When Russell and Wittgenstein were hot on the topic, the term 'logical atomism' was used a lot. Russell (though not an empirical scientist) made appeal to 'direct acquaintance' for getting at the 'atomic units' of meaning.
Some of this was passed on to the logical positivist movement. The LPs saw the Tractatus, at least some of it, as their starting point. Wittgenstein did maintain contact with some of the LPs and the Vienna Circle(especially Neurath and Waismann, though the names Carnap and Ayer are more famous now), so there must have been some mutual understanding there.
If you take the time to read the Tractatus (the much later work, Philosophical Investigations is read much more), you see that it is a far more mystical and transcendental work than anything Russell or the VC were capable of. Even German-speakers who didn't understand that approach to philosophy and logic, upon reading it in German, found its use of the language breathtaking and groundbreaking (as groundbreaking as Musil, a fiction writer).
Frege (along with Peano) gets much of the credit for inventing modern logic, which had hitherto largely been trapped in Aristotle's syllogism for formalisms (though Peirce, an American pragmatist/pragmaticist developed much of the same thing independently). Still, Russell, Whitehead and Wittgenstein made considerable contributions to the early development of it.
I believe the post-modern episteme finds in Wittgenstein, like Kierkegaard and Nietzsche, a far more amenable mind than either Russell or Popper. And Feyerabend is a true post-modern.
Charles Jannuzi