...I think the correct response is to say that both theories explain the data, and one cannot empirically test which theory is true, but the paleontology theory is more elegant (I am tempted to say “simpler”, but that might imply I have a rigorous mathematical definition of the form of simplicity involved, which I don’t).
The concept Scott seems to be looking for is “lower Kolmogorov complexity”. Well, there might be debate about whether Kolmogorov complexity is exactly the right metric, but it seems clearly a vast improvement over having no mathematical definition.
...there is no unambiguous algorithm according to which we can feed in these criteria, a list of theories, and a set of data, and expect the best theory to pop out. The way in which we judge scientific theories is inescapably reflective, messy, and human. That’s the reality of how science is actually done; it’s a matter of judgment, not of drawing bright lines between truth and falsity or science and non-science.
Carrol’s position seems much too pessimistic, giving up without even trying. Why “inescapably”? Before Newton someone might have said, the way to guess the trajectory of a falling rock in inescapably messy and human. Now we know how to describe physics by mathematical equations but not metaphysics. This is not a state of affairs we should just accept.
Algorithmic information theory and AI theory show a clear path towards formalizing metaphysics. I think it is entirely plausible that in the future we will have tools for rigorously comparing scientific theories. Perhaps in cases such as Atlantis a fully rigorous analysis would still be intractable, because of the “messy” domain, but when comparing competing theories of fundamental physics I see no reason why it can’t be done. Even in the messier cases having a rigorous theory should lead to tools for making comparison less subjective.
Algorithmic information theory and AI theory show a clear path towards formalizing metaphysics.
If you define metaphysics as being concerned with deciding between natural and supernatural explanations, the techniques we currently have that are based algorithmic complexity aren’t doing a great job.
The problem is that our standard notions of computational limits is based on physical limitations - - the topic of hypercomputation deals, with the computation that might be possible absent physical limits - - so there is a question begging assumption of physicalism built in.
I don’t think hypercomputation is an issue for algorithmic information theory as foundation for metaphysics/induction. The relevant question is, not whether the world contains hypercomputation, but whether our mind is capable of hypercomputation. And here it seems to me like the answer is “no”. Even if the answer was “yes”, we could probably treat the hypercomputing part of the mind as part of the environment. I wrote a little about it here.
Since the topic is metaphysics , and metaphysics is about what reality really is, the relevant question is whether the world contains hypercomputation.
Well, I am a “semi-instrumentalist”: I don’t think it is meaningful to ask what reality “really is” except for the projection of the reality on the “normative ontology”.
But you still don’t have an apriori guarantee that a computable model will succeed—that doesn’t follow from the claim that the human mind operated within computable limits. You could be facing evidence that all computable models must fail, in which case you should adopt a negative belief about physical/naturalism, even if you don’t adopt a positive belief in some supernatural model.
Well, you don’t have a guarantee that a computable model will succeed, but you do have some kind of guarantee that you’re doing your best, because computable models is all you have. If you’re using incomplete/fuzzy models, you can have a “doesn’t know anything” model in your prior, which is a sort of “negative belief about physical/naturalism”, but it is still within the same “quasi-Bayesian” framework.
The concept Scott seems to be looking for is “lower Kolmogorov complexity”. Well, there might be debate about whether Kolmogorov complexity is exactly the right metric, but it seems clearly a vast improvement over having no mathematical definition.
Carrol’s position seems much too pessimistic, giving up without even trying. Why “inescapably”? Before Newton someone might have said, the way to guess the trajectory of a falling rock in inescapably messy and human. Now we know how to describe physics by mathematical equations but not metaphysics. This is not a state of affairs we should just accept.
Algorithmic information theory and AI theory show a clear path towards formalizing metaphysics. I think it is entirely plausible that in the future we will have tools for rigorously comparing scientific theories. Perhaps in cases such as Atlantis a fully rigorous analysis would still be intractable, because of the “messy” domain, but when comparing competing theories of fundamental physics I see no reason why it can’t be done. Even in the messier cases having a rigorous theory should lead to tools for making comparison less subjective.
If you define metaphysics as being concerned with deciding between natural and supernatural explanations, the techniques we currently have that are based algorithmic complexity aren’t doing a great job.
The problem is that our standard notions of computational limits is based on physical limitations - - the topic of hypercomputation deals, with the computation that might be possible absent physical limits - - so there is a question begging assumption of physicalism built in.
I don’t think hypercomputation is an issue for algorithmic information theory as foundation for metaphysics/induction. The relevant question is, not whether the world contains hypercomputation, but whether our mind is capable of hypercomputation. And here it seems to me like the answer is “no”. Even if the answer was “yes”, we could probably treat the hypercomputing part of the mind as part of the environment. I wrote a little about it here.
Since the topic is metaphysics , and metaphysics is about what reality really is, the relevant question is whether the world contains hypercomputation.
Well, I am a “semi-instrumentalist”: I don’t think it is meaningful to ask what reality “really is” except for the projection of the reality on the “normative ontology”.
But you still don’t have an apriori guarantee that a computable model will succeed—that doesn’t follow from the claim that the human mind operated within computable limits. You could be facing evidence that all computable models must fail, in which case you should adopt a negative belief about physical/naturalism, even if you don’t adopt a positive belief in some supernatural model.
Well, you don’t have a guarantee that a computable model will succeed, but you do have some kind of guarantee that you’re doing your best, because computable models is all you have. If you’re using incomplete/fuzzy models, you can have a “doesn’t know anything” model in your prior, which is a sort of “negative belief about physical/naturalism”, but it is still within the same “quasi-Bayesian” framework.