Differentiate between synthetic a-priori and Analytic a-priori.

Synthetic a priori and analytic a priori are terms used in epistemology and philosophy to distinguish between types of knowledge propositions.

1. Analytic a priori:

   • Analytic a priori propositions are statements whose truth is determined by the meanings of the terms involved, and their truth can be known independently of experience.
   • Examples include tautologies or truths by definition, where the predicate is already contained within the subject. For instance, "All bachelors are unmarried" is analytic a priori because the concept of being unmarried is inherent in the definition of a bachelor.

2. Synthetic a priori:

   • Synthetic a priori propositions involve statements whose truth is not solely dependent on the meanings of the terms but requires empirical validation. These propositions are not derived from the subject's definition alone and extend our knowledge beyond mere linguistic analysis.
   • Immanuel Kant introduced the idea of synthetic a priori knowledge, such as mathematical truths and certain metaphysical principles. For example, the proposition "7 + 5 = 12" is synthetic a priori because it adds something to our understanding beyond the concepts of 7, 5, and 12.

In summary, the key distinction lies in whether the truth of a proposition can be determined through analysis of the terms (analytic a priori) or if it requires empirical input for validation (synthetic a priori). Analytic a priori propositions are true by virtue of language and meaning, while synthetic a priori propositions involve non-empirical but informative truths.