I am not proposing a dichotomy.
Nevertheless, there does seem to be some hostility from people who pride themselves on empiricism towards the value of logical argument (from axioms to theorems).
I want to discuss this. I believe this is the correct forum. The philosophy forum would not invite as any empiricists.
People seem to believe that the heart of science is in its empiricism. I think the empirical approach is important. But I see a lot of people dismiss the logical-philosophical aspects of science due to the "lack of empiricism."
If you are one of these people, can you explain your position?
Consider the success of geometry (in all its forms, not just Euclidean). What makes it so successful?
Consider the failure of empirical approaches to things like the stock market. What makes them so unsuccessful? Can the approaches taken by the Santa Fe Institute help in this regard?