Conceptual containment The philosopher
Immanuel Kant uses the terms "analytic" and "synthetic" to divide propositions into two types. Kant introduces the analytic–synthetic distinction in the Introduction to his
Critique of Pure Reason (1781/1998, A6–7/B10–11). There, he restricts his attention to statements that are affirmative subject–predicate judgments and defines "analytic proposition" and "synthetic proposition" as follows: •
analytic proposition: a proposition whose predicate concept is contained in its subject concept •
synthetic proposition: a proposition whose predicate concept is
not contained in its subject concept but related Examples of analytic propositions, on Kant's definition, include: • "All bachelors are unmarried." • "All triangles have three sides." Kant's own example is: • "All bodies are extended": that is, they occupy space. (A7/B11) Each of these statements is an affirmative subject–predicate judgment, and, in each, the predicate concept is
contained within the subject concept. The concept "bachelor" contains the concept "unmarried"; the concept "unmarried" is part of the definition of the concept "bachelor". Likewise, for "triangle" and "has three sides", and so on. Examples of synthetic propositions, on Kant's definition, include: • "All bachelors are alone." • "All creatures with hearts have kidneys." Kant's own example is: • "All bodies are heavy": that is, they experience a gravitational force. (A7/B11) As with the previous examples classified as analytic propositions, each of these new statements is an affirmative subject–predicate judgment. However, in none of these cases does the subject concept contain the predicate concept. The concept "bachelor" does not contain the concept "alone"; "alone" is not a part of the
definition of "bachelor". The same is true for "creatures with hearts" and "have kidneys"; even if every creature with a heart also has kidneys, the concept "creature with a heart" does not contain the concept "has kidneys". So the philosophical issue is: What kind of statement is "Language is used to transmit meaning"?
Kant's version and the a priori–a posteriori distinction In the Introduction to the
Critique of Pure Reason, Kant contrasts 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. Moreover, the proposition can be validated by experience, but is not grounded in experience. Therefore, it is logically necessary. •
a posteriori proposition: a proposition whose justification does rely upon experience. The proposition is validated by, and grounded in, experience. Therefore, it is logically contingent. Examples of
a priori propositions include: • "All bachelors are unmarried." • "7 + 5 = 12." The justification of these propositions does not depend upon experience: one need not consult experience to determine whether all bachelors are unmarried, nor whether . (Of course, as Kant would grant, experience is required to understand the concepts "bachelor", "unmarried", "7", "+" and so forth. However, the
a priori–
a posteriori distinction as employed here by Kant refers not 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 include: • "All bachelors are unhappy." • "Tables exist." Both of these propositions are
a posteriori: any justification of them would require one's experience. The analytic–synthetic distinction and the
a priori–
a posteriori distinction together yield four types of propositions: • analytic
a priori • synthetic
a priori • analytic
a posteriori • synthetic
a posteriori Kant posits the third type as obviously self-contradictory. Ruling it out, he discusses only the remaining three types as components of his epistemological frameworkeach, for brevity's sake, becoming, respectively, "analytic", "synthetic
a priori", and "empirical" or "
a posteriori" propositions. This triad accounts for all propositions possible. Examples of analytic and examples of
a posteriori statements have already been given, for synthetic
a priori propositions he gives those in mathematics and physics.
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 needs merely to take the subject and "extract from it, in accordance with the principle of contradiction, the required predicate" (B12). In analytic propositions, the predicate concept is contained in the subject concept. Thus, to know 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 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 only need to consult our concepts in order to determine that they are true.
The possibility of metaphysics After ruling out the possibility of analytic
a posteriori propositions, and explaining how we can obtain knowledge of analytic
a priori propositions, Kant also explains how we can obtain knowledge of synthetic
a posteriori propositions. That leaves only the question of how knowledge of synthetic
a priori propositions is possible. This question is exceedingly important, Kant maintains, because all scientific knowledge (for him Newtonian physics and mathematics) is made up of synthetic
a priori propositions. If it is impossible to determine which synthetic
a priori propositions are true, he argues, then metaphysics as a discipline is impossible. The remainder of the
Critique of Pure Reason is devoted to examining whether and how knowledge of synthetic
a priori propositions is possible.
Mathematics and Synthetic Apriori Propositions. One example Kant gives of a possibly synthetic apriori propositions are the propositions of mathematics. The mathematical equation that 10 = 0.2x 50 is true regardless of experience thus making it a priori, but not analytic. Mathematical propositions are not analytic in that 10 does not self evidently contain 0.2x50, in the same way that the concept bachelor contains the categories of unmarried and male.
The Importance of Synthetic Apriori Propositions to Kant's metaphysics Kant's advocacy for his metaphysics in
Critique of Pure Reason can be seen as relying on the possibility of synthetic apriori claims. If synthetic apriori propositions are possible, it supposes a certain metaphysical worldview, much of the Critique of Pure reason then relies on the possibility of synthetic apriori propositions to justify a worldview. One could reduce Kant's argument into a simple form: If Kant's metaphysics is true, then synthetic apriori propositions are possible. ==Frege and the logical positivists==