I had written:
in my scheme of things begin refuted is the only reason not to believe (tentatively accept) a theory,And Peter D had replied:
That would leave you believing multiple incompatible theories, since there are multiple incompatible unrefuted conjectures.This is a good issue to raise.
The outline of the answer is: you can and must always reach a state of having exactly one non-refuted theory/idea/conjecture (for any single issue). (Note: theory/idea/conjecture are basically interchangeable, see: http://fallibleideas.com/ideas )
You are correct that if it weren't for this then our epistemology would not work (pending a brilliant new idea). We have known that for a long time and solved the problem.
Around 20 years ago, David Deutsch was creating a new educational philosophy called Taking Children Seriously.
One of the core ideas of that philosophy is a concept he calls "coercion". Be careful b/c it is defined differently than the dictionary. When clarity is desired, it can be called TCS-coercion.
TCS-coercion is the state of having multiple contradicting and unrefuted conjectures active in your mind, and acting or choosing, using one as against the others, while the conflict is still unresolved.
This issue has been important to David's views on epistemology and education for some 20 years. In that time, it has been addressed!
TCS-coercion is a crucial concept which is connected not only to epistemology and education, but also to psychology, to the issue of force and the issue of suffering. It is consequently connected to politics and to morality. I will not be surprised if connections to other fields are found too.
As an example of a possible major consequence of these ideas, we have conjectured that TCS-coercion A) always causes suffering B) is the only cause of suffering.
TCS-coercion is not an easy to understand concept. Many people interested in TCS have failed to grasp it, and there have been many conversations on the topic.
Another big idea, which is pretty easy to understand the gist of and may be interesting (but which is much harder to substantiate) is this: coercion-theory is basically the theory of disagreements (conflicts between theories) and how to resolve them. The rational truth-seeking method for approaching disagreements is the same when the ideas are in one mind or in two separate minds. Disagreement in one mind is TCS-coercion and disagreement in two minds is conflict between people and in both cases the conflict should be resolved by the same truth seeking methods that create harmony/cooperation.
The problem Peter brings up about multiple unrefuted and incompatible conjectures, and the issue of TCS-coercion, are closely related. They basically share a single answer to the question: how does one avoid being coerced?
Addressing it is not simple. My guess is you (Peter, and most of the audience) will not be able to understand the topic before you understand the more basic points of Popperian epistemology like induction being a fictitious process, justificationism being a mistake, the impossibility of positive support, that all observation is theory laden, fallibilism, the communication gap, that all learning is by C&R, and so on.
However if you are interested the best place to start, for purposes of getting straight to the meat of the issue and skipping the prerequisites, is by reading these:
If you don't understand them, or think you see a flaw in them, and you wish to comment, please try to make your comments simple and narrow and aim to focus on one important thing at a time. I think if we talk about everything at once it will be very confusing.
Besides reading those pages, it would also help to read all the other pages on that website, all of my blog posts, and all of David Deutsch's posts that you can find in the FoR list archives. Plus various books.
If you think that's a lot of reading you are correct. But it helps one learn. I myself read every single one of David's TCS emails in addition to his FoR emails and everything else I could find. That was around a decade worth of old emails from before I joined the list. Reading them helped me to understand things better.
Anyone interested in learning more these topics can also join the email list for it: http://groups.yahoo.com/group/fallible-ideas/