A Priori Knowledge
Some kinds of knowledge are not readily understandable in terms of adequate information if for no other reason than they seem not to be linked with specific truths. Knowledge of people, places, and things and knowledge how are examples.
S knows Jimmy Carter from the time she spent working in the White House. She lived for a year in an apartment near the Eiffel Tower and in that year came to know the seventh arrondissement of Paris. She regularly sees her boss in the firm’s parking lot and hence knows his car. In addition, she knows how to ski, how to use the London underground, and how to rewire an electrical socket.
For S to have such knowledge, she no doubt needs to believe various truths, but there is no single, particular truth she has to believe. By contrast, for S to know that Jimmy Carter was the thirty-ninth president of the United States or that Paris is the capital of France, the truth that has to be believed is straightaway evident.
There may be ways of arguing that despite initial appearances, knowledge how and knowledge of people, places, and things are always identified with specific true beliefs, and at bottom are even species of knowledge that. It requires ingenious arguments to defend such views, however,1 whereas with factual knowledge, the connection with at least one believed truth is immediate and obvious. S knows that P only if she believes P and P is true.
A priori knowledge is sometimes thought to be a species of knowledge requiring separate treatment, but unlike knowledge how and knowledge of people, places, and things, when S knows something a priori, there is a readily identifiable truth she believes. She knows a priori that 2 + 3 = 5 only if she has a true belief that 2 + 3 = 5; she knows a priori that every square is a rectangle only if she has a true belief that every square is a rectangle; and so on. There is thus a foothold for understanding a priori knowledge in terms of adequate information.
The a priori is to be distinguished from the necessary. A proposition’s being known a priori does not ensure that it is necessary, nor does a proposition’s being necessary ensure that it can be known a priori. Nevertheless, the paradigmatic examples of a priori knowledge are of necessary truths, for example, truths of arithmetic, truths of logic, and conceptual truths.
As with contingent truths, it is possible for S to believe a necessary truth but not know it, and the explanation is also the same, namely, there are important truths of which she is unaware. With necessary truths as with contingent ones, there are inevitably gaps in S’s understanding. The relevant question is whether the gaps are important enough to keep her from knowing.
Consider the theorem that the area inside a circle is equal to that of a right triangle whose base is equal to the circumference of the circle and whose height is equal to its radius. Suppose S believes this theorem. Although her belief is true, we may be reluctant to grant that she knows the theorem if she is not aware that the circumference of a circle is 2πr, or that the formula for calculating the enclosed area of a circle is πr2. There is too much important neighboring information she lacks.
By contrast, with the simplest of necessary truths, such as 2 + 3 = 5, little may be required for knowledge beyond belief. Insofar as S doesn’t believe the truths most immediately in the neighborhood, for example, the truth that 5 – 3 = 2, it becomes doubtful whether she really understands and hence really believes the proposition that 2 + 3 = 5.2 On the other hand, related but more distant truths—for example, many of the theorems of number theory—don’t seem critical. S can be unaware of them and yet still seem to have enough information to know that 2 + 3 = 5. Stories involving beliefs about very simple necessary truths thus tend to be stories of narrow knowledge, with the truth that is the center of attention overshadowing associated truths.