Epistemology has a second, justificatory, or normative, function. Philosophers concerned with that function ask themselves what kinds of belief (if any) can be rationally justified. The question has normative import since it asks, in effect, what one ought ideally to believe. (In that respect, epistemology parallels ethics, which asks normative questions about how one ought ideally to act.) The normative approach quickly takes one into the central domains of epistemology, raising questions such as: “Is knowledge identical with justified true belief?,” “Is the difference between knowledge and belief merely a matter of probability?,” and “What is justification?” Knowledge and certainty
Philosophers have disagreed sharply about the complex relationship between the concepts of knowledge and certainty. Are they the same? If not, how do they differ? Is it possible for someone to know that p without being certain that p, or to be certain that p without knowing that p? Is it possible for p to be certain without being known by someone, or to be known by someone without being certain?
In his 1941 paper “Certainty,” Moore observed that the word certain is commonly used in four main types of idiom: “I feel certain that,” “I am certain that,” “I know for certain that,” and “It is certain that.” He pointed out that there is at least one use of “I know for certain that p” and “It is certain that p” on which neither of those sentences can be true unless p is true. A sentence such as “I knew for certain that he would come, but he didn’t,” for example, is self-contradictory, whereas “I felt certain he would come, but he didn’t” is not. On the basis of such considerations, Moore contended that “a thing can’t be certain unless it is known.” It is that fact that distinguishes the concepts of certainty and truth: “A thing that nobody knows may quite well be true but cannot possibly be certain.” Moore concluded that a necessary condition for the truth of “It is certain that p” is that somebody should know that p. Moore is therefore among the philosophers who answer in the negative the question of whether it is possible for p to be certain without being known.
Moore also argued that to say “A knows that p is true” cannot be a sufficient condition for “It is certain that p.” If it were, it would follow that in any case in which at least one person did know that p is true, it would always be false for anyone to say “It is not certain that p,” but clearly this is not so. If one says that it is not certain that Smith is still alive, one is not thereby committing to the statement that nobody knows that Smith is still alive. Moore is thus among the philosophers who would answer in the affirmative the question of whether it is possible for p to be known without being certain. Other philosophers have disagreed, arguing that if a person’s knowledge that p is occurrent rather than merely dispositional, it implies certainty that p.
The most radical position on such matters was the one taken by Wittgenstein in On Certainty. Wittgenstein held that knowledge is radically different from certitude and that neither concept entails the other. It is thus possible to be in a state of knowledge without being certain and to be certain without having knowledge. For him, certainty is to be identified not with apprehension, or “seeing,” but with a kind of acting. A proposition is certain, in other words, when its truth (and the truth of many related propositions) is presupposed in the various social activities of a community. As he said, “Giving grounds, justifying the evidence comes to an end—but the end is not certain propositions striking us immediately as true—i.e., it is not a kind of seeing on our part; it is our acting which lies at the bottom of the language game.” The origins of knowledge
Philosophers wish to know not only what knowledge is but also how it arises. That desire is motivated in part by the assumption that an investigation into the origins of knowledge can shed light on its nature. Accordingly, such investigations have been one of the major themes of epistemology from the time of the ancient Greeks to the present. Plato’s Republic contains one of the earliest systematic arguments to show that sense experience cannot be a source of knowledge. The argument begins with the assertion that ordinary persons have a clear grasp of certain concepts—e.g., the concept of equality. In other words, people know what it means to say that a and b are equal, no matter what a and b are. But where does such knowledge come from? Consider the claim that two pieces of wood are of equal length. A close visual inspection would show them to differ slightly, and the more detailed the inspection, the more disparity one would notice. It follows that visual experience cannot be the source of the concept of equality. Plato applied such reasoning to all five senses and concluded that the corresponding knowledge cannot originate in sense experience. As in the Meno, Plato concluded that such knowledge is “recollected” by the soul from an earlier existence.
It is highly significant that Plato should use mathematical (specifically, geometrical) examples to show that knowledge does not originate in sense experience; indeed, it is a sign of his perspicacity. As the subsequent history of philosophy reveals, mathematics provides the strongest case for Plato’s view. Mathematical entities—e.g., perfect triangles, disembodied surfaces and edges, lines without thickness, and extensionless points—are abstractions, none of which exists in the physical world apprehended by the senses. Knowledge of such entities, it is argued, must therefore come from some other source. Innate and acquired knowledge
The problem of the origins of knowledge has engendered two historically important kinds of debate. One of them concerns the question of whether knowledge is innate—i.e., present in the mind, in some sense, from birth—or acquired through experience. The matter has been important not only in philosophy but also, since the mid-20th century, in linguistics and psychology. The American linguist Noam Chomsky, for example, argued that the ability of young (developmentally normal) children to acquire any human language on the basis of invariably incomplete and even incorrect data is proof of the existence of innate linguistic structures. In contrast, the experimental psychologist B.F. Skinner (1904–90), a leading figure in the movement known as behaviourism, tried to show that all knowledge, including linguistic knowledge, is the product of learning through environmental conditioning by means of processes of reinforcement and reward. There also have been a range of “compromise” theories, which claim that humans have both innate and acquired knowledge. Rationalism and empiricism