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thomblake comments on Don't Believe You'll Self-Deceive - Less Wrong
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Maybe we need to split this into two words. Belief for when it is not supported by fact, or even against the evidence. I mean I've never heard anybody say, "I believe in gravity". Maybe use the phrase "I accept" for supported ideas, as in "I accept quantum mechanics" or "I accept that god does not exist". "Accept" also seems to have less affect than "believe", which may make it easier to change your mind if the evidence changes.
No, in ordinary English, 'believe' means believe - but it also means 'accept' or 'endorse' or various other sorts of things. If we're going to be entrusted with eradicating a common usage (ha) then I say let 'believe' only mean believe. Thus, here, the assertion "I believe X" should be taken to be equivalent to the assertion "X".
"Thus, here, the assertion "I believe X" should be taken to be equivalent to the assertion "X"."
We can believe something without asserting it to be true. "I assert X to be true", likewise, doesn't require that we believe X to be true. All sorts of arguments involve assertions of truth that we don't necessarily extend beyond the argument.
It's something like the empty set: when the null symbol is bracketed, the result doesn't mean "the empty set". Empty brackets, or the null by itself, means that.
Asserting something one does not believe is lying. By the principle of charity we should assume our fellows are not lying, in which case "X" implies "I believe X". Obviously, that's only halfway to equivalence.
If I were to say, "I believe that the president is John McCain", and you responded by disputing my claim that the president is John McCain, I would be out of line to respond that I had never asserted that the president is John McCain. Similarly for the exchange "I believe that Annoyance is Caledonian" "But I'm not Caledonian" "I didn't say you were".
And so they are equivalent, unless you deny the principle of charity or have a counterexample for my second point.