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In what sense do you mean this exactly, and what evidence for it do you have? I've spoken to people like Elliot, but all they said was things like 'humans can function as a Turing Machine by laboureously manipulating symbols'. Which is nice, but not really relevant to anything in real-time.
On a more general note, you should probably try to be a little clearer: 'conjectures and refutations' doesn't really pick out any particular strategy from strategy-space, and neither does the phrase 'explanation' pick out anything in particular. Additionally, 'induction' is sufficiently different from what people normally think of as myths that it could do with some elaboration.
Similarly, some of these issues we do take seriously; we know we're fallible, and it sounds like you don't know what we mean by probability.
Finally, welcome to Less Wrong!
Edit: People, don't downvote the parent; there's no reason to scare the newbies.
Where 'real-time' can be taken literally to refer to time that is expected to exist in physics models of the universe.
Another way of saying it is that human beings can solve any problem that can be solved. Does that help?
Careful here - as I mentioned above, evidence never supports a theory, it just provides a ready stock of criticisms of rival theories. Let me give you an argument: If you hold that human beings are not universal knowledge creators, then you are saying that human knowledge creation processes are limited in some way, that there is some knowledge we cannot create. You are saying that humans can create a whole bunch of knowledge but whole realms of other knowledge are off limits to us. How does that work? Knowledge enables us to expand our abilities and that in turn enables us to create new knowledge and so on. Whatever this knowledge we can't create is, it would have to be walled off from all this other expanding knowledge in a rather special way. How do you build a knowledge creation machine that only has the capability to create some knowledge? That would seem much much more difficult than creating a fully universal machine.
I don't know what point Elliot was answering here, but I guess he is saying that humans are universal Turing Machines and illustrating that. He is saying that humans are universal in the sense that they can compute anything that can be computed. That is a different notion of universality to the one under discussion here (though there is a connection between the two types of universality). Elliot agrees that humans are universal knowledge creators and has written a lot about it (see, for example, his posts on The Fabric of Reality list).
'Conjectures and refutations' is an evolutionary process. The general methodology (or strategy, if you prefer) is: When faced with a problem try to come up with conjectural explanations to solve the problem and then criticise them until you find one (and only one) that cannot be knocked down by any known criticism. Take that as your tentative solution. I guess what you are looking for is an explanation of how human conjecture engines work? That is an unsolved problem. We do know some things, eg: no induction is involved.
Explanations are valuable: they help you understand something. Are you looking for an explanation of how we generate "explanations"? Again, unsolved problem.
It's not really different. It's something that people believe is true that in fact isn't. Hume was the first to realize that there was a "problem of induction" and philosophers have for years and years been trying to justify induction. It took Karl Popper to realize that induction isn't actually how we create knowledge at all: induction is a myth.
Yes, you are called "Less Wrong" after all! I was off-beam with that.
Actually, I am quite familiar with the Bayesian conception of probability. I just don't think probability has a role in the realm of epistemology. Evidence does not make a theory more probable, not even from a subjective point of view. What evidence does, as I have said, is provide a stock of criticisms against rival theories. Also, evidence only goes so far: what really matters is how theories stand up to criticism as explanations. Evidence plays a role in that. I am quite happy to talk about the probability of events in the world, but events are different from explanatory theories. Apples and oranges.
Of course evidence makes theories more probable:
Imagine you have two large opaque bags full of beans, one 50% black beans and 50% white beans and the other full of white beans. The bags are well shaken, you are given one bag at random. You take out 20 beans - and they are all white.
That is clearly evidence that confirms the hypothesis that you have the bag full of white beans. If you had the "mixed" bag, that would only happen one time in a million.
Notice that the counterfactual event is possible (that you have the mixed bag). And even if you hold the bag full of white beans, the counterfactual event that you hold the mixed beans does occur elsewhere in the multiverse. This is what distinguishes events from theories. A false theory never obtains anywhere: it is simply false. So a theory being true or false is not at all like the situation with counterfactual events. You cannot assign anything objective to a false theory.
The actual theory you hold in your example is approximately the following: I have made a random selection from a bag and I know that I have been given one of two bags: one 50% black beans and 50% white beans and the other full of white beans and: I have been honestly informed about the setup, am not being tricked, no mistakes have been made etc. This theory predicts that if I take 20 white beans out of the bag, then the chance of that would be one in a million if I had the mixed bag. Do you understand? The real situation is that you have a theory that is making probabilistic predictions about events and, as I have said several times, I have no problem with probabilistic predictions of theories about events.
As briefly as possible:
Firstly, this seems like a step forwards to me. You seem to agree that induction and confirmation are fine 90% of the time. You seem to agree that these ideas work in practice - and are useful - including in some realms of knowledge - such as knowledge relating to which bag is in front of you in the above example. This puts your anti-induction and anti-confirmation statements into a rather different light, IMO.
Confirmation theory has nothing to do with multiverses. It applies equally well for agents in single deterministic universes - such as can be modelled by cellular automata. So, reasoning that depends on the details of multiverse theories is broken from the outset. Imagine evidence for wavefunction collapse was found. Not terribly likely - but it could happen - and you don't want your whole theory of epistemology to break if it does!
Treating uncertainty about theories and uncertainty about events differently is a philosophical mistake. There is absolutely no reason to do it - and it gets people into all kinds of muddles.
We have a beautiful theory of subjective uncertainty that applies equally well to uncertainty about any belief - whether it refers to events, or scientific theories. You can't really tease these categories apart anyway - since many events are contingent upon the truth of scientific theories - e.g. Higgs boson observations. Events are how physical law is known to us.
Instead of using one theory for hypotheses about events and another for hypotheses about universal laws you should - according to Occam's razor - be treating them in the same way - and be using the same underlying general theory that covers all uncertain knowledge - namely the laws of subjective probability.
"Bayesian Confirmation Theory"
http://plato.stanford.edu/entries/epistemology-bayesian/#BayTheBayConThe
Tim - In the example we have been discussing, no confirmation of the actual theory (the one I gave in approximate outline) happens. The actual theory makes probabilistic predictions about events (it also makes non-probabilistic predictions) and tells you how to bet. Getting 20 white beans doesn't make the actual theory any more probable - the probability was a prediction of the theory. Note also that a theory that you are being tricked might recommend that you choose the mixed bag when you get 20 white beans. Lots of theories are consistent with the evidence. What you need to look for is things to refute the possible theories. If you are concerned with confirmation, then the con man wins.
So I am not agreeing that induction and confirmation are fine any percentage of the time (how did you get that 90% figure?). When you consider the actual possible theories of the example, all that is happening is that you have explanatory theories that make predictions, some probabilistic, and that tell you how to bet. The theories are not being induced from evidence and no confirmation takes place.
You haven't explained how we assign objective probabilities to theories that are false in all worlds.
What you're talking about here is a strategy for avoiding bias which Bayesians also use. It is not a fundamental feature of any particular epistemology.
We don't assign objective probabilities, full stop.
I think you are too lost for me :-(
You don't seem to address the idea that multiverse theories are an irrelevance - and that in a single deterministic automaton, things work just the same way.
Indeed, scientists don't even know which (If any) laws of physics are true everywhere, and which depend on the world you are in.
You don't seem to address the idea that we have a nice general theory that covers all kinds of uncertainty, and that no extra theory to deal with uncertainty about scientific hypotheses is needed.
If you don't class hypotheses about events as being "theories", then I think you need to look at:
http://en.wikipedia.org/wiki/Scientific_theory
Also, your challenge doesn't seem to make much sense. The things people assign probabilities to are things they are uncertain about. If you tell me a theory is wrong, it gets assigned a low probability. The interesting cases are ones where we don't yet know the answer - like the clay theory of the origin of life, the orbital inclination theory of glacial cycles - and so on.
Distinguishing between scientific theories and events in the way that you do apparently makes little sense. Events depend on scientific theories. Scientific theories predict events. Every test of a scientific theory is an event. Observing the perihelion precession of Mercury was an event. The observation of the deflection of light by the Sun during an eclipse was an event. If you have probabilities about events which are tests of scientific theories, then you automatically wind up with probabilities about the theories that depend on their outcome.
Basically agents have probabilities about all their beliefs. That is Bayes 101. If an agent claims not to have a probability about some belief, you can usually set up a bet which reveals what they actually think about the subject. Matters of fundamental physics are not different from "what type of beans are in a bag" - in that respect.
Yes, scientific theories predict events. So there is a distinction between events and theories right? If the event is observed to occur, all that happens is that rival theories that do not predict the event are refuted. The theory that predicted the event is not made truer (it already is either true or false). And there are always an infinite number of other theories that predict the same event. So observing the event doesn't allow you to distinguish among those theories.
In the bean bag example you seem to think that the rival theories are "the bag I am holding is mixed" and "the bag I am holding is all white". But what you actually have is a single theory that makes predictions about these two possible events. That theory says you have a one-in-a-million chance of holding the mixed bag.
No, General Relativity being true or false is not like holding a bag of white beans or holding a bag of mixed beans. The latter are events that can and do obtain: They happen. But GR is not true in some universes and false in others. It is either true or false. Everywhere. Furthermore, we accept GR not because it is judged most likely but because it is the best explanation we have.
Popperians claim that we don't need any theory of uncertainty to explain how knowledge grows: uncertainty is irrelevant. That is an interesting claim don't you think? And if you care about the future of humanity, it is a claim that you should take seriously and try to understand.
If you are still confused about my position, why don't you try posting some questions on one of the following lists:
http://groups.yahoo.com/group/Fabric-of-Reality/
http://groups.yahoo.com/group/criticalrationalism/
It might be useful for other Popperians to explain the position - perhaps I am being unclear in some way.
Edit: Just because people might be willing to place bets is no argument that the epistemological point I am making is wrong. What makes those people infallible authorities on epistemology? Also, if I accept a bet from someone that a universal theory is true, would I ever have to pay out?
Popper's views are out of date. I am somewhat curious about why anyone with access to the relevant information would fail to update their views - but that phenomenon is not that interesting. People fail to update all the time for a bunch of sociological reasons.
Check with the terms of the bet. Or...
Consider bets on when a bridge will fail. It might never fail - and if so, good for the bridge. However, if traders think it has a 50% chance of surviving to the end of the year, that tells you something. The market value of the bet gives us useful information about the expected lifespan of the bridge. It is just the same with scientific theories.
That's a really powerful general argument against Bayesianism that I hadn't considered before: any prior (edit: I should have said "prior information") necessarily constitutes a hypothesis in which you have confidence 1.
I claim that the distinction you make between events and theories is not nearly so clear-cut as you seem to think. You have already made the point that distinguishing between two or more apparent theories can readily be replaced by a parameterized theory. You restrict yourself to to the case where the parameterization is due to an "event". I think most such cases can be tortured into such a view, particularly with your multiverse model. One of the earliest uses of probability theory was Laplace's use in estimating orbital parameters for Jupiter and Saturn. If you take these parameters as themselves the theory, you would view it as illegitimate. If they are more akin to events, this seems fine. But your conception of events as "realizable" differently in the multiverse (i.e. all probabilities should be seen as indicial uncertainty) seems to be greatly underspecified. Given your example of GR as a theory rather than an event, why don't you want to accept a multiverse model where GR really could hold in some universes, but not others? And of course, there's a foundational issue that whatever multiverse model you take for events is itself a theory.
What about the problem of building pyramids on alpha-centuri by 2012? We can't, but aliens living there could.
More pressingly though, I don't see why this is important. Have we been basing our arguments on an assumption that there are problems we can't solve? Is there any evidence we can solve all problems without access to arbitrarily large amounts of computational power? Something like AIXI can solve pretty much anything, but not relevantly.
How about a neural network that can't learn XOR?
The manner in which explanations are knocked down seems under-specified, if you're not doing Bayesian updating.
Nope, I just don't know what in particular you mean by 'explanation'. I know what the word means in general, but not your specific conception.
Well, that's different from there being no such thing as a probability that a theory is true: your initial assertion implied that the concept wasn't well defined, whereas now you just mean it's irrelevant. Either way, you should probably produce some actual arguments against Jaynes's conception of probability.
Meta: You want to reply directly to a post, not its descendants, or the other person won't get a notification. I only saw your post via the Recent Posts list.
Also, it's no good telling people that they can't use evidence to support their position because it contradicts your theory when the other people haven't been convinced of your theory.
Criticism enables us to see flaws in explanations. What is under-specified about finding a flaw?
In your way, you need to come up with criticisms and also with probabilities associated with those criticisms. Criticisms of real world theories can be involved and complex. Isn't it enough to expose a flaw in an explanatory theory? Must one also go to the trouble of calculating probabilities - a task that is surely fraught with difficulty for any realistic idea of criticism? You're adding a huge amount of auxilliary theory and your evaluation is then also dependent on the truth of all this auxilliary theory.
My conception is the same as the general one.
You don't seem to be actually saying very much then; is LW really short on explanations, in the conventional sense? Explanation seems well evidenced by the last couple of top level posts. Similarly, do we really fail to criticise one another? A large number of the comments seem to be criticisms. If you're essentially criticising us for not having learn rationality 101 - the sort of rationality you learn as a child of 12, arguing against god - then obviously it would be a problem if we didn't bare in mind the stuff. But without providing evidence that we succumb to these faults, it's hard to see what the problem is.
Your other points, however, are substantive. If humans could solve any problem, or it was impossible to design an agent which could learn some but not all things, or confirmation didn't increase subjective plausibility, these would be important claims.
Elliot has informed me that he doesn't think he said: "humans can function as a Turing Machine by laboriously manipulating symbols", except possibly in reply to a very specific question like "Give a short proof that humans have computational universality".
Why do you say "people like Ellliot"? Elliot has his own views on things and shouldn't be conflated with people who you think are like him. It seems to me you don't understand his ideas so wouldn't know what the people who are like him are like.