Could you explain how a Popperian disputes such an assertion? [(50% probability of humanity surviving the next century)]
e.g. by pointing out that whether we do or don't survive depends on human choices, which in turn depends on human knowledge. And the growth of knowledge is not predictable (exactly or probabilistically). If we knew its contents and effects now, we would already have that knowledge. So this is not prediction but prophecy. And prophecy has build in bias towards pessimism: because we can't make predictions about future knowledge, prophets in general make predictions that disregard future knowledge. These are explanatory, philosophical arguments which do not rely on evidence (that is appropriate because it is not a scientific or empirical mistake being criticized). No corresponding calculation is made at all.
You ask about how Popperians make decisions if not with such calculations. Well, say we want to decide if we should build a lot more nuclear power plants. This could be taken as gambling with a lot of lives, and maybe even all of them. Of course, not doing it could also be taken as a way of gambling with lives. There's no way to never face any potential dangers. So, how do Popperians decide? They conjecture an answer, e.g. "yes". Actually, they make many conjectures, e.g. also "no". Then they criticize the conjectures, and make more conjectures. So for example I would criticize "yes" for not providing enough explanatory detail about why it's a good idea. Thus "yes" would be rejected, but a variant of it like "yes, because nuclear power plants are safe, clean, and efficient, and all the criticisms of them are from silly luddites" would be better. If I didn't understand all the references to longer arguments being made there, I would criticize it and ask for the details. Meanwhile the "no" answer and its variants will get refuted by criticism. Sometimes entire infinite categories of conjectures will be refuted by a criticism, e.g. the anti-nuclear people might start arguing with conspiracy theories. By providing a general purpose argument against all conspiracy theories, I could deal with all their arguments of that type. Does this illustrate the general idea for you?
You seem to be arguing that Bayesianism is wrong, which is a very different thing.
I think it's wrong as an epistemology. For example because induction is wrong, and the notion of positive support is wrong. Of course Bayes' theorem is correct, and various math you guys have done is correct. I keep getting conflicting statements from people about whether Bayesianism conflicts with Popperism or not, and I don't want to speak for you guys, nor do I want to discourage anyone from finding the shared ideas or discourage them from learning from both.
Would you never take a bet?
Bets are made on events, like which team wins a sports game. Probabilities are fine for events. Probabilities of the truth of theories is problematic (b/c e.g. there is no way to make them non-arbitrary). And it's not something a fallibilist can bet on because he accepts we never know the final truth for sure, so how are we to set up a decision procedure that decides who won the bet?
Would never take an action that could possibly be bad and could possibly be good, which requires weighing two uncertain outcomes?
We are not afraid of uncertainty. Popperian epistemology is fallibilist. It rejects certainty. Life is always uncertain. That does not imply probability is the right way to approach all types of uncertainty.
This brings me back to my initial query: give a specific case where Popperian reasoning diverges from Bayesian reasoning, explain why they diverge, and explain why Bayesianism is wrong. Explain why Bayesian's willingness to bet does harm. Explain why Bayesians are slower than Popperians at coming to the same conclusion. Whatever you want.
Bayesian reasoning diverges when it says that ideas can be positively supported. We diverge because Popper questioned the concept of positive support, as I posted in the original text on this page, and which no one has answered yet. The criticism of positive support begins by considering what it is (you tell me) and how it differs from consistency (you tell me).
And the growth of knowledge is not predictable (exactly or probabilistically). If we knew its contents and effects now, we would already have that knowledge.
You're equivocating between "knowing exactly the contents of the new knowledge", which may be impossible for the reason you describe, and "know some things about the effect of the new knowledge", which we can do. As Eliezer said, I may not know which move Kasparov will make, but I know he will win.
I was directed to this book (http://www-biba.inrialpes.fr/Jaynes/prob.html) in conversation here:
http://lesswrong.com/lw/3ox/bayesianism_versus_critical_rationalism/3ug7?context=1#3ug7
I was told it had a proof of Bayesian epistemology in the first two chapters. One of the things we were discussing is Popper's epistemology.
Here are those chapters:
http://www-biba.inrialpes.fr/Jaynes/cc01p.pdf
http://www-biba.inrialpes.fr/Jaynes/cc02m.pdf
I have not found any proof here that Bayesian epistemology is correct. There is not even an attempt to prove it. Various things are assumed in the first chapter. In the second chapter, some things are proven given those assumptions.
Some first chapter assumptions are incorrect or unargued. It begins with an example with a policeman, and says his conclusion is not a logical deduction because the evidence is logically consistent with his conclusion being false. I agree so far. Next it says "we will grant that it had a certain degree of validity". But I will not grant that. Popper's epistemology explains that *this is a mistake* (and Jaynes makes no attempt at all to address Popper's arguments). In any case, simply assuming his readers will grant his substantive claims is no way to argue.
The next sentences blithely assert that we all reason in this way. Jaynes' is basically presenting the issues of this kind of reasoning as his topic. This simply ignores Popper and makes no attempt to prove Jaynes' approach is correct.
Jaynes goes on to give syllogisms, which he calls "weaker" than deduction, which he acknowledges are not deductively correct. And then he just says we use that kind of reasoning all the time. That sort of assertion only appeals to the already converted. Jaynes starts with arguments which appeal to the *intuition* of his readers, not on arguments which could persuade someone who disagreed with him (that is, good rational arguments). Later when he gets into more mathematical stuff which doesn't (directly) rest on appeals to intution, it does rest on the ideas he (supposedly) established early on with his appeals to intuition.
The outline of the approach here is to quickly gloss over substantive philosophical assumptions, never provide serious arguments for them, take them as common sense, do not detail them, and then later provide arguments which are rigorous *given the assumptions glossed over earlier*. This is a mistake.
So we get, e.g., a section on Boolean Algebra which says it will state previous ideas more formally. This briefly acknowledges that the rigorous parts depend on the non-rigorous parts. Also the very important problem of carefully detailing how the mathematical objects discussed correspond to the real world things they are supposed to help us understand does not receive adequate attention.
Chapter 2 begins by saying we've now formulated our problem and the rest is just math. What I take from that is that the early assumptions won't be revisted but simply used as premises. So the rest is pointless if those early assumptions are mistaken, and Bayesian Epistemology cannot be proven in this way to anyone who doesn't grant the assumptions (such as a Popperian).
Moving on to Popper, Jaynes is ignorant of the topic and unscholarly. He writes:
http://www-biba.inrialpes.fr/Jaynes/crefsv.pdf
> Karl Popper is famous mostly through making a career out of the doctrine that theories may not be proved true, only false
This is pure fiction. Popper is a fallibilist and said (repeatedly) that theories cannot be proved false (or anything else).
It's important to criticize unscholarly books promoting myths about rival philosophers rather than addressing their actual arguments. That's a major flaw not just in a particular paragraph but in the author's way of thinking. It's especially relevant in this case since the author of the books tries to tell us about how to think.
Note that Yudkowsky made a similar unscholarly mistake, about the same rival philosopher, here:
http://yudkowsky.net/rational/bayes
> Previously, the most popular philosophy of science was probably Karl Popper's falsificationism - this is the old philosophy that the Bayesian revolution is currently dethroning. Karl Popper's idea that theories can be definitely falsified, but never definitely confirmed
Popper's philosophy is not falsificationism, it was never the most popular, and it is fallibilist: it says ideas cannot be definitely falsified. It's bad to make this kind of mistake about what a rival's basic claims are when claiming to be dethroning him. The correct method of dethroning a rival philosophy involves understanding what it does say and criticizing that.
If Bayesians wish to challenge Popper they should learn his ideas and address his arguments. For example he questioned the concept of positive support for ideas. Part of this argument involves asking the questions: 'What is support?' (This is not asking for its essential nature or a perfect definition, just to explain clearly and precisely what the support idea actually says) and 'What is the difference between "X supports Y" and "X is consistent with Y"?' If anyone has the answer, please tell me.