Using my epistemology I have learned not to do that kind of thing. Would that serve as an example of a practical benefit of it, and a substantive difference?
No. It provides an example of a way in which you are better than me. I am overwhelmingly confident that I can find ways in which I am better than you.
Do you assert that? It is wrong and has real world consequence. In The Beginning of Infinity Deutsch takes on a claim of a similar type (50% probability of humanity surviving the next century) using Popperian epistemology. You can find Deutsch explaining some of that material here: http://groupspaces.com/oxfordtranshumanists/pages/past-talks
Could you explain how a Popperian disputes such an assertion? Through only my own fault, I can't listen to an mp3 right now.
My understanding is that anyone would make that argument in the same way: by providing evidence in the Bayesian sense, which would convince a Bayesian. What I am really asking for is a description of why your beliefs aren't the same as mine but better. Why is it that a Popperian disagrees with a Bayesian in this case? What argument do they accept that a Bayesian wouldn't? What is the corresponding calculation a Popperian does when he has to decide how to gamble with the lives of six billion people on an uncertain assertion?
I wonder if you think that all mathematically equivalent ways of thinking are equal. I believe they aren't because some are more convenient, some get to answers more directly, some make it harder to make mistakes, and so on. So even if my approach was compatible with the Bayesian approach, that wouldn't mean we agree or have nothing to discuss.
I agree that different ways of thinking can be better or worse even when they come to the same conclusions. You seem to be arguing that Bayesianism is wrong, which is a very different thing. At best, you seem to be claiming that trying to come up with probabilities is a bad idea. I don't yet understand exactly what you mean. Would you never take a bet? Would never take an action that could possibly be bad and could possibly be good, which requires weighing two uncertain outcomes?
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.
I do not plan to continue this discussion except in the pursuit of an example about which we could actually argue productively.
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...
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.