Deduction, Induction, and Hypothesis

Where a guess at an explanation stops being a weak generalisation and becomes a third kind of inference: the last instalment of the 1877–78 series.

by Charles Sanders Peirce23 passages held

English, the original language, and your language

First published: 1878(aged 39)
Original language: English

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Overview

This paper carried a third kind of reasoning to a popular audience: neither proof nor generalisation, but a guess at what would account for a surprising fact. Peirce made his case with a bag of beans. Every argument, he says, has three parts: a Rule, a Case and a Result. All the beans in this bag are white; these beans are from this bag; therefore these beans are white. That is deduction, and it merely applies a rule. Now permute. Start from the Case and the Result — these beans came from the bag, these beans are white — and conclude the Rule: that is induction, the inversion of the syllogism. Start from the Rule and the Result — the bag holds only white beans, and here on the table is a handful of white ones — and conclude the Case, that the handful came from that bag. Peirce calls this third move hypothesis, and insists it is not a weak induction. Induction moves from facts to more facts of the same kind; hypothesis crosses to facts of another kind, which is why our belief in Napoleon is a hypothesis and not a generalisation from the documents. He then matches the three forms to habit, emotion and attention, and sorts the sciences by which of the three each chiefly uses. The series stopped there, in August 1878, after ten months. The third form outlived it. Peirce went on working at the logic of guessing, and in the essay he published in 1908 it reappears as the opening stage of any scientific inquiry at all.

Key concepts

What are Rule, Case and Result?

The three parts Peirce says every argument has. "All the beans in this bag are white" is a Rule; "these beans are from this bag" is a Case; "these beans are white" is a Result. Which two you start from decides which inference you are making, and the whole classification comes out of permuting them.

Why does Peirce call induction the inversion of a syllogism?

Because it begins where a deduction ends. Deduction takes Rule and Case and concludes the Result; induction takes the Case and the Result — these beans came from the bag, these beans are white — and concludes the Rule. The sample is what you are given and the generalisation is what you reach, so the syllogism runs backwards.

Does 'hypothesis' here mean what people now call abduction?

It is the same move under an older name. In this paper the third inference is called hypothesis: start from the Rule and the Result and conclude the Case. Peirce kept renaming it across his career and the later labels belong to later writings, so anyone reading this essay for the word abduction will not find it in it.

Why does Peirce pair the three inferences with habit, emotion and attention?

Because he wants them grounded in something besides logic books. Induction, he says, corresponds to the formation of a habit; hypothesis to an emotion, a single feeling that takes the place of a tangle of separate impressions; deduction to attention, which holds a relation in view. His classification of the sciences at the end rests on the same split between induction and hypothesis.

Why is the kinetic theory of gases a hypothesis rather than an induction?

Because it infers something nobody observes — molecules in motion — from the behaviour of gases, which is what those molecules would explain. An induction could only have told us that further gases behave as these did. Peirce uses the case to show what a scientific theory characteristically is, and why the third form does work the second cannot.

Themes of the book

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

Guessing, Treated as an Inference

A guess at what would account for a surprising fact is neither proof nor generalisation, and Peirce denies it is a feeble version of either: it is a third form of reasoning with rules of its own.

Rule, Case and Result are the parts of any argument, and permuting which two are given generates the three forms — deduction applies a rule, induction concludes to the rule, hypothesis concludes to the case. The difference that matters is direction. Induction moves from facts to further facts of the same kind, while hypothesis crosses to facts of another kind, which is why believing in Napoleon is a guess rather than a generalisation from documents.

abduction
hypothesis
induction
deduction
syllogism
inference
explanation
scientific method
evidence
classification
scientific reasoning

Enter a dialogue

Within this work

passages held: 23
distinct concepts: 48
by passages held, corpus-wide: #765

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: “deduction” and “induction”.

Concept co-occurrence, strongest first 6 concepts, joined by 12 pairings. 28 pairings reach beyond these concepts and are not drawn.
Concept	Paired concept	Shared passages
deduction	induction	8
abduction	induction	7
induction	logic	6
deduction	logic	5
abduction	deduction	4
deduction	syllogism	4
hypothesis	induction	4
induction	syllogism	4
logic	syllogism	4
abduction	logic	3
abduction	syllogism	2
deduction	hypothesis	1

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.

1867 On a New List of Categories
The earliest item on this shelf, and the root of everything after it: the three-part scheme of quality, relation and representation reappears in the logic papers of 1877–78 and again in the evolutionary cosmology of the 1890s.
EN
1868 Questions Concerning Certain Faculties Claimed for Man
Where Peirce clears the ground. The four denials reached here — no intuition, no introspection, no thought without signs, no conception of the incognizable — are restated as premisses at the head of the sequel.
EN
1868 Some Consequences of Four Incapacities
The sequel, and where the argument arrives. The preceding article asked whether we have certain faculties; this one takes its four denials as premisses and follows them out to a theory of reality and of the self.
EN
1877 The Fixation of Belief
Written for readers with no philosophy behind them: the first instalment of a six-part course in the logic of science, serialised in a general-interest monthly. Everything the other 1877–78 papers do rests on the account of doubt, belief and inquiry set out here.
EN
1878 Deduction, Induction, and Hypothesis you are here EN
1878 How to Make Our Ideas Clear
The second instalment of the 1877–78 series, nominally about a dead distinction in the logic textbooks. Two decades after it was printed, the American pragmatists took it as their charter.
EN
1878 The Doctrine of Chances
Third in the series, and the point where the account of inquiry acquires a price. Half of it is arithmetic — card packs, whist hands, insurance offices — and the other half asks whether a creature who never lives to complete a run of trials may reason from probabilities at all.
EN
1878 The Order of Nature
The religious instalment of the 1877–78 series. It reaches forward to the essay Peirce published at the end of his life: both ask what a scientific habit of mind is entitled to say about God, and they give different answers.
EN
1878 The Probability of Induction
A general magazine's readers are asked here to check a table of black and white balls for themselves. It is the most technical stretch of the 1877–78 series, and the one that takes on the probability textbooks directly.
EN
1891 The Architecture of Theories
A prospectus rather than a treatise, and the first of the five articles of Peirce's metaphysical series in Paul Carus's Monist, 1891–93 — the run in which the cosmology it sketches was built.
EN
1892 Man's Glassy Essence
Three things that do not obviously belong together — the constitution of matter, the chemistry of living tissue, and the question whether a church or a crowd can think — joined by the argument that mind and matter differ only in which side you look from.
EN
1892 The Doctrine of Necessity Examined
It stands second in the series, and it is the one that started a quarrel: Carus attacked it twice in his own journal and Peirce defended it once, so that the argument about chance occupied The Monist for fifteen months.
EN
1892 The Law of Mind
Where tychism acquires its partner. The chance of the April paper needed continuity to work in, and continuity gets its name and its defence here — the idea Peirce came to regard as the one his philosophy could least do without.
EN
1893 Evolutionary Love
Here the cosmology turns into an argument about how people ought to live: chance, necessity and love applied to the history of ideas, and to the ethics of a commercial century. It closed the Monist series.
EN
1893 What is Christian Faith?
Addressed past the theologians to two audiences at once — churchmen keeping their membership narrow, and the scientifically educated, shut out of the churches, who were talking about founding one of their own.
EN
1899 Leibniz Rewritten
The one book review on this shelf, from the years after the Coast Survey when Peirce lived partly by notices and dictionary work. It is the only piece here in which he is weighing someone else's system rather than building his own.
EN
1908 A Neglected Argument for the Reality of God
Thirty years after the logic papers and fifteen after the cosmology, Peirce turns the machinery of hypothesis on the question the 1878 series had left open.
EN

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