[kerkeslager]

Popper did not do anything of the sort.

First, I think Popper did not fundamentally disagree with the Bayesian approach: ultimately his critique of Bayesianism is a small adjustment to Bayesianism. When presented with a set of competing hypotheses { h_0, h_1, h_2... }, Bayesianism says that we assign a probability to each, whereas Popper points out that experiments and observation never really actually add credence to a hypothesis, they rather only decrease the probability of a hypothesis.

In theory, decreasing the probability of hypothesis h_0 does not increase the probability of hypothesis h_1, because the set of hypotheses is infinite--that is to say for any n there is always a potential h_{n+1} which has not been thought of by scientists. We know that the sum of the probabilities of hypotheses must be 1, but since the set of hypotheses is an infinite set, decreasing the probability of h_0 does not necessarily increase the probability of h_1, because the probability of any h_n in the set could be increasing.

I think Popper is right in theory, but in practice, I think this is less important than philosophers think it is. Pragmatically, we can treat the set of hypotheses as finite, operating only on the hypotheses humans have... hypothesized. We have no way to operate on hypotheses nobody has thought of, so we just operate on the set of hypotheses we have thought of. Since the sum of this set of probabilities must be 1, decreasing the probability of one hypothesis does increase the probability of all the other hypotheses in the set. Where Popper's critique becomes important is if we keep decreasing the probabilities of all the hypotheses in the set--this indicates that the hypothesis which is true is not in the set (i.e. nobody has come up with the correct hypothesis to test). This indicates a need for new hypotheses. But in a lot of cases, experimentation keeps decreasing the probability of all the hypotheses except one in the finite set of hypotheses humans have thought of, while numerous attempts to decrease the probability of that one hypothesis fail. While Popper would say this does not increase the probability of that one hypothesis, operating as if it does increase the probability of that hypothesis seems to work. We've been able to go to the moon, eradicate smallpox, and build intelligent-seeming machines, all based on hypotheses that we "increased the probability of" in this way, even though increasing the probability of a hypothesis is theoretically impossible.

This all goes back to philosophers' favorite navelgazing claim: that nothing is knowable. Ultimately, I think this is a dishonest argument which even philosophers don't believe. I've offered to punch many a philosopher in the face: after all, it's not knowable that it's going to hurt. But strangely, philosophers who claim to believe that nothing is knowable DO seem to know that will hurt, and none have taken me up on my offer.*

* Unlike the philosophers, I do believe in (probablistic) knowability, and I'm highly confident that punching them in the face would hurt them, so if anyone actually takes me up on this offer, I (probably) won't punch them. So far, no one has called my bluff.

[Mizza]

The first part is is precisely correct, and then the second part is precisely wrong:

> We have no way to operate on hypotheses nobody has thought of, so we just operate on the set of hypotheses we have thought of. Since the sum of this set of probabilities must be 1, decreasing the probability of one hypothesis does increase the probability of all the other hypotheses in the set.

We've been able to go to the moon because we understood general relativity, which absolutely could not have been created from a purely Bayesian approach for the reasons you made clear - it required new ideas.

[kerkeslager]

Did you read the very next sentence, or did you just stop at the first thing you found to disagree with? I said:

> Where Popper's critique becomes important is if we keep decreasing the probabilities of all the hypotheses in the set--this indicates that the hypothesis which is true is not in the set (i.e. nobody has come up with the correct hypothesis to test). This indicates a need for new hypotheses.

I'll add that once relativity was hypothesized, it was added to the finite set of hypotheses that humans had hypothesized. Your "counterexample" is well within the scientific process I described.

[Mizza]

Then it's not a very useful framework, is it.

[kerkeslager]

Inasmuch as the entire field of epistemology isn't useful, sure, science was doing just fine without philosophers attempting to describe it. I mean, what were you planning to use it for? What does the word "useful" mean to you in this context?

The thing here is that whether or not the model of Bayesian epistemology is "useful", it's a fairly accurate description of how scientists approach the acquisition of knowledge, so when you attack that you're attacking science. And the thing is, outside of the brains of philosophers, science works--Bayesian epistemology does describe a process of knowledge acquisition that is effective. Planes still fly, smallpox is still eradicated, microchips still direct electricity to perform computation. Popper can say, "well ackchyually, we haven't actually increased confidence in the hypothesis of acquired immunity, we've only decreased confidence in the other hypotheses," but smallpox isn't going to say, "You know what, Popper, you're right," and reappear to decimate Europe. So de facto it sure seems like we do often know things with some degree of confidence when we eliminate other hypotheses, Popper notwithstanding.

And as I've said over and over: we need science more than ever. Polio just re-emerged in the US, and vaccine denialism is prevalent. While philosophers are sitting in their ivory towers saying "well ackchyually nothing is knowable" people are dying of diseases for which the prevention is not only knowable but known. So you'll excuse me not liking philosophers much here.

[Mizza]

This is Adderall-brained LessWrong gibberish. Bayesian epistemology is not "a fairly accurate description of how we acquire knowledge" compared to critical rationalism. There's only a small, specific community of extremely online people who think otherwise.

[kerkeslager]

Since you've provided no basis for saying that, I guess we'll just have to take your word against my explanation. :shrug: