kaz comments on Mach's Principle: Anti-Epiphenomenal Physics - Less Wrong
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That's not a logical impossibility; it's just a property of the way we change our models. When you observe that X always seems to equal Y, that's redundancy in your model; if you find a model that matches all known observations equally but also compresses X to be the same thing as Y, your new model is the same as the old model except for having lower complexity - i.e. higher probability. Any predictions that are different in your new model from in your old model, you should now expect to be more likely to act according to the new model.