The post-World War II intellectuals were a remarkable crew. Their thinking was motivated by the apocalyptic experience of the war, and sharpened by their experiences in the war, at the front or in back offices, and they learned a bit about tragedy but a great deal about planning; but it also matured after it, in self-critical reflection on the work that that motivation provoked in them. In fact the super-confidence of the post-war generation in the social sciences was fuelled by large government and foundation funding--think about people like Albert Hirschman, Edward Shils, Daniel Bell, among many others. Their confidence meant they thought they had something serious and important that could be communicated outside of their disciplinary bounds. David Riesman's The Lonely Crowd was not only a bestseller, as were many other books of this sort (such as John Kenneth Galbraith's The Affluent Society), it even made it into later popular culture; Riesman's book's title became a line in an Eagles song.
A few thinkers were more skeptical, like Hannah Arendt and Raymond Aron, Albert Camus and Lionel Trilling (and, slightly older than them, Reinhold Niebuhr and Ernst Kantorowicz), but even they thought of themselves as having something direct to contribute to society, something to say beyond the confines of their professional discourses. If they did not have a direct metaphysical confidence, at least they had an epistemic confidence.
Alongside these two ways of being intellectual, there were others; consider the tremendous work of the social scientist WEB DuBois and, after him, writers like Zora Neale Hurston (a trained anthropologist), Howard Thurman, Ralph Ellison, James Baldwin; these intellectuals were pretty much cut out of the funding game by racism, so they developed their own critiques and visions of society from the outside; they were joined by postcolonial and anti-colonial writers too, from Gandhi and Frantz Fanon and Aimé Césaire to CLR James. (DuBois in particular is an American social and cultural thinker of the first class; because he finally left the US, and because of our racism, he's massively ignored here, but he shouldn't be--books like Darkwater, Dusk of Dawn, and Black Reconstruction in America merit everyone's attention.) These thinkers had less confidence of getting a hearing from the overall public, but it was not because their work was professionally narrow, it was because the overall public was effectively white, and deeply unreceptive to their words. Nonetheless, all of them wrote for an audience that was not simply professional. And many of their works remain vital for an understanding of today, perhaps in ways that the works of the "post war intellectuals" are not, precisely because this more marginal group was gripped by issues that the post war intellectuals studiously avoided--most obviously, empire and race.
Anyway, back to the first group, the ones we can safely call "post-war intellectuals," most of whom were social scientists of a humanistic bent (or humanists open to social theory). In a way they were at the heart of the early cold-war consensus that intellectual effort could be usefully directed to common life and would produce useful knowledge. It seems to me that theirs was effectively a deeply anti-tragic mindset; the problem was fundamentally that we needed to apply intelligence to the world, and the world would be bent to our will. Their predecessors were folk like Dewey and Walter Lippmann, whose own newspaper column continued through the 60s. (Group # 2 had another view, and the third group was a vital public culture that lacked the audience it deserved, though it had some audience for itself anyway.)
The Great Society was their apotheosis, that and the Space Race. What destroyed this group's self-understanding, not just in the United States, was Vietnam, with an assist from the racialized "Crisis of the cities" that happened in the 1960s. At best, Vietnam was a tragedy; at worst, it suggested a malicious heart driving the modernizing project itself. The recognition of "urban poverty" as an intractable problem suggested that the Civil Rights struggles of the 1950s, which they had all supported, not at great cost to themselves, would not be enough to grapple with the core sins of the United States, that more would need to be done. (The fact that rural poverty didn't occupy as much attention seems related to the whiteness of the majority of these intellectuals, and thus their ability to see the (racial) other as a "problem" needing addressing, while the white poor, they perhaps believed, they would always have with them.) A study of this era of American intellectual life would be enormously interesting; while we have studies of the so-called "New York Intellectuals," we don't have anything that grapples with this intellectual era, so far as I know.
All of this is simply prolegomenon to invite you to read this fine summary of Lévi-Strauss's life and intellectual trajectory. Lévi-Strauss was in some ways a French analogue to the American Big Social Science of the post-war era. He began with ambitions to render anthropology, and broadly the "human sciences," more "scientific," but ended with a good deal more skepticism about that project. As the review put it, "[w]hat began as an appeal to scientific rigour in the humanities in the 1950s ended as an interpretative philosophical exercise." In a way, Lévi-Strauss's Vietnam was Michel Foucault, and the larger French intellectual reaction against the earnestness of systematicity. This was sparked by the student and labor unrest in Paris and around the country in the spring of 1968, but it had been emerging before that, too.
I wonder if the energy of Lévi-Strauss and those other post-war public intellectuals could be recaptured or redeployed now. We are far from having the kind of well-bounded, clearly policed, unified public culture in which they flourished, for good and ill. Then again, there are lots of voices out there, though they often seem to couch their arguments less in a humanistic idiom and more in a scientistic one; even the economists present themselves as scientists. (That reminds me of a line delivered by the late great sociologist Edward Shils. "A political scientist," he said. "With the 'science' there understood in the same sense as 'Christian Science.'")
Public intervention by thinkers who do not present themselves as scientists these days seems hard. I suspect that also has something to do with the ideologizing and partisanship which has been attached to academics since the 1960s. More to think about still.
UPDATE: I've found another, nice review of the Lévi-Strauss biography, which emphasizes the imperial and post-colonial context of Lévi-Strauss's work. I highly recommend it.