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Ishaan comments on The dangers of zero and one - Less Wrong
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"Tautologies are tautological" is the statement for which I am most certain.
Certainly, if the fate of humanity was the consequence of a false positive and a slap on my wrist was the consequence of a false negative for an affirmative answer to "tautologies are tautological", I would give a negative answer...so by that litmus test, I don't really have 100% confidence. But I've still have a strong logical intuition that I aught to be that confident, and that my emotional underconfidence in the proposed scenario is a bit silly.
The problem is, the above hypothetical scenario involves weird and self contradictory stuff (an entity which knows the right answer, my 100% certainty that the entity knows the right answer and can interpret my answer, etc). I think it may be best to restrict probability estimates to empirical matters (I'm 99.99% certain that my calculator will output "2" in response to the input "1+1=") and keep it away from pure logic realms.
+1 for the thought experiment test. I haven't seen that one before; any source or is it something you came up with?
thanks! the specific thought experiment is something I came up with but the general notion of using hypothetical scenarios to gauge one's true certainty is something that I think many people have done at one time or another, though I can't think of a specific example.