My Philosophical Development — Chapter-by-Chapter Outline

Author: Bertrand Russell First published: 1959 Edition covered: George Allen & Unwin first edition, London, 1959 (with the appendix "Russell's Philosophy: A Study of Its Development" by Alan Wood). The US edition (Simon and Schuster, New York, 1959) has identical content; the Routledge Classics reprint (2007) reproduces the same text. Chapter titles below follow the printed table of contents of the 1959 first edition (verified against a full-text scan of that edition on the Internet Archive and the HathiTrust catalog record, which includes the contents field). The book has 18 chapters plus an index and the Wood appendix.

Central thesis

My Philosophical Development is a late-career intellectual autobiography, written when Russell was eighty-six, in which he retraces the major stages of his philosophical life from adolescent religious doubt to the technical logic of Principia Mathematica to the neutral monism and theory of knowledge of his later decades. It is not a memoir in the manner of his three-volume Autobiography (1967–1969): it is a history of ideas, with the personal material — the 1888 diary, the Hegelian notes, the war years — admitted only where it explains why the ideas changed. The book is structured as a series of self-corrections, each recorded in the past tense with the later Russell commenting on the earlier one.

The book's guiding claim is that there is one constant preoccupation running through all the changes: the question of how much we can know and with what degree of certainty. Around that preoccupation, Russell draws one major division: in the years 1899–1900 he adopted logical atomism and Peano's mathematical technique, a change he calls a revolution; everything after that was evolution. The narrative arc runs from absolute idealism through the revolt into pluralism, the two Principia Mathematica chapters, the theory of the external world, Wittgenstein's impact, and the later theory of knowledge, language, truth, and non-demonstrative inference, ending with the "retreat from Pythagoras" and four polemical replies to the ordinary-language school. Russell repeatedly insists that analysis, not system-building, is the only road of philosophical progress, and that philosophy must be continuous with science and common sense rather than an autonomous study of language.

There is only one constant preoccupation: I have throughout been anxious to discover how much we can be said to know and with what degree of certainty or doubtfulness.

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Chapter 1 — Introductory Outline

Central question

How should Russell's philosophical development be divided into stages, and what single question motivated all of them?

Main argument

The one major division Russell opens by mapping his own development onto the problems that occupied him. He identifies a single turning point: in 1899–1900 he adopted the philosophy of logical atomism and the technique of Peano in mathematical logic. This was so great a revolution, he says, that his earlier work — except what was purely mathematical — became irrelevant to everything he did later; all subsequent changes were evolutionary. He then names the one constant: the desire to discover how much we can be said to know, and with what degree of certainty or doubtfulness.

The two original interests His interest in philosophy had two adolescent sources: a wish to find a defence, however vague, for religious belief; and a wish to persuade himself that something could be known, in pure mathematics if nowhere else. As regards religion, he came to disbelieve first in free will, then in immortality, and finally in God. As regards mathematics, he could not believe that "two plus two equals four" is an inductive generalization from experience, but got nowhere beyond that negative conclusion.

Cambridge and the doctrine of external relations At Cambridge, Russell was indoctrinated with Kant and Hegel, but he and G. E. Moore came to reject both. Moore was chiefly interested in the independence of fact from knowledge; Russell was more concerned with what he called the doctrine of external relations — the thesis that relatedness does not imply any corresponding complexity in the related terms and is not a property of the whole they compose. Monists had maintained the opposite, and this made mathematics inexplicable to him. He developed the view in his book on Leibniz and then encountered Peano's mathematical logic, which supplied a new technique and a new philosophy of mathematics. Reacting against the Hegelian habit of "proving" the impossibility of space, time, and matter, he swung to the opposite extreme and believed in the reality of whatever could not be disproved — points, instants, particles, Platonic universals.

Occam's razor and the physical world After 1910, under Whitehead's influence, he applied Occam's razor to physics: one need not deny points and instants, but one can abstain from asserting them, since physics gives no reason to suppose they exist. The stuff of the physical world could consist of events, each occupying a finite amount of space-time. At the same time he became interested in how we come to know the physical world, and here his philosophy underwent its last substantial change: under William James's influence he ceased to regard perception as a two-term relation of subject and object, greatly increasing the difficulty of connecting experience with the outer world.

Language and inference About 1917 he became interested in the relation of language to facts — vocabulary and syntax — having previously treated language as transparent. He stresses that he has never treated language as an autonomous province: its essential thing is that it means something non-linguistic. His most recent work concerned non-demonstrative inference, where he argues that induction by simple enumeration, without common sense, leads more often to error than to truth, so some other principle must underwrite science. The chapter closes with his methodological creed: ever since abandoning Kant and Hegel he has sought solutions by analysis, and he believes analysis can completely solve the problem of the relation of mind and matter — a solution nobody has accepted, he adds, only because it has not been understood.

Key ideas

• The 1899–1900 adoption of logical atomism and Peano's technique is a revolution; all later changes are evolution.
• One constant preoccupation unites every phase: how much we can know, and with what degree of certainty.
• The doctrine of external relations, developed in the Leibniz book, is the pivot of Russell's break with monism.
• Occam's razor licenses abstaining from asserting points, instants, and particles, replacing them with finite events.
• Perception, under James's influence, ceased to be a two-term subject–object relation.
• Language matters only because it means something non-linguistic; it is not an autonomous realm.
• Induction cannot justify non-demonstrative inference, since it leads to error more often than truth.
• Analysis, not system-building, is the only method of philosophical progress.

Key takeaway

The book announces itself as an error-correcting intellectual autobiography whose one fixed question — what can be known and how certainly — is pursued through a single revolutionary break in 1899–1900 and an evolution afterward.

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Chapter 2 — My Present View of the World

Central question

What is the view Russell has been gradually led to, and why does it dissolve the traditional problem of the relation of mind and matter?

Main argument

The synthesis of four sciences Russell states his mature view "as simply and clearly as I possibly can" because it has been "almost universally misunderstood." It results from a synthesis of physics, physiology, psychology, and mathematical logic. He deliberately reverses the procedure common since Kant: instead of beginning with how we know and proceeding to what we know, he begins with what we know. Knowing how we know is only a small department of knowing what we know, and the Kantian order wrongly gives knowing a cosmic importance. He accepts without qualification the picture from astronomy and geology: mind appears only in a tiny fragment of space-time.

What physics actually says Theoretical physics no longer speaks with Newtonian clarity. Newton's four concepts — space, time, matter, force — have all been swept away: space and time became the relational system of space-time; matter was replaced by series of events; force became energy, which is indistinguishable from the ghost of matter; cause has become decrepit. Yet physics must be believed "on pain of death": a community that rejected it could be exterminated by physicists employed by a hostile government. Physics is exceedingly abstract: it gives equations describing the logical structure of events but says nothing about their intrinsic character. We know intrinsic character only in the events that happen to us.

The photographic plate, the cine-cameras, the gramophone Russell argues from purely physical analogies to perception. Photographic plates exposed to the same portion of the sky must each contain events individually connected with each photographed star; cine-cameras filming a play, or gramophones and radio receiving a speech, receive events whose intrinsic qualities differ from the originals but preserve their structure. These processes are purely physical — we do not suppose the cine-cameras have minds — and they show that in most places a vast assemblage of overlapping events is taking place, many connected by causal chains ("heredity") to an original event.

Events as the fundamental notion Russell takes "event" as fundamental: each event occupies a finite amount of space-time and overlaps with innumerable others. Mathematicians can construct point-instants out of assemblages of overlapping events, but that is a technical convenience. The difference between the world of physics and the world of daily life is a difference of degree of abstraction — like population statistics that strip people of their characteristics.

Private world and inferred world; the Leibniz comparison The world of physics is entirely inferred. Data are the things we know without inference — our observed sensations. Common sense is right that sensations have external causes but wrong to suppose inanimate objects resemble, in intrinsic quality, the perceptions they cause — as groundless as supposing a gramophone record resembles the music it causes. Russell then compares his view with Leibniz's: the monads mirror the universe each from its own point of view; private space vs. physical space; but Russell rejects the pre-established harmony in favor of causal action. With the Second Law of Thermodynamics comes directed causality, and on this he grounds his notorious opinion: "people's thoughts are in their heads." The brain consists of thoughts, using "thought" in Descartes's widest sense; when you look at a brain through a microscope, what you see is part of your private world, a remote effect of the physical brain. He quotes H. Hudson's article "Why we cannot witness or observe what goes on 'in our heads'" (Mind, April 1956) and inverts it: we can observe what goes on in our heads, and nothing else at all.

Mind defined, and three key points A mind is defined as a collection of events connected with each other by memory-chains backwards and forwards. Three key points: (1) the entities of mathematical physics are not the stuff of the world but constructions composed of events; (2) everything we perceive without inference belongs to our private world — here he agrees with Berkeley — while the external world is inferred; (3) causal lines peter out "like rivers in the sand," which is why we do not perceive everything at all times. He claims for the theory only what a physicist claims: it cannot be proved, but it cannot be disproved, and it answers puzzles other theories leave.

Key ideas

• The correct order of inquiry is from what we know to how we know it, not the reverse.
• Newton's space, time, matter, force, and cause have all been displaced by modern physics.
• Physics transmits structure but is silent about the intrinsic character of events.
• Photographic plates, cine-cameras, and gramophones demonstrate structure-preserving causal chains without minds.
• The entities of physics are constructions out of events, not the world's raw stuff.
• Everything perceived without inference belongs to a private world; the external world is inferred (agreement with Berkeley).
• Thoughts are in the head: the brain is composed of "thoughts" in Descartes's wide sense.
• A mind is a collection of events bound together by memory-chains.

Key takeaway

Russell's present view is a neutral, event-based realism in which physics describes only structure, perception gives us only our private world, and the mind–matter gulf dissolves because both are constructions from the same events.

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Chapter 3 — First Efforts

Central question

What did Russell think, and how did he think, between the ages of fifteen and eighteen, before he went to Cambridge?

Main argument

A solitary adolescent philosophy Russell began thinking about philosophical questions at fifteen, reading no philosophical books until Mill's Logic in the months before going up to Trinity. Mathematics dominated his time; the emotional drive was doubt about the fundamental dogmas of religion. He wrote down his beliefs and unbeliefs just before and after his sixteenth birthday, using Greek letters and phonetic spelling for concealment, and the bulk of the chapter quotes this 1888 diary.

The diary extracts The diary is a record of religious doubt moving through stages. On March 3 he has "scarcely" a belief in immortality. On March 19 he calls himself a theist and vows to consider only scientific arguments for God. On March 22 he proves God's existence from the uniformity of nature — an argument that at the same time disproves miracles. On April 2 he argues that without free will there can be no immortality, and that man is a machine "endowed, unhappily for himself, with consciousness." On April 14 he recoils at the thought that all human greatness depends on "some one molecule hitting up against some other a little oftener than in other men," but finds the alternative — a miracle endowing one ape with reason — worse. On April 18 he derives conscience from evolution and education, citing the Ten Commandments as rules for the preservation of the species. On April 20 he commits himself to the greatest-happiness principle. On April 29 he vows to follow reason rather than instinct or education. On May 3 he notes that the soul grows with the body, calling Wordsworth's Intimations "humbug." On June 3 he doubts even that truth is a good: the search for truth has shattered his beliefs, estranged his family, and, "in my individual case, I should say the effects of a search for truth have been more bad than good."

Three centuries at once Russell's mind, he says, was a confusion of seventeenth-century knowledge, eighteenth-century beliefs, and nineteenth-century enthusiasms. His thinking was crude Descartes — he knew Descartes only as the inventor of Cartesian co-ordinates; his rejection of free will on grounds of God's omnipotence might have led him to Spinoza. After losing belief in God he advanced to a position like that of the French Philosophes: a passionate rationalist who loved Laplace's calculator, hated superstition, and believed in the perfectibility of man by reason and machinery. Alongside this ran an emotional life with no intellectual support: he regretted the loss of religion, loved natural beauty, and was moved by Carlyle's rhetoric and Tennyson's sentiment though he rejected them. Shelley was the only writer wholly congenial, in his merits and his faults.

Mathematical doubts His doubts extended to mathematics: Euclid's proofs using superposition seemed shaky; the mere existence of non-Euclidean geometry was exciting but disquieting; the infinitesimal calculus worked in practice but its official proofs were sophistries. Some doubts were laid to rest by W. K. Clifford's Common Sense of the Exact Sciences. He hoped for "a perfected mathematics which should leave no room for doubts," and to extend the sphere of certainty from mathematics to the other sciences bit by bit. The chapter ends with relief at discarding the last vestiges of theological orthodoxy.

Key ideas

• At fifteen to eighteen Russell philosophized in solitude, without books, driven by doubt about religion.
• His 1888 diary already contains a worked-out materialism: no free will, no immortality, conscience from evolution.
• He reasoned in the style of Descartes, Spinoza, and the eighteenth-century Philosophes before knowing any of them.
• Rationalism and romantic sentiment coexisted without reconciliation: "seventeenth-century knowledge, eighteenth-century beliefs and nineteenth-century enthusiasms."
• Mathematical doubts about Euclid and the calculus pushed him toward the problem of the foundations of mathematics.
• He believed a perfected mathematics could anchor certainty and that it could be extended to other sciences.

Key takeaway

Russell's philosophical development begins in solitary adolescent conflict — religious doubt and mathematical scepticism — out of which came the lifelong conviction that certainty, if it exists anywhere, is to be found and extended through mathematics.

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Chapter 4 — Excursion into Idealism

Central question

How did Russell become a Hegelian, and what did he actually believe during his idealist period?

Main argument

Cambridge and the influence of the idealists Russell came across professional philosophers only at Cambridge in October 1890. All the influences were Kantian or Hegelian, with one exception — Henry Sidgwick, the last Benthamite, whom the young dismissed as "Old Sidg." James Ward was a Kantian, G. F. Stout a Hegelian who said Bradley's Appearance and Reality accomplished as much as is humanly possible in ontology, and McTaggart influenced Russell most of all, claiming he could prove by logic that the world is good and the soul immortal. Russell stood out against McTaggart with "gradually diminishing resistance" until, just before his Moral Sciences Tripos in 1894, he went over completely to a semi-Kantian, semi-Hegelian metaphysic.

The foundations of geometry His Fellowship dissertation, "The Foundations of Geometry," took up Kant's question "how is geometry possible?" and answered that it is possible if and only if space is one of the three recognized varieties — Euclidean or one of two non-Euclidean geometries with constant curvature. Einstein's General Theory of Relativity, he says, swept away everything resembling this view: it uses exactly the geometry Russell had declared impossible. "Apart from details, I do not think that there is anything valid in this early book."

The Hegelian dialectic of the sciences Worse followed: he plunged into the Hegelian dialectic, writing "On the Relations of Number and Quantity," which he calls "unadulterated Hegel" and now "nothing but unmitigated rubbish," although Couturat called it "ce petit chef d'œuvre de dialectique subtile." He was by then a full-fledged Hegelian aiming at a complete dialectic of the sciences proving that all reality is mental. Every science abstracts, and every abstraction leads to contradictions; wherever Kant and Hegel conflicted, he sided with Hegel. Two problems specially interested him: the antinomy of absolute vs. relative motion (which he used as a dialectical convenience, since matter was an unreal abstraction anyway), and whether matter consists of atoms separated by empty space or of a plenum — he adopted the Maxwellian plenum over Boscovitch's punctual atoms, dressed in Hegelian form as a dialectical transition from Leibniz to Spinoza.

The unpublished notes The chapter reproduces extensive notes for a "dialectic of the sciences," including "On the Idea of a Dialectic of the Sciences" (January 1, 1898), "Note on Transition from Geometry to Dynamics," "Some Definitions of Matter," "Dynamics and Absolute Motion," "Note on Matter and Motion," "Short Statement of the Antinomy of Absolute Motion," "Can We Make a Dialectical Transition from Punctual Matter to the Plenum?" and "Note on the Logic of the Sciences." These notes show the method: each science is an attempt to construct a universe out of its own ideas; contradictions show the science is not self-subsistent; the dialectic then passes to a new science. The antinomy of absolute motion is the engine: matter is defined as that which moves and is moved by other matter, but motion can only be measured relative to matter free of dynamical relations to the measured matter — impossible by the definition itself — so dynamics is "dialectically untenable" and matter cannot constitute Reality. The transition to the plenum concludes that "the same matter... is present in every point of space," with the whole universe present in every point of space and time.

The verdict Re-reading the philosophy of physics from 1896–1898, Russell says, it seems "complete nonsense," and he finds it hard to imagine how he ever thought otherwise — adding only that his notes were no more misguided than the writings of Hegel. He emphasizes his youthful optimism about the finality of his own theories, and remarks that his Hegelian dress even let him prefer logical order over chronology.

Key ideas

• Cambridge idealism was total — Kantian and Hegelian — with McTaggart as the decisive influence.
• His first book, on the foundations of geometry, was a Kantian answer to "how is geometry possible?" later demolished by Einstein.
• He became a full-fledged Hegelian whose project was a dialectic of the sciences culminating in the proof that all reality is mental.
• The antinomy of absolute motion was the pivot of his Hegelian philosophy of physics.
• The 1898 notes construct a dialectical transition from punctual matter to the plenum in which the Whole is the only reality.
• He ultimately judged the whole period "complete nonsense," no worse but no better than Hegel.
• A near-unbelievable optimism about the finality of his own theories marked his early work.

Key takeaway

Russell's excursion into idealism was a deep one — complete with an unpublished dialectic of the sciences that treated the antinomy of absolute motion as proof that matter cannot be real — and he later judged it a total failure, which is why the next chapter's rebellion mattered.

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Chapter 5 — Revolt into Pluralism

Central question

Why and how did Russell and Moore abandon idealism at the end of 1898, and what did the new pluralist philosophy amount to?

Main argument

The rebellion Towards the end of 1898, Moore and Russell rebelled against both Kant and Hegel, Moore leading the way. The first published account was Moore's "The Nature of Judgement" in Mind, whose negative part — that fact is in general independent of experience — both still accepted. Moore was most concerned with rejecting idealism; Russell was most interested in rejecting monism. The two were connected through the doctrine about relations that Bradley had distilled from Hegel: the doctrine of internal relations, against which Russell set his own doctrine of external relations.

Internal vs. external relations The doctrine of internal relations held that every relation between two terms expresses intrinsic properties of the terms and, in ultimate analysis, a property of the whole they compose. With some relations this is plausible — love or hate are states of the subject. But for the abstract relations that interest logic it fails: if A is earlier than B, nothing in A's intrinsic nature requires this; Leibniz's example of the man whose wife dies in India without his knowing is the doctrine pushed to absurdity. Asymmetrical relations — those that hold one way but not the other — are the decisive case: reducing "A is earlier than B" to dates of A and B fails because the dates must again stand in the relation "earlier than," and reducing it to a property of the whole A-and-B fails because the whole has no order, so it cannot distinguish "A is earlier than B" from "B is earlier than A." Since asymmetrical relations are essential in most of mathematics, the doctrine was important.

The 1907 Aristotelian Society paper Russell reprints a long passage from his 1907 paper on Harold Joachim's The Nature of Truth: the axiom of internal relations ("every relation is grounded in the natures of the related terms") is equivalent to the monistic theory of truth, and to the conclusion that there are no relations at all. The argument turns on diversity: if A and B are diverse, this cannot be reduced to difference of adjectives without an endless regress; hence, if the axiom were true, there could be no diversity and only one thing. He argues that the axiom's supposed grounds — the law of sufficient reason, and the claim that related terms "cannot but" be related as they are — are either misformulated or question-begging, and that the axiom is incompatible with all complexity and with the idealists' own doctrine of "identity in difference," which collapses "like an opera-hat."

The liberation The new philosophy felt like liberation: "as if I had escaped from a hot-house on to a wind-swept headland." He hated the stuffiness of supposing space and time were only in his mind; he liked the starry heavens even better than the moral law. In the first exuberance he became a naive realist, rejoicing that grass is really green. He began to believe everything the Hegelians disbelieved: all the numbers sitting in a row in a Platonic heaven, points and instants as actually existing entities, a world of universals consisting mostly of what verbs and prepositions mean, and mathematics as not-quite-true no longer — the Hegelians meant "the Absolute can find better things to occupy its mind than doing sums." Gradually Occam's razor gave him a "more clean-shaven picture of reality": he still thinks it impossible to disprove integers, points, instants, or the Gods of Olympus, but there is no reason to think they exist.

The unity of the sentence The early years of the new philosophy were occupied with largely linguistic questions: what makes the unity of a complex, and especially of a sentence? The verb binds the sentence together, yet the verbal noun means the same thing without binding. He troubled himself with the difference between is and being; his mother-in-law, a famous religious leader, assured him philosophy is only difficult because of long words, and he confronted her with: "What is means is, and therefore differs from is, for 'is is' would be nonsense." These problems arose from the belief that if a word means something, there must be some thing that it means — a mistake swept away by the theory of descriptions in 1905.

What survived He lists what has not changed: the doctrine of external relations and pluralism; that an isolated truth may be quite true; that analysis is not falsification; that any non-tautological proposition, if true, is true in virtue of a relation to fact; that facts are in general independent of experience; and that experience is a very restricted and cosmically trivial aspect of a tiny portion of the universe.

Key ideas

• The revolt against Kant and Hegel at the end of 1898 was led by Moore, followed closely by Russell.
• Moore rejected idealism; Russell rejected monism, through the doctrine of external relations.
• Asymmetrical relations cannot be reduced to predicates of their terms or of the whole, which is fatal to internal relations.
• The axiom of internal relations entails that there are no relations and only one thing — ontological monism.
• The rebellion produced a period of naive realism and a Platonic luxuriance of entities, later trimmed by Occam's razor.
• The unity of the sentence (the verb vs. the verbal noun) was an early puzzle later dissolved by the theory of descriptions.
• External relations, pluralism, and the independence of fact from experience survived every later change.

Key takeaway

The rejection of the doctrine of internal relations was the hinge of Russell's whole career: once relations were real and external, pluralism, mathematics, and an isolationist, fact-based theory of truth all became possible.

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Chapter 6 — Logical Technique in Mathematics

Central question

What did Russell learn from Peano in 1900, and how does it yield a definition of number that dissolves the old puzzles of arithmetic?

Main argument

The divorce of logic and mathematics Russell opens with a complaint: since Aristotle, logic has been treated by people proficient in Greek, and mathematics by people who knew no logic, and the divorce has been disastrous. At the International Congress of Philosophy in Paris in 1900 he became aware of the importance of logical reform for the philosophy of mathematics through Peano of Turin, who in every discussion showed more precision and logical rigour than anyone else. Russell asked to read all his works, immediately read them, and was given the impetus for his own views. Mathematical logic was not new — Leibniz had made attempts thwarted by respect for Aristotle, Boole published his Laws of Thought in 1854, Peirce developed a logic of relations, and Schröder summarized the field in three volumes — but none of it threw light on the grammar of arithmetic.

The two advances Two purely technical advances (both made earlier by Frege, unknown to Russell until later) mattered most. First: the separation of "Socrates is mortal" from "All Greeks are mortal." The second is not subject-predicate at all but a connection of two propositional functions: for all values of x, if x is Greek, x is mortal. It names no one, extends over the whole universe, cannot be proved by enumeration, and is true even if there are no Greeks — "All Lilliputians are mortal" is true. Second: a class with one member is not identical with that member. "Satellite of the Earth" would not change its meaning if a second satellite were discovered, and can be understood by someone who has never heard of the Moon; statements about the Moon as a name require acquaintance with the Moon.

Counting, classes, and propositional functions The old philosophy of arithmetic thought of numbers as resulting from counting, and got into hopeless puzzles because things counted as one can be counted as many: football clubs, their members, and the molecules of Mr A are all countable units depending on the question "of what is this an instance?" Counting a collection presupposes a propositional function under which its members fall. A propositional function — "x is a man" — is an expression containing a variable that becomes a proposition when a value is assigned. One is not a characteristic of things but of certain propositional functions — those true of exactly one value of the variable; zero belongs to null functions. The Scholastic maxim that one and being are convertible made it impossible to define 1; the truth is that being is a useless word.

The definition of number Numbers are sets of classes with "similarity": two classes are similar when their terms can be coupled one to one. In a monogamous country, the number of married men equals the number of married women without counting either; so for shoes, chairs and people, and couples. The number of a class is the class of all classes similar to it: 2 is the class of all couples, 3 of all trios, 0 the class of null classes, 1 the class of unit classes. This definition (formulated by Frege sixteen years earlier) disposes of 0 and 1, dissolves the one-and-many problem, and — most importantly — gets rid of numbers as metaphysical entities: they become "merely linguistic conveniences with no more substantiality than belongs to 'etc.' or 'i.e.'" Kronecker said God made the integers and mathematicians made the rest; on this definition even that prerogative of the integers disappears, and the primitive apparatus reduces to such purely logical terms as or, not, all, and some.

The infinite and the extensions of number Because numbers no longer come from counting, infinite collections lose their terror: counting is only one way of discovering how many terms a collection has, applicable only to finite collections. Rational fractions are relations between whole numbers; real numbers are sets of rational numbers — the square root of 2 is all rationals whose square is less than 2, a definition Russell believes he invented and which "puts an end to a puzzle which had perplexed mathematicians ever since the time of Pythagoras"; complex numbers are ordered couples of reals. He also admired Peano's geometry without figures, which displayed the needlessness of Kant's Anschauung, and Peano's space-filling curve. In September 1900 he wrote his paper on the logic of relations; by December 31, 1900 he had finished the first draft of The Principles of Mathematics — "an intellectual honeymoon such as I have never experienced before or since" — followed early in 1901 by intellectual sorrow.

Key ideas

• Logic and mathematics had been divorced since Aristotle; Peano's rigour at the 1900 Paris Congress reunited them for Russell.
• "Socrates is mortal" and "All Greeks are mortal" have completely different logical forms; the latter involves propositional functions and no named subject.
• A class with one member is not identical with that member.
• Numbers are classes of similar classes; 2 is the class of all couples.
• Numbers turn out to be linguistic conveniences, not metaphysical entities; only or, not, all, some remain primitive.
• Counting is not essential to number, which opens the way to infinite numbers.
• The square root of 2 is defined as the class of rationals whose square is less than 2 — ending a puzzle going back to Pythagoras.
• The months from July to December 1900 were an "intellectual honeymoon" that ended with Russell's paradox.

Key takeaway

Peano's technique, and the definition of numbers as classes of similar classes, reduced arithmetic to logic, eliminated numbers as entities, and made infinity tractable — at the cost of the contradictions that would soon follow.

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Chapter 7 — Principia Mathematica: Philosophical Aspects

Central question

What were the philosophical problems of Principia Mathematica — Russell's paradox, the theory of types, and the theory of descriptions — and how were they solved?

Main argument

The project From 1900 to 1910 Whitehead and Russell gave most of their time to Principia Mathematica. The Principles of Mathematics (finished May 23, 1902) was a "crude and rather immature draft" of the later work, differing in containing controversy with other philosophies of mathematics. The primary aim was to show that all pure mathematics follows from purely logical premisses and uses only concepts definable in logical terms — an antithesis to Kant. Whitehead invented most of the notation; Russell did most of the work on series; and every part was done three times over, so that "there is hardly a line in all the three volumes which is not a joint product." Two developments followed: a pleasant one — the logical apparatus needed turned out smaller than expected, since classes proved unnecessary — and an unpleasant one.

Russell's paradox In the spring of 1901, considering Cantor's proof that there is no greatest cardinal number, Russell applied it to the number of all the things there are, and was led to consider the class of all classes that are not members of themselves. Is this class a member of itself? Each alternative leads to its opposite — a contradiction. He inspected each step "under a logical microscope" and could find nothing wrong. He wrote to Frege, who replied that arithmetic was tottering and that his Law V was false; Frege gave up the attempt to deduce arithmetic from logic and took refuge in geometry. Russell felt the trouble lay in logic, not mathematics, and found a recipe for manufacturing infinitely many contradictions. Poincaré gleefully said mathematical logic was no longer sterile — it begat contradiction. Older puzzles seemed similar: the Epimenides liar paradox ("I am lying") and Burali-Forti's contradiction about the greatest ordinal. In The Principles of Mathematics he stated the difficulties without professing a solution, suggesting in an appendix the crude beginnings of the doctrine of types.

The theory of types A satisfying solution had three requisites: the contradictions must disappear; as much of mathematics as possible must be left intact; and the solution should appeal to "logical common sense" — which is why Russell found Quine's ad hoc systems unsatisfactory. He explains the theory of types by the homely example of the three sweets: offered any one, two, or all three, you have eight courses of conduct — 2 to the power 3 — and a class of n terms has 2ⁿ subclasses; Cantor proved 2ⁿ is greater than n even for infinite n. Applying this to all the things in the universe, there must be more classes of things than things, so classes are not things. Classes, therefore, are a convenience of discourse: given a propositional function there is a range of values for which it is significant, and a class is only a way of talking about the values for which the function is true. As for the vicious-circle problem — "the process is like trying to jump on to the shadow of your head" — the liar's "everything that I assert is false" refers to a totality of assertions and only becomes paradoxical by being included in it. Distinguish first-order propositions (referring to no totality of propositions), second-order (referring to totalities of first-order propositions), and so on; the liar's statement is then simply false, and all the paradoxes are seen to contain the same condemned kind of reflexive self-reference. Russell admits the doctrine has not won wide acceptance, but he has seen no cogent argument against it.

The theory of descriptions Set forth in "On Denoting" (Mind, 1905) — which the editor thought so preposterous he begged Russell to reconsider — the theory of descriptions came to be thought Russell's most important contribution to logic. The contrast is between the name "Scott" and the description "the author of Waverley." "Scott is the author of Waverley" is an identity, not a tautology: George IV wished to know whether Scott was the author of Waverley, but not whether Scott was Scott, though substituting one for the other in a true proposition can turn it false. Meinong had argued that "the golden mountain" must subsist in some shadowy world of being, since otherwise "the golden mountain does not exist" would be meaningless. The theory of descriptions dissolves this: "the golden mountain does not exist" becomes "the propositional function 'x is golden and a mountain' is false for all values of x," where the phrase no longer occurs as subject. Existence, in this analysis, can only be asserted of a description: "the author of Waverley exists" means that the function "x wrote Waverley" is true of exactly one value; "Scott exists" is bad grammar. The central point: a phrase may contribute to the meaning of a sentence without having any meaning at all in isolation — proved by the fact that if "the author of Waverley" meant anything other than Scott the identity would be false, and if it meant Scott it would be a tautology; hence it means neither, Q.E.D.

Key ideas

• The primary aim of Principia Mathematica was to show all pure mathematics follows from purely logical premisses — an antithesis to Kant.
• Russell's paradox (the class of classes not members of themselves) ended the 1900 "logical honeymoon" and shattered Frege's system.
• A solution must make the contradictions disappear, preserve mathematics, and satisfy logical common sense.
• The theory of types bans self-reference: propositions form an order hierarchy, and the liar's sentence is simply false at its own order.
• Classes are not things but logical conveniences — discourse about the values for which a propositional function is true.
• The theory of descriptions (1905) shows descriptions are incomplete symbols contributing to meaning without meaning in isolation.
• "The golden mountain does not exist" no longer forces acceptance of Meinong's subsistence realm.
• Existence is only properly asserted of descriptions; "Scott exists" is bad grammar.

Key takeaway

The two great tools of Principia Mathematica's philosophy — the theory of types against the paradoxes and the theory of descriptions against fictitious entities — both work by showing that apparent subjects of propositions are not what grammar suggests.

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Chapter 8 — Principia Mathematica: Mathematical Aspects

Central question

What were the mathematical — as opposed to philosophical — achievements of Principia Mathematica, above all the logic of relations and relation-arithmetic?

Main argument

The neglected mathematics Whitehead and Russell were disappointed that Principia Mathematica was viewed only philosophically. Russell knew of only six people who had read the later parts: three Poles, "subsequently (I believe) liquidated by Hitler," and three Texans, "subsequently successfully assimilated." Results worked out in Part IV were published ten years later in Mathematische Annalen with inaccuracies the authors had avoided; Reichenbach told Russell he had invented "transfinite induction," which was fully treated in Volume III. This chapter explains the mathematical aspects.

Relations in intension The prejudice against relations had harmed mathematics as well as philosophy. Boole's logic, like Leibniz's attempts, was concerned with class-inclusion and was a development of the syllogism. Peirce treated a relation as a class of couples, which is technically possible but misdirects attention. Russell thought of relations as intensions — "x precedes y," "x is greater than y," "x is north of y" — and held that the intension alone gives unity to a class or a set of ordered couples: the class of earwigs cannot be enumerated, yet we speak about all earwigs in virtue of its defining intension. Ordered couples require a relation in intension to distinguish (x, y) from (y, x). The calculus of relations then symbolizes: the terms having R to y; the terms to which x has R; the domain of R; the converse domain; the field; the converse; the relative product — "grandparent" is the relative product of "parent" with itself, "brother or sister" the relative product of "child" and "parent"; and plurals, such as "parents of Etonians."

Three kinds of relations (1) One-many relations give rise to descriptive functions — phrases with "the": "the father of x," "the wife of x" (ambiguous where polygamy exists), "the square of x" but not "the square-root of x," which has two values. (2) One-one relations establish correlations: in a monogamous country the number of husbands equals the number of wives, and men's noses equal men. An ordinal correlator preserves order: precedence among married officials and among their wives. (3) Relations that generate series: a series is a set of terms ordered by a relation that is asymmetrical (husband, not spouse), transitive (ancestor, not father), and connected (of any two terms, one bears it to the other — true of ancestor within a royal line of succession). "I think I was the first person to give [series] an exact meaning."

The generalized formal laws and the multiplicative axiom Mathematics is not just the science of number and quantity: much of the reasoning establishing arithmetic has little to do with number, and the formal laws — associative, commutative, distributive — were to be proved generally, including for infinite cases. Multiplication of infinitely many factors uses "selections," illustrated by Members of Parliament, each a representative of a constituency; three classes of three give twenty-seven selections. But when the number of classes is infinite, no finite act of choice guarantees a selection — the millionaire with infinitely many pairs of shoes can choose always the right shoe, but with socks, where there is no right or left, no rule exists. Russell proposed the "multiplicative axiom" (equivalent to Zermelo's principle of election) but, unlike Zermelo, did not regard it as self-evident: Peano's verdict is quoted — "Is this principle true or false? Our opinion has no value" — and Russell included it explicitly in the hypotheses of any proposition using it.

The ancestral relation and mathematical induction The word "and so on" hides a deep problem: "ancestor" cannot be defined as "parent, parent of parent, and so on" because "finite" is not yet defined. Frege's notion of the ancestral relation solves it: the posterity of x with respect to R is the class of things belonging to every hereditary class to which x belongs; "being called Smith" is hereditary in the father–son relation, being human in the parent–child relation. Applying this to the successor relation, the finite numbers are the posterity of 0 — which makes mathematical induction not a principle but a definition: a finite number is one increased by adding 1; an infinite number is not.

Relation-arithmetic and structure The second half of Volume II, Russell's most important mathematical contribution, contains what he called relation-numbers, of which ordinal numbers are a specialized example. Ordinal similarity ("likeness") between relations P and Q means their fields can be correlated without change of order — precedence among married officials and their wives — and the relation-number of P is the class of relations ordinally similar to P. All the formal laws true of ordinals are true of relation-numbers generally, except that the commutative law fails for infinite fields: add two terms at the beginning of the natural-number series and the new series is like the old; add them at the end and it is not. Well-ordered series (every sub-class with members has a first term) give the ordinals; relation-numbers in general were first defined in the Principia. Series of series of series — the gold bricks stacked at Fort Knox in rows, layers, and stacks, symbolized by relative products of the membership relation — are needed for the associative laws. Structure is thereby given a precise definition: two relations have the same structure when their fields can be correlated so that corresponding terms have corresponding relations; the gramophone record and the music it plays are indistinguishable in logical properties; and the notion generalizes to triadic relations such as "between" and "jealousy." Russell argues that those who do not know mathematical logic go astray on "structure," and notes that relation-arithmetic found one application in the lexicographical problem — defining alphabetical order in a language with an infinite alphabet — as Jürgen Schmidt informed him in a letter of 1956.

Key ideas

• The calculus of relations, treating relations as intensions, was the mathematical core of Principia Mathematica.
• Domain, converse domain, field, converse, relative product, and plurals are the key constructions of the calculus.
• Series are precisely defined by asymmetry, transitivity, and connectedness.
• Infinite multiplication requires "selections," and the multiplicative axiom is an unproved assumption, not a self-evident truth.
• The ancestral relation defines "finite" and turns mathematical induction from a principle into a definition.
• Relation-numbers generalize ordinal numbers; ordinal similarity defines structure exactly.
• The commutative law of arithmetic fails for infinite relation-numbers.
• Mathematical logic is the tool for understanding structure, on which understanding of the empirical world depends.

Key takeaway

The mathematical achievement of Principia Mathematica was the exact logic of relations, culminating in relation-arithmetic — a general theory of structure that Russell regarded as his most important contribution to the work and the key to understanding the empirical world.

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Chapter 9 — The External World

Central question

How can perception give knowledge of an external world, given that what we directly experience is not the object physics deals with?

Main argument

The popular book and the retained doctrines Invited by Gilbert Murray to write a popular outline of his philosophy for the Home University Library, Russell produced The Problems of Philosophy (1912), written at a moment when his opinions had a "clear-cut definiteness" they did not have earlier or later. He still agrees with much of it: "knowledge" is not a precise conception but merges into "probable opinion"; self-evidence has degrees; and we can know a general proposition without knowing any single instance — "all the pairs of numbers that have never been multiplied together have products greater than 1,000." But he no longer thinks the laws of logic are laws of things (they are purely linguistic); points, instants, and particles are no longer part of the raw material of the world; what he said about induction was crude; and his confident assurance about universals has gone.

Whitehead's construction and the Lowell Lectures Whitehead's method of constructing points, instants, and particles as sets of finite events awakened Russell from his "dogmatic slumbers" and suggested that all the smoothness of theoretical physics belongs to the ingenuity of mathematicians rather than the nature of the world. For the Lowell Lectures in Boston, spring 1914 — Our Knowledge of the External World — Russell set out to use the novel apparatus. The problem of perception: two people looking at an object see differently owing to perspective, with no reason to single out one percipient; the physicist says we do not see atoms and molecules; the physiologist shows an elaborate causal chain from eye to brain; the man with an amputated leg feels pain in his great toe. What we directly experience cannot be the external object, yet only what we directly experience gives reason to believe in the world of physics.

Solipsism and the impossible programme Solipsism as a hypothesis — that there is no valid reason to assert or deny anything except my own experiences — cannot be refuted, but nobody can sincerely believe it. The full-fledged theory, in which naive realist and physicist agree, demands inference from the experienced to the unexperienced, validated only by principles outside deductive logic. In "The Relation of Sense-Data to Physics" (Scientia, 1914), Russell posed the problem: physics exhibits sense-data as functions of physical objects, but verification requires physical objects to be exhibited as functions of sense-data — "we have therefore to solve the equations." He soon became persuaded this is an impossible programme and allowed two sorts of inference: the sense-data of other people, and "sensibilia" — appearances of things at places where there are no minds to perceive them. He gave up trying to construct matter out of experienced data alone, and contented himself with a picture of the world fitting physics and perception into a single whole.

Six-dimensional space and perspectives On New Year's Day 1914 the theory burst upon him: space has six dimensions, not three. What counts as a point — or rather a "minimal region" — in the space of physics is really a three-dimensional complex of which the total of one man's percepts is an instance. The photographic plate argument shows why: a plate anywhere photographs the stars visible there, so in one tiny region of physical space there is at every moment a vast multiplicity of occurrences, each spatially related to the others as the corresponding objects are. When I see a star, three places are involved: the star's place in physical space, my place in physical space, and my percept's place among my percepts in my private space. Events can be collected into bundles in two ways: all the appearances of one thing (the sun's percepts, photographs, and unperceived occurrences, changing regularly by the inverse-square law and irregularly through mist and cloud) — this way suits physics; or all the appearances at one physical place, a "perspective," the total of my percepts at a given time — this way suits psychology, since one perspective in a brain is a man's momentary percepts. All the puzzles about different people's perceptions, about the causal relation of a thing to its appearances, and about mind and matter are cleared away by distinguishing these three places.

The status of the theory Russell did not offer the theory as necessarily true, but as consistent with all known facts — so far the only theory of which this can be said, on the same level as Einstein's General Theory of Relativity: it solves puzzles and is incompatible with no known facts, and that is as much as any scientific theory ought to claim. He closes with a technical caution: Whitehead's construction of points from finite events, and his own variant using classes of events none smaller than an assigned minimum, work only on certain assumptions; without them we can reach very small regions but not points — hence "minimal regions" rather than points, a difference he thinks unimportant.

Key ideas

• Perception cannot give us the physical object directly; the causal chain from object to brain intervenes.
• Solipsism as a hypothesis cannot be refuted, but cannot be sincerely believed.
• Constructing physical objects wholly out of experienced data is an impossible programme; sensibilia and other minds must be inferred.
• On the 1914 theory, physical space has six dimensions: each point is a three-dimensional complex of percepts.
• Events can be bundled as appearances of one thing (physics) or as one perspective (psychology).
• Every percept has three places: the thing's place, the percipient's place, and its place in the percipient's perspective.
• The theory claims no more than consistency with known facts and the power to dissolve puzzles.
• Points, instants, and particles are constructions from finite events, and only "minimal regions" are guaranteed.

Key takeaway

The problem of the external world is solved by taking perception seriously: the world of physics is inferred, the world of data is private, and the two are connected by causal lines whose structure — not intrinsic quality — is preserved.

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Chapter 10 — The Impact of Wittgenstein

Central question

What did Russell take from Wittgenstein's Tractatus Logico-Philosophicus, and what, on reflection, did he reject?

Main argument

The two schools from without Principia Mathematica at first had an unfavourable reception. The Formalists, led by Hilbert, held that arithmetical symbols are merely marks on paper manipulated by arbitrary rules like chess — which avoids philosophical controversy but cannot explain the application of numbers: "there are three men in this room" or "there were twelve apostles." The Intuitionists, led by Brouwer, denied the law of excluded middle, holding that a proposition can be counted true or false only when there is a method of ascertaining which; their stock example is "there are three successive sevens in the decimal determination of π," which could be proved true if found but never proved false. Without "lawless" decimals the theory of real numbers and almost all higher mathematics collapses, and Brouwer faced the disaster unflinchingly. Russell rejects the identification of "true" with "verifiable": "It snowed on Manhattan Island on the 1st January in the year 1 A.D." has no conceivable method of decision, but it is preposterous to say it is neither true nor false. These were attacks from without; Wittgenstein's were attacks from within.

The two waves of influence Wittgenstein's impact came in two waves: before the First World War, through a typescript of notes given in early 1914 and long conversations; and immediately after the Armistice, when he sent the manuscript of the Tractatus from captivity at Monte Cassino. His later doctrines, as in the Philosophical Investigations, have not influenced Russell at all. Russell disarmingly notes that he is not sure the views he believed himself to have derived from Wittgenstein were in fact his views — Wittgenstein "always vehemently repudiated expositions of his doctrines by others." In the 1918 London lectures (printed in The Monist), Russell first adopted the name "logical atomism," acknowledging his debt to Wittgenstein.

The picture theory and logical mysticism The basic doctrine of the Tractatus is that a proposition is a picture of the facts it asserts: the symbol "aRb" works because it establishes a relation between "a" and "b" representing the relation between a and b. Wittgenstein emphasizes structure: "The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world" (4.014). Russell still thinks Wittgenstein was right about the importance of structure, but is very doubtful that a true proposition must reproduce the structure of its fact, and thinks that even if true, it has no great importance. On the mysticism — logical form "can only be shown, not said" (4.12) — Russell demurs: a language of higher order can say what a given language cannot, and so on ad infinitum. This suggestion, then new, has become a commonplace of logic, and disposes of Wittgenstein's mysticism and, he thinks, of the newer puzzles presented by Gödel.

Identity and the counting argument In Principia Mathematica, identity was defined as having all the same "predicative" properties (properties not referring to any totality of properties). Wittgenstein objected (5.5302, 5.5303): to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing. Russell accepted this at one time but soon concluded it makes mathematical logic impossible. If a and b have all their properties in common, you can never mention a without mentioning b or count them as two; Wittgenstein's position assumes diversity is an indefinable relation without knowing it. The definition of 2 requires "x is not identical with y," and the whole apparatus of intensions common and peculiar to enumerated objects collapses. Wittgenstein also refused to permit any statement about all the things in the world — at The Hague in 1919 Russell made three blobs of ink on white paper and besought him to admit there must be at least three things in the world; he refused resolutely. This was connected with his mysticism and justified by his refusal to admit identity, and it also outraged his view of the axiom of infinity: Russell treated as purely empirical the question how many things there are, making all higher mathematics hypothetical; Wittgenstein called even that meaningless.

Extensionality and atomicity Wittgenstein announced two general principles. The principle of extensionality says the truth of any statement about a proposition p depends only on the truth or falsehood of p — which seems obviously false for "A believes p," since a man may believe some true propositions and not others. Wittgenstein's cryptic answer (5.54): "A believes p" is not a function of p but of the words in which A expresses the proposition; "there is no such thing as the soul — the subject, etc." The principle of atomicity (2.0201): every statement about complexes can be analysed into statements about their constituent parts, so that if you knew all atomic facts and knew that they were all, you could infer all other truths by logic alone. The difficulty is again "A believes that B is hot," which contains two verbs and a subordinate complex. Russell's conclusion, from An Inquiry into Meaning and Truth, was cautious: the analysis of such sentences does not show extensionality false, and does not prove atomicity true.

Logic as tautology and the second edition Russell agrees with Wittgenstein that logic consists wholly of tautologies — "I did not think so until I read what he had to say on the subject" — and that atomic propositions are mutually independent. In the second edition of Principia Mathematica (1925) he adopted the principle of extensionality and minimized the uses of the axiom of reducibility. He explains the axiom: a property referring to a totality of properties (like "typical Englishman" — defined by reference to all properties, it would be untypical by its own definition) may be called non-predicative; the axiom asserts every non-predicative property is formally equivalent to a predicative one. In the first edition the axiom was defended on inductive grounds — self-evidence is never more than part of the reason for accepting an axiom — and in the second edition admitted to be "purely pragmatic," while Chwistek's heroic course of dispensing with it sacrificed a great deal of ordinary mathematics, and Wittgenstein's alternative (that functions of propositions are always truth-functions) made the theory of real numbers largely collapse.

Ramsey F. P. Ramsey took up the problem in "The Foundations of Mathematics" (1925) and "Mathematical Logic" (1926). His main thesis: mathematics must be rendered purely extensional, and the troubles of the Principia arose from an illegitimate intrusion of the intensional point of view. He held that an infinite class can be defined by enumeration — our mortality is an empirical fact logicians should ignore — making the multiplicative axiom a tautology; and he redefined propositional functions as arbitrary correlations of propositions with individuals, so that "φ(Socrates) may be Queen Anne is dead, φ(Plato) may be Einstein is a great man." This dispensed with the axiom of reducibility while preserving the symbolic part of Principia Mathematica almost unchanged — saving mathematics "from the Bolshevik menace of Brouwer and Weyl." Russell finds it very difficult to make up his mind: with Ramsey's functions, general propositions lose their raison d'être, since "fx is true for all values of x" could not be known without enumerating every value. Ramsey also distinguished two classes of contradictions: the semantic ones (the liar), dissolved by distinguishing a word from its meaning, and the mathematical ones (the greatest cardinal), which require the theory of types. Russell hopes Ramsey's theories are valid; Ramsey himself doubted they were altogether satisfactory.

Key ideas

• Hilbert's formalism cannot explain the applications of number; Brouwer's intuitionism identifies truth with verifiability, which is preposterous.
• The Tractatus's picture theory and its emphasis on structure influenced Russell profoundly, though he later doubted the picture doctrine.
• Wittgenstein's logical mysticism — form can only be shown, not said — is disposed of by hierarchies of languages.
• Wittgenstein's rejection of identity would make mathematical logic impossible; counting requires it.
• The principles of extensionality and atomicity were accepted by Russell only in qualified form, following his Inquiry.
• Logic consists of tautologies, and atomic propositions are mutually independent — both Wittgensteinian doctrines Russell adopted.
• The axiom of reducibility was a blot on Principia Mathematica, reduced but not eliminated in the second edition.
• Ramsey's extensional reconstruction dispensed with the axiom of reducibility but cost general propositions their point.

Key takeaway

Russell absorbed the Tractatus's structure-emphasis, its account of logic as tautology, and its two principles, but rejected its mysticism, its doctrine of identity, and its prohibition on totality statements — while Ramsey's extensionalism remained a promising, unproven alternative.

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Chapter 11 — Theory of Knowledge

Central question

With what prejudices and method did Russell, after the war, turn to the theory of knowledge — and what did he conclude about experience, behaviour, and meaning?

Main argument

The turn to epistemology From August 1914 to the end of 1917 Russell was wholly occupied with anti-war work; by early 1918, having finished Roads to Freedom, he returned to philosophy. In prison he wrote a polemical criticism of Dewey and the Introduction to Mathematical Philosophy, after which his thoughts turned to theory of knowledge and the relevant parts of psychology and linguistics — a more or less permanent change of interest. The outcome is embodied in three books: The Analysis of Mind (1921), An Inquiry into Meaning and Truth (1940), and Human Knowledge: Its Scope and Limits (1948). He began with "no fixed convictions, but only a certain store of maxims and prejudices," and he enumerates six.

The six prejudices First: the continuity between animal and human minds. This led him to animal psychology, where he found "animals always behave in a manner showing the rightness of the philosophy entertained by the man who observes them" — seventeenth-century ferocity, Rousseau's noble savage, Victorian apes as virtuous monogamists, deteriorated morals in the dissolute twenties. Americans' animals rush about frantically until they hit on the solution by chance; Germans' animals sit still and scratch their heads — and both sets of observations are entirely reliable, since what an animal does depends on the problem. Pavlov's conditioned reflexes led to behaviourism, which he never accepted as a philosophy but valued as a method to be pushed as far as possible while knowing it has limits. Second: explanations in terms of physics wherever possible. He quotes Ramsey against himself — "I don't feel the least humble before the vastness of the heavens... My picture of the world is drawn in perspective" — and replies that he is happier thinking about the nebula in Andromeda than about Genghis Khan; "the attempt to humanize the cosmos... is displeasing to me quite independently of the question whether it is true or false." Third: "experience" has been over-emphasized. If you are on a pebbly beach you may be quite sure there are pebbles you have not seen; everyone accepts innumerable propositions about things not experienced, and the view that we have no knowledge transcending experience is "utterly untenable." Fourth: nevertheless, all knowledge of what exists, if not directly reporting perception or memory, must be inferred from premisses at least one of which is so known; but there are forms of probable inference which must be accepted although they cannot be proved by experience. Fifth: meaning and linguistic problems had been neglected; just as there are formalists in arithmetic, there are formalists in language who think truth is a matter of following rules rather than correspondence with fact — but except in logic and mathematics no other theory of truth has any chance of being right; and belief and knowledge have pre-verbal forms. Sixth — "perhaps the most important in all my thinking" — method: start from something vague but puzzling, something that seems indubitable but cannot be precisely expressed, and examine it "like that of first seeing something with the naked eye and then examining it through a microscope": the bacilli in impure water, the object approaching through a thick fog. Analysis gives new knowledge without destroying the old. "Belief in the above process is my strongest and most unshakable prejudice as regards the methods of philosophical investigation."

Key ideas

• The post-war turn to epistemology produced The Analysis of Mind, An Inquiry into Meaning and Truth, and Human Knowledge.
• Animal psychology shows the observer's philosophy dictates the animal's behaviour; behaviourism is a method, not a philosophy.
• Explanations in terms of physics are to be preferred wherever possible; experience is cosmically unimportant.
• The concept of "experience" has been over-emphasized: we know propositions about things we have never experienced.
• Yet all knowledge of existence traces back to perception or memory as premisses, plus unprovable probable inferences.
• Meaning and language had been neglected; truth outside logic and mathematics is correspondence with fact.
• The philosophical method is analysis: fix attention on the vague but certain until structure appears, as with a microscope.
• Belief and knowledge have pre-verbal forms, continuous with animal intelligence.

Key takeaway

Russell entered his theory-of-knowledge period armed with six prejudices — behaviourism as method, physics-mindedness, suspicion of "experience," empiricist provenance of existence claims, the importance of meaning, and above all the microscope-like method of analysis — which set the agenda for his last three major philosophical books.

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Chapter 12 — Consciousness and Experience

Central question

What follows from abandoning the relational theory of sensation — the view that sensation is an act of a subject directed at an object?

Main argument

The abandonment of the subject During 1918 Russell's view of mental events underwent an important change. He had originally accepted Brentano's threefold analysis of sensation into act, content, and object; he had given up the content–object distinction but retained the relational structure: a subject "aware" of an object, expressed by "awareness" or "acquaintance." He had criticized James's denial of this in "On the Nature of Acquaintance" (The Monist, 1914), but after the logical atomism lectures he became convinced James was right. James's essay "Does 'Consciousness' Exist?" (1904) contended that the supposed subject is "the name of a nonentity... a mere echo, the faint rumour left behind by the disappearing 'soul'". Russell accepted this in 1918, fourteen years after it was published.

The disappearance of sense-data In The Analysis of Mind (1921) Russell explicitly abandoned "sense-data": the subject appears to be "a logical fiction, like mathematical points and instants," introduced not because observation reveals it but because grammar demands it. Once the subject is dispensed with, the distinction between sensation and sense-datum vanishes: "the sensation that we have when we see a patch of colour simply is that patch of colour, an actual constituent of the physical world." A patch of colour is certainly not knowledge; pure sensation is not cognitive, though through its psychological effects it is the cause of cognitions. New problems arose at once: "awareness," "acquaintance," and "experience" had to be re-defined. He quotes the opening of An Inquiry into Meaning and Truth: asked how you know I have two eyes, the plain man replies "What a silly question! I can see you have"; the inquiry substitutes "articulate hesitation for inarticulate certainty."

Behaviour and the limits of behaviourism Part of the problem yields to behaviourist methods. A burnt child dreads the fire: living matter changes its response to a repeated stimulus, dead matter and machines do not; an automatic machine never learns to respond to the sight of a penny. Habit consists essentially in the conditioned reflex. Pavlov's dogs learned to treat one thing as a sign of another — choosing the door with the circle for dinner and avoiding the ellipse for a shock, until the ellipse was made so nearly circular that the dog suffered a nervous breakdown, "much the same thing happens to schoolboys" asked what six times nine is. But behaviourism cannot cover everything: you could make a machine that groans and says "This is unendurable," but you would not believe it was undergoing what you undergo with toothache.

Neutral monism The question whether sensation is essentially relational decides the fate of neutral monism. So long as the subject was retained there was a mental entity with nothing analogous in the material world; without it, a mind and a piece of matter can both be logical constructions from materials not differing vitally — sometimes actually identical. The Post Office Directory analogy: the same names appear twice over, alphabetical and geographical; a sensation grouped by memory-chains is part of a mind, grouped with its causal antecedents it is part of the physical world. "This view affords an immense simplification. I was glad when I realized that abandonment of the 'subject' made it possible to accept this simplification and to regard the traditional problem of the relation of mind and matter as definitively solved."

The duality that must be re-introduced There is a duality essential to knowledge: knowing is distinct from the known, and after being banished from sensation it must be re-introduced. Perception is the first form: smells and bodily feelings do not suggest externality as forcibly as sight and touch; when a dog sees a rabbit, we can hardly suppose it says "I am having a visual sensation which probably has an external cause" — yet on the James–Mach view the occurrence has only an indirect and causal relation to the rabbit. In An Inquiry Russell replaced "acquaintance" with "noticing," accepted as an undefined term. He quotes the Inquiry's analysis at length: the puddle you avoid without saying anything; "know" is highly ambiguous; if knowing were distinct from the experience, "I feel hot" would multiply events ad infinitum — so, as a rule, we do not know our present experiences; "knowing" may be defined as "acting appropriately" (the dog knows his name, the carrier pigeon knows the way home), but a thermometer would then know when it is cold; what must happen to an experience to be known is that it be noticed — "noticing" is a matter of degree, mainly isolating from the sensible environment, as you notice the cello part of a piece of music; every empirical proposition is based on sensible occurrences that were noticed when they occurred. Perception, as opposed to sensation, involves habit: sensation is the part of experience due to the stimulus alone, a "theoretical core"; the total occurrence is an interpretation with accretions of habit — when you see a dog, the sensational core is a patch of colour stripped of recognition, and the accretions make perception possibly misleading (Walt Disney might make a "real" dog crow or vanish). A further duality arises in imagination and memory, which cannot be interpreted without introducing belief: remembering is a relation of image to prototype, with a credence less than that given to noticed sensations. Finally "consciousness" and "experience" themselves need definitions: experience is behaviour modified by the event (open to external observation); consciousness is knowledge that something is happening to me or has happened — noticing. The idealists' exaggeration of experience — the view that there can be nothing which is not experienced — could not have flourished, Russell says, if people had taken the trouble to find out what "experience" can mean.

Key ideas

• Brentano's act–content–object analysis collapsed into the non-relational sensation of James and Mach.
• The subject is a logical fiction demanded by grammar; with it, the sensation–sense-datum distinction vanishes.
• The sensation simply is the patch of colour — an actual constituent of the physical world.
• Conditioned reflexes explain much learning, but behaviourism cannot account for toothache.
• Neutral monism becomes possible: mind and matter are arrangements of the same events, as in a postal directory.
• "Noticing" replaces "acquaintance"; as a rule we do not know our present experiences.
• Perception is sensation plus accretions of habit; only the sensational core is due to the stimulus alone.
• The mind–body problem is "definitively solved" by treating minds and bodies as logical constructions from one neutral stuff.

Key takeaway

Abandoning the relational subject dissolves the mind–matter distinction into neutral monism — the same events arranged as a mind by memory-chains and as matter by causal antecedents — at the cost of re-introducing knowledge's duality through perception, memory, and noticing.

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Chapter 13 — Language

Central question

What is meaning, and how is language related to the non-linguistic facts it expresses?

Main argument

Words are universals Russell first became interested in the definition of "meaning" in 1918, having previously treated language as transparent. The first thing that struck him was obvious but ignored: a word is a universal of which the instances are the occasions on which it is spoken, heard, written, or read. Philosophers realized that dog is a universal because there are many dogs, but failed to notice that the word "dog" is a universal in exactly the same sense — the word itself has the metaphysical status of the Platonic dog "laid up in heaven." Meaning, therefore, is a relation between an individual instance of a word and an individual instance of what the word means.

Meaning as habit Proceeding as far as possible on behaviourist principles, Russell explains object-words. The child hears "dog" uttered while attending to a dog; by telescoping, a dog gives him an impulse to say "dog," and hearing the word makes him expect a dog. These two habits are active and passive understanding: passive (expecting a dog on hearing the word) comes earlier and is shared with dogs and horses; parrots utter words without knowing what they mean. A word is used correctly when the average hearer will be affected by it in the way intended — "a psychological, not a literary, definition"; the relation of a word to its meaning is of the nature of a causal law, and there is no more reason why a person who uses a word correctly should be able to tell what it means "than there is why a planet which is moving correctly should know Kepler's laws." The essential point: the word shares some of the causal properties of what it means — waked by a cry of "Fire!" you behave much as if you smelt burning; the word cannot make you hot, but the causal similarities are what define meaning. The definition is limited to object-words: there is no zoo where you can show a child the meaning of "than" — and to the indicative or exclamatory use. The elementary uses of a word are indicative, imperative, and interrogative — "mother," "mother!", "mother?" — and the imperative use shows that "thinking of" an object ante-dates language and is made communicable by it.

The autonomy of language rejected Russell attacks the view that words should never be confronted with facts — that "the cat is a carnivorous animal" means only that zoology books classify cats among carnivora. "This is one of those views which are so absurd that only very learned men could possibly adopt them." Language consists of sensible phenomena just like eating or walking; the superstitious awe of words is prehistoric — the man who knows his enemy's name acquires magic power over him; "in the beginning was the Word" underlies the philosophies of Plato and Carnap alike. The stuff of mental occurrences consists of sensations and images; behaviourists refuse images because unobservable from without, but memory and imagination are inexplicable without them.

Sentences, facts, and belief Words like "the," "is," and "than" only acquire significance as parts of sentences, so meaning cannot be analysed further without considering sentences. The verb confers unity upon the sentence — "A is greater than B" is complex and must correspond to a complexity in the fact — and a sentence also has the duality of truth and falsehood. Truth and falsehood cannot be defined without facts: "I think one must say that there are facts and that 'truth' consists in one sort of relation to facts while 'falsehood' consists in another sort of relation." Facts are whatever there is except what is completely simple — "A table consists of legs and a flat top"; sentences express an analysis of a complex, and sentences that all contain "Socrates" — "Socrates was wise," "Socrates was Athenian," "Socrates loved Plato," "Socrates drank the hemlock" — are about Socrates because the facts that make them true contain him as a constituent. The structure of a whole is the way its parts are interrelated, and every account of structure is relative to units treated for the time being as devoid of structure — the skeleton's bones, cells, molecules, atoms, and so on; points may be defined as classes of events without falsifying geometry. A sentence in the indicative may be uttered from belief or to arouse belief: when an actor says "This is I, Hamlet the Dane," nobody believes him and nobody thinks he is lying — truth and falsehood belong only to sentences expressing belief or intended to cause belief. Beliefs can exist without words: a cat seeing a dog expresses its belief by arching its back and hissing, exactly as you express yours by saying "dog." A belief is "a certain state of body or mind or both" — a state of an organism which can, in theory, be fully described without mentioning what is believed. Verbal expression derives its importance from communicability and precision.

Key ideas

• A word is a universal whose instances are its utterances; "meaning" relates instances of words to instances of objects.
• Understanding an object-word consists in two acquired habits — active and passive — forming a causal law.
• Language is a form of bodily behaviour; the "autonomous language" doctrine is absurd because language itself is part of the world of fact.
• The verb confers unity on the sentence; sentences presuppose facts for their truth and falsehood.
• "Socrates" occurs in many true sentences because the man is a constituent of the corresponding facts.
• Structure is relative to units treated as unanalysed at a given stage of analysis.
• Truth and falsehood belong primarily to beliefs, which are states of an organism that can exist without words.
• Images are indispensable for memory and imagination, contra behaviourism.

Key takeaway

Meaning is a causal habit connecting words to the world; sentences express beliefs about facts; and language, far from being an autonomous realm, is itself part of the world of fact — which is why Russell could later define truth in terms of belief's relation to fact.

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Chapter 14 — Universals and Particulars and Names

Central question

Are there universals as well as particulars, what are particulars, and what is a proper name?

Main argument

The problem is not merely verbal The problems of universals and particulars occupied Russell ever since he abandoned monistic logic. He illustrates the stakes with a fable he printed in Polemic (No. 2, 1946): a company of philosophers, each of a different school, is served horse-flesh under the name of beef; the nominalist disciple of Roscelin says "beef" and "horse" are only sounds, the Platonist says the joint was a copy of the eternal horse in heaven, the Augustinian says both are ideas in the mind of God — and all agree the innkeeper deserves prosecution for fraud. "The sole point of this parable is that the question of 'universals' is not merely one of words, but one which arises through the attempt to state facts." Russell was led in two directions: by the study of Leibniz, and by the fact that many fundamental mathematical concepts demand asymmetrical relations, which cannot be reduced to predicates.

Four fundamental beliefs Since abandoning monism, Russell has retained four beliefs he cannot doubt: (1) truth depends on some relation to fact; (2) the world consists of many interrelated things; (3) syntax — the structure of sentences — must have some relation to the structure of facts; and (4), less certain, what can be said about a complex can be said without mentioning it, by setting forth its parts and their relations. These assumptions were implicit in the symbolism of Principia Mathematica — small Latin letters for things, Greek letters for classes, capitals for relations — though classes were gradually replaced by properties. His first attempt to state the metaphysics of his symbolism was Chapter IV of The Principles of Mathematics, "Proper Names, Adjectives and Verbs," in which he defined a term as "the widest word in the philosophical vocabulary": "A man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned, is sure to be a term." He later came to think much of this erroneous, altered by the theory of descriptions (a word may contribute to significance without meaning in isolation — "the" is not a curious Platonic object) and the doctrine of types (some words cannot be substituted for others without producing nonsense: "killing no murder" must be expanded into "If A kills B, it does not follow that A murders B," and "Socrates and killing are two" is illegitimate).

The difficulties of particulars If a statement that x has a property is always significant and never analytic, then x is not the sum of its properties and two particulars must be able to differ purely numerically while sharing all their properties — but then x becomes "an invisible peg from which properties would hang like hams from the beams of a farmhouse." His first attempt to deal with this was the 1911 paper "On the Relations of Universals and Particulars" — on which occasion Bergson remarked, with surprise, that Russell seemed to think it was the existence of particulars, not universals, that needed proving. The 1911 paper rejected the bundle hypothesis on two grounds: the relativity of position (two red patches in different places differ only in position, which is not a quality) and the diversity of the contents of different minds (two men believing that two and two are four must have distinct beliefs, and subjects cannot be mere bundles of qualities — "Benevolence, stupidity, and love of puns believe that two and two are four" would not be correct). He came later to think these arguments invalid: position in experienced space is absolute — what is in the centre of the visual field has the quality of centrality, everything else has degrees of up-and-down and right-and-left — so a red patch on the right is the complex of redness and rightness. Similarly, time: when a clock strikes, what makes you recognize two strokes as two is the quality of "subjective pastness" or fading; the noises plus their degrees of fading form the plural complex. The whole question whether there are simples to be reached by analysis is unnecessary: nothing can be known to be simple, and statements naming complexes are not falsified by the later discovery of complexity — molecules are composed of atoms, atoms have structure.

Proper names Russell concedes that the followers of Wittgenstein were right on one point: he originally believed, with Leibniz, that everything complex is composed of simples and that analysis aims at simples — a view he now rejects. On proper names he distinguishes the syntactical from the epistemological. Syntactically, a proper name is a word not denoting a predicate or relation which can occur in a proposition containing no variable. Epistemologically, a name should denote something of which we are immediately aware; "Socrates" is for most of us a substitute for a description (we look him up in the encyclopaedia), while its primitive use was pointing at the man — "That is Socrates." Proper names, unlike descriptions, are meaningless unless there is an object they designate: statements about the present King of France are false but not meaningless; statements pretending the King is called Louis XIX are meaningless, not false. His principle: if we can understand a sentence, it must be composed entirely of words denoting things with which we are acquainted or definable in terms of such words. Words understood without verbal definition must denote things that can be pointed out — "red" and "blue," learned by hearing them pronounced while noticing red or blue things. Names in the restricted sense can only be given to what is experienced; the subject of psychology and the particle of matter, if intelligible, must be bundles of experienced qualities and relations. Hence the syntactical rearrangement: instead of "This is red," "Redness is compresent with centrality." Minimum vocabularies — the smallest number of words in terms of which all the others in a body of sentences can be defined — have as their hard core the words attaching sentences to the non-linguistic world; and among these there are no words with the uniqueness habitually supposed to belong to particulars. "The stuff of the world consists of things like whiteness, rather than of objects having the property of being white." This involves the rejection of minds and bits of matter as the stuff out of which the world is built. In place of particulars he offers "complete complexes of compresence" — complexes whose members are all compresent with each other but not all compresent with anything outside.

The universals that remain The theory does not dispose of all universals: "red is a colour" is a genuine subject–predicate proposition assigning the quality colour to the substance red — you can pass from any colour to any other by imperceptible gradations, but not from a colour to a sound. More important are relational propositions: a language cannot express all we know without "A is before B," "A is to the right of B," "A is more like B than like C" — "It is relation-words that are the most stubborn of words of which the meaning is in some sense universal." And a point overlooked in almost all theorizing: those who dislike universals think they can be merely words, but "a word itself is a universal" — the word "cat" has many instances; if universals are denied as vigorously as some nominalists deny them, there is no such thing as the word "cat," only instances of it. As to the metaphysical status of universals: there certainly are relational facts — "Philip was the father of Alexander" and "Alexander preceded Caesar" — but whether there is an entity named by the relation-word is unclear; "verbs are necessary, but verbal nouns are not." He quotes the last paragraphs of An Inquiry into Meaning and Truth: "similarity exists" is nonsense if "exists" is used as in "the President of the United States exists," but "the word 'yellow' is necessary because there are yellow things; the word 'similar' is necessary because there are pairs of similar things"; and "complete metaphysical agnosticism is not compatible with the maintenance of linguistic propositions" — the study of syntax can yield considerable knowledge of the structure of the world.

Key ideas

• The universals problem is not merely verbal: it arises in the attempt to state facts.
• Four indubitable beliefs: truth relates to fact; the world is many; syntax mirrors fact-structure; complexes are describable by their parts.
• Particulars as bare subjects are unknowable pegs; position in sensible space is absolute, so qualities can do the work.
• Nothing can be known to be simple; the search for simples is unnecessary.
• Proper names are meaningless without an object; descriptions are not.
• Minimum vocabularies attach language to the non-linguistic world through words like "red" — qualities, not bare particulars.
• The stuff of the world consists of things like whiteness; minds and bits of matter are rejected as fundamental.
• A word itself is a universal; relation-words are the most stubborn universals of all.

Key takeaway

Particulars collapse into complexes of compresence and the stuff of the world becomes qualities, while universals — above all relations — survive as irreducible, because even the nominalist's own words are universals.

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Chapter 15 — The Definition of 'Truth'

Central question

What is truth, against the monistic and pragmatist theories, and what relation to fact makes a belief true?

Main argument

The two periods Russell wrote about truth at two periods: four essays of 1906–1909 reprinted in Philosophical Essays (1910), and again in the late 1930s, with the results in An Inquiry into Meaning and Truth (1940) and, slightly modified, Human Knowledge (1948). From the moment he abandoned monism he had no doubt that truth is defined by some kind of relation to fact.

Against the monistic (coherence) theory Joachim's The Nature of Truth (1906) defined truth by coherence: no one truth is independent of another, and each, stated in full, turns out to be the whole truth about the whole universe; error consists in abstraction, in treating parts as independent wholes — the erring subject's confident belief converts partial apprehension into falsity. Russell's reply: on this view, my confident assertion that Bishop Stubbs wore episcopal gaiters is an error, while a monistic philosopher's confident assertion that Bishop Stubbs was hanged for murder is not — the criterion does not distinguish right from wrong judgement as ordinarily understood. The whole of truth is composed of propositions which are true in the ordinary sense, since it is impossible to believe that "Bishop Stubbs was hanged for murder" is part of the whole of truth.

Against pragmatism The pragmatist theory, set forth by William James, holds that a belief is true if it has certain kinds of effects; Russell holds that an empirical belief is true if it has certain kinds of causes. James: "Ideas... become true just in so far as they help us to get into satisfactory relations with other parts of our experience"; "The true... is only the expedient in the way of our thinking"; "truths in the plural, of processes of leading... having only this quality in common, that they pay." Russell paraphrases: "a truth is anything which it pays to believe" — a paraphrase pragmatists called a gross misrepresentation, though he never understood what else the words could mean. The insuperable difficulty: to know whether a belief is true we must first know what its effects are and whether they are good — by the pragmatist's own criterion, which lands us in an endless regress. Was the French Revolution's belief in Rousseau true because its effects made Europe what it is, or false because of the harm? "It is surely far easier to discover by direct investigation that the Contrat Social is a myth than to decide whether belief in it has done harm or good on the whole." And the practical consequences are grim: what pays depends on the Government and the police; the beliefs of the Nazis failed the test only because Germany lost the war; belief in Paradise for those who die in battle for the True Faith has paid "in the long run and on the whole" — and both Moslem and Christian beliefs cannot be true together. He concludes with his 1909 verdict that pragmatism is not only theoretically mistaken but "socially disastrous," developing "by inherent necessity, into the appeal to force and the arbitrament of the big battalions." James's reply ("Two English Critics," in The Meaning of Truth, 1909) accused Russell of supposing he meant what he said: what James meant was not that the consequences are good but that the believer thinks they will be — so A and B may both be believing truly, and "if the critic be both a pragmatist and a Baconian," the Shakespeare belief is "perfectly true for me" while Bacon wrote the plays. Russell finds this unintelligible: whether Shakespeare or Bacon wrote Hamlet "is a question of fact, totally independent of what anybody now living may think." On James's copy of Russell's article, next to the claim that "A exists" may be true even if A does not exist, James had written "silly!" Russell presses the point: James wanted to assert that "God exists" is true without metaphysics, interested only in terrestrial consequences; "I confess that on this point my feelings are with the Pope, who condemned pragmatism as an unsatisfactory way of defending religious belief."

Russell's earlier theory, abandoned His own earlier definition of truth (last chapter of Philosophical Essays) analysed belief as a four-term relation: believing "Socrates loves Plato" relates me to Socrates, love, and Plato, and the belief is true when there is a complex of Socrates and Plato related by love. He abandoned it because he ceased to believe in the subject and because a relation cannot occur significantly as a term except where a paraphrase is possible.

The later theory: belief and verifier The new theory, set forth in An Inquiry into Meaning and Truth, proceeds from the simple and primitive toward the complex. Stages: the sentence; the proposition, that which is common to sentences in different languages saying the same thing ("Caesar is dead" and "César est mort" assert the same proposition); and behind the proposition, belief. Truth and falsehood belong primarily to beliefs, only derivatively to propositions and sentences. A belief is a state of an organism; the expectation of a bang when you see a door blown shut by the wind is a belief expressible in words but not constituted by them; when the event comes, your feeling might be expressed by "Quite so!" or "How surprising" — "surprise is a criterion of error." Philosophers err in starting from the complex and questionable — the law of gravitation, the existence of God, quantum theory — instead of plain matters of fact like "I feel hot." In the simplest case, what a belief expresses and what it indicates are identical: when I say "hot," my utterance is caused by my feeling hot — "the bed-rock upon which all empirical knowledge is based." In general, the fact which makes a statement true is its "verifier": "Caesar crossed the Rubicon" is verified by an event long past; "all men are mortal" has as many verifiers as there are men. General and existential statements go beyond experience: "I met a man on the moor" shares something with each of the states "I met A," "I met B"...; "there are men whom I have never met" is known without an instance — "I have found that even solipsists are surprised by the fact that they have never met any other solipsist." The verifier need not have a logical form closely related to the statement: a disjunction — "that is either Etna or Stromboli" — is verified by one of its halves. The word for a relation is not a relation, so the simplest correspondence occurs with images: a visual memory-image of A to the left of B is verified when A is in fact to the left of B, the image of A like A, the image of B like B, the relation the same. His final definition, from Human Knowledge (page 170): "Every belief which is not merely an impulse to action is in the nature of a picture, combined with a yes-feeling or a no-feeling; in the case of a yes-feeling it is 'true' if there is a fact having to the picture the kind of similarity that a prototype has to an image; in the case of a no-feeling it is 'true' if there is no such fact." The definition of truth does not afford a definition of knowledge: a stopped clock that I believe to be going may give me a true belief as to the time by chance. The theory is fundamentally a correspondence theory: truth is a relation to one or more facts, varying in complexity with the structure of the belief.

Key ideas

• Truth is a relation to fact; the monistic coherence theory cannot distinguish right from wrong judgement.
• Pragmatism's "truth is what pays" requires knowing effects and their goodness first — an endless regress — and makes truth depend on governments, wars, and opinions.
• Russell's earlier four-term analysis of belief was abandoned with the subject.
• Truth and falsehood belong primarily to beliefs; sentences and propositions are derivative.
• A belief is a state of an organism, describable without mentioning what is believed.
• The verifier is the fact or facts that make a belief true; general statements need no instance.
• Surprise is a criterion of error; "I feel hot" is the bed-rock of empirical knowledge.
• The final definition: belief is a picture plus a yes-feeling or no-feeling, true when a fact stands to it as prototype to image.

Key takeaway

Truth is correspondence between belief and fact — the belief is a picture with a yes-feeling or no-feeling, and it is true when a fact stands to that picture as a prototype to its image — and neither coherence nor what "pays" can serve as a criterion.

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Chapter 16 — Non-Demonstrative Inference

Central question

What principles justify the inferences of common sense and science, which are only probable, if induction cannot?

Main argument

The scope of the problem Returning to England in June 1944, Russell chose "Non-Demonstrative Inference" as the subject of his annual lectures at Trinity. He had become aware that all the inferences used in common sense and science are of a different sort from those of deductive logic: with true premisses and correct reasoning, the conclusion is only probable. He found the subject much larger than expected — in most discussions unduly confined to induction. Inductive arguments, unless confined within the limits of common sense, lead to false conclusions more often than true ones; scientific inference needs indemonstrable extra-logical principles, but induction is not one of them.

Probability: frequency and doubtfulness He began with probability. The frequency theory — the probability that a person chosen at random from England will be called "Smith" is the ratio of Smiths to the population — is precise, purely mathematical, and has nothing to do with uncertainty. Keynes's Treatise on Probability held instead that there is an indefinable relation between propositions of making more or less probable, not numerically measurable. Russell's conclusion: wherever probability is definite, the frequency theory applies, but there is another conception — "degree of credibility" or "degree of doubtfulness" — which is what matters in scientific inference, because the premisses themselves are uncertain (Hengist was indubitable, Horsa perhaps a legend).

The instances He collected instances of inferences nobody questions although they are not logically demonstrative: your shadow walks with you and waves its arms when you do, yet a dark patch with an independent existence is logically possible; the solipsist's own memory — he does not remember before age two, yet does not think he began then, and once dreamt he "remembered" that Whitehead and he had murdered Lloyd George — forces even solipsism down to "solipsism of the moment," which no solipsist has ever accepted; two copies of the same book agreeing word for word compel belief in a common cause back to the author, hence other minds; a loud explosion heard at different times by people at different distances makes sound-waves credible; Mount Everest does not cease to exist when unseen, and the room does not "go out with a pop." The principles are distilled out of such instances by analysis; the evidence for the principles is derived from the instances, not vice versa. Empirical knowledge has three stages: knowledge about myself, about other minds (including testimony), and about the physical world.

Causal laws, causal lines, and structure Causal laws are not invariable sequences: in classical dynamics they are differential equations stating acceleration; in modern physics they are statistical. What we mean by a persistent "thing" is a series of sets of occurrences connected by laws statable without mentioning other things. Russell gives the name "causal line" to a series of events from any one of which something can be inferred about its neighbours; causal lines are approximate, impermanent, and not universal, which is why "matter" satisfies physics less and less. The conception of structure is of great utility: seeing red in one direction and blue in another, there must be a corresponding difference in the causes; A reading aloud and B taking down dictation — the printed text, A's noises, B's hearing, B's writing — demands a common structure preserved through four sets of events; the gramophone record and the broadcast speech are the same. All visual and auditory perceptions transmit structure but not intrinsic quality — and we can know a space-time structure without knowing the qualities composing it, just as we know "all the numbers that I have never thought of and never shall think of are greater than a thousand."

Why induction fails as a premiss Keynes showed that induction from the mathematical theory of probability requires two conditions: the generalization must have a finite probability before any instances are examined, and the probability of observing only favourable instances, given the generalization is false, must tend to zero. The first condition is the crux: some principle must confer a finite antecedent probability on some generalizations and not others. Russell's postulates are designed to do exactly this — and they need not be certain, only finitely probable, which distinguishes them radically from idealistic a priori principles.

The five postulates (1) The postulate of quasi-permanence, replacing Newton's first law: given any event A, it very frequently happens that at any neighbouring time there is at some neighbouring place an event very similar to A — the basis of common sense's "persons" and "things," and of the old concept of substance. (2) The postulate of separable causal lines, the most important: it is frequently possible to form a series of events such that, from one or two members, something can be inferred as to all the others — the sound wave and the light wave are the obvious examples. (3) The postulate of spatio-temporal continuity, which denies action at a distance: when there is a causal connection between non-contiguous events, there must be intermediate links — though Russell suspects it may reduce to a tautology, since physical space-time is inferential and its order is dependent upon causality. (4) The structural postulate: when a number of structurally similar complex events are ranged about a centre in regions not widely separated, it is usually the case that all belong to causal lines having their origin in an event of the same structure at the centre — the broadcast speech, the theatre audience, the starry sky; it is because of structure that physics can be about unexperienced occurrences. (5) The postulate of analogy: given two classes of events A and B, and given that whenever both can be observed there is reason to believe A causes B, then if A is observed but B cannot be, it is probable that B occurs — the ground of belief in other minds. The postulates state only probabilities, not certainties; they are justified because they are implied in inferences we all accept, and the whole system of science and everyday knowledge, out of which they are distilled, is within limits self-confirmatory. There is a coherence theory of probability: two facts plus a connecting causal principle may each be more probable together than apart — "without the introduction of principles, no suggested collection of facts... is either coherent or inconsistent." The postulates replace the vague "causality" or "uniformity of nature" with something more precise.

Method: the tunnel Since the Principia days Russell has used a method of which he was at first scarcely conscious: building a bridge between the world of sense and the world of science, "as in making a tunnel through an Alpine mountain, work must proceed from both ends in the hope that at last the labour will be crowned by a meeting in the middle." Analysis exhibits a science as a deductive system whose residual principles and entities are "hostages for the whole science"; common sense, the starting-point, is already infected with crude theory. Mathematical logic is the essential tool, since from a "higgledy-piggledy collection of things destitute of the smooth properties that mathematicians like" it can make structures with the required properties. Universal scepticism cannot be refuted but cannot be accepted; the facts of sense and the broad truth of science are data, since they have a higher degree of probability than anything philosophical speculation is likely to achieve. The outcome of this work is science rather than philosophy: the reasons for accepting it are the ordinary scientific reasons, and there is no claim to certainty.

Key ideas

• All inference outside logic and mathematics is non-demonstrative: probable, not certain.
• Induction by simple enumeration, unconfined by common sense, leads more often to error than to truth.
• Probability is statistical when definite; "degree of doubtfulness" governs scientific inference.
• Inference to other minds, to the physical world, and even to one's own past cannot be validated by experience alone.
• Causal lines — series of events from which neighbours can be inferred — replace "things" and "matter."
• Structure, not intrinsic quality, is preserved through causal chains and is what physics transmits.
• Keynes's conditions show induction needs a finite antecedent probability, which postulates must supply.
• Five postulates — quasi-permanence, separable causal lines, spatio-temporal continuity, structure, analogy — justify the accepted inferences.
• The method is the two-ended tunnel: analysis from science, observation from sense, meeting in the middle.

Key takeaway

Since induction cannot justify the probable inferences of science and common sense, Russell distils from the inferences themselves five indemonstrable postulates of probability — quasi-permanence, causal lines, continuity, structure, and analogy — which together supply what Keynes's analysis of induction requires.

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Chapter 17 — The Retreat from Pythagoras

Central question

What did Russell's youthful Platonism about mathematics mean to him, and why and how did he abandon it?

Main argument

The Pythagorean outlook Russell describes his development since the early years of the century as "a gradual retreat from Pythagoras." The Pythagoreans had a peculiar mysticism bound up with mathematics; it greatly affected Plato, more than is generally acknowledged, and Russell had for a time a very similar outlook, finding in what he then supposed to be the nature of mathematical logic something profoundly satisfying in important emotional respects.

The Thales-like boyhood As a boy his interest in mathematics was more like Thales than Pythagoras: he delighted in finding things in the real world obeying mathematical laws — the lever, the pulley, falling bodies describing parabolas, the theory of billiard balls. When a new tutor asked why a penny spins, he replied "Because I make a couple with my fingers," and was surprised at the reaction. He marked a tennis court using the theorem of Pythagoras; he impressed Tyndall by determining the centre of gravity with two crossed walking-sticks; he hoped for a "parallelogram of motives" analogous to the parallelogram of forces — a foolish idea, since the man equally attracted to two roads does not go across the fields between them; the twentieth century discovered the all-or-nothing principle instead, justifying Dr Johnson's opinion that the Devil, not the Almighty, was the first Whig.

The ascetic Platonism His interest in applications was gradually replaced by interest in the principles of mathematics, through the wish to refute mathematical scepticism — the official sophistries of the infinitesimal calculus, the shaky proofs of Euclid. He came to think of mathematics "as an abstract edifice subsisting in a Platonic heaven and only reaching the world of sense in an impure and degraded form." His outlook was profoundly ascetic: "I disliked the real world and sought refuge in a timeless world, without change or decay or the will-o'-the-wisp of progress." Asked by Logan Pearsall Smith what he particularly liked, he answered "Mathematics and the sea, and theology and heraldry, the two former because they are inhuman, the two latter because they are absurd." He quotes his essay "The Study of Mathematics" (1907): mathematics possesses "supreme beauty — a beauty cold and austere, like that of sculpture"; real life is "a long second-best"; mathematics takes us "into the region of absolute necessity, to which not only the actual world, but every possible world must conform"; retirement into "the cloister of contemplation" was admittedly "somewhat selfish."

Why it all became nonsense "All this, though I still remember the pleasure of believing it, has come to seem to me largely nonsense." Mathematics has ceased to seem non-human: "I have come to believe, though very reluctantly, that it consists of tautologies" — to a sufficiently powerful mind the whole of mathematics would appear trivial, as trivial as "a four-footed animal is an animal." Its timelessness consists merely in the fact that the pure mathematician is not talking about time. The contradictions demanded solutions which "might be true but were not beautiful"; he felt about them "much as an earnest Catholic must feel about wicked Popes," and the splendid certainty he had hoped to find in mathematics was lost "in a bewildering maze." The ascetic mood faded, and was finally dispelled by the First World War: watching young men embarking in troop trains to be slaughtered on the Somme "because generals were stupid," he found himself "united to the actual world in a strange marriage of pain"; the abstract world of ideas seemed thin and trivial before the vast suffering around him.

What was lost and what remained What was lost was the hope of finding perfection, finality, and certainty; what was gained was "a new submission to some truths which were to me repugnant." He retained: that truth depends upon a relation to fact, and that facts in general are non-human; that man is cosmically unimportant — a Being who could view the universe impartially "would hardly mention man, except perhaps in a footnote near the end of the volume." But he no longer thinks intellect superior to sense, or Plato's world of ideas the only access to the real world: "I think of sense, and of thoughts built on sense, as windows, not as prison bars." We can, however imperfectly, mirror the world, like Leibniz's monads; it is the philosopher's duty to make himself "as undistorting a mirror as he can," while recognizing the inevitable distortions of the here and now; "to show the road to this end is the supreme duty of the philosopher."

Key ideas

• The whole development since 1900 is a gradual retreat from Pythagoras and his mathematics-bound mysticism.
• Boyhood mathematics was Thales-like — delight in laws found in the real world.
• The young Russell was ascetic: mathematics was a timeless Platonic refuge from a disliked real world.
• Mathematics has come to seem largely nonsense as an ideal — it consists of tautologies, and its timelessness is merely not talking about time.
• The paradoxes' ugly solutions and the loss of certainty dispelled the mathematical mysticism; the war completed the change.
• The war's suffering "married" Russell to the actual world.
• What survived: truth as relation to non-human facts; man as cosmically unimportant.
• Sense and thought built on sense are windows, not prison bars; the philosopher's duty is to be an undistorting mirror.

Key takeaway

Russell's intellectual autobiography is a retreat from the Pythagorean dream — mathematics as a sublime Platonic world of certainty — into a philosophy that treats sense as a window on the world and the philosopher's job as mirroring reality as undistorted as human finitude allows.

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Chapter 18 — Some Replies to Criticism

Central question

How does Russell answer the criticisms of the later Wittgenstein school, and what does he defend?

Main argument

The polemic against the later Wittgenstein Russell opens wryly: "It is not an altogether pleasant experience to find oneself regarded as antiquated after having been, for a time, in the fashion." Leibniz had said of Berkeley: "The young man in Ireland who disputes the reality of bodies seems neither to explain himself sufficiently nor to produce adequate arguments." Russell could not say the same of Wittgenstein, by whom he was superseded in the opinion of many British philosophers — "It was not by paradoxes that he wished to be known, but by a suave evasion of paradoxes." He likens Wittgenstein to Pascal and Tolstoy — geniuses who threw away their talent from an impulse of pride: Wittgenstein "debased himself before common sense as Tolstoy debased himself before the peasants." He admired the Tractatus but not the later work, which seemed an abnegation of the man's own best talent. The chapter reprints four polemical articles already published in learned journals: (1) "Philosophical Analysis," a review of J. O. Urmson's book of that name; (2) "Logic and Ontology," an examination of G. J. Warnock's chapter "Metaphysics in Logic"; (3) "Mr Strawson on Referring," a rebuttal of P. F. Strawson's criticism of the theory of descriptions; and (4) "What is Mind?", a review of Gilbert Ryle's The Concept of Mind. Russell says he has been unable, in spite of serious efforts, to see any validity in the school's criticisms of him, and hopes the reader will judge from the articles.

Article 1: "Philosophical Analysis" Russell surveys the three philosophies that dominated Britain since 1914: the Tractatus (which he calls WI), logical positivism, and the Philosophical Investigations (WII). He had general sympathy with the logical positivists despite disagreeing with distinctive doctrines; WII "remains to me completely unintelligible. Its positive doctrines seem to me trivial and its negative doctrines unfounded." If WII were true, "philosophy is, at best, a slight help to lexicographers, and at worst, an idle tea-table amusement." His own fundamental aim, common to all philosophers before WII, is to understand the world and separate knowledge from unfounded opinion; WII tells us to understand only sentences. He attacks the view that sentences must never be confronted with facts — Neurath, Hempel, and at one time Carnap held that assertions are compared with assertions, not with experiences. He retells the Hempel fable: the restaurant in Paris, the menu, the order of beef — all language — and then the mouthful, confrontation with fact; the restaurateur replies "the scientists of my culture circle include the sentence 'this is beef' among those that they accept" — absurd, as Carnap in due course came to realize. His own method: taking it for granted that science and common sense are broadly capable of being interpreted as true, ask what are the minimum hypotheses from which that broad measure of truth results. The reduction of mathematics to logic confined "Divine Creation" to or, not, all, and some. Truth in pure mathematics is syntactical; truth in empirical matters has a different basis — relation to one or more facts. He works through the everyday example "Professor Z goes for a walk every afternoon unless it is raining," urging that analysis of the experience — a series of visual impressions, like the film that reproduces seeing him walk — is science, not metaphysics; "metaphysics" has become "a philosophical opinion not held by the present author," like being accused of being a security risk in the public service. To Urmson's two objections: (a) analysis never reaches simples — Russell sees no reason either to assert or deny that simples exist; he quotes his 1918 exchange with Mr Carr ("it might be that analysis could go on forever") and Human Knowledge on the skeleton, bones, cells, molecules, atoms — at no stage is there positive reason to suppose the units are simple, nor is the question important, since structure-accounts are not falsified by later analysis; atomic sentences are a purely syntactical matter. (b) "England declared war in 1939" is not equivalent to any collection of simpler statements — Russell is at a loss: the statement is about something momentous, yet not about an entity "England" apart from the English people; given enough statements about what English people did, including the Cabinet's dictaphone-recorded deliberations and the people's acceptance of the Cabinet's authority, they would logically imply the statement. He defends the "perfect logical language" as a tool of logical dissection, quoting the Principia's own warning: language can represent complex ideas easily ("a whale is big") while the true analysis of "one is a number" leads to intolerable prolixity; no logician imagines the logical language has practical utility. Empirical evidence: the illusions of sense (the voice from the next room, the restaurant mirrors, the buzzing telegraph wires, the madman's voices) are an ancient problem; philosophy that ignores the physics and physiology of perception "chooses to ignore" science. The argument that you cannot know "all A is B" except through experience of As that are Bs rests on a false analysis of general propositions: no particular A is a constituent of the proposition, so "All the whole numbers which no one will have thought of before the end of the present century are greater than 1,000" is knowable with no instance — and the Nautical Almanack's prophecies are not questionable metaphysics. Two opposite misconceptions of experience: crude experience tells us less than we think, and inference from the experienced to the unexperienced — even the unexperienceable — is essential to retain common-sense beliefs. The essential truth of empiricism: every piece of empirical knowledge a person possesses depends on some sensation in his own life; but the sensation is part of the cause of the belief, not part of what is believed. The denial of inference to unexperienced causes would be "absolutely devastating." Urmson's discussion of logical atomism ignores its later developments, including Human Knowledge on proper names. Analysis is the road of all scientific progress — water as two parts hydrogen, the conductor hearing the symphony, the alphabet against Chinese ideograms. The most serious objection: the new philosophy has abandoned "that grave and important task which philosophy throughout the ages has hitherto pursued" — understanding the world; it concerns itself "not with the world and our relation to it, but only with the different ways in which silly people can say silly things." Philosophy must be built on a wide foundation of non-philosophical knowledge: "Such knowledge is the soil from which the tree of philosophy derives its vigour."

The remaining articles The chapter continues with the other three articles — "Logic and Ontology" (against Warnock's claim that logic rests on metaphysics-free ground, defending the notion that syntax reveals world-structure), "Mr Strawson on Referring" (rebutting Strawson's objection to the theory of descriptions, which Russell maintains is a matter of the logical form of the proposition, not of usage), and "What is Mind?" (against Ryle's behaviourist account of mind, defending the privacy of mental events and the legitimacy of introspection) — reprinted as the record of Russell's final exchanges with the ordinary-language movement.

Key ideas

• Russell was superseded by the later Wittgenstein, whom he likens to Pascal and Tolstoy — genius abandoning itself from pride.
• WII is unintelligible to him: positive doctrines trivial, negative doctrines unfounded.
• Language cannot be divorced from fact: the Hempel fable shows the absurdity of the culture-circle criterion.
• His method: minimum hypotheses from which the broad truth of science and common sense follows.
• Analysis need not reach simples to be valid; atomic sentences are syntactical, atomic facts are not required.
• "England declared war in 1939" is analysable in principle into statements about what English people did.
• Every piece of empirical knowledge depends on some sensation in one's own life — the essential truth of empiricism.
• The new philosophy abandoned philosophy's task: understanding the world, not sentences.

Key takeaway

The final chapter defends the analytic method and the correspondence theory of knowledge against the later Wittgenstein school — the philosophy of sentences rather than the world — while reaffirming Russell's lifelong conviction that philosophy must grow from the soil of science.

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The book's overall argument

1. Chapter 1 (Introductory Outline) — establishes the book's frame: an intellectual autobiography with one constant preoccupation (how much can be known, and how certainly), divided by the 1899–1900 revolution into an earlier and a later Russell.
2. Chapter 2 (My Present View of the World) — states the destination reached: a synthesis of physics, physiology, psychology, and logic in which events are fundamental, physics describes only structure, the perceived world is private, and minds are memory-chains of events.
3. Chapter 3 (First Efforts) — establishes the origin: adolescent religious doubt and mathematical scepticism, argued in solitary diary entries that already contain the deterministic, empiricist leanings of the mature philosopher.
4. Chapter 4 (Excursion into Idealism) — establishes the error corrected: Russell became a full-fledged Hegelian who built an unpublished dialectic of the sciences proving matter unreal, and later judged the whole period nonsense.
5. Chapter 5 (Revolt into Pluralism) — establishes the break: the rejection of the doctrine of internal relations in favor of external relations, which entails pluralism, real asymmetrical relations, and the independence of fact from experience.
6. Chapter 6 (Logical Technique in Mathematics) — establishes the technique: Peano's logic, propositional functions, and the definition of numbers as classes of similar classes, reducing arithmetic to logic and eliminating numbers as entities.
7. Chapter 7 (Principia Mathematica: Philosophical Aspects) — establishes the tools for the paradoxes: the theory of types against self-reference and the theory of descriptions against fictitious entities, each showing that grammar misleads about logical form.
8. Chapter 8 (Principia Mathematica: Mathematical Aspects) — establishes the mathematics: the calculus of relations, the definition of series, the multiplicative axiom, the ancestral relation, and relation-arithmetic, which defines structure exactly.
9. Chapter 9 (The External World) — establishes the theory of perception: solipsism is irrefutable but unbelievable; physical objects cannot be constructed from experienced data alone; perspectives and sensibilia connect physics and perception in six-dimensional space.
10. Chapter 10 (The Impact of Wittgenstein) — establishes the post-Principia logic: the Tractatus supplied structure, tautology, and the two principles of extensionality and atomicity, but its mysticism and its doctrine of identity must be rejected, and the axiom of reducibility remains a blot.
11. Chapter 11 (Theory of Knowledge) — establishes the turn: after the war Russell made epistemology his subject, guided by six prejudices — animal–human continuity, physics-mindedness, suspicion of "experience," empiricist provenance, the importance of meaning, and the method of analysis.
12. Chapter 12 (Consciousness and Experience) — establishes the metaphysics of mind: with the subject abandoned, sensations are non-relational and neutral; mind and matter are arrangements of the same events, and the mind–body problem is definitively solved by neutral monism.
13. Chapter 13 (Language) — establishes the philosophy of language: meaning is causal habit, words are universals, sentences express beliefs about facts, and language is part of the world of fact, not an autonomous realm.
14. Chapter 14 (Universals and Particulars and Names) — establishes the ontology: particulars collapse into complexes of compresence, the stuff of the world is qualities, and universals — above all relations — are irreducible because even words are universals.
15. Chapter 15 (The Definition of 'Truth') — establishes the epistemology: truth is the relation of belief to fact — a belief is a picture with a yes-feeling or no-feeling, true when a fact stands to it as prototype to image — against coherence and pragmatism alike.
16. Chapter 16 (Non-Demonstrative Inference) — establishes the foundations of empirical knowledge: induction is not a premiss of probable inference; five postulates — quasi-permanence, separable causal lines, spatio-temporal continuity, structure, and analogy — justify what nobody doubts.
17. Chapter 17 (The Retreat from Pythagoras) — establishes the emotional and intellectual arc: the whole development is a retreat from the Platonic, ascetic worship of mathematics into a philosophy for which sense is a window, not a prison bar.
18. Chapter 18 (Some Replies to Criticism) — establishes Russell's final position: analysis and correspondence to fact are defended against the later Wittgenstein school, and philosophy is reaffirmed as the attempt to understand the world from the soil of science.

Common misunderstandings

Misunderstanding: My Philosophical Development is an autobiography like the three-volume Autobiography. It is an intellectual autobiography — a history of ideas and arguments. Only chapters 3 and 4 are substantially personal, and the personal material (the 1888 diary, the war years) is admitted to explain changes of doctrine.

Misunderstanding: The chapter titles are "First Efforts at Generalisation" and "Escape from Idealism." The printed table of contents of the 1959 edition gives "First Efforts" (chapter 3) and "Excursion into Idealism" (chapter 4). The longer forms are catalog abbreviations that have circulated and should not be trusted; Russell's own title for chapter 4 is an "excursion," not an escape.

Misunderstanding: Russell was always an empiricist and atomist. Chapter 4 shows he was a committed Hegelian for several years, complete with a dialectic of the sciences, and only rebelled at the end of 1898 — a fact central to the book's argument that his career is a record of self-correction.

Misunderstanding: Logical atomism claims the world is composed of simples at which analysis finally arrives. Chapter 18 (and 14) explicitly deny this: Russell says there is no reason to expect analysis to reach simples, that nothing can be known to be simple, and that atomic sentences are a purely syntactical matter.

Misunderstanding: The theory of descriptions says descriptions are meaningless. It says the opposite of what it is sometimes accused of: a descriptive phrase contributes to the meaning of a sentence without having any meaning in isolation — it is an incomplete symbol, not a name of an entity.

Misunderstanding: Russell's neutral monism is a form of idealism. It is neither idealism nor materialism: the neutral stuff is intrinsically neither mental nor physical, and "mental" and "physical" are arrangements. His claim that "the brain consists of thoughts" uses "thought" in Descartes's wide sense and is part of the dissolution of the mind–matter distinction, not a mentalism.

Misunderstanding: The book endorses induction as the foundation of science. The opposite: chapter 16 argues that induction by simple enumeration, unconfined by common sense, leads more often to error than to truth, and substitutes five postulates of non-demonstrative inference.

Misunderstanding: My Philosophical Development is Russell's final settled system. Russell repeatedly presents conclusions as probable, provisional, and "not to be proved"; he says of his present view that no prudent person claims more for a theory than that it cannot be disproved and answers puzzles.

Misunderstanding: Russell accepted the Tractatus wholesale. Chapter 10 shows him accepting structure, tautology, extensionality (in qualified form), and atomicity (cautiously), but rejecting the picture theory's importance, the doctrine of identity, the prohibition on totality statements, and the mysticism.

Misunderstanding: The final chapter is a review of ordinary-language philosophy as a whole. It is four reprinted polemical articles — against Urmson, Warnock, Strawson, and Ryle — plus a new introduction; the school's general attitude ("the different ways in which silly people can say silly things") is Russell's stated reason for the polemic.

Central paradox / key insight

The book's most counterintuitive idea is that an honest philosopher's intellectual autobiography is a record of error correction: Russell's career — the one the book narrates — is a sequence of positions (idealism, Platonism about mathematics, the relational theory of sensation, induction as the foundation of science) each of which he explicitly repudiates in these pages, and he presents the repudiations as the substance of progress. The paradox deepens with the "retreat from Pythagoras": the more rigorous his logic became, the less certainty he could find; the philosopher who began by seeking a perfected mathematics that would leave no room for doubts ends by declaring that mathematics consists of tautologies, that its timelessness is merely not talking about time, and that even his own final view cannot be proved — only shown not to be disprovable. Certainty, the original goal, turns out to be the one thing philosophy cannot deliver, and the book's method — analysis from both ends, like a tunnel through an Alpine mountain — is offered precisely because no single foundation can be taken as given.

I have throughout been anxious to discover how much we can be said to know and with what degree of certainty or doubtfulness.

Important concepts

Logical atomism — The philosophy Russell adopted in 1899–1900 (the name came later, in his 1918 lectures): the world consists of many independent things with properties and relations, and analysis breaks complexes down toward atoms. Russell insists the doctrine does not require that analysis ever reach simples.

Doctrine of internal relations / external relations — The idealist thesis that every relation is grounded in the natures of its terms (or of the whole they compose) vs. Russell's thesis that relatedness implies no corresponding complexity in the relata. Rejecting internal relations is the hinge of the 1898 revolt and, for Russell, the foundation of mathematics.

Doctrine of types (theory of types) — The solution to Russell's paradox: propositions and classes form an order hierarchy, and reflexive self-reference — including the totality in the defined totality — is banned, dissolving the liar and the class of non-self-membered classes.

Axiom of reducibility — The axiom of Principia Mathematica that every non-predicative property is formally equivalent to a predicative one; admitted by Russell to be a "blot" on the system, minimized in the second edition, and dispensed with (at a cost he judged unacceptable) by Ramsey.

Propositional function — An expression containing a variable that becomes a proposition when a value is assigned ("x is a man"); the basis of the analysis of "all" and "some," of classes, and of the definition of number.

Theory of descriptions — The 1905 doctrine that definite descriptions are incomplete symbols: "the author of Waverley" contributes to the meaning of sentences without meaning anything in isolation, so "the golden mountain does not exist" needs no Meinongian realm of being, and existence is properly asserted only of descriptions.

Incomplete symbol — An expression that is meaningful only in the context of a sentence, not as a name: descriptions, classes, and (later) points, instants, minds, and material things are all treated as such.

Occam's razor / logical constructions — "Wherever possible, logical constructions are to be substituted for inferred entities": numbers, classes, points, instants, and physical objects are constructions, so one may abstain from asserting their existence rather than deny it.

Event — Russell's fundamental entity: something occupying a finite amount of space-time, overlapping with innumerable others; point-instants are mathematical constructions from events; physics describes only the structure of events, never their intrinsic character.

Sense-data / sensibilia / perspectives — The data of perception (abandoned as an act–object pair in 1921); the appearances things present where there is no mind; and the totality of appearances at one physical place, of which one man's percepts are an instance. The 1914 theory makes physical space six-dimensional, each "point" a three-dimensional complex of percepts.

Neutral monism — The doctrine, adopted in 1918 under James's influence, that mind and matter are arrangements of one neutral stuff: a sensation grouped by memory-chains is mental, grouped with its causal antecedents it is physical — the Post Office Directory analogy. Russell calls the mind–body problem "definitively solved" by it.

Noticing — The undefined term that replaced "acquaintance" after the abandonment of the subject; empirical propositions rest on sensible occurrences that were noticed, and "consciousness" is defined as knowledge that something is happening to me — noticing.

Verifier — The fact or facts in virtue of which a belief is true; truth is the correspondence of a belief-picture with a yes-feeling or no-feeling to its verifier.

Causal lines / the five postulates — Causal lines are series of events from which neighbouring events can be inferred; the five postulates of non-demonstrative inference (quasi-permanence, separable causal lines, spatio-temporal continuity, structure, analogy) replace induction as the justification of probable inference.

Compresence / complete complex of compresence — Qualities compresent in experience ("redness is compresent with centrality"); a complete complex is one whose members are all compresent with each other but not with anything outside — Russell's substitute for particulars, making "the stuff of the world" things like whiteness.

Minimum vocabulary — The smallest set of words in terms of which all others in a body of sentences can be defined; its hard core attaches language to the non-linguistic world, and contains no proper names in the traditional sense.

Relation-number — The class of relations ordinally similar to a given relation; ordinal numbers are the subclass applying to well-ordered series, and relation-arithmetic is Russell's precise definition of structure.

References and Web Links

Full text and editions

• Full text of the 1959 George Allen & Unwin first edition (open scan on the Internet Archive; the item title says "Routledge Classics" but the scanned book is the 1959 first edition, including the prefatory note and the Alan Wood appendix): https://archive.org/details/my-philosophical-development-routledge-classics-bertrand-russell
• Internet Archive scan of the 1959 London edition (Allen & Unwin, restricted): https://archive.org/details/myphilosophicald0000russ
• Internet Archive scan of the 1959 New York edition (Simon and Schuster, restricted): https://archive.org/details/myphilosophicald00russ
• Open Library work record (16 editions, with publisher's description): https://openlibrary.org/works/OL1088551W
• Open Library record of the 1959 Simon and Schuster edition: https://openlibrary.org/books/OL6270402M

Library catalogs (used to verify the edition and contents)

• HathiTrust catalog record for the 1959 Allen & Unwin edition, including the contents field used to cross-check the chapter list: https://catalog.hathitrust.org/Record/001395965 — MARC view: https://catalog.hathitrust.org/Record/001395965.marc
• Library of Congress record, LCCN 59007264 (Simon and Schuster edition): https://lccn.loc.gov/59007264
• CiNii Books record (Simon and Schuster, 1959, with appendix note): https://ci.nii.ac.jp/ncid/BA29720978
• WorldCat record for the 1959 New York edition: https://search.worldcat.org/title/371328

Reference works (supplements, not substitutes)

• Stanford Encyclopedia of Philosophy, "Bertrand Russell" (A. D. Irvine) — overview of Russell's philosophy, quoting extensively from this book: https://plato.stanford.edu/entries/russell/
• Stanford Encyclopedia of Philosophy, "Descriptions" (P. Ludlow) — the theory of descriptions and its later history: https://plato.stanford.edu/entries/descriptions/
• Stanford Encyclopedia of Philosophy, "Russell's Logical Atomism" (K. Klement) — logical atomism, relations, and analysis: https://plato.stanford.edu/entries/logical-atomism/
• Stanford Encyclopedia of Philosophy, "Neutral Monism" (L. Stubenberg) — Mach, James, and Russell on the one neutral stuff: https://plato.stanford.edu/entries/neutral-monism/
• Wikipedia, "My Philosophical Development" (article with publication history and reviews): https://en.wikipedia.org/wiki/My_Philosophical_Development

Contemporary review

• T. V. Smith, review of My Philosophical Development, Ethics 70(1), 1959, pp. 93–94 (DOI, verified): https://doi.org/10.1086/291259