I'd only like to add a small contribution, concerning Mises's argument that "The human being cannot see the infinitely small step" and thus continuous functions cannot be used as models.

Discretely sampled (digital) signals are used all the time in engineering, and they are analogous to their continuous counterparts (analog). Particular care must be taken when "converting" between one and the other; but for most purposes they're pretty close.

All the appliances you have at home now take discrete samples of continuous quantities (physical quantities like temperature and such). Just because a human can't sample a signal / economic quantity infinitely, it doesn't mean that math must be taken out of the equation entirely. You just need to bend your math a bit to accommodate.

http://en.wikipedia.org/wiki/Sampling_(signal_processing) (And notice how there -is- math despite the fact that such systems cannot discern infinitely small changes in quantity.) (Edit: The link parser doesn't like that ending braces somehow; it should be included in the link.)

As a personal note, some people's narrow views simply blow my mind, how they can dismiss entire subjects with just one fallacious argument.