Traditionally, we come to know things either through sense experience or through rational inquiry. We come to know the concept “chair” by looking at various chairs, and by seeing how chairs are used, namely, for sitting on. We come to define the concept “physical object” through rational thought- a physical object is a tangible entity that casts a shadow, or that is matter- it occupies space and has mass and weight.
A priori knowledge is knowledge that is derived independently of sense experience. For example, that bachelors are unmarried men is a priori knowledge. A posteriori knowledge is known viz sense experience, for instance, that crows are black. Analytic propositions are true by virtue of the meanings of the words used, for instance, that triangles have three sides. Synthetic propositions are true by virtue of the way the world is, for instance, that rain is wet.
Are there synthetic a priori propositions? That is, are there truths which are known via reason, but also true of the way the world is? Take mathematical truths for example. The proposition that “1 + 1 = 2” can only be known if we know the concept “1” and the concept of “equality”. But how do we come to know these concepts?