The Doctrine of Chances

An essay on card packs, whist and insurance offices that argues, midway, that a man cannot reason well while he cares only about his own fate.

by Charles Sanders Peirce20 passages held

English, the original language, and your language

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

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Overview

A science becomes exact only when it is treated quantitatively: that is where this paper begins. At its centre is the argument that a man who would not give up his own soul to save the world is reasoning badly in everything he does. Three steps take Peirce there. First, probability is not a property of an event but of a way of arguing: the proportion of cases in which inferences of a given form carry truth with them. That is a fact about frequencies and about nothing else, so to speak of the probability of an event without naming the condition under which it is supposed to happen is to say nothing, however universal the habit. Near the end of the paper, a friend who plays whist has counted the spades in a hundred and sixty-five hands for him, and found the pack carrying traces of the last deal that no calculation allowed for. Second, the ratio only settles down over thousands and millions of trials, so a single case considered by itself has no probability at all. That leaves the man who must draw once from a pack, with heaven and hell riding on the colour, unable to justify his obviously sensible choice. Third, given time enough, every run turns against the player: the martingale, the doubling system some believe infallible, does fail, and the insurance company whose expectation looks enormous is ruined. What without death would happen to every man, with death must happen to some man, and death leaves each of us too few trials for the average to be sure. There is one way out, and Peirce takes it: if reasoning is to mean anything, the interests behind it cannot stop at the reasoner; they must extend to the whole community, beyond this geological epoch and beyond all bounds. Logic, he writes, is rooted in the social principle. The paper ran third in the series, in March 1878. It reached the general reader again in 1923, when the philosopher Morris Raphael Cohen gathered Peirce's essays as Chance, Love and Logic, with a supplement by John Dewey — eight years before the Collected Papers began.

Key concepts

Why is it called the doctrine of chances — is this about gambling?

It was the ordinary name for probability theory in Peirce's century, taken from the study of games. He works with card packs, whist hands and insurance offices because those are the cases where the condition of the inference is actually stated, which is precisely what ordinary talk about probability leaves out.

Does this paper claim that chance is anything real in nature?

No, and the two are easily confused. Chance here is a matter of frequency: how often arguments of a given form come out true. Nothing in the paper says the world is loose or undetermined. The doctrine that there is real spontaneity in nature belongs to papers written fourteen years later and is a separate claim with separate evidence.

What is the martingale, and why does Peirce bring it up?

The doubling system — after every loss stake twice as much, and you must eventually come out ahead. Peirce grants that the player will probably gain at first, then points out that if he plays long enough a run against him will exhaust his fortune; an insurance company meets the same end. Without death that fate would come to every man; with death it must come to some man.

What does Peirce mean by saying logic is rooted in the social principle?

That the interests behind an inference must reach past the reasoner himself. A single case has no probability; the ratio appears only across an endless run that no individual lives to complete. So a man whose interests stop at his own fate has no warrant for the inferences he draws, because his run ends and the community's does not.

Why do faith, hope and charity turn up midway through a probability essay?

Because Peirce thinks a reasoner cannot do without them. Interest in an indefinite community, the hope that it will continue, and the willingness to sacrifice one's own fate to it are not piety added to logic; on his argument they are conditions of drawing a probable inference at all. He calls them three sentiments indispensable to logic.

Themes of the book

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

Probability Belongs to the Argument

A card pack, a whist hand or a patient has no probability of its own; the number measures the proportion of cases in which inferences of a given form carry truth with them.

Put that way, speaking of an event's probability without naming the condition under which it is supposed to happen says nothing at all, however universal the habit of so speaking. A friend's count of a hundred and sixty-five whist hands made the point against the calculation: real packs carry traces of the last deal that no formula allowed for. And because a ratio settles only across thousands of trials, the single case considered by itself has no probability whatever.

probability
statistics
chance
averages
conditional-probability
multiplication-rule
independence
gambling
measurement
inference
mathematical reasoning

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Why Logic Needs More Than One Life

Every run of trials is cut short by death, so a reasoner who cares only about his own fate can never justify the inference he is drawing. Peirce widens the interests rather than the mathematics.

The doubling system that some believe infallible does fail given time enough, and the insurance office that cannot be ruined is ruined; finitude is the condition under which every probable inference is actually made, not a detail to be idealised away. The way out is an ethical premiss placed inside logic itself: the interests behind an inference must reach past the reasoner to the community, beyond this geological epoch and beyond all bounds.

ethics
sociality
community
hope
faith
risk
decision theory
continuity

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Within this work

passages held: 20
distinct concepts: 51
by passages held, corpus-wide: #776

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: “logic” and “probability”.

Concept co-occurrence, strongest first 3 concepts, joined by 3 pairings. 27 pairings reach beyond these concepts and are not drawn.
Concept	Paired concept	Shared passages
logic	probability	8
probability	statistics	4
logic	statistics	3

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
The paper that ends the series. Its central idea — guessing, treated as an inference with rules of its own rather than as a lack of them — is what Peirce kept working at for the rest of his life.
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 you are here 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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