Suppose I admit that there is a difference between propositions which are self-evidently true in themselves, and propositions which I take to be self-evidently true, such that there may be self-evidently true propositions which I do not recognize to be self-evidently true (or even true for that matter), and also that I may take some propositions to be self-evidently true which are not self-evidently true (and possibly not true).
Am I justified in believing that those beliefs which I think to be self-evidently true are self-evidently true, or else at least are true? There are two ways I could go about providing justification: the first is to claim that all or at least some propositions which I take to be self-evidently true must of logical necessity be self-evidently true. The second is to claim that my commitment to some proposition which I take to be self-evidently true being true is a properly basic commitment. That is to say, in the absence of a defeater, (which admits not of a defeater-defeater or cancelling defeater) we ought to say that we are justified in maintaining beliefs which we take to be self-evident as foundationally basic beliefs.
Problem is, if I say that there are some beliefs which I should recognize to be properly basic in virtue of seeming to be self-evidently true, then is my commitment to their being properly basic itself self-evident, properly basic, or neither? I think it can’t be properly basic (one could see the beginning of an infinite regress). But, an appeal to some set of beliefs being ‘Properly Basic’ in Plantinga’s sense, and thus justified in the absence of arguments, is not plausibly self-evidently true. If neither, then can my suggestion that beliefs which appear self-evidently true to us qualify as properly basic beliefs (and which are thus justified)?
Perhaps an appeal to proper basicality is itself properly basic in a non-vicious way (in a basic way). It makes no sense to ask how one justifies a belief in proper basicality itself if that is just a properly basic belief, and it can make no sense to ask for a justification for that properly basic belief.