In defense of the <i>a priori</i>
Mathematics suffers from the same so-called faults as Austrian economics. It is nevertheless useful. Let me explain. "Apodictically certain" principles play the same role in Austrian economics as axioms play in mathematics.
 Economics teaches that one finds more value in what one receives than in what one gives up in exchange. (says an Austrian)
That can be taken as axiomatically true, in the following way: to say that someone values A over B is nothing other than to say that, if he had a choice between A and B, he would choose A. This can be simply a matter of definition. Is that bad or useless? No, because mathematics is full of stuff that is true by definition but math is nevertheless not at all useless. Let's look at the attempted rebuttal to the above:
sometimes I buy something only to discover that it’s not as good as I thought it would be and that I’d probably have been better off spending my money on something else instead
But that does not contradict , because what it concerns is a change in preference. Before, when he was ignorant, he valued A over B, meaning he would have chosen A over B (proven by the fact that he did choose A over B). After, when he knew a bit more about A, he valued B over A, meaning that (had he had the choice to do over again) he would have chosen B over A.
Seems to me that the proper answer to an Austrian is not to contradict a straw man version of his assertion, not to contradict an artificially weakened version of his assertion. Or to put it another way, interpret your opponent's statement as if he meant the strongest, most defensible interpretation of his statement, rather than as if he meant a weak interpretation of his statement. I believe Popper recommended this approach: strengthen your opponent's case before answering it. If you interpretively weaken your opponent's case before answering it you will convince only yourself, because your opponent will see you as having addressed a straw man.
So how can the Austrian be answered? By pointing out to him that a person's preferences change over time, and that what he prefers today may not be what he prefers tomorrow, and so an action that maximizes his benefit today does not thereby maximize his benefit tomorrow.
He might acknowledge that.
I have to admit, one doesn’t usually see the argument from personal incredulity hanging out there all pink and naked like this outside of Creationist circles.
And yet mathematical axioms often are accepted largely because we cannot imagine them not being true. Indeed, mathematics is persuasive largely not only because the theorems follow from some arbitrary set of axioms, but because the theorems follow from axioms which we cannot imagine not being true.
If that's what's supposedly wrong with Austrian economics, then it's really just a matter of style. If there is something I'd criticize the Austrians for, it's not their own economics, but their intolerance to other economics: they are not taking the other economics on its own terms. But the same criticism applies in the opposite direction.
"We can deduce whatever we like a priori, but but this does not make any of it a priori true about the world we live in."
But some things are true a priori. It is true a priori that if you weigh less than I do, then I weigh more than you do. You can ask, "sure, that's a priori true, but what is the point of saying something so blindingly obvious?" The point is that sometimes people *deny tautologies*, in fact often their thinking amounts to denying tautologies. There is a name for this. It's called "muddled thinking". And aside from muddled thinking, there simply are limits to our capacity to draw logical inferences. Even if we know all the laws of physics, it takes a lot of labor to deduce the necessary consequences even for very simple systems, so difficult that people who go to the trouble deserve respect and a title - how about "economist"?
A large number of errors about economics are in fact errors of logic and reasoning, i.e., muddled thinking. It is not merely that people have empirically false beliefs, but that they *aren't making sense*, they are failing to rigorously apply logic. And in any case, mere a priori mathematics can be a tremendously powerful tool of inference. How can we draw the powerful inferences that we do from math, if it is a priori and therefore, supposedly, empirically empty? The reason is simple: the logical equivalence of two statements is only in the simplest cases blindingly obvious to us; often it is far from obvious - enter mathematics.