Varieties of Thickness
Mark,
The debate between “thick” and “thin” conceptions of libertarianism encompasses several interrelated but more specific debates, having to do with (1) correct application of the non-aggression principle in hard cases; or (2) libertarian strategy and the possibility of there being cultural, intellectual, or other causal preconditions for a free society to emerge, survive, or flourish; or (3) views about the likely effects of liberty, and whether freedom will tend to produce more of certain rare positive goods, or to undermine certain prevalent (but non-coercive) positive evils; or (4) whether the best logical grounds for libertarianism (whatever that may be) also justify some further set of voluntarily-adopted beliefs, principles, projects, practices, traditions, institutions, etc. If you’re interested, I’ve discussed (1), (2), and (4) at some more length in my remarks from the Molinari Society symposium on thickness, and (3) briefly towards the end of my remarks on Matt MacKenzie’s paper on libertarian theories of exploitation.
Because the debate involves a lot of smaller debates that are interrelated but logically distinct from each other, and because many people who consider their conception of libertarianism to be “thin” (e.g. Jan Narveson) often actually end up endorsing a thicker conception in at least one of these respects (the “thinness” that they have in mind in their self-identification usually just amounts to accepting fewer thick commitments in total than are accepted by most self-identified advocates of a “thick” conception), I don’t think there is any good single formula to separate the thick from the thin. The closest that you can come to would be something like this: if you believe that libertarians should (in some sense or another, yet to be discussed) concern themselves (in some sense or another, yet to be discussed) with stuff other than just the non-aggression principle, and ought (in some sense or another, yet to be discussed) try to non-aggressively promote stuff other than just consistent non-aggression as part of their libertarian program, then you’re advocating a thick conception of libertarianism. If not, then you’re promoting a thin conception.
For what it’s worth, the internecine battle you’re thinking of, between paleolibertarians and so-called “cosmopolitan” libertarians, is not really a battle between thick and thin libertarians. Both those who think (1) that voluntarily cultivating some form of parochial traditionalism is (in some sense) vital to libertarianism, and those who think (2) that voluntarily cultivating some form of anti-traditionalist “cosmopolitanism” is (in some sense) vital to libertarianism, are advancing a thick conception of libertarianism, and battling over which thick conception is the right conception. (There are also those, like me, who think (3) that the battle, such as it is, is largely founded on a confusion, and who advance quite different claims about the best social-intellectual context for liberty from either of the two warring parties. There are also those who think (4) that libertarians shouldn’t be feuding over this stuff at all, and should just push the non-aggression principle and nothing else, wherever they go, whether to rock-ribbed but non-violent white supremacists, or to cocktail parties by snooty but non-violent New York intellectuals, or to rabble-rousing but non-violent popular liberation movements, or to kooky but non-violent survivalist-conspiracy theory types, or whatever. Only those who advocate (4) are advancing a thin conception of libertarianism.)
Hope this helps.