A Theorem Concerning God

by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 Copyright Robert G. Brown, 2024

It is rare in the history of mankind that an actual theorem has been stated, let alone proven, concerning God. This lack of provable results has been one of the major stumbling blocks to rational religion, and of course that which is not, or cannot, be made rational remains irrational to our great dismay and mutual destruction.

This document proves an actual theorem concerning God and the Universe that might be of interest in the eternal conflict between those that allege that God "created" the Universe and those that allege that there is no God and that the Universe didn't require a creator. The theorem does not resolve the question of whether or not there is a God (as Hume showed long ago that neither reason nor inference are sufficient to prove God's existence), but it puts an end rather nicely to the question of whether or not any consistently proposed God could have created the Universe.

By analyzing the question of God using information theory and Godel's theorems, by using set theory in straightforward ways, it demonstrates that only one model of God can be made to satisfy the "standard properties of God": Omniscience, Omnipresence, Omnipotence. It therefore establishes strict constraints on theisms. Most theistic religions of the world are, to put it bluntly, not in accord with this theorem. Because the theorem is based on reason, and indeed its axioms are such that they can hardly be challenged and end up with a system of rational knowledge at all, this is simply too bad for those religions. They are wrong! Not just incorrect at their periphery, flawed in some relatively minor manner of scripture. Not just flawed in their scripture. Flawed at the core -- the basic conception of God they advance is self-contradictory and impossible.

In most cases this is painfully obvious from even a cursory examination of their theistic mythology anyway, but again the lack of an actual constructive theorem concerning God has left a tiny window of possibility that the core belief and description of God as a dualistic creator of the Universe it isn't actually unreasonable, irrational, impossible so that those theism could be correct. This window is now closed.

Be Warned! The article contains a gratuitous polemic against theist scripture-based religions, especially those whose mythological roots lie in the Bronze Age, a time when life on earth was ugly, nasty brutish, and short (the mean life expectancy in central Eurasia was only around 18). To quote Thomas Jefferson:

The priests of the different religious sects ... dread the advance of science as witches do the approach of daylight, and scowl on the fatal harbinger announcing the subdivision of the duperies on which they live.

The advances of science have long since diced all of the duperies (contained in the supposedly "divinely inspired" scriptures that define their creed) upon which they live, demonstrating (for example) that the entire book of Genesis is pure myth and is absolutely disproven by science. It is precisely as reasonable to believe that the computer screen upon which you are reading these words will transmogrophy into a cloud of butterflies (violating any number of laws of physics) than it is to believe Genesis. Simple common sense and everyday experience suffices to reject it. Yet recent surveys suggest that as much as 60% of the population of the United States still believes that the events in Genesis actually happened!

This kind of self-deluded belief is not harmless, and is not without consequences. We live in an age where single individuals can control destructive powers that vastly exceed all of the armies in all of the world of the Bronze Age, and to attempt to govern that power with a Bronze Age morality, the morality expressed by Moses in Numbers 31 as he commanded his troops to commit genocide and slaughter the Midianite captive women and children, sparing only the young virgin girls whom he gave to his troops as sex-slaves, is unthinkable. The world currently lives in a perpetual state of global war -- religious war, founded in ancient conflicts between competing mythological superstitions. No country is immune, no person is safe as long as these superstitions are insulated from the forces of reason by common custom.

Those who choose to believe these fantasies have every right to do so, but they have no right at all to expect that their beliefs should be safe from being questioned by their neighbors in public forums, as this too is a natural right of all freethinking humans. To again quote Jefferson:

Of publishing a book on religion, my dear sir, I never had an idea. I should as soon think of writing for the reformation of Bedlam, as of the world of religious sects. Of these there must be, at least, ten thousand, every individual of every one of which believes all wrong but his own.

A hallmark of science, that is to say, reasonable belief founded in a mixture of empirical observation and consistency with a network of equally well founded beliefs with detailed predictive and explanatory power, is that when presented with the same data and arguments, two reasonable humans will, in general, agree on the correctness or plausibility of the conclusions that are drawn from them. Every student that studies Euclidean geometry proves the same theorems from the sufficient axioms of the theory. A Muslim, a Hindu, a Christian, and a Jew may disagree violently about precisely which foods are unclean and forbidden by God (through divinely inspired scriptures written by ignorant male humans in the dark ages of the past) to eat, but presented with a telescope and verifiable astronomical data and taught the calculus they will all agree that Newton's Law of Gravitation correctly describes the motions of the little lights that seem to move about the night sky, and that upon closer examination those tiny lights are actually enormous worlds that companion our own as it orbits the truly enormous sun.

Reason leads them to a common answer, and takes a dogmatic theistic assertion of Genesis and proves it false. To continue to hold to a belief that the sun goes around the earth, or the belief that Genesis itself is still divinely inspired truth, is insane. This work is therefore advanced in the pious hope that if humans wish to continue to hold to a religious belief in God -- something that is a matter of purely personal choice, given the evidence of their own lives and observations -- they begin by applying the test of reason to any theistic system they wish to adhere to by ensuring that its core theology is compatible with the theorem.