All of them are lovely and extremely useful in my world-models. And all of them have failed me at one time or another. Here are some modes where I’ve thought I understood and it was obvious, but I was missing important assumptions:
Intermediate Value Theorem: Obvious, incontrovertible. A knockout punch in any disagreement. Except, a lot of things aren’t quite as continuous as you think, when you really get formal about them.
Net Present Value: Also clearly the right tool for most comparisons of value. And figuring out the correct discount rate to take into account differing risks is quite nontrivial.
Local linearity: this one I lean on a bit less, but it still bites me when I get too loose with “locally”.
Theory of Mind: I’m getting better, but I’m still a master of Typical Mind Fallacy.
Grice’s Maxims (and Crocker’s Rule): Great when a target I strive for, very misleading when I expect that it’s common.
All of them are lovely and extremely useful in my world-models. And all of them have failed me at one time or another. Here are some modes where I’ve thought I understood and it was obvious, but I was missing important assumptions:
Intermediate Value Theorem: Obvious, incontrovertible. A knockout punch in any disagreement. Except, a lot of things aren’t quite as continuous as you think, when you really get formal about them.
Net Present Value: Also clearly the right tool for most comparisons of value. And figuring out the correct discount rate to take into account differing risks is quite nontrivial.
Local linearity: this one I lean on a bit less, but it still bites me when I get too loose with “locally”.
Theory of Mind: I’m getting better, but I’m still a master of Typical Mind Fallacy.
Grice’s Maxims (and Crocker’s Rule): Great when a target I strive for, very misleading when I expect that it’s common.