classes of equally numerous collections. In physics the same method constructs the "thing": a table presents different shapes to different observers — "no two of these people have exactly the same sense-data" — and since the phrase "in the same place" is ambiguous, the different appearances do not conflict. "The 'thing' of common sense may in fact be identified with the whole class of its appearances," by Occam's razor.

Private space and perspective space. No sensibile is ever a datum to two people at once; each person lives in a private world. The space of perspectives arranges whole private worlds as points — the penny that looks circular from some perspectives and elliptical from others orders them. Every sensibile has two places: the place from which it appears (the perspective, interesting to the psychologist) and the place at which it appears (the thing, interesting to the physicist).

Matter and time. "The matter of a given thing is the limit of its appearances as their distance from the thing diminishes" — tentatively; the infinite divisibility of matter arises because one appearance at a distance represents many things at the limit. Time, like space, is a construction: histories are divided into biographies, correlated by assuming a velocity of sound or light.

Illusions, hallucinations, and dreams. Russell argues that "existence" is only applicable to descriptions, not to data: "Given any datum x, it is meaningless either to assert or to deny that x 'exists'" — though "My present sense-datum exists" is significant. Dream-objects are "there" in the dreamer's private space; a door banging may produce a dream of a naval engagement, and "his sense-data are still physical, and are such as a completed physics would include and calculate." The bent stick "is straight to the touch, though bent to sight. There is no 'illusion,' but only a false inference." Abnormal sense-data differ from normal ones "as regards their correlations," not intrinsically.

Key ideas

  • Physics can only be verified if physical objects are exhibited as functions of sense-data.
  • Sensibilia are objects with the status of sense-data that need not be data to any mind.
  • Sense-data are physical; the sensation is mental; the subjectivity of sense-data is physiological.
  • "Wherever possible, logical constructions are to be substituted for inferred entities."
  • The thing is the class of its appearances; its appearances to different observers occupy different private spaces.
  • Matter is the limit of a thing's appearances as their distance from the thing diminishes.
  • Existence applies to descriptions, not to data; dream-objects are as "given" as waking ones.
  • Abnormal sense-data are physical too — they differ only in their correlations with other sensibilia.

Key takeaway

By substituting logical constructions for inferred entities — the thing as a class of its appearances, matter as a limit, the one space and time as constructions — physics is shown to be verifiable through sense-data alone, which are themselves part of the physical world.

Chapter 9 — On the Notion of Cause

Central question

Is there a law of causality, and if not, what principle does science actually employ in its place?

Main argument

The word "cause" should be extruded. Russell announces three aims: to show "cause" is "so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable"; to discover what principle science actually uses; and to exhibit confusions about teleology and determinism. He cites Baldwin's Dictionary, which gives three mutually incompatible definitions of causality. Analysis of "necessary" shows it can only apply to propositional functions, not propositions: "Charles I's head was cut off" is "just as true in summer as in winter." The third definition's temporal contiguity is impossible: "No two instants are contiguous"; the dilemma of the finite duration of cause and effect "is fatal to the view that cause and effect can be contiguous in time."

The law is false and unemployable. "An 'event,' in the statement of the law, is obviously intended to be something that is likely to recur" — hence not a particular but "some universal of which there may be many instances." But then the time-interval between cause and effect creates "insuperable difficulties": "I put my penny in the slot, but before I can draw out my ticket there is an earthquake which upsets the machine and my calculations." To secure the effect one must include the whole environment, and then repetition becomes almost impossible. The principle "same cause, same effect, which philosophers imagine to be vital to science, is therefore utterly otiose." Even Bergson — who rightly saw the philosophical law is worthless — wrongly supposes science uses it; "philosophers ... are too apt to take their views on science from each other, not from science."

Five maxims refuted. Russell dismantles the folklore of causation:

  • Cause and effect must resemble each other — science shows causes and effects are "usually very widely dissimilar."
  • Cause is analogous to volition, with an intelligible nexus — "Nothing is less 'intelligible' ... than the connection between an act of will and its fulfilment."
  • The cause compels the effect — compulsion involves thwarted desire; "there can be no question of compulsion" where desire does not come in.
  • A cause cannot operate after it has ceased to exist — this rests on the supposition that causes "operate" at all; causes, if any, act after ceasing to exist.
  • A cause cannot operate where it is not — urged against Newton, the source of the prejudice against action at a distance.

What replaces causality. In an advanced science "there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula." The law of gravitation is a set of differential equations: "sameness of differential equations" is the only correct phrase. The "uniformity of nature" is not "same cause, same effect" but "the principle of the permanence of laws" — and that is an empirical generalisation, accepted only on inductive grounds, never a major premiss. Science works with relatively isolated systems — "one which, within some assignable margin of error, will behave in the same way ... however the rest of the universe may be constituted" — and the case of one event causing another "is really only the most simplified instance of a practically isolated system."

Determinism, teleology, free will. A deterministic system is defined functionally: given certain determinants, the state at any time is a function of them. A system may have many sets of determinants: if psycho-physical parallelism holds, states of one man's mind determine the whole material universe as much as the reverse — "it must be exactly as true to regard matter as subject to mind as it would be to regard mind as subject to matter." A mechanical system may also be a teleological system, in which purposes are realised — mechanism throws "no light whatever" on teleology. On free will: whether volitions are determined "is a mere question of fact; no a priori considerations ... can exist on either side." The "subjective sense of freedom ... has no bearing on the question whatever," for "we feel that our will is not compelled, but that only means that it is not other than we choose it to be." The past and the future are symmetrical: "You cannot make the future other than it will be; this again is an application of the law of contradiction." The three meanings of "necessity" are separated, and the problem of free will versus determinism is judged "mainly illusory, but in part not yet capable of being decisively solved."

Key ideas

  • "The law of causality, I believe, ... is a relic of a bygone age."
  • Baldwin's Dictionary offers three mutually incompatible definitions of cause; none survives analysis.
  • "Same cause, same effect" is otiose: fully specified antecedents never recur, so the principle would make science sterile.
  • The word "cause" should be completely extruded from the philosophical vocabulary.
  • Scientific laws are functional relations — "sameness of differential equations" — not uniformities of sequence.
  • The uniformity of nature is the permanence of laws, an empirical generalisation, not an a priori necessity.
  • Determinism is a functional notion; a system may have purely material and purely mental determinants alike.
  • The problem of free will versus determinism is mainly illusory: compulsion requires thwarted desire.

Key takeaway

There is no such thing as the cause of an event: the supposed law of causality is a relic, and science replaces it with functional laws relating determinants, which dissolve the apparent conflict between determinism and freedom.

Chapter 10 — Knowledge by Acquaintance and Knowledge by Description

Central question

What do we know when we know that "the so-and-so" is thus-and-so, without knowing who or what the so-and-so is?

Main argument

Acquaintance defined. Russell begins: "I say that I am acquainted with an object when I have a direct cognitive relation to that object, i.e. when I am directly aware of the object itself." Acquaintance is the relation of subject to object that constitutes presentation; the word is chosen to "preserve the dualism of subject and object," which "seems to me a fundamental fact concerning cognition." We are acquainted with sense-data; with universals (awareness of universals is conceiving, and a universal of which we are aware is a concept — we are aware of the universal yellow, and of relations such as before, else we could not know that "if one thing is before another, and the other before a third, then the first is before the third"); and possibly with ourselves. "Among the objects with which we are acquainted are not included physical objects (as opposed to sense-data), nor other people's minds."

Description defined. A description is any phrase of the form "a so-and-so" (ambiguous) or "the so-and-so" (definite). We know an object by description "when we know that it is 'the so-and-so', i.e. when we know that there is one object, and no more, having a certain property." The examples: the man with the iron mask; "the candidate who gets most votes will be elected, though I do not know who is the candidate." Common words, "even proper names, are usually really descriptions": Bismarck himself could use his name as a genuine proper name, but a friend who knew him was acquainted only with sense-data connected with his body — "His body as a physical object, and still more his mind, were only known as the body and the mind connected with these sense-data. That is, they were known by description."

The fundamental principle. "Every proposition which we can understand must be composed wholly of constituents with which we are acquainted." Judgments are not composed of mental entities called "ideas": the idea-theory makes ideas "a veil between us and outside things" and leads to a vicious regress. In a judgment about Julius Cæsar, the actual man is not a constituent; we substitute "the man whose name was Julius Cæsar," and the judgment "the man whose name was Julius Cæsar was assassinated" is analysed as "one and only one man was called Julius Cæsar, and that one was assassinated" — "there is no constituent corresponding to the phrase."

Meaning and denotation. The duality of meaning and denotation ("the author of Waverley" has meaning and denotes Scott) is "misleading if taken as fundamental": the denotation is not a constituent of the proposition, since we may know the proposition without knowing the denotation, and since "the golden mountain does not exist" and "the round square is self-contradictory" are significant though their subjects denote nothing — against Meinong's realm of non-existent objects. The correct analysis: "the author of Waverley was the author of Marmion" means "some one wrote Waverley and no one else did, and that some one also wrote Marmion and no one else did." Descriptions are analysed away; the real subjects are propositional functions. Only "this" — and, with a 1917 footnote's correction, no longer "I" — is a strictly proper name of a particular. The conclusion: "All propositions intelligible to us ... are composed wholly of constituents with which we are acquainted," and our knowledge of physical objects and other minds is only knowledge by description, "the descriptions involved being usually such as involve sense-data."

Key ideas

  • Acquaintance is direct awareness of the object itself; description is knowledge of "the so-and-so."
  • We are acquainted with sense-data and universals, possibly with ourselves — not with physical objects or other minds.
  • A description is "the so-and-so"; an object is known by description when we know that exactly one object has a property.
  • "Every proposition which we can understand must be composed wholly of constituents with which we are acquainted."
  • Judgments contain the actual objects judged about, not "ideas"; the idea-theory is a veil and a regress.
  • The denotation of a description is not a constituent of propositions containing it — Meinong's golden mountain is a mistake.
  • "The author of Waverley" is analysed away: "one and only one man wrote Waverley, and he was Scott."
  • Knowledge of Bismarck, of Julius Cæsar, and of other minds is descriptive knowledge rooted in acquaintance with sense-data.

Key takeaway

All understanding rests on acquaintance with particulars and universals, and knowledge by description — including our entire knowledge of physical objects and other minds — is reducible to it, with descriptive phrases analysed away into propositional functions.

The book's overall argument

  1. Chapter 1 (Mysticism and Logic) — establishes the frame: metaphysics arises from the union and conflict of mysticism and science, and mysticism is to be commended as an attitude toward life but rejected as a creed about the world.
  2. Chapter 2 (The Place of Science in a Liberal Education) — establishes the scientific spirit as the core of intellectual culture: the refusal to regard our desires as a key to the world.
  3. Chapter 3 (A Free Man's Worship) — draws the ethical consequence: within a purposeless universe, freedom lies in renouncing desire and worshipping the good our own conscience builds.
  4. Chapter 4 (The Study of Mathematics) — establishes the paradigm of exact thought as an end in itself, coldly beautiful and independent of us.
  5. Chapter 5 (Mathematics and the Metaphysicians) — establishes that pure mathematics is formal logic, dissolving the ancient paradoxes of infinity, continuity, space, and motion.
  6. Chapter 6 (On Scientific Method in Philosophy) — establishes the method: philosophy becomes the piecemeal, analytic, a priori study of logical forms — "the science of the possible."
  7. Chapter 7 (The Ultimate Constituents of Matter) — establishes the ontology: the world is momentary particulars, and matter is a logical construction from them, not a persistent substance.
  8. Chapter 8 (The Relation of Sense-Data to Physics) — establishes the epistemology of physics: sense-data are physical, and logical constructions substituted for inferred entities secure physics' verifiability.
  9. Chapter 9 (On the Notion of Cause) — establishes that the law of causality is a relic: science employs functional laws relating determinants, and determinism so understood is compatible with freedom.
  10. Chapter 10 (Knowledge by Acquaintance and Knowledge by Description) — establishes the theory of knowledge: every proposition we can understand is composed wholly of constituents with which we are acquainted, and description extends knowledge beyond acquaintance.

Common misunderstandings

Misunderstanding: The book rejects mysticism entirely.

Russell's first essay argues the opposite of a dismissal: "mysticism is to be commended as an attitude towards life, not as a creed about the world." The mystical emotion is "the inspirer of whatever is best in Man," and the very reverence of mysticism may nourish the patient investigation of science. What is rejected is only the creed — the four metaphysical beliefs — built on the emotion.

Misunderstanding: "A Free Man's Worship" is an atheist's manifesto of despair.

Despair is its foundation, not its conclusion. The essay moves from "unyielding despair" through renunciation to freedom: "the free man's worship" is the worship of the good and the building of ideals in a world that does not support them. Its final movement is the obligation of kindness to fellow-sufferers.

Misunderstanding: The book is anti-science or anti-philosophy.

It is a manifesto for a kind of philosophy. The targets are ethical metaphysics, evolutionism, and intuitionism (Bergson); the method recommended — logical analysis, constructions in place of inferences — is an early statement of what became analytic philosophy.

Misunderstanding: Russell denies causation.

He denies the word and the law: "cause" is "so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable," and "same cause, same effect" is false. He affirms that science rests on functional laws, empirical uniformities, and the inductive "permanence of laws."

Misunderstanding: Russell is an idealist or solipsist who thinks the world is in our minds.

The opposite. The whole point of the sense-data essays is that "sense-data are part of the actual substance of the physical world"; matter is a logical construction from particulars — a way of grouping them, not a mental fiction. The subjectivism of sense is "physiological not psychical."

Misunderstanding: "Mysticism and Logic" is a book of mathematics only.

The first five essays are explicitly popular (Russell calls them "entirely popular" in the preface), and only the last five are "somewhat more technical." The mathematics essays (4 and 5) serve the larger argument about the nature of logic and reality.

Misunderstanding: The title essay is "A Free Man's Religion."

No such essay exists in this collection. The essay is "A Free Man's Worship" — a common conflation in secondary sources.

Misunderstanding: The 1910 Philosophical Essays and this book are the same collection.

They share only three essays (including "A Free Man's Worship" and "The Study of Mathematics"). The 1917/1918 edition retitled and substantially rearranged the collection, dropping and adding essays, and the 1910 edition's table of contents does not match this one.

Central paradox / key insight

The collection's most counterintuitive theme is that mysticism and logic are complements, not enemies. The two impulses that pull metaphysics apart — the mystic's demand for sudden, total insight and the scientist's demand for patient, partial analysis — are, in Russell's handling, mutually necessary: the mystic's reverence supplies the motive for the disinterested pursuit of truth, and logical analysis supplies the discipline that turns insight into knowledge. The same structure appears in ethics: the philosophy that refuses to impose its own good and evil on the world is itself "the outcome of a higher ethical standpoint."

"Insight, untested and unsupported, is an insufficient guarantee of truth, in spite of the fact that much of the most important truth is first suggested by its means."

"A philosophy which does not seek to impose upon the world its own conceptions of good and evil is not only more likely to achieve truth, but is also the outcome of a higher ethical standpoint."

Important concepts

Mysticism — The impulse toward sudden, coercive insight into a reality behind appearance; characterised by belief in intuition over analysis, in unity, in the unreality of time, and in the illusoriness of evil. Russell commends it as an attitude toward life, not as a creed about the world.

Scientific spirit — "The refusal to regard our own desires, tastes, and interests as affording a key to the understanding of the world"; the suppression of hopes, fears, loves, and hates in the interest of the desire to know.

Sense-datum — A particular immediately given in sense, such as a patch of colour or a noise; the epistemological basis of all our knowledge of external particulars.

Sensibile — An object with the same metaphysical and physical status as a sense-datum, without necessarily being given to any mind; the relation of a sensibile to a sense-datum is "like that of a man to a husband."

Acquaintance — The direct cognitive relation of a subject to an object itself; knowledge of things (as opposed to truths), which brings the object itself before the mind. We are acquainted with sense-data, universals, and possibly ourselves.

Description — A phrase of the form "a so-and-so" (ambiguous) or "the so-and-so" (definite); knowledge by description is knowledge that exactly one object has a certain property. Physical objects and other minds are known only by description.

Logical construction — A class or series of particulars substituted, wherever possible, for inferred entities ("symbolic fictions"). Matter, the thing, points, instants, and the one space and time are logical constructions; "Wherever possible, logical constructions are to be substituted for inferred entities" is "the supreme maxim in scientific philosophising."

Particulars and universals — Particulars are existents and complexes of existents; universals (concepts) are objects of which no particular is a constituent, known by conceiving. The world is a pattern of momentary particulars; their relations make up the arrangement.

Perspective and biography — A perspective is the totality of particulars simultaneous with a given particular (a private world, whether or not any percipient views it); a biography is everything directly earlier, later than, or simultaneous with a given particular. "Things" and "perspectives" are two classifications of the same particulars.

Logical atomism / absolute pluralism — The view, stated in "On Scientific Method in Philosophy," that "while maintaining that there are many things, it denies that there is a whole composed of those things."

Propositional function — An expression containing a variable, becoming a proposition when a value is assigned to the variable; the subject-matter into which definite descriptions are analysed ("the author of Waverley" becomes "one and only one man wrote Waverley, and he …").

Uniformity of nature — Not "same cause, same effect," but the permanence of laws; an empirical generalisation accepted on inductive grounds, never an a priori necessity.

Determinism — A functional notion: a system is deterministic when, given certain determinants, its state at any time is a function of them; a system may have several quite different sets of determinants (material or mental).

Matter — "The limit of its appearances as their distance from the thing diminishes" (tentatively); the persistent particles of physics are logical constructions, and the immediate objects of sense are among the ultimate constituents of the physical world.

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