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randallsquared comments on Supernatural Math - Less Wrong
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No, I'm not holding that there actually is such a world, only that there would be no reason to apply our reality's rules to such a world. My real point is that the logical follows in actual historical fact from the physical, rather than being some sort of special knowledge that can be deduced without reference to anything physical.
Really, our beliefs about the logical follow from the physical. Don't confuse the map with the territory.
Heh. This is precisely the question, isn't it? Are logic and mathematics in the territory somewhere or are they the language of the map?
The way I see it is that logic is a territory, my beliefs about logic form a corresponding map, and that map is useful for constructing maps of other territories (and the accuracy of those maps is evidence of the accuracy of the logic map).
If nothing else this is a really well phrased statement of position. Maybe I'm just committing the philosopher's fallacy (deciding things are necessary because I'm not creative enough to think up alternatives) but I really just can't see what it would mean for there to be a world in which A didn't = A, in which the middle wasn't excluded, in which triangles are round, etc. What criteria are you using to decide on one view over the other?