In David Griffin’s book, God Exists but Gawd Does Not, the seventh chapter is called “Mathematics.” It’s the longest chapter in the book, and over its 40 pages Griffin presents his case that the reality and efficacy of mathematics provide a strong argument for the existence of God.
He begins by defending Platonic realism that affirms the reality of an abstract realm of mathematical objects, as opposed to the prevailing scientific view of sensate empiricism which denies that such an abstract realm exists. Mathematical objects are abstract entities such as numbers, the truth that 2 + 2 = 4, and Einstein’s famous equation.
If mathematical objects and other Platonic forms are nonphysical and outside space and time, where exactly do they exist? If they are located in an abstract realm “somewhere in the universe,” or in “Plato’s Heaven,” that could account for their reality, but not for their efficacy.
As to the efficacy of mathematical objects or how they can influence our minds and the world (the so-called Benacerraf problem), it is required that:
Mathematical objects must exist somewhere in an actuality because, by Whitehead’s ontological principle, only actualities have causal agency. That actuality, whose locus is the entire universe although an entity distinct from the universe, is God, or the universal mind.
To intuit or grasp these objects, our minds cannot be strictly limited to sensate empiricism with its doctrine that perception is only by means of our physical senses, since mathematical objects are, by definition, not physical. So, if not by our physical senses, what is it that enables us to perceive them?
Whitehead invites us to realize that there is a deeper and more fundamental mode of perception that we share with all actualities, a nonsensory perception that he calls causal efficacy. Your body itself illustrates how this works:
For example, what happens when you see a tree before you? As Whitehead says, a datum of information is passed from the excited “cells of the retina, through the train of actual entities forming the relevant nerves, up to the brain. Any direct relation of eye to brain is entirely overshadowed by this intensity of indirect transmission . . . the predominant basis of perception is perception of the various bodily organs, as passing on their experiences by channels of transmission and enhancement.” What you are seeing is a presentation made possible by many antecedent processes of nonsensory perception occurring in your body.
“There are many things we know about the world,” says Griffin, “that come from nonsensory, rather than sensory, perception, such as knowledge of the external world, causation, our own bodies, memory, the past, and time.” Speaking of another mode of nonsensory perception, mathematician Kurt Gödel said, “I don’t see any reason why we should have less confidence in . . . mathematical intuition, than in sense perception.” A relevant example of nonsensory perception, with considerable research backing it up, is mental telepathy. As Griffin writes, “A significant number of philosophers and scientists have expressed their acceptance of the reality of telepathy . . . on the basis of various types of evidence: anecdotal, sustained studies of apparently exceptional individuals, and laboratory experiments.” If one human mind can, through nonsensory perception, perceive the thoughts of another mind, then, by analogy, nothing stands in the way of human minds perceiving mathematical objects, or other Platonic forms, in the universal mind.
Another facet of mathematics is the sheer wonder it can inspire since, in all the workings of the universe, mathematics plays so fundamental a role that astrophysicist Mario Livio wonders why its powers seem omnipresent, a term he notes that is usually associated only with a deity. Such wonderings apparently inspired Livio, for he has written a book whose title asks the question, Is God a Mathematician?
That the universe is so deeply rooted in mathematics is, for many scientists, a great mystery. Nobel laureate Richard Feynman said, “Why nature is mathematical is a mystery; the fact that there are rules at all is a kind of miracle.” And in a famous essay called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” mathematician Eugene Wigner described this as “something bordering on the mysterious, because there is no rational explanation for it.”
Wigner deepens the mystery by noting how, in advanced mathematics, “the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.” Mario Livio adds: “Concepts and relations explored by mathematicians only for pure reasons—with absolutely no application in mind—turn out decades (or sometimes centuries) later to be the unexpected solutions to problems grounded in physical reality!”
The omnipresence of mathematics is still a mystery, but perhaps not so great, and a rational explanation becomes possible, if it is understood, as Whitehead suggested drawing on Plato, that there is “a basic Psyche whose active grasp of ideas conditions impartially the whole process of the Universe.” Thus, these mysteries of mathematics suggest the reality and efficacy of an all-inclusive mind, or God.
Griffin concludes the chapter with this summation:
“Mathematics points to the existence of God, understood as the mind or soul of the universe, in four ways.
“1. The reality of God provides a place where Platonic mathematical forms can exist.
“2. The idea that these forms are actively prehended by God can explain the causality behind them that allows human beings to perceive them.
“3. God as the unity of the universe, ‘conditioning impartially the whole process of the Universe,’ can explain, as Newton had emphasized, the universality of the laws of nature.
“4. By saying that the laws of nature and the human mind are rooted in the same divine mind, we render less mysterious the fact that mathematical ideas formulated for their interest and beauty often turn out to be uncannily useful in physics.”
It should be mentioned that the chapter on mathematics is only one part of Griffin’s eight-part cumulative argument for the existence of God, followed by chapters that explicate the other seven parts: morality, logic and rationality, truth, religious experience, metaphysical order, cosmological order, and teleological order.
HyC