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Exactly.
My view is that embracing the branches of mathematics that map onto their methods of analysis would benefit them, by immediately integrating a bunch of known results from those fields, and would make it easier for mainstream academics to embrace their work.
The empirical methods of mainstream econ work with data, once data has been collected. The a priori methods of Austrians have the benefit that they're suitable for analyzing new phenomena, such as Bitcoin, before there is data on it. Satoshi had to use Austrian, a priori thinking, to create it.
But now we have 16 years of data too, and I think it's easier to spike most people's interest by showing them the data in the form of an NGU chart, than it is by getting them to read the white paper and understand the game theory :) Which is an example of how empiricism can be useful.
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Yes, Austrians acknowledge the usefulness of empiricism for doing economic history and demonstrating how economic principles played out in the past.
I think they do themselves a disservice in seeming to oppose the use of empirics at all, when what they oppose is the use of empirics for proving theory.
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It may benefit them, however, that is not the way Austrians have pursued their theories from Menger to the present. It is outside of their methods of theoretical exploration.
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