Sit with the demand for certainty and it quickly turns corrosive. Descartes, looking for one thing he could not doubt, imagined an all-powerful deceiver bending every perception — the sky, his hands, even mathematics. Nothing he could see or feel proved the demon absent. The senses, it turned out, could all be counterfeit.
And yet the doubt destroyed itself at one point. However thoroughly he was deceived, something was being deceived; there had to be a thinker for the deception to land on. Cogito, ergo sum — I think, therefore I am. Whatever else collapses, the existence of the doubter survives the doubt. It is the closest thing philosophy has to bedrock, and notably it is delivered by reason, not the senses. That is the rationalist wager: the mind's own operations are more trustworthy than anything the eyes report.
The empiricist answerEverything through the senses.
The empiricists pushed the other way. Locke called the mind a blank slate written on by experience; there are no ideas we did not first take in through the senses. It is the method of science, and it works — but Hume found the crack in its foundation. We believe the future will resemble the past, that causes will keep producing their effects. Yet no argument proves it. Every attempt to justify induction has to assume induction. We trust the sun will rise on habit, not on proof.
The modern ruptureThe three pages that broke knowledge.
For over two thousand years, knowledge had a tidy definition: justified true belief. To know something was to believe it, to be right, and to have good reason. Then in 1963 Edmund Gettier published a three-page paper of counterexamples in which someone has a belief that is true, and justified, and yet plainly not knowledge — they were right by luck, their justification pointing at the truth by accident. The definition cracked, and epistemology has been trying to repair or replace it ever since.
Where does that leave the original question? With a useful distinction. Certainty — the demon-proof kind — we have almost none of, beyond our own existence as thinking things. Knowledge in the ordinary, workable sense we have in abundance, provided we drop the demand that it be immune to every conceivable doubt. Most of living happens in that second register, and always has.