In a discussion on method, namely on whether there should be an empirical approach to economics, it’s common to invoke the arguments of economists like Menger and Mises. The latter, especially, spent a lot of time developing his own method and criticizing positivism. But, these were the methodological debates of the late 19th century and the first 2–3 decades of the 20th. Not only did pure theory (logic, deduction) win, but it did so because clearly the majority of well-known economists followed that route: Marshall, Keynes, Pigou, Fisher, et cetera. The empirical approach of today is not the same method.
Empirical economics today is mostly economic history, but it does go a little beyond this. Scientists say they can’t prove anything, but they can falsify their theories. This is an acceptance of human fallibility, and it assigns to any given theory some probability of being right — this probability is subjective, because two rivals may place two different probabilities on the same theory. What the empirical approach allows for is to look at and test the evidence, and based on this evidence we can revise that probability we attach to the theory. When economists want to falsify something, a downward revision in the probability of the theory being right is what they really have in mind.
There is no pure theory–empirical dichotomy. Most economists, except those on the fringe (is my guess), are theorists first, empiricists second. Empiricists test theories, they don’t develop them based on their tests (the test can make them re-think the theory, though). Economists are theorists first for a good reason. The bulk of good economic theory has been developed deductively, from Richard Cantillon and Adam Smith down to Paul Krugman and more modern economists. But, deduction isn’t perfection, and there were debates (e.g. J.B. Clark v. Böhm-Bawerk; Keynes v. Hayek; etc.) with no obvious winner, even before statistical empiricism was a big thing. Deductive economics has not been able to achieve consensus on important topics, and the number of topics grows as they become more complicated.
Empiricism provides a little bit of a safety net, providing us with another tool when there’s disagreement. It’s especially handy when we’re talking about complex phenomena, where the probability of logical error increases. The point isn’t to displace pure theory, but to reinforce it.
I think people who are skeptical of empiricism in economics do often implicitly acknowledge its strengths. There is an intuitive incentive to using empirical evidence to support your theory, not just as an illustration but as evidence. You want to persuade your rival that your theory is right and relevant, and empirical evidence does this. It works in reverse too. When we’re surprised by the data — it doesn’t look the way we thought it would —, most of us rethink our priors. This is empirical economics.