The Logical Positivists
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:
analytic proposition: a proposition whose truth depends solely on the meaning of its terms
analytic proposition: a proposition that is true (or false) by definition
analytic proposition: a proposition that is made true (or false) solely by the conventions of language
(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:
synthetic proposition: a proposition that is not analytic
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 Willard Van Orman 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:
analytic propositions – propositions grounded in meanings, independent of matters of fact.
synthetic propositions – propositions grounded in fact.
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.