We cannot fully prove the external world exists beyond our own minds

Nagel opens with the classic skeptical puzzle: everything we know about a world outside our own mind comes to us through sensory experience, and since we only ever directly access those experiences rather than the world itself, we cannot rule out the possibility that our entire perceived reality is some kind of elaborate illusion, dream, or deception. He walks through why common responses, like appealing to the consistency of our experiences or the testimony of others, don't actually escape the problem, since consistency and testimony are themselves only available to us as further experiences that could equally be part of the illusion. Nagel isn't arguing we should actually doubt the external world in daily life, since doing so is practically impossible and not how humans function, but he uses the puzzle to show that our confidence in an external world rests on something other than airtight logical proof. This distinction between practical certainty and logical certainty recurs throughout philosophy whenever intuition and rigorous reasoning diverge. Takeaway: some of our most basic beliefs rest on trust rather than proof, and recognizing that is not the same as abandoning them.