This paper compares Wittgenstein's conception of ?objective certainty? with Descartes's ?metaphysical certainty?. According to both conceptions if you are certain of something in these senses, then it is inconceivable that you are mistaken. But a striking difference is that for Descartes, if you are metaphysically certain of something it follows both that the something is so and that you know it is so; whereas on Wittgenstein's conception neither thing follows. I try to show that there is a form of ?scepticism? (...) in Wittgenstein's outlook on the concept of certainty, although it is not the familiar Philosophical Scepticism. The Appendix takes issue with a recent essay by John Cook which argues that the ?hinge propositions? of On Certainty are based on ?the metaphysics of phenomenalism? (shrink)