The analytic-synthetic distinction, (also called the analytic-synthetic dichotomy), is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are those which are true simply by virtue of their meaning while synthetic propositions are not; however, philosophers have used the terms in very different ways. Furthermore, whether there is a legitimate distinction to be made has been widely debated among philosophers since Willard Van Orman Quine's critique of the distinction in his 1951 article "Two Dogmas of Empiricism".
The philosopher Immanuel Kant was the first to use the terms "analytic" and "synthetic" to divide propositions into types. Kant introduces the analytic/synthetic distinction in the Introduction to the Critique of Pure Reason (1781/1998, A6-7/B10-11). There, he restricts his attention to affirmative subject-predicate judgments, and defines "analytic proposition" and "synthetic proposition" as follows:
Examples of analytic propositions, on Kant's definition, include:
Kant's own example is:
Each of these is an affirmative subject-predicate judgment, and in each, the predicate concept is contained with 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:
Kant's own example is:
As with the examples of analytic propositions, each of these 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 "unhappy"; "unhappy" 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."
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:
Examples of a priori propositions include:
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:
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:
Kant thought the third type is self-contradictory, so he discusses only three types as components of his epistemological framework. However, Stephen Palmquist treats the analytic a posteriori not only as a valid epistemological classification, but as the most important of the four for philosophy.
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 to take the subject and "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.
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, as all important metaphysical knowledge is 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.
Over a hundred years later, a group of philosophers took interest in Kant and his distinction between analytic and synthetic propositions: the logical positivists.
Part of Kant's examination of the possibility of synthetic a priori knowledge involved the examination of mathematical propositions, such as
Kant maintained that mathematical propositions such as these were synthetic a priori propositions, and that we knew them. That they were synthetic, he thought, was obvious: the concept "12" is not contained within the concept "5," or the concept "7," or the concept "+." And the concept "straight line" is not contained within the concept "the shortest distance between two points." (B15-17) From this, Kant concluded that we had knowledge of synthetic a priori propositions. He went on to maintain that it was extremely important to determine how such knowledge was possible.
The logical positivists agreed with Kant that we had knowledge of mathematical truths, and further that mathematical propositions were a priori. However, they did not believe that any fancy metaphysics, such as the type Kant supplied, were necessary to explain our knowledge of mathematical truths. Instead, the logical positivists maintained that our knowledge of judgments like "all bachelors are unmarried" and our knowledge of mathematics (and logic) were basically the same: all proceeded from our knowledge of the meanings of terms or the conventions of language.
Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the "analytic/synthetic distinction." They provided many different definitions, such as the following:
(While the logical positivists believed that the only necessarily true propositions were analytic, they did not define "analytic proposition" as "necessarily true proposition" or "proposition that is true in all possible worlds.")
Synthetic propositions were then defined as:
These definitions applied to all propositions, regardless of whether they were of subject-predicate form. Thus under these definitions, the proposition "It is raining or it is not raining," was classified as analytic, while under Kant's definitions it was neither analytic nor synthetic. And the proposition "7 + 5 = 12" was classified as analytic, while under Kant's definitions it was synthetic.
With regard to the issues related to the distinction between analytic and synthetic propositions, Kant and the logical positivists agreed about what "analytic" and "synthetic" meant. This would only be a terminological dispute. Instead, they disagreed about whether knowledge of mathematical and logical truths could be obtained merely through an examination of one's own concepts. The logical positivists thought that it could be. Kant thought that it could not.
In 1951, W.V. Quine published his famous essay "Two Dogmas of Empiricism" in which he argued that the analytic-synthetic distinction is untenable. In the first paragraph, Quine takes the distinction to be the following:
In short, Quine argues that the notion of an analytic proposition requires a notion of synonymy, but these notions are parasitic on one another. Thus, there is no non-circular (and so no tenable) way to ground the notion of analytic propositions.
While Quine's rejection of the analytic-synthetic distinction is widely known, the precise argument for the rejection and its status is highly debated in contemporary philosophy. However, some (e.g., Boghossian, 1996) argue that Quine's rejection of the distinction is still widely accepted among philosophers, even if for poor reasons.