I'm a lowly grad student but even I find this post to be quite ridiculous, especially when the OP claims himself to be a top-10 tenured professor.
Really just taking an example, you insist that utility functions and indifference curves don't exist. Well, if you know the existence of utility functions (up to regularity conditions), then there's no issue in deriving indifference curves. Note here I'm using the microeconomic definition of utility functions and indifference curves, not the laymen's intuitive feel on what "ought" to be an indifference curve. So the issue boils down to showing to you the existence of utility functions. Let's not be that restrictive, as it is possible that utility functions can not exist (i.e. lexicographic preferences). So let's talk about more abstractly in preference relations.
So you probably now have issues with the existence of preference relations. You're probably going to argue that a lot of experiments have shown that people violate the axioms of preferences (i.e. transitivity, completeness). Ok fine. And then you're going to cite a bunch more other neuroscience studies to say that people do all this crazy shit. Fine, I know that. Hell, even I know I don't obey the axioms of preferences on a day-to-day basis. But for things that matter (i.e. not trivial experiments on undergrads where the only thing at risk is probably like $10), how many examples and studies can you cite that people violate these things?
Here, since you like rhetorical questions so much, here's a question to you. You seem to think that physics is supreme of all of sciences. Modern physics is based on mathematics. Have you heard of Godel's Incompleteness Theorem (http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems)? But this doesn't seem to bother physicists that much now does it?