Synthetic a priori judgments

Synthetic a priori judgments are statements that are necessarily true and provide new information, even though they are known independently of experience. For example, "7 + 5 = 12" is considered synthetic a priori because it is universally valid and we arrive at it through reasoning, not just by definitions or experience. These judgments expand our knowledge without needing to observe the world directly, yet they are necessarily true and foundational to our understanding. Immanuel Kant introduced this concept to explain how certain fundamental truths about space, time, and causality are known independently of sensory experience but are still informative.