"Applied Rationality Training Regime" #9: Double-Crux

 

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January 9 brings us to "Training Regime Day 9: Double-Crux" which startled me considerably; I'd read some other essays which talked about this technique, and now I think I know why I had a problem with them. 

  An argument (which may be embedded in something more complicated) is a sequence of statements where each is supposedly justified, whether because it's just plain obvious ( = an axiom) or because it follows from previous statements ( = an inference.) If you accept (the conclusion of) an argument, the crux of that argument for you is simply a crucial point...one for which you're aware that you'd change your mind if that point's justification failed. If Joe doesn't believe your argument, then there are one or more specific points you disagree at. The double-crux claim is that you and Joe should normally be able to find some one point which is crucial to both of you: a double-crux. (It might be a conjunction: (the sun is a fried egg AND 2+2=17)). If you can convince him it's true, he'll change his mind about the overall argument, but if he can convince you it's false, then you'll change yours.  Something like that; a point on which to focus. And with a little luck, it'll be something you can look up or otherwise settle easily. Without that luck, at least you'll have identified the disagreement, which is progress anyway. You can start looking for parts of the crux to serve as sub-cruxes.

  Mark suggests two kinds of crux-searching. The first, "proposer/listener", has you taking your argument and thinking which steps are cruxes for you...and you propose these to Joe, to see if they are crucial for him too. If nothing comes up, swap roles and try again. The second crux-search, "model unpacking", may involve exactly the same argument-steps, but the change in focus is total. Instead of thinking of a proposition as coming directly from data, assertions about the world, think of it as reflecting a model which is influenced by that data. Instead of thinking about the argument as a sequence of justifications, think of it as a traversal, an exposition, of your underlying model. The crucial statements are those which expose crucial aspects of that model -- so that if Joe accepted them he'd accept the conclusion.

  I'm not sure how much difference it should make in practice, but over the years I have moved away from thinking about arguments as step-by-step justifications. Perhaps it comes from actually teaching proof techniques in computer science classes long ago, or perhaps it comes from further back ...  My wife says some of our college seminar classmates were really annoyed that they couldn't tell what I actually supported, since I would argue pretty much any side of anything. But I was stunned by one who said "I just don't feel the need to believe the logical consequences of my beliefs." I'm not sure how double-crux would have found something to work with there. 

  Nowadays, I tend to think of almost everything through models, models which I express to myself, when I want to get explicit, as Bayesian bookshelves where each model is an imaginary book whose width is the probability I assign it. Evidence makes them thicker or thinner...it doesn't generally make them go away. There might be a crux somewhere, but it's not the focus of the enterprise, it's not the way I generally try to think. So I've been thinking, today, about how to unpack models; thinking about models that I've depended on for a lifetime, and about models that have changed a lot quite recently. My views on minimum wage have changed sharply...but not because I've rejected some set of previously convincing-to-me arguments or even changed mechanisms in the model, but rather as a function of gradual and continuing changes in my models of the prospects for AI alignment. Tentative and indirect, but it seems to have become the way I think.Changes happen, yes, but are cruxes really the right way to think about it? This is not clear to me, except in a trivial sense. Well, I'll go on thinking.

Changes happen; today is National Balloon Ascension Day, and it's Karel Čapek's birthday. We keep dreaming up new tech, and the dreams keep coming true. Happy birthday, Karel.