People have discovered many different ways to reduce the likelihood of making an error in reasoning. One way is to obey the rules of formal logic—rules for reasoning that can be described in purely abstract terms without making any contact at all with real-world facts. If the structure of your argument can be mapped directly onto one of the valid forms of argument that logic specifies, you’re guaranteed a deductively valid conclusion. Whether your conclusion is true is a different matter entirely and depends on the truth of your premises—the statements that precede your conclusion. Formal logic is a type of deductive reasoning—“top-down” argument forms that produce conclusions that follow necessarily from the premises on which they are based.
Two kinds of formal logic have received a great deal of attention historically. The oldest is the syllogism. Syllogisms are used for some kinds of categorical reasoning. For example: All A are B, X is an A, therefore X is a B. (Most famously: All men are mortal, Socrates is a man, therefore Socrates is mortal.) Syllogisms have been around for at least twenty-six hundred years.
Formal logic also includes propositional logic, which is somewhat more recent, having first been treated seriously by fourth-century B.C. Greek Stoic philosophers. This kind of logic tells us how to reach valid conclusions from premises, such as with the logic of the conditional. For example: If P is the case, then Q is the case. P is the case, therefore Q is the case. (If it snows, the schools will be closed. It snowed. Therefore the schools will be closed.) P is a condition requiring Q, or, differently put, P is a sufficient condition for Q.
In contrast to deductive logic, inductive reasoning is a “bottom-up” type of reasoning. Observations are collected that suggest or support some conclusion. One type of inductive reasoning consists of observing facts and reaching a general conclusion about facts of their particular kind. This book is full of different types of inductive reasoning. The scientific method nearly always involves—in fact often is completely dependent on—inductive reasoning of one kind or another. All of the types of inductive reasoning in this book are inductively valid, but their conclusions are not deductively valid, merely probable. On the basis of observation and calculation we induce that the mean of the population of some events is X plus or minus Y standard deviations. Or we induce from observing the results of our experiment that A causes B, since we observe that every time A is the case B is also the case; when A is not the case, B is not the case. It’s more probable that A causes B if these things are true than if we’re missing those observations, but it’s not certain that A causes B. For example, something associated with A might be causing B. Inductive conclusions aren’t guaranteed to be true even if all the observations they are based on are true, there are many of them, and there are no exceptions. The generalization “all swans are white” is inductively valid but, as it turns out, not true.
Deductive and inductive reasoning schemas essentially regulate inferences. They tell us what kinds of inferences are valid and what kinds are invalid. A very different kind of system of reasoning, also developed about twenty-six hundred years ago in Greece, and developed at the same time in India, is called dialectical reasoning. This form of reasoning doesn’t so much regulate reasoning as suggest ways to solve problems. Dialectical reasoning includes the Socratic dialogue, which is essentially a conversation or debate between two people trying to reach the truth by stimulating critical thinking, clarifying ideas, and discovering contradictions that may prompt the discussants to develop views that are more coherent and more likely to be correct or useful.
Eighteenth- and nineteenth-century versions of dialectical reasoning, owing primarily to the philosophers Hegel, Kant, and Fichte, center on the process of “thesis” followed by “antithesis” followed by “synthesis”—a proposition followed by a potential contradiction of that proposition, followed by a synthesis that resolves any contradiction.
Other types of reasoning that have been labeled “dialectical” were developed in China, also beginning around twenty-six hundred years ago. Chinese dialectical reasoning deals with a much broader range of issues than Western or Indian versions of dialectical reasoning. The Chinese version suggests ways of dealing with contradiction, conflict, change, and uncertainty. For example, whereas the Hegelian dialectic is “aggressive” in the face of contradiction in the sense that it seeks to obliterate contradictions between propositions in favor of some new proposition, Chinese dialectical reasoning often seeks to find ways in which the conflicting propositions can both be true.
Dialectical reasoning isn’t formal or deductive and usually doesn’t deal in abstractions. It’s concerned with reaching true and useful conclusions rather than valid conclusions. In fact, conclusions based on dialectical reasoning can actually be opposed to those based on formal logic. Relatively recently, psychologists both in the East and in the West have begun to study dialectical reasoning, developing systematic descriptions of prior formulations and proposing new dialectical principles.
Chapter 13 presents two common types of formal reasoning, and Chapter 14 presents an introduction to some forms of dialectical reasoning that I find most interesting and helpful. All of the scientific tools discussed in this book depend to some degree on formal logic. Many of the other tools appeal to dialectical precepts.