Conceptual containment
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:

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
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," i.e. take up space. (A7/B11)
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 concepts "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 happy."
"All creatures with hearts have kidneys."
Kant's own example is:

"All bodies are heavy," i.e. have mass. (A7/B11)
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 "happy"; "happy" 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


FROM WIKIPEDIA