You haven’t yet given me a reason to care about “objective probability” in my inferences. Leaving that aside—if I understand your view correctly, your claim is that in order for a system to have an “objective probability”, a system must have an “intrinsic geometry”. Gotcha. Not unreasonable.
What is “intrinsic geometry” when translated into math? (Is it just symmetry? I’d like to tease apart the concepts of symmetry and “objective probability”, if possible. Can you give an example of a system equipped with an intrinsic geometry (and therefore an “objective probability”) where symmetry doesn’t play a role?)
Why does your reasoning not apply to the coin toss? What’s the mathematical property of the motion of the coin that motion in my system does not possess?
I want to know the ingredients that will help me build a system that meets your standards. Until I can do that, I can’t truly claim to understand your view, much less argue against it.
Constant,
You haven’t yet given me a reason to care about “objective probability” in my inferences. Leaving that aside—if I understand your view correctly, your claim is that in order for a system to have an “objective probability”, a system must have an “intrinsic geometry”. Gotcha. Not unreasonable.
What is “intrinsic geometry” when translated into math? (Is it just symmetry? I’d like to tease apart the concepts of symmetry and “objective probability”, if possible. Can you give an example of a system equipped with an intrinsic geometry (and therefore an “objective probability”) where symmetry doesn’t play a role?)
Why does your reasoning not apply to the coin toss? What’s the mathematical property of the motion of the coin that motion in my system does not possess?
I want to know the ingredients that will help me build a system that meets your standards. Until I can do that, I can’t truly claim to understand your view, much less argue against it.