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SilasBarta comments on Counterfactual Mugging and Logical Uncertainty - Less Wrong
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If a theory of logical counterfactuals is to apply to statements of the form "If X was true, then Y would be true", do we need to restrict the forms of X and Y, or can they be arbitrary mathematical propositions?
For example, does it make sense to ask something like, "What is 13*3, if 3*3 was 8?" An obvious answer is "38", but what if you're doing multiplication in binary?
I don't see why a theory of counterfactuals couldn't apply to mathematical propositions. After all, our cognitive architectures use causality at a primitive level, and the same architecture is taught math.
And certainly, while learning math, you were taught results that didn't "seem" right at the time, so you worked backwards until you could understand why that result (like 2+6 = 8) makes sense.
So you just have to imagine yourself in such a similar situation about math, learning it for the first time. If everyone in class seemed to understand multiplication but you, and it were also a fact that 3*3 = 8, what process would you figure was actually going on when you multiply? Then, apply that to 13*3.