Kant's version and the a priori/a posteriori distinction
In the Introduction to the Critique of Pure Reason, Kant combines his distinction between analytic and synthetic propositions with another distinction, the distinction between a priori and a posteriori propositions. He defines these terms as follows:
a priori proposition: a proposition whose justification does not rely upon experience
a posteriori proposition: a proposition whose justification does rely upon experience
Examples of a priori propositions include:
"All bachelors are unmarried."
"7 + 5 =12."
The justification of these propositions does not depend upon experience: one does not need to consult experience in order to determine whether all bachelors are unmarried, or whether 7 + 5 = 12. (Of course, as Kant would have granted, experience is required in order to obtain the concepts "bachelor," "unmarried," "7," "+," and so forth. However, the a priori / a posteriori distinction as employed by Kant here does not refer to the origins of the concepts, but to the justification of the propositions. Once we have the concepts, experience is no longer necessary.)
Examples of a posteriori propositions, on the other hand, include:
"All bachelors are happy."
"Tables exist."
Both of these propositions are a posteriori: any justification of them would require one to rely upon one's experience.
The analytic/synthetic distinction and the a priori/a posteriori distinction together yield four types of propositions:
1. analytic a priori
2. synthetic a priori
3. analytic a posteriori
4. synthetic a posteriori
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The ease of knowing analytic propositions
Part of Kant's argument in the Introduction to the Critique of Pure Reason involves arguing that there is no problem figuring out how knowledge of analytic propositions is possible. To know an analytic proposition, Kant argued, one need not consult experience. Instead, one need merely "extract from it, in accordance with the principle of contradiction, the required predicate..." (A7/B12) In analytic propositions, the predicate concept is contained in the subject concept. Thus in order to know that an analytic proposition is true, one need merely examine the concept of the subject. If one finds the predicate contained in the subject, the judgment is true.
Thus, for example, one need not consult experience in order to determine whether "All bachelors are unmarried" is true. One need merely examine the subject concept ("bachelors") and see if the predicate concept "unmarried" is contained in it. And in fact, it is: "unmarried" is part of the definition of "bachelor," and so is contained within it. Thus the proposition "All bachelors are unmarried" can be known to be true without consulting experience.
It follows from this, Kant argued, first: all analytic propositions are a priori; there are no a posteriori analytic propositions. It follows, second: there is no problem understanding how we can know analytic propositions. We can know them because we just need to consult our concepts in order to determine that they are true.
