SEP does a very good job of putting Passmore's claim into context:
In 1967 John Passmore reported that: “Logical positivism, then, is dead, or as dead as a philosophical movement ever becomes.” (1967, 57) Earlier in the same article he had equated logical positivism with logical empiricism, so presumably that was dead too. At that time few would have disagreed with Passmore, even though Carnap was still alive and active. But in speaking of this movement Passmore was referring not to a movement but to specific doctrines, and his interpretation of them was much influenced by Ayer. Even so, Passmore conceded that the movement had left a legacy and that “the spirit which inspired the Vienna circle” persisted. It still does.
Part of the movement's legacy lies in contemporary philosophy of science. In the US nearly all philosophers of science can trace their academic lineages to Reichenbach. Most were either his students or students of his students and so on. His scientific realism inspired a generation of philosophers, even those clearly outside the movement. Even the reaction against various forms of realism that have appeared in recent decades have roots in the logical empiricist movement. Moreover, philosophers of science are expected to know a great deal of the science about which they philosophize and to be cautious in telling practicing scientists what concepts they may or may not use. In these respects and others contemporary philosophers promote a kind of naturalism, and by so doing they follow both the precept and the example of the logical empiricists.
There are other issues where the legacy of logical empiricism is still visible. Two different approaches to probability are still under discussion. One of them explores the objective chances of external events; this investigation follows in the tradition of the frequency theory of Reichenbach and von Mises. The second approach has an epistemic conception of probability as exemplified by Carnap. S.L. Zabell summarizes the current situation as follows:
But although the technical contributions of Carnap and his school remain of considerable interest today, Carnap's most lasting influence was more subtle but also more important: he largely shaped the way current philosophy views the nature and role of probability, in particular its widespread acceptance of the Bayesian paradigm (as, for example, in Earman, 1992; Howson and Urbach, 1993; and Jeffrey, 2004). (Zabell 2007, 294)
There is also a continuing concern for how the various sciences fit together. Some have scouted theoretical unification and others a more pluralistic model, just as the logical empiricists did. There was for a while a vogue for the disunity of science. Some even said that their conception of the disunity of science is just what Neurath meant by the unity of science. Parts of the discussion were intended as challenges to logical empiricism, but often the arguments used were pioneered by the logical empiricists themselves.
For the 30 years after Passmore's report metaphysics became ever more visible in philosophy. It was a diverse development, but in the self-conceptions of many of its most prominent practitioners there was no attempt to shun science or logic or to think that metaphysics had access to facts that were deeper than or beyond those that a proper science could reach. So the metaphysics that blossomed was not necessarily of the sort that Carnap and others combated. Most recently there are some in meta-ontology that want to reconsider and reconnect with Carnap's ontological caution.
Even in its heyday many philosophers who on either doctrinal or sociological grounds can be grouped with the logical empiricists did not see themselves that way. We should not expect philosophers today to identify with the movement either. Each generation finds its place by emphasizing its differences from what has gone before. But the spirit of the movement still has its adherents. There are many who value clarity and who want to understand the methodology of science, its structure, and its prospects. There are many who want to find a natural home within a broad conception of science for conceptual innovation, for logic and mathematics, and for their own study of methodology. And importantly there are those who see in science a prospect for intellectual and social reform and who see in their own study of science some hope for freeing us all from the merely habitual ways of thinking “by which we are now possessed” (Kuhn 1962, 1). These are the motives that define the movement called logical empiricism. As Twain might have said, the reports of its death are greatly exaggerated.