My proofs for Islam

[Angrboda]

I am saying it perhaps is properly basic and all we can do is appeal to other proper basic facts that would contradict it. 

One of the properties of some properly basic beliefs is that they are incorrigible. That to deny them would result in a contradiction or logical inconsistency. It wouldn't be conclusive, whether your belief were incorrigible or not, but if it were, you would have a strong argument for your belief, and if it weren't, then at least you've narrowed the field with respect to what you can argue on its behalf.

Properly basic beliefs, justification, foundationalism and the corresponding epistemology in general are very broad topics, so a discussion of what makes a belief properly basic could easily get mired in detail and go nowhere. But at a minimum, I would have to ask whether you are appealing to some form of reformed epistemology, or more classical foundationalism. The distinction matters, and the term 'basic belief' is used in both.

Beyond that, the purpose of argument is to persuade. If you think that something is properly basic, and those you are attempting to persuade do not, you're not going to succeed in persuading them. So if we have a difference over what is and is not properly basic, and the rest depends upon that, then we have to stop right here. We can go no further and further attempts to persuade us on the basis of it being a properly basic belief is just spamming. You will have stopped talking to us, and simply be talking to yourself.

The only additional thing I would add is that reasonable and healthy adults disagree as to whether something is or is not properly basic, then that is a strong prima facie case against that being a properly basic belief, so assuming it is without any additional evidence that it is in the face of that disagreement is substituting a weak case for a strong one, and that's simply illogical. You need a lot more than "I believe it is properly basic" if there is considerable disagreement as to the fact, and that's a bar, which, simply from an impressionistic standpoint as someone familiar with the epistemological issues, a very high bar, and one that you are unlikely to meet.