Define Analytic a-priori.

Analytic a priori refers to a category of knowledge or propositions within epistemology, a branch of philosophy that deals with the nature and scope of knowledge. Coined by Immanuel Kant, this term signifies a type of statement that is both analytic and known independently of experience.

1. Analytic: Analytic propositions are those in which the predicate is contained within the subject. In other words, the truth of the statement can be determined by analyzing the meanings of the terms involved. An example is the statement "All bachelors are unmarried," where the concept of being unmarried is inherent in the definition of a bachelor.

2. A Priori: A priori knowledge is knowledge that is independent of experience or empirical observation. It is based on reason and conceptual analysis rather than sensory experience. A priori knowledge is considered foundational and is not derived from specific instances in the external world.

Analytic a priori knowledge, then, represents statements that are true by virtue of their meanings and can be known independently of empirical observation. Kant used this concept to distinguish certain types of necessary and universal truths, such as those in mathematics and logic, from synthetic a posteriori knowledge, which is contingent on experience. Analytic a priori knowledge plays a central role in Kant's epistemological framework, emphasizing the inherent and non-experiential nature of certain fundamental truths.