You seem to think it is somehow not 'hard science' to study dynamic nonlinear systems, and that no good can come of such study. [ ... ]You answer does not address whether it is possible that there might exist a hard science of economics, as opposed to a mere philosophy, which was the original point. Characterizing economics as a dynamic nonlinear system (which it certainly is), does not invalidate it as a subject of hard science.
The problem is not that the economy is non-linear, the problem is that the system is too big and complex, and it has so many unpredictable external inputs, that we cannot build a useful scientifically sound model for it. To have any hope of being predictive, the model would have to include corporations and consumers of all size, governments, religions, the media, greedy dishonest bankers, etc. etc. One cannot predict predict its behavior with a few simple equations of three or four variables whose values have to be guessed. That is not science, it is pseudo-science.
Science isn't about making models that perfectly replicate the systems they model (that would be duplicating a system).
It's about making models that work within relevant constraints, with sufficient descriptive and prescriptive power. For instance, if I want to predict where a billiard ball goes, I can use Newtonian physics, without worrying about the quantum states of each particle that composes it. I'm concerned with the macro system--getting a ball into the pocket, and the Newtonian model does the trick.
Or worry about modeling the interactions of gazillions of water molecules that flow past the blades of a hydro turbine to make the thing work.
Would you call that pseudo-science? Am I missing your point?