For Bayes: No Exceptions to Cromwell's Rule

[Lawrence Crocker]

For Bayesian subjective probabilities, Cromwell's Rule has it that a prior probability x, is in the range 0 < x < 1. However Lindley, who gets credit for enunciating the rule and providing its name, of colorful history, made an exception for logical and mathematical propositions. These he permitted to take the values 0 or 1.

I contend that Lindley was wrong and Cromwell exceptionlessly right. Considering four different strengths of the mathematical exception, I argue that none is acceptable. For non-omniscient beings, not even simple logic or mathematics is certain in the very demanding sense of “certain” appropriate to the Bayesian project. For the argument please see www.LawrenceCrocker.blogspot.com.

[Dalek Prime]

So, you didn't like my answer to your other thread?

viewtopic.php?f=17&p=220200#p220200

Otay. But just say so in the original thread. No need to open a new one.

[dionisos]

For Bayesian subjective probabilities, Cromwell's Rule has it that a prior probability x, is in the range 0 < x < 1. However Lindley, who gets credit for enunciating the rule and providing its name, of colorful history, made an exception for logical and mathematical propositions. These he permitted to take the values 0 or 1.

I contend that Lindley was wrong and Cromwell exceptionlessly right. Considering four different strengths of the mathematical exception, I argue that none is acceptable. For non-omniscient beings, not even simple logic or mathematics is certain in the very demanding sense of “certain” appropriate to the Bayesian project. For the argument please see http://www.LawrenceCrocker.blogspot.com.

If you apply Bayesian probabilities even to math rules, you should apply it to every steps that build Bayesian probabilities.
It is bad, because it is self referential.

Assume X the chance that Bayesian probabilities (BP) is right.(by example X=(1-10^(-100000)))
Then look at a mathematical propositions(MP) you use to deduce Bayesian probabilities, the probability that this proposition is true is Y.
If we know MP is false, then BP have great chance to be false (and if it is true, you don’t know why).
If we know MP is true, it improve the probability of BP only a little (given all the other things we use to deduce BP)
The validity of BP don’t have too much impact on the probability of MP.
It follow that Y>X.
Then whenever you doubt MP because of Bayesian probabilities (BP), you should doubt Bayesian probabilities even more, and then, you should doubt MP less.

I will not make the real argument i would do here, i confess i wanted to do it, but it happened to be more confused that i thought.
Still, what i think, is that this kind of self-referential construction, are unstable, we can believe them because we are human that didn’t see the consequences, but when we see it, it just explode in madness.

[Obvious Leo]

Still, what i think, is that this kind of self-referential construction, are unstable, we can believe them because we are human that didn’t see the consequences, but when we see it, it just explode in madness.

A lovely way of putting it, dionisos. We can twist our minds into pretzels for no good reason once we start looking for complications where no complications exist. There are no certainties in nature because that's just not the way the real world works.

[Philosophy Explorer]

I don't know if this pertains. I often read that quantum computing wouldn't be limited to 0 or 1, but can take on many values so I favor Cromwell's rule (question: does this mean that the computer can go beyond 1?)

PhilX

[dionisos]

I don't know if this pertains. I often read that quantum computing wouldn't be limited to 0 or 1, but can take on many values so I favor Cromwell's rule (question: does this mean that the computer can go beyond 1?)

PhilX

A classical computer could do everything that a quantum computer can do. (there are libraries to simulate quantum computing in classical computer)
But the quantum computer can do it in a weaker time complexity.
If you don’t know what time complexity is, we could abusively say that weaker time complexity mean that you do it much faster. (but remember it is not exactly that).

But i assure you this have nothing to do with the actual discussion.

does this mean that the computer can go beyond 1?

No, fortunately any computer could go "beyond 1", it would be hard to do any calculus without that.
Data are represented by series of "0" and "1", you could easily build a computer that represent data by series of "0", "1", and "2", but it would be useless.