To know something, in the ordinary sense, is to be in a position to say "I know" with justification — to have grounds, to be responsive to evidence, to acknowledge the possibility that one might be wrong. Knowledge claims are embedded in practices of inquiry, verification, and correction. "I know there is a goldfinch in the garden" is the kind of claim I make when I have looked, and another person might reasonably challenge me on. This is what "know" ordinarily means.
Moore tried to refute the sceptic by saying: "I know I have two hands — here they are." But Wittgenstein argues that Moore's use of "know" is grammatically displaced. To know one has two hands is to be in a position to check, to find out, to discover — as if "I have two hands" were the sort of thing one might be uncertain about. But in ordinary life, "I have two hands" is not discovered; it is not even believed in the ordinary sense. It simply does not belong to the language game of knowledge and doubt. Moore gave scepticism too much credit by taking it seriously on its own terms.
Certainty is not a heightened form of knowledge but something prior to it. It is the unreflective, unjustified, and unjustifiable trust that makes any inquiry possible. Wittgenstein's move is to show that scepticism and common-sense refutation both misplace their ground: both treat certainty as if it were a species of knowledge, subject to the same logic of evidence and justification. But certainty is woven into our form of life in a different way — it shows itself in action before it can be stated in a proposition.
On Certainty engages directly with Moore's "Proof of an External World" and "Certainty" throughout. The distinction between certainty and knowledge is most explicitly stated at §§166–175. Wittgenstein's remark "I know — seems to describe a state of affairs which guarantees what is known, guarantees it as a fact. One always forgets the expression 'I thought I knew'" (§12) is the most compressed statement of the problem.
