One thing that I always like to be clear about.... is that there is nothing special to a ph.d. it just produces scholarship and scholars, and scholarship and scholars do not need the ph.d. The doctoral degree is only a credential, there is nothing more, nothing particular that differentiates it from other forms of expertise or even similar forms of expertise gained outside of the institution.
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So i would and have argued that the 'credentials' have no relation to intellectual life. Credentials matter to the institutions and the holders. Similarly, 'intellectual life' does not require credentials and should not be seen as different from the everyday lives of large sections of the population. I think sometimes we idealize intellectual life to mean the lives of a certain form of scholar, and I find that model of intellectual life to not actually exist for most people, even most scholars.
So we have credentials and institutions in my view, and both are part of a capitalist system, market. The market is co-constructed to the benefit of the institutions and credentialed individuals. The problem has nothing to do with intellectual life at all really. We add the term to make a claim about greater purpose, much as sociology does with its claim for a public sociology. That is an attempt to legitimize or justify through appeal to practical worth, but what I've argued above is that there is no necessary practical worth to the ph.d. It only has worth in terms of the institutions that require it. Thus I think you can conclude that the appeal to greater worth will likely be received internally as adding additional requirements, and externally with a degree of credulousness.
The original impetus behind the reforms of higher education instituted most memorably by Charles Eliot of Harvard, and the creation of graduate research universities like Johns Hopkins in Baltimore, the University of Chicago, and Cornell, in Ithaca, NY was not only to update the curriculum - as society not only secularized, but became increasingly dependent upon a type of knowledge not limited to reading dead languages - but to create a set of standards by which that knowledge could be judged as credible. Being publicly available, open to serious criticisms from peers, a furious and free exchange of views and ideas - these ideals set the stage for the institutionalization of an entire set of professions whose entire purpose was for the benefit of the larger society.
Over time, however, as specialization increased and intellectuals became more and more concerned with the twin goals of protecting their little fiefdoms and ensuring their on-going participation in their institutions (as well, I should add, as the glut of students in graduate programs in the 1960's, thanks in no small part to the education deferments from the draft), the link between much of what constitutes "intellectual life" is completely divorced from the larger society. In part, the original "culture wars" began with such a bang precisely because so much of the discourse in the humanities is unfamiliar to the general public. It is parodied and dismissed easily enough because it doesn't serve the interest of the larger society, but the individuals and institutions of which they are a part. Reconnecting the humanities and their researches to the needs of society at large - and please don't give me the whole, "but-pure-research-is-necessary-because-you-never-know-what-will-come-of-it" bit; in physics, chemistry, engineering that may be true, but not in the study of 19th century French poetry - includes starting with differentiating between "participating in the intellectual life of the society" and "getting a Ph.D.".
If we start with that distinction, accept it as a guide, we might very well have some interesting and innovative ways of imagining not just higher education, but the place of the life of the mind in American society.