To talk about the universalism vs particularism issue, one of the issues with universalism is that it’s trying to solve either provenly hard problems, in the sense that it requires exponential or worse efficiency for an algorithm to do it, or we suspect that it’s really hard to do, and we just haven’t proved it.
One of the best examples here is learning efficiently from data, and there’s a line in a paper that talks about one of the issues for universalism in practice:
Any polynomial-time algorithm for finding a hypothesis consistent with the data would
imply a polynomial-time algorithm for breaking widely-used cryptosystems such as RSA!
And this is considered unlikely by complexity theorists and cryptographers.
This seems similar to the issue mentioned below:
This feels importantly different from, idk, a working mathematician’s view of math? Hypothesizing that somewhere out there are all the true propositions and all the false propositions is pretty different from the set of known-true-propositions, and the methodology for determining what goes in that set. Or a working software engineer’s understanding of computation, in which runtime considerations are important instead of ignorable.
The problem for mathematics in general is at least in the RE complexity class, which is wildly intractable, and even propositional logic is NP-complete in satisfiability. These are really hard problems in the general case, so hard that without radical assumptions about physics will likely remain intractable in the general case.
Universalism is a currently impractical doctrine, but one that is sometimes useful.
To talk about the universalism vs particularism issue, one of the issues with universalism is that it’s trying to solve either provenly hard problems, in the sense that it requires exponential or worse efficiency for an algorithm to do it, or we suspect that it’s really hard to do, and we just haven’t proved it.
One of the best examples here is learning efficiently from data, and there’s a line in a paper that talks about one of the issues for universalism in practice:
And this is considered unlikely by complexity theorists and cryptographers.
This seems similar to the issue mentioned below:
The problem for mathematics in general is at least in the RE complexity class, which is wildly intractable, and even propositional logic is NP-complete in satisfiability. These are really hard problems in the general case, so hard that without radical assumptions about physics will likely remain intractable in the general case.
Universalism is a currently impractical doctrine, but one that is sometimes useful.