Also, trying to have preferences about abstractions, especially infinite ones, seems bound to end in tears, i.e. a complete mess of an ontology problem. You’d import all the problems of philosophy of mathematics in and heap them on top of the problems of ethics. Not to mention Godelian problems, large cardinal axiom problems, etc. Just the thought of trying to sort all that out fills me with dread.
Also, trying to have preferences about abstractions, especially infinite ones, seems bound to end in tears, i.e. a complete mess of an ontology problem. You’d import all the problems of philosophy of mathematics in and heap them on top of the problems of ethics. Not to mention Godelian problems, large cardinal axiom problems, etc. Just the thought of trying to sort all that out fills me with dread.
Scary, and I haven’t even finished converting myself into a pure mathematician yet. :-) I was hoping to avoid these issues by somehow limiting preference to programs, but investigation led me back to the harder problem statement. Ultimately, a simpler understanding has to be found, that sidesteps the monstrosity of set-theoretical infrastructure and diversity of logics. At this point though, I expect to benefit from conceptual clarity brought by standard mathematical tools.
Also, trying to have preferences about abstractions, especially infinite ones, seems bound to end in tears, i.e. a complete mess of an ontology problem. You’d import all the problems of philosophy of mathematics in and heap them on top of the problems of ethics. Not to mention Godelian problems, large cardinal axiom problems, etc. Just the thought of trying to sort all that out fills me with dread.
Scary, and I haven’t even finished converting myself into a pure mathematician yet. :-) I was hoping to avoid these issues by somehow limiting preference to programs, but investigation led me back to the harder problem statement. Ultimately, a simpler understanding has to be found, that sidesteps the monstrosity of set-theoretical infrastructure and diversity of logics. At this point though, I expect to benefit from conceptual clarity brought by standard mathematical tools.