Deduction

Deduction is the sort of rationality that is the central concern of traditional logic. It involves deductively valid arguments, or arguments in which, if the premises are true, then the conclusion must also be true. In a deductively valid argument, it is impossible for the premises to be true and the conclusion false. Some standard examples are:

(1) All human beings are mortal; all women are human beings; therefore, all women are mortal.

(2) Some angels are archangels; all archangels are divine; therefore, some angels are divine.

These simple arguments (deductive arguments can be infinitely more complex) illustrate two important features of deductive reasoning: it need not be about real things, and it can be applied to any subject matter whatsoever—i.e., it is universal.

One of the significant achievements of philosophy in the 20th century was the development of rigorous ways of characterizing such arguments in terms of the logical form of the sentences they comprise. Techniques of formal logic (also called symbolic logic) were developed for a very large class of arguments involving words such as and, or, not, some, all, and, in modal logic, possibly (or possible) and necessarily (or necessary). (See below The computational account of rationality.)

Although deduction marks a kind of ideal of reason, in which the truth of the conclusion is absolutely guaranteed by the truth of the premises, people’s lives depend upon making do with much less. There are two forms of such nondeductive reasoning: induction and abduction.

Induction

Induction consists essentially of statistical reasoning, in which the truth of the premises makes the conclusion likely to be true, even though it could still be false. For example, from the fact that every death cap mushroom (Amanita phalloides) anybody has ever sampled has been poisonous, it would be reasonable to conclude that all death cap mushrooms are poisonous, even though it is logically possible that there is one such mushroom that is not poisonous. Such inferences are indispensable, given that it is seldom possible to sample all the members of a given class of things. In a good statistical inference, one takes a sufficiently large and representative sample. The field of formal statistics explores myriad refinements of arguments of this sort.

Abduction

Another sort of nondeductive rationality that is indispensable to at least much of the higher intelligence displayed by human beings is reasoning to a conclusion that essentially contains terms not included in the premises. This typically occurs when someone gets a good idea about how to explain some data in terms of a hypothesis that mentions phenomena that have not been observed in the data itself. A familiar example is that of the detective who infers the identity of a certain criminal from the evidence at the scene of the crime. Sherlock Holmes erroneously calls such reasoning “deduction”; it is more properly called abduction, or “inference to the best explanation.” Abduction is also typically exercised by juries when they decide whether the prosecution has established the guilt of the defendant “beyond a reasonable doubt.” Most spectacularly, it is the form of reasoning that seems to be involved in the great leaps of imagination that have taken place in the history of scientific thought, as when Isaac Newton (1642–1727) proposed the theory of universal gravitation as an explanation of the motions of planets, projectiles, and tides.

Practical reason

All the forms of rationality so far considered involve proceeding from one belief to another. But sometimes people proceed from belief to action. Here desire as well as belief is relevant, since successful rational action is action that satisfies one’s desires. Suppose, for example, that a person desires to have cheese for dinner and believes that cheese can be had from the shop down the street. Other things being equal—that is, he has no other more pressing desires and no beliefs about some awful risk he would take by going to the shop—the “rational” thing for him to do would be to go to the shop and buy some cheese. Indeed, if this desire and this belief were offered as the “reason” why the person went to the shop and bought some cheese, one would consider it a satisfactory explanation of his behaviour.

Although this example is trivial, it illustrates a form of reasoning that is appealed to in the explanation of countless actions people perform every day. Much of life is, of course, more complex than this, in part because one often has to choose between competing preferences and estimate how likely it is that one can actually satisfy them in the circumstances one takes oneself to be in. Often one must resort to what has come to be called cost-benefit analysis—trying to do that which is most likely to secure what one prefers most overall with as little cost as possible. At any rate, engaging in cost-benefit analysis seems to be one way of behaving rationally. The ways in which people can be practically rational are the subject of formal decision theory, which was developed in considerable detail in the 20th century in psychology and in other social sciences, especially economics.

None of the foregoing should be taken to suggest that people are always rational. Many people report being “weak-willed,” failing to perform what they deem to be the best or most rational act, as when they fail to diet despite their better judgment. In the case of many other actions, however, rationality seems to be simply irrelevant: jumping up and down in glee, kicking a machine that fails to work, or merely tapping one’s fingers impatiently are actions that do not seem to be performed for any particular reason. The claim here is only that rationality forms one important basis for thinking that something has genuine mental states.