[Wissmania]

"Philosophers, he posited, would be better off if they stopped trying to prove things like scientists, an impulse he believed led thinkers to overlook how philosophy might stimulate the ‘mind’s excitement and sensuality’. Rather, they ought to limit themselves to explaining how a system of thought is possible."

Can someone explain what this last sentence means?

[bobwaycott]

In simplest terms that don't depend too heavily on philosophical references or terminology, I believe he means the philosophical task shouldn't be to prove a thing is or isn't, but that a thing could be—that a set of plausible explanations exist or could exist to provide enough convincing power that a given system of thought or a different state of affairs is not impossible to conceive of or consider capable of existing.

[earljwagner]

It sounds like Foucault's concept of a "discursive formation", basically a Kuhn-style paradigm. Foucault was interested in the social conditions and context that enable certain statements to be uttered, and interpreted as meaningful.

More broadly, Nozick's focus shifted away from logical proof as a form of argument, the hallmark of Anglo-American Analytic philosophy. It seems to shift to a more Continental (European) style, in which philosophers point to patterns, aiming to evoke insights (e.g. Foucault and more recently Žižek).

[hyperpape]

It's pretty much meaningless without more context than the article gives. It's similar to phrases that've been used in connection with historical philosophers like Kant, the purest analytic philosophers like Carnap, and many others of different schools.