It's common to see arguments in philosophy of religion that aim to establish the existence of a perfect being, where the perfections are taken to be maximal expressions of a special subset of personal qualities (e.g., omnipotence, omniscience, and moral perfection). Standard arguments include ontological arguments and so-called "Stage Two" reasoning in cosmological arguments.
A standard objection to such arguments is that it's not at all clear that such properties are individually possible and/or collectively compossible. But I want to raise a deeper problem that, so far as I've been able to tell, has never been put directly. The problem is that such arguments not only assume that such properties are compossible, but also that they are instantiable as basic or foundational properties. But of course the non-theist will have principled worries, based on what they take to be our best theories about the world, that personal attributes are not properties that can be instantiated as basic our foundational properties -- i.e. they're not ground-floor properties, but rather derivative properties that are grounded (at least in part) in the physical. They will thus have non-trivial, substantive worries that it's metaphysically impossible for personal attributes to exist at the metaphysical ground floor -- at least unaccompanied by physical properties (or whatever the physical is ultimately composed of).