I think you regard innate/genetic ideas as important. I do not. Because people are universal knowledge creators, and can change any idea they start with, it doesn't matter very much.
You misunderstand. I bring it up as a model of learning, and my choice was based on your own remarks. You said that knowledge is created by an evolutionary process. That way of putting it suggests an analogy with Darwin's theory of evolution as proceeding by random variation and natural selection. And indeed there is an analogy between Popper's conjectures and refutations and variation and natural selection, and it is this: a conjecture is something like variation (mutation), and refutation is something like natural selection.
However, what I found was that the closer I looked at knowledge which is actually acquired through natural selection - what we might call innate knowledge or instinctive knowledge - the more the process of acquisition resembled Bayesian updating rather than Popperian conjecture and refutation. I explained why.
In Bayesian updating, there are competing hypotheses, and the one for which actual events are less of a surprise (i.e., the hypothesis Hi for which P(E|Hi) is higher) is strengthened relative to the one for which events are more of a surprise. I find a parallel to this in competition among alleles under natural selection, which I described.
Essential to Bayesian updating is the coexistence of competing hypotheses, and essential to natural selection is the coexistence of competing variants in a species. In contrast, Popper talks about conjecture and refutation, which is a more lonely process that need not involve more than one conjecture and a set of observations which have the potential to falsify it. Popper talks about improving the conjecture in response to refutation, but this process more resembles Lamarckian evolution than Darwinian evolution, because in Lamarckian evolution the individuals improve themselves in response to environmental challenges, much as Popper would have us improve our conjectures in response to observational challenges. Also, in Lamarckian evolution, as in the Popperian process of conjecture and refutation, competing variants (compare: competing hypotheses) do not play an essential role (though I'm sure they could be introduced). Rather, the picture is of a single animal (compare: a single hypothesis) facing existential environmental challenges (compare: facing the potential for falsification) improving itself in response (which improvement is passed to offspring).
The Popperian process of conjecture, refutation, and improvement of the conjecture, can as it happens be understood from a Bayesian standpoint. It does implement Bayesian updating in a certain way. Specifically, when a particular conjecture is refuted and the scientist modifies the conjecture - at that point, there are two competing hypotheses. So at that point, the process of choosing between these two competing hypotheses can be characterized as Bayesian updating. The less successful hypothesis is weakened, and the more successful hypothesis is strengthened.
In short, if you want to take seriously the analogy that does exist between evolution through natural selection and knowledge acquisition of whatever type, then you may want to take a closer look at Bayesian updating as conforming more closely to the Darwinian model.
In short, if you want to take seriously the analogy
I wasn't talking about an analogy.
Evolution is a theory which applies to any type of replicator. Not by analogy by literally applies.
Make sense so far?
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.