Teaching Theory of Knowledge
10. A Priori Knowledge
Since most of the issues involved in this module require a grasp of elementary symbolic logic, we recommend that an introductory logic course be required as a prerequisite to any course emphasizing these issues.
Literally construed, 'a prior' is an adverb which means 'in a manner which is independent of experience'. Thus one may be said to reason or know a priori. However, the term is also used adjectivally to describe a type of knowledge, that is, knowledge which is gained independently of sense experience. Although it is possible to conceive a number of non-sensible modes of knowledge (e.g., mystical insight, prescience), the module will be restricted to knowledge gained by reason, somehow independently of the information provided by the senses. The types of knowledge can be divided according to well-known means of classifying the kinds of propositions said to be known a priori. Some kinds of allegedly a priori knowledge, most notably mathematical knowledge, must also be given a proper place in the classification. Finally, the classification itself can be called into question.
Division of the field:
- Reason as a Source of Knowledge
- Types of Knowledge
- Necessary truths
- Analytic truths
- Propositions of logic
- Propositions true by virtue of meaning
- Framework principles
- Synthetic propositions
- Contingent truths
- A Special Case of A Priori Knowledge: Mathematics
Reason as a Source of Knowledge: Innate ideas. The linguistic theory of Noam Chomsky rekindled interest in whether humans have some kind of innate knowledge which could be called a priori. Historical links to Descartes were suggested by Chomsky himself.
Chomsky, N. "Cartesian Linguistics: Acquisition and Use of Language." In Stich, 89-106.Harman, G. "Psychological Aspects of the Theory of Syntax." In Stich, 165-80.
Hart, W. D. "Innate Ideas and A Priori Knowledge." In Stich, 107-110.
Mackie, J. L. 'The Possibility of Innate Knowledge." Proceedings of the Aristotelian Society 70 (1969-70), 181-96.
Nagel, T. "Linguistics and Epistemology." In Sidney Hook (ed.), Language and Philosophy. New York: New York University Press, 1979.
Stich, S. (ed.) Innate Ideas. Berkeley: University of California, 1975. Hereafter referred to as 'Stich'.
Stich, S. "Introduction." In Stich, 1-24.
Reason as a Source of Knowledge: Logical rules. Recent work on the psychology of inference has had a bearing on questions of our knowledge of the validity of patterns of deductive inference. The implications of this work for a priori knowledge are just beginning to be worked out.
Cherniak, C. "Computational Complexity and the Universal Acceptance of Logic." Journal of Philosophy 81 (1984), 739-58.Goldman, A. I. Episternology and Cognition. Cambridge, Mass.: Harvard University Press, 1986. See especially chapter 13, 278-304.
Johnson-Laird, P. Mental Models. Cambridge, Mass.: Harvard University Press. 1983.
Rips, L. "Cognitive Processes in Reasoning." Psychological Review 90 (1983). 38-71.
Types of Knowledge. There is not universal agreement regarding the categories of the a priori, a posteriori, synthetic, analytic, necessary and contingent. Each of the articles listed considers at least some of these distinctions.
Bradley, R. and Swartz, N. Possible Worlds. Indianapolis: Hackett. 1979. See especially chanters 3.4-3.6, 142-78.Kripke, S. "Naming and Necessity." In Davidson and Harman (eds.), Setnantics of Natural Languages. Dordrecht Reidel, 1972. 254-355.
McGinn, C. "A Priori and A Posteriori Knowledge." Proceedings of the Aristotelian Society 76 (1975-76), 195-208.
Necessary truths: Analytic propositions (propositions of logic). Logical propositions are the likeliest candidates for a priori knowledge. There are several theories about the acquisition of logical knowledge, including conventionalism, intuitionism, and platonism. The most significant challenge to the a priori status of logical truths has been the development of alternatives to the standard logic (first-order predicate logic). This raises questions about the possibility of denying such principles as the excluded middle and even non-contradiction.
Dummett, M. "The Philosophical Basis of Intuitionistic Logic." In Logic Colloquia '73. Rose, H. and Shepherdson, (eds.). Amsterdam, 1975.Pap, A. Semantics and Necessary Truth. New Haven: Yale 1958. See especially chanters 5, 6 and 7.
Putnam, H. Mathematics, Matter, and Method; Philosophical Papers, Vol. 1. Cambridge: Cambridge University Press, 1975.
Putnam, H. "There Is At Least One A Priori Truth." Erkenntnis 13 (1978), 153-70.
Quine, W. V. Philosophy of Logic. Englewood Cliffs, N.J.: Prentice-Hall, 1970. See especially chapters 4 and 6.
Quine, W. V. "Carnap on Logical Truth." In Schilpp (ed.), The Philosophy of Rudolf Carnap. La Salle: Open Court, 1963. See "A Philosopher Looks at Quantum Mechanics" (130-58) and "The Logic of Quantum Mechanics" (174-97).
Necessary truths: Analytic truths (propositions true by virtue of meaning). Quine cast a pall over the prospects for determining identity conditions for meanings. His criticisms of one of the best-known suggestions, Carnap's 'meaning postulates', is indicative of the problems for this species of allegedly analytic truths.
Carnap, R. "Meaning Postulates." In Carnap, Meaning and Necessity. (2nd ed.). Chicago: University of Chicago, 1956.Grice, P. and Strawson, P. "In Defense of a Dogma." The Philosophical Review 65 (1956), 2, 141-58.
Pap, A. Semantics and Necessary Truth. See especially chapters 8, 9 and 10.
Quine, W. V. "Truth by Convention."
Quine, W. V. "Two Dogmas of Empiricism." In Quine, From a Logical Point of View. (2nd ed.). Cambridge, Mass.: Harvard University Press. 1961.
White, Morton. "The Analytic and the Synthetic: An Untenable Dualism." In his Essays and Reviews in Philosophy and Intellectual History, New York: Oxford University Press, 1973, 121-37. Also reprinted in Semantics and the Philosophy of Language, L. Linsky, (ed.), 1952, and in Analyticity: Selected Readings, J. F. Harris, Jr., and R. H. Severens, (eds.), 1970.
Framework principles. The question of the epistemic status of the principles of our 'conceptual framework' is a very general form of issue surrounding a priori knowledge. It is the ground on which Kant took his stand in defense of the a priori. However, contemporary philosophy has been pessimistic about our ability to isolate such principles and about their epistemic status even if they are found.
Carnap, R. "Empiricism, Semantics and Ontology." In Carnap, Meaning and Necessity.Davidson, D. "On the Very Idea of a Conceptual Scheme." In Davidson, Inquiries into Truth and Interpretation. Oxford: Oxford University Press, 1984.
Putnam, H. "The Analytic and the Synthetic." In Feigl, H. and Maxwell, G. (eds.), Minnesota Studies in the Philosophy of Science. Minneapolis: University of Minnesota Press, 358-97. Reprinted in Putnam's Mind, Language, and Reality: Philosophical Papers, vol. 2, Cambridge: Cambridge University Press, 1975, 33-69.
Quine, W. V. "Two Dogmas of Empiricism". In Quine, From a Logical Point of View. (2nd ed.) Cambridge, Mass.: Harvard University Press, 1961.
Quine,W.V. Word and Object. Cambridge,Mass.: MIT, 1960.
Synthetic propositions. In the second half of the twentieth century, attention to the issue of synthetic a priori propositions has been confined largely to Kant exegesis. Through the late 40's and 50's there has been a controversy over whether certain propositions concerning colors are synthetic a priori truths, .e.g., can something be red and green all over?
Chisholm, R. Theory of Knowledge. (2nd ed.). Englewood Cliffs: Prentice-Hall, 1977. See especially chapter 3, 34-61.Contingent truths. Until the beginning of the 70's it was assumed almost universally that all a priori propositions are necessarily true. This thesis was challenged by Kripke, who claimed that there is a class of contingent a priori propositions, e.g., 'I exist'.
Donnellan, K. "The Contingent A Priori and Rigid Designators." Midwest Studies in Philosophy 2 (1977), 12-27.Kripke, S. "Naming and Necessity." In Davidson and Harman (eds.), Semantics of Natural Languages. Dordrecht: Reidel, 1972. 254-355.
A Special Case of A Priori Knowledge: Mathematics (19th century). Throughout the 19th century, it seemed clear that mathematical knowledge is a priori, and according to Kant, synthetic a priori. A lone holdout was J. S. Mill, who believed that mathematical truths are very general empirical propositions. The classical position that all mathematical knowledge is a priori and that arithmetical knowledge, in particular, is so, was laid down by Frege.
Frege, G. Foundations of Arithmetic. J. L. Austin. (tr.). Oxford: Blackwell, 1950. See especially preface, introduction, chapter 1.Kant, I. Prolegomena to any Future Metaphysics. L. W. Beck. (ed.). Indianapolis: Bobbs-Merrill, 1950. See Part One.
Kant, I. Critique of Pure Reason. N. K. Smith. (tr.). London: Macmillan Press, 1933. See the Introduction, Transcendental Aesthetic, Anticipations of Perception.
Mill, J. S. Systems of Logic. London: Longmans, 1843. See Book II: Of Reasoning.
Twentieth Century. Often it was suggested that a priori mathematical knowledge turned on the formal conventions underlying mathematical systems (von Neumann, Curry). This view, whether it was called formalism or conventionalism, received a serious setback as a result of Godel's discoveries. It was also criticized on more general philosophical terms (Quine). A priorism survived as an epistemology of mathematics by associating with a Platonistic or a constructivist metaphysics (Godel, Dummett).
Curry, H. "Remarks on the Definition and Nature of Mathematics." In Benacerraf, P. and Putnam, H. (eds.), Philosophy of Mathematics. Englewood Cliffs: Prentice-Hall, 1964. Hereafter cited as 'Benacerraf and Putnam'Dummett, M. "The Philosophical Basis of Intuitionistic Logic." In Rose, H. and Shepherdson (eds.), Logic Colloquia '73 Amsterdam, 1975.
Godel, K. "What is Cantor's Continuum Problem?" in Benacerraf and Putnam.
von Neumann, J. "Formalism" in Benacerraf and Putnam.
Quine, W. V. "Truth By Convention" in Benacerraf and Putnam.
Quine, W. V. "Two Dogmas of Empiricism" in Benacerraf and Putnam
Current Views. At present, a number of philosophers are trying to defend the a priori character of mathematical knowledge (Steiner, Bealer, Padlock, Rosenkrantz). On the other hand, a growing minority of philosophers is challenging the view that mathematical knowledge is a priori (Lakatos, Putnam, Tymoczko, Kitcher).
Bealer, George. Content and Quality. Oxford: Clarendon Press, 1982.Kitcher, P. The Nature of Mathematical Knowledge. New York: Oxford, 1984.
Lakatos, I. "A Renaissance of Empiricism in Recent Philosophy of Mathematics." In Tymoczko.
Lakatos, I. "What Does a Proof Prove?" In Tymoczko.
Pollock, J. Knowledge and Justification. Princeton: Princeton University Press, 1974. See especially chapter 10.
Putnam, H. "Mathematical Truth." In Tymozzko.
Rosenkrantz, G. "The Nature of Geometry." American Philosophical Quarterly 18, 2 (1981), 101-110.
Steiner, M. Mathematical Knowledge. Ithaca, N.Y.: Cornell University Press, 1975.
Tymoczko, T. New Directions in the Philosophy of Mathematics. Boston: Birkhauser, 1986. Hereafter cited as 'Tymoczko'.
Tymoczko, T. "The 4-Color Problem and its Philosophical Significance." In Tymoczko.
Cross References For a discussion of some of the classical positions in the controversy over a priori knowledge, see also "A Priori/A Posteriori Knowledge" in the "Historical Sources" section.
For an example of a course that considers whether recent results in linguistics support some version of a priori knowledge, see also "Language and Knowledge" in the "Bridge Courses" section.