Über die Autorinnen und Autoren

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

THE GAME OF PROBABILITY

STANFORD UNIVERSITY PRESS

Contents

Introduction..............................................................................................................................................................11 Theology and the Law: Dice in the Air...................................................................................................................................152 Numbers and Calculation in Context: The Game of Decision—Pascal...................................................................................................373 Writing the Calculation of Chances: Justice and Fair Game—Christiaan Huygens......................................................................................734 Probability, a Postscript to the Theory of Chance: Logic and Contractual Law—Arnauld, Leibniz, Pufendorf..........................................................975 Probability Applied: Ancient Topoi and the Theory of Games of Chance—Jacob Bernoulli..............................................................................1186 Continued Proclamations: The Law of logica probabilium—Leibniz....................................................................................................1477 Defoe's Robinson Crusoe, or, The Improbability of Survival..............................................................................................................1728 Numbers and Tables in Narration: Jurists and Clergymen and Their Bureaucratic Hobbies...................................................................................1959 Novels and Tables: Defoe's A Journal of the Plague Year and Schnabel's Die Insel Felsenburg.............................................................................22010 The Theory of Probability and the Form of the Novel: Daniel Bernoulli on Utility Value, the Anthropology of Risk, and Gellert's Epistolary Fiction.....................24811 "Improbable Probability": The Theory of the Novel and Its Trope—Fielding's Tom Jones and Wieland's Agathon.......................................................27312 The Appearance of Truth: Logic, Aesthetics, and Experimentation—Lambert..........................................................................................30513 "Probable" or "Plausible": Mathematical Formula Versus Philosophical Discourse—Kant..............................................................................33814 Kleist's "Improbable Veracities," or, A Romantic Ending................................................................................................................369Conclusion................................................................................................................................................................391Notes.....................................................................................................................................................................399Bibliography..............................................................................................................................................................465

Chapter One

DICE IN THE AIR

A Prehistory of Probability: How Probability and Verisimilitude Came to Be Linked with Games of Chance

Jacob Bernoulli's Ars conjectandi (The Art of Conjecturing), which founded modern probability theory with its 1713 publication, includes a first and brief history of mathematical probability. According to the Basel mathematician, those who invented games of chance had, unbeknownst to themselves, already invented ways to measure probability. Bernoulli's point is that the idea of measuring probability seems implied in the invention of games of chance. If we look more closely, however, we see two different phases in his brief account. In a first step, Bernoulli's inventors prepare contrivances to engineer equally likely chance events (e.g., the hardware of regular-sided cubes—dice). In a second step, they come up with symbols for determining winners and losers (e.g., the software of the numbers carved on the cubes' sides). The two phases thus encompass the construction of strict contingency: first, the chance event; second, the additional strategic context in which chances appear as probabilities. How are the two phases connected to each other? In his redefinition of probability theory in the first decades of the twentieth century, Richard von Mises (1883–1953) developed the notion of "dice in the air" to illustrate how, in order to be subject to measurement, probability has to be radically removed from any everyday intuition of probability. The binary logic of events that are equally likely to happen or not to happen exists only in the "collectivity" of repeatable throws, and hence as if "in the air." For Bernoulli, however, the invention of dice is an ingenious act that detects and implements strict binary contingency and its measure within our everyday world. The second step, the strategic weighing of probability, seems to follow immediately from the first step of creating dice. The fact that the mathematical formula for probability had been discovered by inventing dice to produce chance events remained unnoticed, or at least unmentioned. Beyond the triumph of cracking pure chance—of being able to calibrate and measure probabilities—Bernoulli and his contemporaries do not seem even to consider how the everyday, the literary, or the logical meaning of the probable might weigh in on the use of dice as a measuring device.

Today's histories of probability have not solved the problem. In what sense can something that has no relation to anything beyond itself enter into a historical account—how can "dice in the air" emerge in the course of a story to be told? This book suggests that this very problem gives the literary history of probability—the history of probability and verisimilitude in rhetoric and poetics—a chance to intervene in the history of epistemological probability. Or to put it even more boldly: because of this problem, a literary history of probability has to supplement the history of probability in science. How did probability come to be associated with mathematical gaming theory? This inquiry, which is fundamental for understanding the emergence of probability, will lead back to probability in logic, rhetoric, and literary works. But only when an answer to this question can be provided does it make sense to reverse it: how did the emergence of mathematical probability influence the verisimilitude of the poets? This question then leads directly to the center of the traditional concept of poetry and its transformation into an understanding of literature as concerned with reality, an understanding that came about with the modern novel. In order to look into the effects of science in literary works, we must be able to account for the use of the poetological and logical category of probability within the history of mathematics. The two investigations work to complement each other, and differ only in respect to where we choose to begin the inquiry. They are both part of a history of writing that encompasses numbers and letters, the space of alphanumeric notation.

A cursory view of more recent histories of probability reveals the urgency of an investigation that traces the relationship between gambling calculations and their interpretation as a theory of probability and verisimilitude. In his reconstruction of the history of mathematics, Ivo Schneider clearly distinguishes...