A tautology's truth is certain, a proposition's possible, a contradiction's impossible. (TLP 4.464)
Indee people even surmised that there must be a 'law of least action' before they knew exactly how it went.
(Here, as always, what is certain a priori proves to be something purely logical.) (6.3211)
and contrast them with his final thoughts on certainty,
Am I not getting closer and closer to saying that in the end logic cannot be described? (OC 501)and we'll see that Wittgenstein's thoughts on certainty seem not to have changed much in the intervening thirty years. The logical, the certain and the a priori. Wittgenstein says in the TLP that "there are no pictures that are true a priori" (2.225). But that makes sense: A picture is tied up with sense, the empirical, and as such cannot be a priori--by definition. The only avenue to knowledge is the empirical--"It is always by favor of Nature that one knows something" (OC 505). The facts must line up with with a proposition, case-ness must map onto one's picture. Truth and falsity constitute knowledge, and therefore, the subject of any sentence of the form, 'I know ____.'
The indefensible, non-propositional bedrock of our action--certainty--is logic(al). I was surprised to come across Wittgenstein making this move in his last thoughts. Had he reverted to his youthful Tractarian days? I think not. If I were to look into the PI, for example, I'm sure his thought would still align. Wittgenstein didn't change so much as grow. If you have a limp or a hairlip as a child, you'll probably have it for the rest of your life.
When Wittgenstein says, the "propositions of logic describe the scaffolding of the world, or rather they represent it" is he maybe talking about the understanding (TLP 6.124)? One could interpret him as trying to map out the understanding in a manner similar to Kant. Induction is that which goes without saying, must go without saying. For how could one derive the law of induction? By induction? I think that this is the point, but I don't think there's a similarity to Kant, per se.
What is the relation between my being certain I have two hands and logic? Does this certainty represent a logical framework without which I would be thrust into retard-like apoplexy? This may be approaching the right way. Speaking about a proposition on which all other propositions hinge, Wittgenstein makes the parenthetical remark that it calls to mind Frege's remarks on the law of identity (494). A's do not become ~A's while one isn't looking; your car won't just disappear. If you gave this up then you'd have to give up everything.
There is more, though. Wittgenstein's remark supra, that logic can't be described: That might be exactly right. Even though advances in logic were made (after two thousand years) I would be tempted to say that advances in our notation were made. What is logic? Logic is the invisible hand guiding our actions. Putting my hand in a wood-chipper is not logical; nor is walking in front of a moving bus. Logic can be seen in our actions, when we act with certainty.