From How to Think About God, by Mortimer J. Adler:
“To say that God’s existence is essentially like that of everything else known by us to exist is tantamount to saying that God’s existence is physical, material, or corporeal, and that, consequently, it is a mode of existence which can be known to us either by direct perceptual acquaintance or by scientific inference from empirical evidence.
“What is wrong with saying this? The simple indisputable fact is that the existence of God has never been a subject of scientific inquiry. It has never been supposed that the problem of whether or not God exists can be solved by the means and methods at the disposal of the experimental or empirical natural sciences.
“Why not? Because the means and methods of natural science are applicable only to physical, material, or corporeal objects and God is not a physical, material, or corporeal object.
“‘How’s that again?’ or ‘Not so fast,’ some of my more critical readers may interject at this point. In saying that the existence of God cannot be an object of scientific investigation because God is immaterial or incorporeal, have I not assumed the very point that needs to be established?
“The fact that natural science so far has not used its means and methods to investigate the existence of God does not preclude the possibility of its doing so in the future, by techniques not now imaginable by us. Hence, there must be some other reason for thinking that God cannot be essentially like the physical things of this world, known by us to exist.
“Another line of reasoning is available. It takes its departure from our understanding of the cosmos as the totality of material or corporeal things and all physical occurrences and processes. As a totality, it is all-embracing. Nothing can be physical, material, or corporeal and exist outside the cosmos, for if it did, the cosmos would not be the totality of all such things.
“Now, if we think of God as physical, material, or corporeal, God must be thought of either (1) as a part of the physical cosmos, or (2) as identical with the cosmos as a whole. Or, (3), the cosmos must be thought of as part of God.
“The cosmos cannot be a part of God and remain the totality of physical things, occurrences, and processes. A part of something that is itself physical or material cannot be the totality of all physical or material things. This eliminates the third alternative.
“God cannot be thought of as a part of the physical cosmos and also be thought of as the supreme being; for then the physical cosmos as a whole, which includes God as a part of itself, would be greater than God. This eliminates the first alternative.
“We are left with the second alternative–that God is identical with the physical cosmos as the totality of all physical things, occurrences, and processes. But the physical cosmos, vast totality that it is, is certainly not that than which no greater can be thought of. Hence, if we identify God with the physical cosmos, we are no longer thinking of God as the supreme being–that than which no greater can be thought of.
“The elimination of all three alternatives as impossible brings us to the conclusion that God cannot be thought of as physical, material, or corporeal.”
How to Think About God, by Mortimer J. Adler, pp. 82-83.
[Note that earlier in the book, Adler had started with the premise that whatever God is specifically, he must be “that than which nothing greater can be thought of” as per St. Anselm.]