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WorkJohn Stuart Mill

A System of Logic, Ratiocinative and Inductive

Six books to show that all knowledge, arithmetic included, comes from experience. Mill built them on material supplied by the Cambridge philosopher he set out to refute.

by John Stuart Mill1,475 passages held

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(aged 37)
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Overview

William Whewell, Master of Trinity College, Cambridge, taught that science does not simply collect facts: the mind adds an idea of its own to what it observes, and some truths, those of arithmetic and geometry among them, are known to be necessary without any appeal to experience. Mill owed him a debt. He had been stuck for five years at the threshold of induction, the reasoning that passes from observed cases to a general law, when Whewell's History of the Inductive Sciences appeared in 1837 and gave him the scientific material he lacked. Within two months he had drafted the hardest third of his book. A System of Logic was published in 1843 and turned that material against its supplier. Mill argues that all knowledge rests on experience, mathematics included: that two and one make three is a generalisation from things counted, trusted because nothing has ever contradicted it. A syllogism, the classic form of deduction, proves nothing new, since its general premise is only a record of particular cases already observed. What observation can establish is causes, and the book sets out methods for isolating a cause by comparing cases that agree and cases that differ; they are still taught under Mill's name. The sixth and last book extends those methods to human conduct and society, with help from the French philosopher Auguste Comte. More was at stake for Mill than a theory of science. A truth known by intuition cannot be challenged by evidence, and he held that the appeal to intuition protected established opinion in morals and politics from examination. Whewell replied in 1849 with a pamphlet, Of Induction, with Especial Reference to Mr. J. Stuart Mill's System of Logic, objecting that Mill could show few real discoveries made by his methods. Mill went on revising in answer to his critics through eight editions, the last in 1872. In 1884 the German mathematician Gottlob Frege took up the account of arithmetic in The Foundations of Arithmetic and observed that, if numbers were facts about heaps of things, zero would be a puzzle, since nobody has ever seen or touched zero pebbles.

Key concepts

What is the difference between what a name denotes and what it connotes?

A name denotes the things it applies to and connotes the attributes that make it apply. 'White' denotes snow, paper and foam, and connotes whiteness. Mill holds that proper names such as John or Dartmouth denote without connoting: they point at an individual and say nothing about it. The meaning of a general name lies in its connotation, and a definition is the statement of it.

What are Mill's methods for finding a cause?

They are rules for comparing cases so that one circumstance can be singled out as the cause. The Method of Agreement looks for the one circumstance shared by every case in which the effect occurs. The Method of Difference compares two cases alike in everything except one circumstance and the effect. The Method of Residues subtracts what known causes explain, and the Method of Concomitant Variations watches what rises and falls together. Mill's showpiece is dew.

What does Mill mean by the uniformity of nature?

It is the assumption that what happens once will happen again whenever the circumstances are the same. Mill calls it the ultimate premise of every induction, since any inference from observed to unobserved cases presupposes it. He denies that it is known before experience: people arrived at it slowly, from countless narrower regularities that were never contradicted, and it is certain only in the way the widest experience is certain.

What is an empirical law?

An empirical law is a regularity that has been observed to hold while its cause is still unknown. Mill's examples include the local times of the tides and the weather that follows certain appearances of the sky. Such a law can be trusted only within the range of times, places and circumstances where it was observed, because nobody knows what it depends on. It becomes a law of nature in the full sense once it is derived from causes.

What is the doctrine of necessity in the System of Logic?

It is the claim that human actions follow from motives and character as regularly as other events follow from their causes. Mill accepts it and separates it from fatalism, the belief that nothing a person does can alter the outcome. Character is formed by circumstances, he says, and a person's own wish to be different is one of those circumstances. People can therefore work on their characters, and that ability is what the feeling of freedom reports.

Themes of the book

What this book returns to, gathered into themes and ordered by how much of the text each one occupies.

What a name says and what an argument proves

Does a deductive argument ever teach anything that its premises did not already contain? Mill answers that the real inference runs from case to case, and the general statement is a note made along the way.

Proper names, Mill argues, mark a thing without describing it: Dartmouth would keep its name if the river Dart changed its course. General names carry attributes, and a definition merely unfolds them. From there he turns on the syllogism. Whoever asserts that all men are mortal has already asserted it of the Duke of Wellington, so the premise cannot prove the conclusion. The village matron who treats a neighbour's child by what cured her own Lucy reasons from particulars to particulars, and in the end so does everyone. General propositions are registers of such inferences and short formulae for making more.

  • logic
  • language
  • meaning
  • connotation
  • definition
  • propositions
  • reasoning
  • inference
  • deduction
  • deductive reasoning

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Arithmetic and geometry learned from things

If two and one make three only because counting has never shown otherwise, is anything known for certain before experience? Here Mill meets the doctrine of necessary truths at its strongest point.

William Whewell held that the axioms of geometry and arithmetic are seen to be necessary, because their contrary cannot be conceived. Mill replies that what people cannot conceive records their habits of association and nothing about the world: educated men once found the antipodes inconceivable. Two pebbles and one pebble make three because the senses have shown it at every trial, and the axiom that two straight lines cannot enclose a space is a generalisation from looking at lines. Mathematical certainty is the certainty of very wide and very uniform experience, and what is deduced from definitions holds only so far as things answer to them.

  • geometry
  • empiricism
  • epistemology
  • belief
  • perception

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How a cause is found

On what grounds may a few observed cases stand for all the cases nobody has observed? Everything a science claims depends on the answer, and Mill looks for it in the search for causes.

Induction, for Mill, rests on the uniformity of the course of nature, which is itself learned by induction of the loosest kind. A cause is the antecedent on which an effect follows invariably and unconditionally, which is why day is not the cause of night. To isolate one he gives four methods: compare cases that agree in a single circumstance, cases that differ in one only, what is left when known causes are subtracted, and what varies together. Against Whewell he holds that Kepler's ellipse described the path of a planet and inferred nothing beyond the facts. The book on fallacies shows the same rules being broken.

  • induction
  • causation
  • scientific method
  • laws of nature
  • evidence
  • observation
  • generalization
  • scientific explanation
  • probability
  • philosophy of science
  • classification
  • fallacies
  • empirical laws

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A science of human nature and society

Can human conduct be studied as a science if people are to remain free? Mill has to show that a caused action is not a compelled one before his last book can begin.

The sixth book opens with liberty and necessity. Actions follow from character and motives, Mill says, but a person can alter his own character if he wishes, and the doctrine is wrongly taken for fatalism. On that footing he proposes a science of how character is formed, which he names ethology, and a science of society. Politics cannot be reasoned like geometry from one premise, as Bentham's school tried, nor tested by experiment like chemistry. With Comte he recommends generalising from history and then checking the result against the laws of human nature. The closing chapter separates science from the Art of Life, which sets the ends.

  • social science
  • metaphysics

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Within this work

passages held
1,475
distinct concepts
866
by passages held, corpus-wide
#43

What this book thinks together

The wheel takes this book’s leading concepts and shows how often they come up together. The wider the band between two, the more of its passages speak of both. Among them, most often together: “causation” and “induction”.
Concept co-occurrence, strongest first 8 concepts, joined by 28 pairings. 84 pairings reach beyond these concepts and are not drawn.
ConceptPaired conceptShared passages
causationinduction172
inductionscientific method88
causationscientific method70
causationscientific explanation64
evidenceinduction60
classificationinduction27
classificationlanguage25
causationevidence24
classificationscientific method23
inductionlogic23
inductionscientific explanation21
evidencescientific method19
languagelogic18
classificationlogic15
evidencelogic14
inductionlanguage10
logicscientific method8
causationclassification7
causationlanguage7
causationlogic6
classificationevidence4
evidencescientific explanation4
languagescientific method4
evidencelanguage2
languagescientific explanation2
classificationscientific explanation1
logicscientific explanation1
scientific explanationscientific method1

Works held

The author's work in order, this book marked in place. Your-language title first, the original beneath it where the two differ; side chips show which full texts are held.

  1. 1843 A System of Logic, Ratiocinative and Inductive you are here EN
  2. 1844 Essays on Some Unsettled Questions of Political Economy (Essays on some unsettled Questions of Political Economy)

    Written at twenty-three and twenty-four, these five essays waited until the System of Logic had found him readers. Their argument on trade returns, four years later, in the Principles of Political Economy.

     EN
  3. 1848 Principles of Political Economy

    Seven editions carried this treatise from 1848 to 1871, revised as his view of socialism moved. It is read here in the text of the seventh, the last Mill revised himself.

     EN
  4. 1859 On Liberty

    One of the two books Mill expected to outlast the rest, the other being the System of Logic. Its defence of individuality against majority opinion runs on into Considerations on Representative Government and The Subjection of Women.

     EN
  5. 1861 Considerations on Representative Government

    Written two years after On Liberty, it faces the same danger, a majority that overrides everyone else, and meets it with electoral machinery. It is his fullest statement on how a free people should be governed.

     EN
  6. 1861 Utilitarianism

    A defence of the ethics he inherited from Bentham and from his father, assembled from papers of the 1850s. Short as it is, it supplies the standard of right and wrong that his political books take for granted.

     EN
  7. 1862 The Contest in America

    Occasional journalism from Fraser's Magazine, written in haste before a journey to Greece. It shows Mill as a polemicist, arguing against the prevailing opinion of his own class.

     EN
  8. 1865 Auguste Comte and Positivism

    Two essays from the Westminster Review of 1865, written eight years after Comte's death. They close a relationship that began with admiring letters in 1841 and left its mark on the System of Logic.

     EN
  9. 1869 The Subjection of Women

    The most contested of his books in its day, published in 1869 after his one term in Parliament. It carries the reasoning of On Liberty into marriage and the household.

     EN
  10. 1879 Socialism

    Left unfinished at his death, these are the posthumous "Chapters on Socialism", first drafts for a book planned in 1869. They return to a question that the Principles of Political Economy had reopened from one edition to the next.

     EN
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