Chapter 48
Induction: reasoning from particulars and observations to general conclusions.
106 passages · 27 principal · Covers the 49 volumes of primary texts
Induction is the reasoning by which the mind passes from particular things observed to general conclusions about things not observed. It moves from these cases to all cases, and from what has happened to what will happen. It is a great idea for these books because nearly every author who claims to know something about nature, disease, the earth, or human conduct must at some point make that passage, and because a smaller number stop to ask whether it can be justified. In the Harvard Classics the idea appears in three ways. Bacon and Mill set out its method. Hume questions its ground. Darwin, Lyell, Jenner, Holmes, Faraday, Pasteur, and many others practise it. Taken together, these writers give a fairly full picture of what induction promises and what it risks.
Bacon presents induction as the instrument of a reformed philosophy. He holds that it keeps close to the senses and “closes with nature.” He complains that logicians have neglected it, and says he uses it throughout his own work1. He insists, however, that induction comes in two kinds. The common kind proceeds by simple enumeration, piling up agreeing instances. Bacon calls this puerile, and he proposes in its place a true induction that analyses experience by exclusion and rejection2. His point is that agreeing cases alone never compel a conclusion. One must also eliminate the natures that fail to accompany the effect. This method has a remedial purpose as well. The innate idols of the mind cannot be uprooted, only pointed out, and the intellect becomes qualified to judge only through induction in its legitimate form3. In the New Atlantis the same ideal appears as an institution: observations, axioms, and aphorisms are raised step by step from tabulated experiments4.
The image of a stepwise ascent recurs well outside natural philosophy. Burke, writing on the sublime and beautiful, urges that the ingredients of an effect be examined one by one, and that many similar and contrary cases be compared so that knowledge rests on a wider induction5. He explicitly follows what he calls Newton’s rule. He concludes from many observations while keeping the exceptions in view6. Burke thus brings into aesthetics the Baconian demand that contrary instances be attended to, and not only confirming ones.
Mill’s Autobiography records the effort to make this procedure exact, and the difficulty of doing so. Mill understands induction as the finding of causes of effects, an ascent by generalization from particulars to the tendencies of causes7. Yet he tells us that he halted for five years, unable to make anything satisfactory of the subject8. He resumed only when he had acquired a broader view of physical science, and Whewell’s history of the inductive sciences supplied much of the material9. Whewell’s later philosophy of those sciences then gave Mill an antagonist against whom to sharpen his own theory10. Mill’s ambition was large. He claims that his theory reduces the inductive process to strict rules and a scientific test, just as the syllogism does for ratiocination11. He applies the same distinction to political thought. He praises Tocqueville’s treatment of government as wholly inductive and analytical, and contrasts it with the purely ratiocinative method of his own father12. For Mill, then, induction is a rival to deduction that can be given an equal formal rigour, and not merely a source of premises for it.
Hume poses the question that both Bacon’s and Mill’s confidence leave untouched. We expect similar effects from similar causes, but Hume argues that this expectation cannot be grounded in reason. It presupposes the uniformity of nature and does not prove it13. Every inference from uniform past experiments to like future effects assumes that the future will resemble the past. Experience therefore cannot establish that assumption without arguing in a circle14. Even a long-continued regularity does not show that it will continue, since the hidden nature of bodies might change while their sensible qualities stay the same15. Bacon had treated induction as the cure for the mind’s errors. Hume finds at its root a habit of expectation that no rule can certify. Mill’s hope of a scientific test for induction must face this objection, and the passages here do not show it answered.
Within the practice of induction a narrower question arises: how many instances are enough? Hume himself grants that the completeness of an enumeration can be assured only by examining many instances16. He also holds that when the past is mixed, inference weighs the possible outcomes by how often each has occurred17. The physicians make the force of numbers the substance of their case. Jenner offers a great number of instances in support of an extraordinary claim18. He lets particular cases accumulate toward the conclusion that cowpox gives lasting protection against smallpox19,20. Eventually he appeals to uniform results across thousands of cases21,22,23. Holmes argues the same way. He shows puerperal fever confined to particular practitioners24. He treats the clustering of the disease around them as pointing to contagion as its only cause25. He contrasts one midwife’s cases with hundreds attended by others26. And he cites a case series that brought a sceptical physician round to the conclusion of contagion27.
The authors agree that numbers matter, and they agree just as firmly that a single case proves little. Harvey holds that sound general conclusions require many cases, not one particular proposition28. Hume says that one experiment cannot justify a general rule, and that only uniform repeated conjunction entitles us to foretell29. Jenner, for all his enthusiasm, warns that no positive conclusion can be drawn from a solitary instance or a few cases30. Pascal states the logical asymmetry most sharply. A claim resting on experiment cannot be universal unless all cases have been enumerated, while one contrary case is enough to overturn the generalization31. Pascal’s point gives Bacon’s preference for rejection over enumeration a stricter logical form: confirming instances only add up, but one contrary instance refutes.
If one contrary case overturns a rule, the treatment of apparent exceptions becomes crucial, and here the authors divide. Jenner infers preventive power from success in many cases without exception. He then argues that the apparent failures must not have been true cow-pox32. This move protects the generalization by redefining its instances, and it raises the worry of whether a rule saved in this way still says anything about the world. Burke’s course is more candid: he keeps the exceptions in view rather than explaining them away6. Darwin does the same when he draws a general rule from careful measurements of several breeds and openly notes the short-faced tumbler as an exception33. He also concludes that sterility is general but not universal34, so that the qualification becomes part of the law itself. Rousseau, arguing in a moral rather than a natural context, holds that a general induction from the concurrence of all nations should not be invalidated by a few local customs35. Pascal’s strict rule and Rousseau’s tolerance of exceptions show that the force of a counterexample depends partly on whether the claim was meant as a universal law or as a general tendency.
The authors also recognize that inductions can go wrong in many ways. Hume calls the forming of general maxims from particular observations a delicate operation, liable to error from haste or narrowness36. Darwin compares the geologist who generalizes from a scanty record to a naturalist who judges a whole country from one barren point37. Manzoni’s narrator observes that judging by induction without knowledge of the facts leads to wrongful accusations, even of real villains38. Elsewhere he uses the word ironically, of a man persuading the Venetians “by induction” of a boldness he only professes39. Dryden claims to argue by “plain inductions” about the incompetence of the crowd and the wits40. He says he could prove the morals of his fables by induction but finds it too tedious41. In such passages the word has become a mark of authority more than a method.
Analogy and inference from absence carry special risks. Hume holds that inference from observed to unobserved cases is stronger the closer the resemblance, as in the circulation of the blood across animals42. Rousseau questions inferring human behaviour from the battles of animals whose sexual relations differ from ours43. Darwin shows how an inference from the abundance and good preservation of fossils to the absence of a group can fail44. On the Beagle he warns that inferring a tropical climate from shells could be mistaken, judging from South American evidence45.
The sciences in these volumes show induction in use, and Darwin is its most persistent practitioner. He tabulates varieties in floras to determine which species vary most46. His tables of plants and beetles show that larger genera have more varieties, which tests an expectation against the data47. He uses Watson’s catalogue figures on restricted ranges48 and recorded cases of rapid increase49. He infers laws from large bodies of fact and experiment50. He reaches a universal law of occasional crossing from many cases and consultation with Huxley51. His rule about cirripedes rests on a long array of observations, with sources of error allowed for52. He predicts intermediate gradations in nests and then finds them53, and he draws general rules from Gartner’s particular cases54. On geographical distribution he argues from comparisons across continents55,56 and from the composition of island faunas57. He reasons from limited experimental samples of seeds to their passage across wide seas58,59,60. He concludes from many naturalists’ instances that an organ’s importance for classification varies61. Without written pedigrees, he infers community of descent from many concurring resemblances62. He reflects that the habit of comparison is what leads from isolated facts to generalization63. Darwin’s practice combines enumeration with anticipation and test, and so departs from pure Baconian induction.
Geology faces a particular difficulty, because its past cannot be observed directly. Lyell recounts how comparing fossils with living analogues, together with Donati’s dredging of the Adriatic, overturned old dogmas about the origin of fossils64. Since change is too slow to watch, the geologist must compare fossil shells across formations65. He must also read successive disturbances from unconformable strata66,67. Lyell’s principle is that present changes are the key to past events, and that past deposits in turn illuminate present processes68. Here the uniformity Hume called unprovable becomes a working rule of method. Darwin applies the principle on the Beagle. He reasons from shells and strata to an ancient estuary69 and from terraces to the history of upheaval70,71,72. From soundings he concludes that reef corals live only to limited depths, and he extends this to vast ocean areas73. From mapped correlations of reefs and volcanoes he generalizes that continents rise and ocean floors sink74. He uses existing analogies from Africa and Siberia to argue that great extinct mammals needed no luxuriant vegetation75,76. Geikie reads a shallow-water origin into ripple marks and desiccation cracks77. He takes meteoric granules in deep clay as evidence of extremely slow sedimentation78, and he fixes sequence across regions by strata and their fossils79. Helmholtz notes that geologists infer the former extent of glaciers from boulders, moraines, and polish80. Long before any of these, Herodotus argued that Egypt is made by the river, from shells on the mountains, salt efflorescence, and black soil unlike that of Libya or Arabia81.
In physics and chemistry the ascent is quicker but no different in kind. Faraday generalizes from several experiments that all things gravitate82. From iron filings, lime, phosphorus, and charcoal he concludes that all bright flames contain solid particles, and he invites his audience to carry the reasoning further themselves83,84,85. Newcomb samples a small region of the heavens and infers the whole, much as a farmer judges his field from part of it86. Newcomb’s procedure raises Darwin’s worry about the barren point on the scale of the universe.
Medicine supplies the inductions with the most at stake. Voltaire reports conclusions about immunity drawn from repeated observation87. Holmes reasons from the disproportion between cases of fever and the number of autopsies performed to the presence of a special poison88. Pasteur extends his findings on ferments toward plants and perhaps animals89. From observations across patients and animal inoculations he moves toward principles about the organisms of disease90,91. Even outside science the same pattern of reasoning appears. Smith tests a claim by comparing production records across years92. Haskell estimates enemy casualties from burial counts and the ratio of killed to wounded observed in many battles93.
What remains open is the relation between these two bodies of writing. The working inductions of Darwin, Lyell, and Jenner seem untroubled by Hume’s objection. They proceed on the assumption that nature is uniform and are rewarded by discovery. Bacon and Mill hoped to give such reasoning a certified form. Pascal and Hume show that no finite enumeration reaches certainty, and that the expectation of uniformity is presupposed rather than proved. Between the strict refutation by one contrary case and the practical habit of allowing for exceptions, the authors leave unsettled when a generalization should yield to an exception and when the exception should be explained away.
Introductory essay written by Claude Opus 5.5 from the outline and the notes on every passage below; quotations are checked against this edition.
See also: Logic 2c
See also: Medicine 8c · Experience 9c
See also: Experience 9d
See also: Cause 8a · Change 5a · Geology 6a
See also: Geology, Cause, Experience, Evolution, Science, Medicine