timelets

"We are prone to think that we have here are degrees of certainty, with 2+2=4 enjoying the highest certainty. We don't realize that what we have here are not degrees of certainty, but kinds of certainty. And the kinds of certainty are as various as the kinds of proposition in question. *"

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This crucial point is often lost in probability calculations. Nassim Taleb gets it though.

* “Different kinds of certainty have different kinds of grounds. And what it is that is certain is, in each such case, a categorially different kind of proposition. The grounds for mathematical certainty are deductive proofs, and mathematical propositions are rules, not descriptions. The certainty of a perceptual statement such as ‘The curtains are red’ lies in its being evident to the senses – look and see! The certainty of an empirical prediction is determined by its conclusive empirical evidence. And the certainty of a highly theoretical proposition of science, such as e = mc2, is determined by the holistic confirmation of the theory of which it is a part.
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What applies to certainty applies also to truth.
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Empirical propositions, mathematical propositions, logical propositions and ethical propositions are categorially different. And that’s why what it is for propositions of categorially different kinds to be true is also so different, even though the term ‘true’ is unequivocal.”

Peter Hacker;. “A Beginner's Guide to the Later Philosophy of Wittgenstein.”

A couple of good quotes about how a problem statement shapes its potential solution.
https://youtu.be/sje2AZOrww0?t=1051

He [Wittgenstein] does not mean by this that the doubt in question is spurious or deceitful, only that it is not real doubt – it is not what we mean by doubt. We doubt when we have reason to doubt, not because we are at leisure to doubt: ‘The question is this: how is doubt introduced into the language-game? One doubts on specific grounds’ (OC 458). Moreover, the philosophical sceptic’s doubt purports to be obsessive or radical: from the fact that we sometimes have reason to doubt, he concludes that we are always entitled to doubt. It is, again, precisely in this that the sceptic’s doubt is not real doubt: ‘A doubt that doubted everything would not be a doubt’ (OC 450); ‘If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty’ (OC 115).
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According to Wittgenstein, the sceptic is making two grave mistakes – and these are connected. One, we have just seen, is that he is mistaking the behaviour of doubt for genuine doubt; and the other is that he is mistaking hinges for propositions (either empirical or epistemic).

Daniele Moyal-Sharrock, Understanding Wittgenstein's On Certainty.

Reasoned vs at leisure doubt is a key distinction that emerges from OC.

Откуда советские люди знают про расизм, которого в СССР не было и быть не могло:

http://bse.sci-lib.com/article095507.html

В теории языка Витгенштейна сегодняшние обсуждения в русскоязычном сообществе вопроса "расист ли Трамп?" можно было бы считать experimentum crucis.

The clearest summary I've ever read on the subject:

Although in detail the Tractatus is among the most difficult of philosophical works, its rough outlines are well known. To each sentence there corresponds a (possible) fact. If such a fact, obtains, the sentence is true; if not, false. For atomic sentences, the relation between a sentence and the fact it alleges is one of a simple correspondence or isomorphism. The sentence contains names, corresponding to objects. An
atomic sentence is itself a fact, putting the names in a certain relation; and it says that (there is a corresponding fact that) the corresponding objects are in the same relation. Other sentences are (finite or infinite) truth-functions of these.

-- Saul Kripke, "Wittgenstein on Rules and Private Language. (1984).