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curi comments on Bayesian Epistemology vs Popper - Less Wrong Discussion
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That is not Popper's position. That is not even close. In various passages he explicitly denies it like "not certain or probable". To Popper, the claims that the evidence tells us something is certainly true, or probably true, are cousins which share an underlying mistake. You're assuming Popper would agree with you about probability without reading any of his passages on probability in which he, well, doesn't.
Arguing what books say with people who haven't read them gets old fast. So how about you just imagine a hypothetical person who had the views I attribute to Popper and discuss that?
For example, the answers to all questions that have a "why" in them. E.g. why is the Earth roughly spherical? Statements with "because" (sometimes implied) is a pretty accurate way to find explanations, e.g. "because gravity is a symmetrical force in all directions". Another example is all of moral philosophy. Another example is epistemology itself, which is a philosophy not an empirical field.
Yes
This does not solve the problem to my satisfaction. It orders theories which make identical predictions (about all our data, but not about the unknown) and then lets you differentiate by that order. But isn't that ordering arbitrary? It's just not true that short and simple theories are always best; sometimes the truth is complicated.
For a formal mathematical discussion of these sorts of problems, read Causality by Judea Pearl. He reduces cause to a combination of conditional independence and ordering, and from this he defines algorithms for discovering causal models from data, predicting the effect of interventions and computing counterfactuals.
Could you give a short statement of the main ideas? How can morality be reduced to math? Or could you say something to persuade me that that book will address the issues in a way I won't think misses the point? (e.g. by showing you understand what I think the point is, otherwise I won't except you to be able to judge if it misses the point in the way I would).
Sorry, I over-quoted there; Pearl only discusses causality, and a little bit of epistemology, but he doesn't talk about moral philosophy at all.
His book is all about causal models, which are directed graphs in which each vertex represents a variable and each edge represents a conditional dependence between variables. He shows that the properties of these graphs reproduce what we intuitively think of as "cause and effect", defines algorithms for building them from data and operating on them, and analyzes the circumstances under which causality can and can't be inferred from the data.
I don't understand the relevance.
Your quote seemed to be saying that that Bayesianism couldn't handle why/because questions, but Popperian philosophy could. I mentioned Pearl as a treatment of that class of question from a Bayes-compatible perspective.
Causality isn't explanation. X caused Y isn't the issue I was talking about.
For example, the statement "Murder is bad because it is illiberal" is an explanation of why it is bad. It is not a statement about causality.
You may say that "illiberal" is a short cut for various other ideas. And you may claim that eventually that reduce away to causal issues. But that would be reductionism. We do not accept that high level concepts are a mistake or that emergence isn't important.
Huh? It may be that I haven't read Logic of Scientific Discovery in a long time, but as far as I remember/can tell, Popper doesn't care about moral whys like "why is murder bad" at all. That seems to be an issue generally independent of both Bayesian and Popperian epistemology. One could be a Bayesian and be a utilitarian, or a virtue ethicist, or some form of deontologist. What am I missing?
He doesn't discuss them in LScD (as far as I remember). He does elsewhere, e.g. in The World of Parmenides. Whether he published moral arguments or not, his epistemology applies to them and works with them -- it is general purpose.
Epistemology is about how we get knowledge. Any epistemology which can't deal with entire categories of knowledge has a big problem. It would mean a second epistemology would be needed for that other category of knowledge. And that would raise questions like: if this second one works where the first failed, why not use it for everything?
Popper's method does not rely on only empirical criticism but also allows for all types of philosophical criticism. So it's not restricted to only empirical issues.
You seem to be assuming that "morality" is a fact about the universe. Most people here think it's a fact about human minds.
(ie we aren't moral realists, at least not in the sense that a religious person is).
Actually, one of the reason I stood by this interpretation of Popper was because one of the quotes posted in one of the other threads here:
Which is apparently from Conjectures and Refutations, pg 309. Regardless, I don't care about this argument overmuch, since we seem to have moved on to some other points.
Remember that in Bayesian epistemology, probabilities represent our state of knowledge, so as you pointed out, the simplest hypothesis that fits the data so far may not be the true one because we haven't seen all of the data. But it is necessarily our best guess because of the conjunction rule.
You are going to have to expand on this. I don't see how the conjunction rule implies that simpler hypotheses are in general more probable. This is true if we have two hypotheses where one is X and the other is "X and Y" but that's not how people generally apply this sort of thing. For example, I might have a sequence of numbers that for the first 10,000 terms has the nth term as the nth prime number. One hypothesis is that the nth term is always the nth prime number. But I could have as another hypothesis some high degree polynomial that matches the first 10,000 primes. That's clearly more complicated. But one can't use conjunction to argue that it is less likely.
Imagine that I have some set of propositions, A through Z, and I don't know the probabilities of any of these. Now let's say I'm using these propositions to explain some experimental result--since I would have uniform priors for A through Z, it follows that an explanation like "M did it" is more probable than "A and B did it," which in turn is more probable than "G and P and H did it."
Yes, I agree with you there. But this is much weaker than any general form of Occam. See my example with primes. What we want to say in some form of Occam approach is much stronger than what you can get from simply using the conjunction argument.
There are so many problems here that it's hard to choose a starting point.
1) the data set you are using is biased (it is selective. all observation is selective)
2) there is no such thing as "raw data" -- all your observations are interpreted. your interpretations may be mistaken.
3) what do you mean by "best guess"? one meaning is "most likely to be the final, perfect truth". but a different meaning is "most useful now".
4) You say "probabilities represent our state of knowledge". However there are infinitely many theories with the same probability. Or there would be, except for your solomonoff prior about simpler theories having higher probability. So the important part of "state of our knowledge" as represented by these probabilities consists mostly of the solomonoff prior and nothing else, because it, and it alone, is dealing with the hard problem of epistemology (dealing with theories which make identical predictions about everything we have data for).
5) you can have infinite data and still get all non-emprical issues wrong
6) regarding the conjunction rule, there is miscommunication. this does not address the point i was trying to make. i think you have a premise like "all more complicated theories are merely conjunctions of simpler theories". But that is to conceive of theories very differently than Popperians do, in what we see as a limited and narrow way. To begin to address these issues, let's consider what's better: a bald assertion, or an assertion and an explanation of why it is correct? If you want "most likely to happen to be the perfect, final truth" you are better off with only an unargued assertion (since any argument may be mistaken). But if you want to learn about the world, you are better off not relying on unargued assertions.