If maths is supposed to apply to the universe and doesn't then, that is a problem. But most of it doesn't apply to the universe, And it is physics that is supposed to apply to the universe.
And physics runs on math. If math didn't work, then physics wouldn't be able to run on it. The fact that the same results which you get when you perform a mathematical operation on purely abstract symbols also hold when you apply that mathematical operation to real, concrete things suggests that mathematics has some general effectiveness as a method for deriving true statements from other true statements.
We can do this consistently enough that when we fail to get predictive results from mathematical formulas in real life, we assume we're using the wrong ma...
One of the most annoying arguments when discussing AI is the perennial "But if the AI is so smart, why won't it figure out the right thing to do anyway?" It's often the ultimate curiosity stopper.
Nick Bostrom has defined the "Orthogonality thesis" as the principle that motivation and intelligence are essentially unrelated: superintelligences can have nearly any type of motivation (at least, nearly any utility function-bases motivation). We're trying to get some rigorous papers out so that when that question comes up, we can point people to standard, and published, arguments. Nick has had a paper accepted that points out the orthogonality thesis is compatible with a lot of philosophical positions that would seem to contradict it.
I'm hoping to complement this with a paper laying out the positive arguments in favour of the thesis. So I'm asking you for your strongest arguments for (or against) the orthogonality thesis. Think of trying to convince a conservative philosopher who's caught a bad case of moral realism - what would you say to them?
Many thanks! Karma and acknowledgements will shower on the best suggestions, and many puppies will be happy.