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Stuart: "Luke's response to Yoda should have been "I will try and lift it out using the force. If that fails, I will try and lever it out. If that fails ...""
Then Luke would have succeeded at rescuing his craft, but made no progress in learning The Force, and the Dark Side would have ruled the galaxy. :-)
Nick: "I wonder if nerdish literalism is a problem here. Saying "I will do X" when I can't rationally assign a high probability to success feels like dishonest overconfidence - and if I fail, it'll have been an outright lie."
No, that's the point exactly. Your body will adapt its own behavior to be in accord with your mind. (It's the old "Whether you think you can, or think you can't, you're right".) It's easy to demonstrate: run 10 miles saying "I'm a great runner, I'm strong, I'm fast, ...", and then next week run 10 miles saying "I hate running, I'm weak, I'm hungover, I'm slow, ...". Your body doesn't want to live the lie, so it makes your internal monologue true. When you commit completely to something, you can accomplish much more than you think you can. (Damn, I sound like a cheesy motivational speaker.)