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DanielLC comments on Frugality and working from finite data - Less Wrong
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How about this: it doesn't matter.
If we want to build a device that only works if a certain theory is true, we can use it to test the theory. If not, you can do what you want either way, so what does it matter?
There's still similar useful problems. For instance: you can keep getting new data on economics, but there's no way anyone's going to let you do an experiment. In addition, the data you're getting is very bad if you're trying to eliminate bias. It can't be solved in that way, though.
This is somewhat true of macroeconomics, but manifestly untrue of microeconomics. Economists are constantly doing experiments to learn more about how incentives and settings affect behavior. And the results are being applied in the real world, sometimes in environments where alternative hypotheses can be compared.
And even in macroeconomics, work like that explained in Freakonomics shows how people can compare historical data from polities that chose different policies and learn from the different outcomes. So even if no individual scientist will be allowed to conduct a controlled experiment on the macroeconomy, there are enough competing theories that politicians are constantly following different policies, and providing data that sheds light on the consequences of different choices.
Yes; if your theories don't differ in their constraints on expectation, you both can't test the difference and the difference doesn't matter for the future.
The problem is when your theories diverge in the future predictions such that you would take radically different courses of action, depending on which was true.