The philosopher most famously associated with the question "What can I know?" is Immanuel Kant. He explored this question deeply in his seminal work, the "Critique of Pure Reason," where he examined the limits and scope of human knowledge and how our minds perceive and categorize reality. Kant's inquiry into what we can know is foundational in Western philosophy and epistemology.

Another related philosophical stance comes from Socrates, who famously said "I know that I know nothing," highlighting a humble recognition of one's own ignorance as a starting point for philosophical inquiry. However, the specific phrasing and central question "What can I know?" aligns more distinctly with Kant's critical philosophy.