KNOWLEDGE AND MODALITY

The prominence of the modalities (i.e., necessity and contingency) in epistemological discussions is due to the influence of Immanuel Kant (1965), who maintained that:

1. All knowledge of necessary propositions is a priori; and
2. All propositions known a priori are necessary.

Saul Kripke (1971, 1980) renewed interest in Kant's account of the relationship between the a priori and the necessary by arguing that some necessary propositions are known a posteriori and some contingent propositions are known a priori. A cogent assessment of the controversy requires some preliminary clarification.

The distinction between necessary and contingent propositions is metaphysical. A necessarily true (false) proposition is one that is true (false) and cannot be false (true). The distinction between a priori and a posteriori knowledge is epistemic. S knows a priori that p just in case: (a) S knows that p; and (b) S's justification for believing that p does not depend on experience. Condition (b) is controversial. On the traditional reading, (b) is equivalent to (c): S's belief that p is nonexperientially justified. Hilary Putnam (1983) and Philip Kitcher (1983), however, argue that (b) is equivalent to (d): S's belief that p is nonexperientially justified and cannot be defeated by experience. Albert Casullo (2003) rejects the Putnam-Kitcher reading on the grounds that it yields an analysis of a priori knowledge that excludes the possibility that someone knows a posteriori a proposition that can be known a priori.

The expression "knowledge of necessary propositions" in (1) is ambiguous. The following definitions remove the ambiguity:

1. S knows the general modal status of p just in case S knows that p is a necessary proposition (i.e., either necessarily true or necessarily false) or S knows that p is a contingent proposition (i.e., either contingently true or contingently false);
2. S knows the truth value of p just in case S knows that p is true or S knows that p is false (assuming truth is always bivalent);
3. S knows the specific modal status of p just in case S knows that p is necessarily true or S knows that p is necessarily false or S knows that p is contingently true or S knows that p is contingently false. (A) and (B) are logically independent. One can know that Goldbach's Conjecture is a necessary proposition but not know whether it is true or false. Alternatively, one can know that some mathematical proposition is true but not know whether it is a necessary proposition or a contingent proposition. (C), however, is not independent of (A) and (B). One cannot know the specific modal status of a proposition unless one knows both its general modal status and its truth value.

(1) is crucial for Kant, because it is the leading premise of his only argument in support of the existence of a priori knowledge:

• (1) All knowledge of necessary propositions is a priori.
• (3) Mathematical propositions, such as that 7 + 5 = 12, are necessary.
• (4) Therefore, knowledge of mathematical propositions, such as that 7 + 5 = 12, is a priori.

(1), however, is ambiguous. There are two ways of reading it:

• (IT) All knowledge of the truth value of necessary propositions is a priori, or
• (IG) All knowledge of the general modal status of necessary propositions is a priori.

The argument is valid only if (1) is read as (1T). Kant, however, supports (1) with the observation that although experience teaches that something is so and so, it does not teach us that it cannot be otherwise. Taken at face value, this observation states that experience teaches us that a proposition is true and that experience does not teach us that it is necessary. This supports (1G), not (1T).

Kripke rejects (1) by offering examples of necessary truths that are alleged to be known a posteriori. First, he maintains that if P is an identity statement between names, such as "Hesperus = Phosphorus," or a statement asserting that an object has an essential property, such as "This table is made of wood," then one knows a priori that:

• (5) If P then necessarily P.

Second, he argues that because one knows by empirical investigation that Hesperus = Phosphorus and that this table is made of wood, one knows a posteriori that:

• (6) P.

Kripke concludes that one knows by modus ponens that:

• (7) Necessarily P.

(7) is known a posteriori because it is based on (6), which is known a posteriori.

How do Kripke's examples bear on (1)? Once again, a distinction must be made between (1G) and (1T). Kripke's examples, if cogent, establish that (1T) is false: They establish that one knows a posteriori that some necessary propositions are true. They do not, however, establish that (1G) is false: They do not establish that one knows a posteriori that some necessary propositions are necessary. It may appear that Kripke's conclusion that one has a posteriori knowledge that necessarily P entails that (1G) is false. Here a distinction must be made between (1G) and:

• (IS) All knowledge of the specific modal status of necessary propositions is a priori.

Kripke's examples establish that (1S) is false: They establish that one knows a posteriori that some necessary propositions are necessarily true. Because knowledge of the specific modal status of a proposition is the conjunction of knowledge of its general modal status and knowledge of its truth value, it follows from the fact that one's knowledge of the truth value of P is a posteriori that one's knowledge of its specific modal status is also a posteriori. However, from the fact that one's knowledge of the specific modal status of P is a posteriori, it does not follow that one's knowledge of its general modal status is also a posteriori.

(1G) has not gone unchallenged. Kitcher (1983) argues that even if knowledge of the general modal status of propositions is justified by nonexperiential evidence, such as the results of abstract reasoning or thought experiments, it does not follow that such knowledge is a priori because the nonexperiential justification in question can be defeated by experience. Casullo (2003) rejects (1G) on the grounds that the Kantian contention that experience can provide knowledge of only the actual world overlooks the fact that much practical and scientific knowledge involves counterfactual conditionals, which provide information that goes beyond what is true of the actual world.

Kripke also argues that some contingent truths are known a priori. His examples are based on the observation that a definite description can be employed to fix the reference—as opposed to give the meaning—of a term. Consider someone who employs the definition description "the length of S at t₀ " to fix the reference of the expression "one meter." Kripke maintains that this person knows, without further empirical investigation, that S is one meter long at t₀ . Yet the statement is contingent because "one meter" rigidly designates the length that is in fact the length of S at t₀ but, under different conditions, S would have had a different length at t₀ . In reply, Alvin Plantinga (1974) and Keith Donnellan (1979) contend that, without empirical investigation, the reference fixer knows that the sentence "S is one meter long at t₀ " expresses a truth, though not the truth that it expresses. Gareth Evans (1979) disputes this contention.

Bibliography

Casullo, Albert. A Priori Justification. New York: Oxford University Press, 2003.

Donnellan, Keith S. "The Contingent A Priori and Rigid Designators." In Contemporary Perspectives on the Philosophy of Language, edited by P. French et al. Minneapolis: University of Minnesota Press, 1979.

Evans, Gareth. "Reference and Contingency." Monist 62 (1979): 161–189.

Kant, Immanuel. Critique of Pure Reason. Translated by Norman Kemp Smith. New York: St. Martin's Press, 1965.

Kitcher, Philip. The Nature of Mathematical Knowledge. New York: Oxford University Press, 1983.

Kripke, Saul. "Identity and Necessity." In Identity and Individuation, edited by M. K. Munitz. New York: New York University Press, 1971.

Kripke, Saul. Naming and Necessity. Cambridge, MA: Harvard University Press, 1980.

Plantinga, Alvin. The Nature of Necessity. Oxford: Oxford University Press, 1974.

Putnam, Hilary. "'Two Dogmas' Revisited." In Realism and Reason: Philosophical Papers. Vol. 3. Cambridge, U.K.: Cambridge University Press, 1983.

Albert Casullo (1996, 2005)