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dlthomas comments on The Fallacy of Gray - Less Wrong
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I'm trying to imagine the other dimension we could add to this. If we have "more right" and "less right" along one axis, what's orthogonal to it?
I initially felt this comment was silly (the post isn't saying every space can be reasonably modeled as one-dimensional, is it?), but my brain is telling me we actually could come up with a more precise way to represent the article's concept with a Cartesian plane... but I'm not actually able to think of one. False intuition based on my experience with the "Political Compass" graph, perhaps.
Direction of divergence?
Neither (1, 5) nor (5, 1) may be "more wrong" when the answer is (2, 2), but may still be quite meaningfully distinct for some purposes.
That's true. They could be wrong in different ways (or "different directions", in our example), which could be important for some purposes. But as you say, that depends on said purposes; I'm still uncertain as to the fallacy that dspeyer refers to. If our only purpose is determining some belief's level of correctness, absent other considerations (like in which way it's incorrect), isn't the one dimension of the "shades of grey" model sufficient?
Although -- come to think of it, I could be misunderstanding his criticism. I took it to mean he had an issue with the original post, but he could just be providing an example of how the shades-of-grey model could be used fallaciously, rather than saying it is fallacious, as I initially interpreted.