Cognition and Chance: The Psychology of Probabilistic Reasoning

By Raymond S. Nickerson | Go to book overview

CHAPTER
12

Concluding Comments

G ambling, the drawing of lots, and other activities that today we associate with chance go back to antiquity. Whether the ancients had a concept of chance that was very close to what is generally meant by chance today is questionable. The use of chance devices for purposes of divination suggests that users, at least sometimes, believed the outcomes to be revealing of otherwise hidden truths: Was the accused party guilty or not? Would the king's army prevail in battle?…

As a mathematical discipline, probability theory is a relative late-comer; historians of mathematics usually mark its beginning in the middle of the 17th century, with the work of Blaise Pascal, Pierre de Fremat, and some of their contemporaries. It was axiomatized only early in the 20th century as a consequence of the work, primarily, of Andrei Kolmogorov. Today well-formed probability problems generally can be solved straightforwardly with the application of the probability calculus, as laid out, for example, by William Feller (1957, 1966). The usefulness of probability theory has been established beyond doubt in numerous contexts and its impact on the sciences, especially during the 20th century, has been profound.

Despite these facts, the philosophical question of what probability and closely related entities like chance and randomness really are remains a matter of debate. All these terms have been given a variety of connotations, so being explicit about what is intended in specific contexts can help avoid confusion and misunderstanding. Whatever chance is, it is not the antithesis of lawfulness, as the predictability of chance events in the aggregate attests. Probability

-436-

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Cognition and Chance: The Psychology of Probabilistic Reasoning
Table of contents

Table of contents

  • Title Page *
  • Contents vii
  • Preface ix
  • Chapter 1 - Probability and Chance 1
  • Chapter 2 - Randomness 54
  • Chapter 3 - Coincidences 82
  • Chapter 4 - Inverse Probability and the Reverend Tnomas Bayes 109
  • Chapter 5 - Some Instructive Problems 143
  • Chapter 6 - Some Probability Paradoxes Ana Dilemmas 181
  • Chapter 7 - Statistics 232
  • Chapter 8 - Estimation Ana Prediction 283
  • Chapter 9 - Perception of Covariation Ana Contingency 332
  • Chapter 10 - Choice Under Uncertainty 355
  • Chapter 11 - People as Intuitive Probabilists 398
  • Chapter 12 - Concluding Comments 436
  • References 439
  • Author Index 489
  • Subject Index 505
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