An analytic proposition is true by virtue of its meaning. The predicate is contained in the subject. All bachelors are unmarried. The concept bachelor already includes unmarried. You do not need to check the world. The truth is in the words. The proposition is analytic.

The term comes from Immanuel Kant. He distinguished analytic from synthetic propositions. Analytic propositions are true by definition. Synthetic propositions are true by fact. All bachelors are unmarried is analytic. All bachelors are unhappy is synthetic. The first is true by meaning. The second requires evidence.

Analytic proposition examples

• All triangles have three sides.
• A bachelor is an unmarried man.
• Red is a color.
• If it is raining, then it is raining.
• No bachelor is married.

Analytic propositions are necessarily true. They cannot be false. Denying them leads to contradiction. A married bachelor is a contradiction in terms. The proposition is not informative about the world. It tells you about language and concepts. That is the criticism. Analytic propositions are trivial. They do not add to knowledge. They just unpack definitions. Kant agreed that analytic propositions are not informative. But he argued that some propositions are both analytic and informative. He called them synthetic a priori. That is a controversial category. Most philosophers accept the analytic-synthetic distinction. But the boundary is debated. Is water is H2O analytic or synthetic? It was discovered by science, so it seems synthetic. But some argue that water just means H2O. The debate continues. Analytic propositions are true by meaning. But what counts as meaning is not always clear.