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comment by Raemon · 2021-08-29T21:25:00.468Z · LW(p) · GW(p)

i really like this metaphor, but I'm unclear on how much it tracks in the literal idea clarifying world.

I'd be interested in a concrete example of you demonstrating a thought process where this helped?

Replies from: TekhneMakre
comment by TekhneMakre · 2021-08-29T23:27:48.037Z · LW(p) · GW(p)

Feels like the interesting examples would be complicated and contextual, like there's a bunch of subject matter that's being engaged with and there's global deficiencies in that which you can loosen by a bunch of small moves. And in general abstract philosophical propositions have this character. So it feels like it's important for readers to be prepared to supply their own examples, which is what I do when reading.

Any given revolution in thought that's preceded by straining to assimilate anomalies in the old way of thinking is supposed to be an example.

Maybe a source of smaller examples is trying to understand an existing subject deeply. E.g. an area of math. I used to ignore when people would say that linear algebra is properly understood without reference to an a priori fixed basis for your vector space. This sort of works okay, you can get reasonable intuitions for lots of stuff without distinguishing abstract V from V with a basis, but it gets confusing and eventually nonsensical when you try to understand other things. For example, "there's a canonical isomorphism between V and V** (the double dual) but not between V and V*" makes no sense if you think of V as having a basis. Maybe an intermediate case is norms; you can sort of interact with norms while pretending that they're just always the Euclidean norm from an (orthonormal) basis, but it makes more sense if you distinguish everything and understand it on its own terms. In retrospect it would have been better to have made a more breadth-first (breadth in the conceptual dimension, not the "topic" dimension) attempt to clarify stuff, and to listen to the signals in the intermediate cases that there's tension and something different should happen.