I have heard a Strong Reductionist theory, which goes as follows: History is Psychology. Psychology is Biology. Biology is Chemistry. Chemistry is Physics. Physics is Math. In other words, you can (in principle) derive the higher order theory from the more fundamental theory.
For any deterministic interpretation of quantum mechanics, it seems that this would necessarily have to hold (though for MWI, it would not tell you which universe you happen to be in).
As a completely irrelevant aside, the first link is tenuous—it’s awfully hard to explain Pompeii in terms of just psychology—but it would still be true that you could derive all of history from sufficient knowledge of starting conditions, and could possibly work backwards from sufficient knowledge of the present (which, for MWI, would include sufficient knowledge of the state of all worlds).
If for no other reason, I reject that theory because Physics is not Math. Physics is inherently about making statements that have empirical content. Math is inherently about making statements that lack empirical content.
Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?
Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?
I think the answer to your question is “method of construction.”
In principle, a Cartesian skeptic should be able generate the same map of “Math” that we use. In contrast, there is no reason that a Cartesian skeptic’s map of Physics would have any resemblance to the territory at all. (I accept that it is hard to see what could motivate a Cartesian skeptic to generate Math).
I’m almost tempted to say that for a priori truths, the map is the territory. I hesitate because I’m not confident I am using the metaphor correctly.
In principle, a Cartesian skeptic should be able generate the same map of “Math” that we use. In contrast, there is no reason that a Cartesian skeptic’s map of Physics would have any resemblance to the territory at all. (I accept that it is hard to see what could motivate a Cartesian skeptic to generate Math).
I am not convinced this is the case. How do we pick which axioms to use, except by comparison to reality? Certainly, this is how it historically happened.
After describing all possible physics models, the skeptic still has no idea which is right.
In contrast, all the math articulated is right. (There are probably some caveats I should make, like no inconsistent axioms, and some reference to Godel, but I suspect I don’t know enough actual math to make all the necessary caveats).
I’m almost tempted to say that for a priori truths, the map is the territory. I hesitate because I’m not confident I am using the metaphor correctly.
This definitely seems to be a slip up in application of the metaphor. The map is my beliefs, the territory is truth. I know from experience that I can believe something to be a mathematical truth, only to thereafter find a mistake in my proof—I don’t expect “the statement was true for as long as your map represented it” is actually your position.
For any deterministic interpretation of quantum mechanics, it seems that this would necessarily have to hold (though for MWI, it would not tell you which universe you happen to be in).
As a completely irrelevant aside, the first link is tenuous—it’s awfully hard to explain Pompeii in terms of just psychology—but it would still be true that you could derive all of history from sufficient knowledge of starting conditions, and could possibly work backwards from sufficient knowledge of the present (which, for MWI, would include sufficient knowledge of the state of all worlds).
Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?
I think the answer to your question is “method of construction.”
In principle, a Cartesian skeptic should be able generate the same map of “Math” that we use. In contrast, there is no reason that a Cartesian skeptic’s map of Physics would have any resemblance to the territory at all. (I accept that it is hard to see what could motivate a Cartesian skeptic to generate Math).
I’m almost tempted to say that for a priori truths, the map is the territory. I hesitate because I’m not confident I am using the metaphor correctly.
I am not convinced this is the case. How do we pick which axioms to use, except by comparison to reality? Certainly, this is how it historically happened.
What can’t the skeptic say “If you accept the Axiom of Choice, here’s what follows. If you reject the Axiom of Choice, this follows instead.”
And you are right that I misused the map/territory metaphor.
Why can’t the skeptic similarly say, “If you accept that there is a particle at..., here is what follows; otherwise, this follows instead”?
After describing all possible physics models, the skeptic still has no idea which is right.
In contrast, all the math articulated is right. (There are probably some caveats I should make, like no inconsistent axioms, and some reference to Godel, but I suspect I don’t know enough actual math to make all the necessary caveats).
I am not certain that the same objection cannot be made to math, but I at least follow what your objection is.
This definitely seems to be a slip up in application of the metaphor. The map is my beliefs, the territory is truth. I know from experience that I can believe something to be a mathematical truth, only to thereafter find a mistake in my proof—I don’t expect “the statement was true for as long as your map represented it” is actually your position.