Likewise, higher-order game theory promises a normalisation of game theory.
I don’t know why, but this smells correct to me.
I have the same intuition—I agree that this smells correct. I suspect that the answer has something to do with the thing where when you take measurements (for whatever that should mean) of a system, what that actually looks like is some spectactularly non-injective map from [systems of interest in the same grouping as the system we’re looking at] to R, which inevitably destroys some information, by noninjectivity.
So I agree that it smells right, to quantify over the actual objects of interest and then maybe you apply information-destroying maps that take you outside spacetime (into math) rather than applying your quantifiers outside of spacetime after you’ve already applied your map and then crossing your fingers that the map is as regular/well-behaved as it needs to be.
I have the same intuition—I agree that this smells correct. I suspect that the answer has something to do with the thing where when you take measurements (for whatever that should mean) of a system, what that actually looks like is some spectactularly non-injective map from [systems of interest in the same grouping as the system we’re looking at] to R, which inevitably destroys some information, by noninjectivity.
So I agree that it smells right, to quantify over the actual objects of interest and then maybe you apply information-destroying maps that take you outside spacetime (into math) rather than applying your quantifiers outside of spacetime after you’ve already applied your map and then crossing your fingers that the map is as regular/well-behaved as it needs to be.