The Language of Argument

2 3 9

11

Chances

The kinds of arguments discussed in the preceding three chapters are inductive, so they

need not meet the deductive standard of validity. They are, instead, intended to meet the

inductive standard of strength. Whereas deductive validity hinges on what is possible,

inductive strength hinges on what is probable. Roughly, an argument is inductively

strong to the extent that its premises make its conclusion more likely or probable.

Hence, just as we can get a better theoretical understanding of deductive validity by

studying formal logic, as we did in Chapters 6 and 7, so we can get a better theoretical

understanding of inductive strength by studying probability, as we will do in this

chapter. To complete our survey of inductive arguments, this chapter offers an elemen-

tary discussion of probability. It begins by illustrating several common mistakes about

probability. To help avoid these fallacies, we need to approach probability more carefully,

so formal laws of probability are presented along with Bayes’s theorem.

Some Fallacies of Probability

Probability is pervasive. We all assume or make probability judgments through-

out our lives. We do so whenever we form a belief about which we are not

certain, as in all of the kinds of inductive arguments studied in Chapters 8–10.

Such arguments do not pretend to reach their conclusions with certainty, even

if their premises are true. They merely try to show that a conclusion is likely

or probable. Judgments about probability are, thus, assumed in assessing such

arguments and beliefs. Probability also plays a crucial role in our most impor-

tant decisions. Mistakes about probability can then lead to disasters. Doctors

lose patients’ lives, stockbrokers lose clients’ money, and coaches lose games

because they overestimate or underestimate probabilities. Such mistakes are

common and fall into several regular patterns. It is useful to understand these

fallacies, so that we can learn to avoid them.

The Gambler’s Fallacy

Casinos thrive partly because so many gamblers misunderstand probability.

One mistake is so common that it has been dubbed the gambler’s fallacy. When

people have a run of bad luck, they often increase their bets because they

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