Given the context, I interpreted Komponisto’s comment as saying that to the extent that we reason correctly we are using Bayes’ theorem, not that we always reason correctly.
Even if the claim is worded like that, it implies (incorrectly) that correct reasoning should not involve steps based on opaque processes that we are unable to formulate explicitly in Bayesian terms. To take an example that’s especially relevant in this context, assessing people’s honesty, competence, and status is often largely a matter of intuitive judgment, whose internals are as opaque to your conscious introspection as the physics calculations that your brain performs when you’re throwing a ball. If you examine rigorously the justification for the numbers you feed into the Bayes theorem, it will inevitably involve some such intuitive judgment that you can’t justify in Bayesian terms. (You could do that if you had a way of reverse-engineering the relevant algorithms implemented by your brain, of course, but this is still impossible.)
Of course, you can define “reasoning” to refer only to those steps in reaching the conclusion that are performed by rigorous Bayesian inference, and use some other word for the rest. But then to avoid confusion, we should emphasize that reaching any reliable conclusion about the facts in a trial (or almost any other context) requires a whole lot of things other than just “reasoning.”
Even if the claim is worded like that, it implies (incorrectly) that correct reasoning should not involve steps based on opaque processes that we are unable to formulate explicitly in Bayesian terms.
You misunderstand. There was no normative implication intended about explicit formulation. My claim is much weaker than you think (but also abstract enough that it may be difficult to understand how weak it is). I simply assert that Bayesian updating is a mathematical definition of what “inference” means, in the abstract. This does not say anything about the details of how humans process information, and nor does it say anything about how mathematically explicit we “should” be about our reasoning in order for it to be valid. You concede everything you need to in order to agree with me when you write:
You could [justify intuitive judgements in Bayesian terms] if you had a way of reverse-engineering the relevant algorithms implemented by your brain,
In fact, this actually concedes more than necessary—because it could turn out that these algorithms are only approximately Bayesian, and my claim about Bayesianism as the ideal abstract standard would still hold (as indeed implied by the phrase “approximately Bayesian”).
Of course, this does in my view have the implication that it is appropriate for people who understand Bayesian language to use it when discussing their beliefs, especially in the context of a disagreement or other situation where one person’s doesn’t understand the other’s thought process. I suspect this is the real point of controversy here (cf. our previous arguments about using numerical probabilities).
Of course, this does in my view have the implication that it is appropriate for people who understand Bayesian language to use it when discussing their beliefs, especially in the context of a disagreement or other situation where one person’s doesn’t understand the other’s thought process. I suspect this is the real point of controversy here (cf. our previous arguments about using numerical probabilities).
Yes, the reason why I often bring up this point is the danger of spurious exactitude in situations like these. Clearly, if you are able to discuss the situation in Bayesian language while being well aware of the non-Bayesian loose ends involved, that’s great. The problem is that I often observe the tendency to pretend that these loose ends don’t exist. Moreover, the parts of reasoning that are opaque to introspection are typically the most problematic ones, and in most cases, their problems can’t be ameliorated by any formalism, but only on a messy case-by-case heuristic basis. The emphasis on Bayesian formalism detracts from these crucial problems.
If we actually knew how to reason correctly, we could program computers to do it. We reason correctly, better than computers, without understanding how we do it.
Given the context, I interpreted Komponisto’s comment as saying that to the extent that we reason correctly we are using Bayes’ theorem, not that we always reason correctly.
Even if the claim is worded like that, it implies (incorrectly) that correct reasoning should not involve steps based on opaque processes that we are unable to formulate explicitly in Bayesian terms. To take an example that’s especially relevant in this context, assessing people’s honesty, competence, and status is often largely a matter of intuitive judgment, whose internals are as opaque to your conscious introspection as the physics calculations that your brain performs when you’re throwing a ball. If you examine rigorously the justification for the numbers you feed into the Bayes theorem, it will inevitably involve some such intuitive judgment that you can’t justify in Bayesian terms. (You could do that if you had a way of reverse-engineering the relevant algorithms implemented by your brain, of course, but this is still impossible.)
Of course, you can define “reasoning” to refer only to those steps in reaching the conclusion that are performed by rigorous Bayesian inference, and use some other word for the rest. But then to avoid confusion, we should emphasize that reaching any reliable conclusion about the facts in a trial (or almost any other context) requires a whole lot of things other than just “reasoning.”
You misunderstand. There was no normative implication intended about explicit formulation. My claim is much weaker than you think (but also abstract enough that it may be difficult to understand how weak it is). I simply assert that Bayesian updating is a mathematical definition of what “inference” means, in the abstract. This does not say anything about the details of how humans process information, and nor does it say anything about how mathematically explicit we “should” be about our reasoning in order for it to be valid. You concede everything you need to in order to agree with me when you write:
In fact, this actually concedes more than necessary—because it could turn out that these algorithms are only approximately Bayesian, and my claim about Bayesianism as the ideal abstract standard would still hold (as indeed implied by the phrase “approximately Bayesian”).
Of course, this does in my view have the implication that it is appropriate for people who understand Bayesian language to use it when discussing their beliefs, especially in the context of a disagreement or other situation where one person’s doesn’t understand the other’s thought process. I suspect this is the real point of controversy here (cf. our previous arguments about using numerical probabilities).
Yes, the reason why I often bring up this point is the danger of spurious exactitude in situations like these. Clearly, if you are able to discuss the situation in Bayesian language while being well aware of the non-Bayesian loose ends involved, that’s great. The problem is that I often observe the tendency to pretend that these loose ends don’t exist. Moreover, the parts of reasoning that are opaque to introspection are typically the most problematic ones, and in most cases, their problems can’t be ameliorated by any formalism, but only on a messy case-by-case heuristic basis. The emphasis on Bayesian formalism detracts from these crucial problems.
If we actually knew how to reason correctly, we could program computers to do it. We reason correctly, better than computers, without understanding how we do it.