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.”

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