Final answer:
The question of God's existence cannot be resolved as a brute fact without further explanation. Arguments for and against the existence of a supernatural deity both encounter significant challenges, and the Burden of Proof lies with those asserting God's existence. Cosmological and ontological arguments, as well as individual religious experiences, offer logical possibilities but are not definitive proof.
Step-by-step explanation:
The question asks whether we can consider the absence of God as a brute fact, with no need for explanation, and how this compares with theistic claims. In considering the existence of a supernatural deity, arguments both for and against face challenges. The absence of religious experience does not necessarily indicate the non-existence of such an experience or realm. However, when assessing the existence of God, especially within philosophical discourse, the Burden of Proof rests on those making the affirmative claim.
Appeals to ignorance, where absence of evidence is mistakenly taken as evidence of absence, are fallacious. Similarly, the veracity of reports of religious experiences cannot be assumed without strong reason and evidence. Offering a mere logical possibility of a supernatural deity through subjective experiences or ontological arguments does not satisfy the standard of proof required for a rational belief in a supreme being.
The exploration of cosmology and philosophical argumentation, such as Thomas Aquinas' views on knowing God indirectly as a cause in the natural world or the challenges in defining the mind, also touch upon the complexities of proving God's existence. Through these avenues, one cannot conclusively establish the existence of God but can consider the logical possibility.