Dear Roger Schlafly,
Logical/Empirical Positivism is a term notoriously resisting clear definition. I agree that it has a number of interesting and even desirable facets, but overall, I think, that it has led (and under the cover of analytical philosophy still leads) science into a dead end.
Three criticalities:
POSITIVISM: The term implies analysis, affirmation and verification, which it inherited from the linguistic turn (e.g. Frege, Wittgenstein). But already the late Wittgenstein denied language to be positively=affirmatively tractable and Quine's confirmation holism kissed the idea of scientific Positivism goodbye. Only Lego-worlds are affirmatively tractable.
LOGICAL: Today there are more than a dozen of most varied logics in use. Which one is the right one? Moreover, all of them suffer from what is called the foundational or grounding problem of logic. The idea that logic represents something in the world goes into the face of philosophical tradition since Kant, who located it in the mind. This is why the '3-uns' of the contest theme are mere logical pastime and have no effect whatsoever in physics or elsewhere.
EMPIRICAL: Positivism, by discriminating metaphysical ideas like causation, elevated instrument readings, photon counter knacks, etc. to the level of empirical evidence. Ever since scientists verify theories by instrument readings (data). And don't absurdities attributed to data like entanglement, Big Bang and multiverses confirm Kant, i.e. that logical constructions have no existence in the world?
Overall, positivism (unfortunately) isn't dead but has survived in analytical philosophy, which emphasizes analyticity and hence logic, with the consequence that science has adopted the processuality of logic and hence become temporal itself. This - timelessness vs. time - in my opinion, is the key difference between classical and modern science and surfaces in the difference between law and model.
Heinz