I think it should be possible to compute probabilities and expectation values of absolutely anything. However to put it on a sound mathematical basis we need a theory of logical uncertainty.
I think so because conceptually a Bayesian expectation value is your “best effort” to estimate something. Since you can always do your “best effort” you can always compute the expectation value. Of course, for this to fully make sense we must take computing resource limits into account. So we need a theory of probability with limited computing resources aka a theory of logical uncertainty.
conceptually a Bayesian expectation value is your “best effort” to estimate something.
Not quite. Conceptually a Bayesian expectation is your attempt to rationally quantify your beliefs which may or may not involve best efforts. That requires these beliefs to exist. I don’t see why it isn’t possible to have no beliefs with regard to some topic.
Since you can always do your “best effort” you can always compute the expectation value.
That’s not very meaningful. You can always output some number, but so what? If you have no information you have no information and your number is going to be bogus.
If you don’t believe that the process of thought asymptotically converges to some point called “truth” (at least approximately), what does it mean to have a correct answer to any question?
Meta-remark: Whoever is downvoting all of my comments in this thread, do you really think I’m not arguing in good faith? Or are you downvoting just because you disagree? If it’s the latter, do you think it’s good practice or you just haven’t given it thought?
If you don’t believe that the process of thought asymptotically converges to some point called “truth” (at least approximately), what does it mean to have a correct answer to any question?
There is that thing called reality. Reality determines what constitutes a correct answer to a question (for that subset of questions which actually have “correct” answers).
I see no reason to believe that the process of thought converges at all, never mind asymptotically to ‘some point called “truth”’.
Interaction with reality only gives you raw sensory experiences. It doesn’t allow you to deduce anything. When you compute 12 x 12 and it turns out to be 144, you believe 144 is the one correct answer. Therefore you implicitly assume that tomorrow you won’t somehow realize the answer is 356.
Not quite. I can test whether a rock is hard by kicking it.
But this byte-sized back-and-forth doesn’t look particularly useful. I don’t understand where you are coming from—to me it seems that you consider your thought processes primary and reality secondary. Truth, say you, is whatever the thought processes converge to, regardless of reality. That doesn’t make sense to me.
When you kick the rock, all you get is a sensory experience (a quale, if you like). You interpret this experience as a sensation arising from your foot. You assume this sensation is the result of your leg undergoing something called “collision” with something called “rock”. You deduce that the rock probably has a property called “hard”. All of those are deductions you do using your model of reality. This model is generated from memories of previous experiences by a process of thought based on something like Occam’s razor.
Since the only access to truth we might have is through our own thought, if the latter doesn’t converge to truth (at least approximately) then truth is completely inaccessible.
if the latter doesn’t converge to truth (at least approximately) then truth is completely inaccessible.
Why not? Granted that we have access to reality only through mental constructs and so any approximations to “the truth” are our own thoughts, but I don’t see any problems with stating that sometimes these mental constructs adequately reflect reality (=truth) and sometimes they don’t. I don’t see where this whole idea of asymptotic convergence is coming from. There is no guarantee that more thinking will get you closer to the truth, but on the other hand sometimes the truth is right there, easily accessible.
A Bayesian never “knows” anything. She can only compute probabilities and expectation values.
Can she compute probabilities and expectation values with respect to decisions she would make if she had infinite time and information?
I think it should be possible to compute probabilities and expectation values of absolutely anything. However to put it on a sound mathematical basis we need a theory of logical uncertainty.
On the basis of what do you think so? And what entity will be doing the computing?
I think so because conceptually a Bayesian expectation value is your “best effort” to estimate something. Since you can always do your “best effort” you can always compute the expectation value. Of course, for this to fully make sense we must take computing resource limits into account. So we need a theory of probability with limited computing resources aka a theory of logical uncertainty.
Not quite. Conceptually a Bayesian expectation is your attempt to rationally quantify your beliefs which may or may not involve best efforts. That requires these beliefs to exist. I don’t see why it isn’t possible to have no beliefs with regard to some topic.
That’s not very meaningful. You can always output some number, but so what? If you have no information you have no information and your number is going to be bogus.
If you don’t believe that the process of thought asymptotically converges to some point called “truth” (at least approximately), what does it mean to have a correct answer to any question?
Meta-remark: Whoever is downvoting all of my comments in this thread, do you really think I’m not arguing in good faith? Or are you downvoting just because you disagree? If it’s the latter, do you think it’s good practice or you just haven’t given it thought?
There is that thing called reality. Reality determines what constitutes a correct answer to a question (for that subset of questions which actually have “correct” answers).
I see no reason to believe that the process of thought converges at all, never mind asymptotically to ‘some point called “truth”’.
How do you know anything about reality if not through your own thought process?
Through interaction with reality. Are you arguing from a brain-in-the-vat position?
Interaction with reality only gives you raw sensory experiences. It doesn’t allow you to deduce anything. When you compute 12 x 12 and it turns out to be 144, you believe 144 is the one correct answer. Therefore you implicitly assume that tomorrow you won’t somehow realize the answer is 356.
And what does that have to do with knowing anything about reality? Your thought process is not a criterion of whether anything is true.
But it is the only criterion you are able to apply.
Not quite. I can test whether a rock is hard by kicking it.
But this byte-sized back-and-forth doesn’t look particularly useful. I don’t understand where you are coming from—to me it seems that you consider your thought processes primary and reality secondary. Truth, say you, is whatever the thought processes converge to, regardless of reality. That doesn’t make sense to me.
When you kick the rock, all you get is a sensory experience (a quale, if you like). You interpret this experience as a sensation arising from your foot. You assume this sensation is the result of your leg undergoing something called “collision” with something called “rock”. You deduce that the rock probably has a property called “hard”. All of those are deductions you do using your model of reality. This model is generated from memories of previous experiences by a process of thought based on something like Occam’s razor.
OK, and how do we get from that to ‘the process of thought asymptotically converges to some point called “truth”’?
Since the only access to truth we might have is through our own thought, if the latter doesn’t converge to truth (at least approximately) then truth is completely inaccessible.
Why not? Granted that we have access to reality only through mental constructs and so any approximations to “the truth” are our own thoughts, but I don’t see any problems with stating that sometimes these mental constructs adequately reflect reality (=truth) and sometimes they don’t. I don’t see where this whole idea of asymptotic convergence is coming from. There is no guarantee that more thinking will get you closer to the truth, but on the other hand sometimes the truth is right there, easily accessible.
I apologize but this discussion seems to be going nowhere.
Agreed.