Deterministic world and “too much information to process” are uninteresting. All that simply means that due to practical constraints, sometimes the only reasonably thing is to assign no probability.

Better: Sometimes the only reasonable thing is to assign a probability that’s strictly speaking “wrong”, but adequate if you’re only facing opponents who are (approximately) as hampered as you in terms of how much they know and much they can feasible compute. (E.g. Like humans playing poker, where the cards are only pseudo-random.)

If you want to say this is uninteresting, fine. I’m not trying to argue that it’s interesting.

Except uncomputability means it won’t work even in theory. You are always Dutch bookable.

Sorry, you’ve lost me.

Chaitin’s number is not a mathematical entity—it’s creation of pure metaphysics.

Chaitin’s number is awfully tame by the standards of descriptive set theory. So what you’re really saying here is that you personally regard a whole branch of mathematics as “pure metaphysics”. Maybe a few philosophers of mathematics agree with you—I suspect most do not—but actual mathematicians will carry on studying mathematics regardless.

The claim that kth bit of Chaitin’s number is 0 just doesn’t mean anything once k becomes big enough to include a procedure to compute Chaitin’s number.

I’m not sure what you’re trying to say here but what you’ve actually written is false. Why do you think Chaitin’s number isn’t well defined?

Better: Sometimes the only reasonable thing is to assign a probability that’s strictly speaking “wrong”, but adequate if you’re only facing opponents who are (approximately) as hampered as you in terms of how much they know and much they can feasible compute. (E.g. Like humans playing poker, where the cards are only pseudo-random.)

If you want to say this is uninteresting, fine. I’m not trying to argue that it’s interesting.

Sorry, you’ve lost me.

Chaitin’s number is awfully tame by the standards of descriptive set theory. So what you’re really saying here is that you personally regard a whole branch of mathematics as “pure metaphysics”. Maybe a few philosophers of mathematics agree with you—I suspect most do not—but actual mathematicians will carry on studying mathematics regardless.

I’m not sure what you’re

tryingto say here but what you’ve actually written is false. Why do you think Chaitin’s number isn’t well defined?