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a source familiar with the matter
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He's British so nobody can tell one way or the other

They are tautological but not axioms

2+2=4 can be proven as a theorem of mathematics

Another example:

"Every effect has a cause"

Can you think of some way this could be tested?

Can you think of some way the human action claim can be tested?

A more familiar example:

"A binding minimum wage will result in higher unemployment than would otherwise have been the case"

Can you think of some way to test this?

You would have to apply and not apply the minimum wage to the same group of people at the same time (or perhaps you can find a large population of clones in identical circumstances).

if they have this, they are pro-DEI

"Earth's climate alternates between ice ages, and greenhouse periods during which there are no glaciers on the planet. Earth is currently in the ice age called Quaternary glaciation."

https://en.wikipedia.org/wiki/Ice_age

It depends on the nature of the theory.

Suppose the theory is that all unmarried men are bachelors, or that 2+2=4, or (to take an actual example from Mises) that human action is aimed at some goal.

Can you imagine an experiment that could disprove any of these?

On the other hand, suppose the theory is that an electron has a certain mass, or that ice melts at a certain temperature and pressure. It is very easy to imagine an experiment that might disprove such a theory.