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abramdemski comments on Algorithms as Case Studies in Rationality - Less Wrong
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Comments (39)
Because in casual speech the question doesn't actually mean "does that imply that?", but rather "do we have a derivation of that from that, using our set of inference rules?" Not the same, but people seldom realise the distinction.
That is also a fair interpretation, especially for those students who just want to get the homework done with and don't really care about increasing their sureness in the theorem being re-proved.
If we additionally care about the argument and agree with all the inference rules, then I think there is a little more explaining to do.
Not only for the students, I think. Confusion between implication and inference was enough widespread to motivate Lewis Carroll to write an essay, and nothing much changed has since then. I didn't properly understand the distinction even after finishing university.