“Ever since the creation of the world his eternal power and divine nature, invisible though they are, have been understood and seen through the things he has made.”
Romans 1:20 NRSV-CI
Two Ways
Perhaps there is no other question that can elucidate the differences between the objectivist/materialist view on the one hand and those who allow for exploration into metaphysics and mysticism on the other than the question of whether God exists.
The strict objectivist approach denies that anything exists beyond the physical world we can observe, and therefore must conclude that God does not exist.
Often, it is the atheist who demands, “prove that God exists,” without attempting to offer any explanation why God does not or cannot exist beyond their own faith that this universe is all there is. For the atheist, that God does not exist is a given. It is a matter of faith.
For all others who are willing to look beyond into metaphysics, who question whether the universe had a beginning and what caused it, who are capable of the modicum of humility necessary to admit the possibility of a higher power, purpose, and meaning, answering the God question brings rewards proportionate to its challenges.
It’s as if one camp is asking not just whether God exists but what is His nature, and the other is asserting that such questions are nonsensical. From that perspective, there really is no debate, only proverbial ships passing in the night.
Not just a Watchmaker
Many proofs of God’s existence have been offered, and it is not my intention to survey them all or even to delve deeply into any. For some it is as simple as, “The true story of the world must be told by somebody to someone else,”[1] and the storyteller is outside the world.
Others, like Aquinas and Gödel, crave a bit more rigor in the form of logic and reasoning. Gödel offered a proof of God is unique because it is both ontological, that is based on the nature of God’s being, and set forth in the syntax of mathematical logic (see Figure 7 below).
The ontological approach closely follows the reasoning set forth by Gottfried Wilhelm Leibniz, a seventeenth century mathematician who developed the Calculus both independently from and concurrently with Isaac Newton. Gödel, like Leibniz, believed in the Platonic view that, “the order of the world reflects the order of the supreme mind governing it…[and] that all order is a reflection of rationality.”[2]
Although the ranks of theists among scientists in Gödel’s time (the early to mid 1900’s) were dwindling, presumably due to the astonishing acceleration in the pace of scientific understanding of the physical world, Gödel was quick to point out that the founders of modern science were not atheists.
Many were believers in the same vein as Gödel’s close friend, Albert Einstein, who adhered to a pantheistic view of a higher power whom he was perfectly willing to call God, but not a personal God who is involved with our lives or tied to any particular religion or dogma.
In contrast, Gödel believed God is personal and yet more than a person because He can play the role of a person. What Einstein believed is often called the watchmaker God, the idea being that God created a watch, wound it up, and let it go, with no ongoing meddling in human affairs needed.
To Einstein’s credit, the fact that he considered Gödel’s view of God to be naïve did not prevent him from admiring and valuing Gödel’s intellect above all others, including his own, to the point of admitting that he only joined the same Institute as Gödel for the privilege of being able to walk home with him.
To Einstein’s decrement, he did not possess the wisdom to see that a watchmaker God would not have humbled himself to become human, and to suffer and die for the good of his creatures.
Figure 7: In symbol form, Gödel’s ontological proof that God exists
Gödel vs. Dawkins
A rough outline of Gödel’s proof that God exists goes something like this.
Define ‘God-like’ in terms of all positive properties. After some further definition and logical argument, conclude that ‘necessity of existence’ is a positive property. This establishes the key proposition that if God is possible then God is actual. Next, demonstrate that God’s non-existence is not provable. Since God’s non-existence is not provable, then God is possible. Therefore, God exists.
As has become his signature move, Gödel employs strange loops to do his heavy lifting. In this case, the definition of positive properties allows any conjugation of positive properties to also be a positive property. He essentially defined a set of sets, conscripting the power of recursion so that the underlying syntax can talk about itself and the abstraction of itself.
“In this argument, God’s possible existence is identified with the compatibility of the system of all positive properties, which is identified with the consistency of the system of their corresponding propositions.”
Hao Wang, A Logical Journey, p. 115
Richard Dawkins, biologist and perhaps the best know modern evangelist for atheism, argued against God’s existence on the grounds that God is the most improbable hypothesis to explain what we see in the universe.[4]
The Dawkins argument has been effectively countered on at least two grounds. First, the Christian view is that God’s nature is simple because it is unified, whereas Dawkins contends that God would have to be the most complex thing in the universe. Second, Dawkins either forgets or willfully ignores that God would exist outside of space and time.
Gödel’s proof offers another way to counter Dawkins.
The lynch pin of Gödel’s argument is that, if it is possible that there is some God-like object, then it is necessary that there is some God-like object. Dawkins does not make the case that God is impossible, just that God is exceedingly improbable.
But ‘exceedingly improbable’ is still encompassed by ‘possible.’ To overcome Gödel’s logic, it must be shown that God’s existence is not possible in any scenario and for any universe.
“[I]f God is so much as possible, He is actual. This means that one cannot be an atheist unless one is a ‘superatheist,’ i.e., someone who denies not just that God exists but that He is possible.”
Palle Yourgrau, A World Without Time, p. 130
Perhaps it is better to formulate the question ‘Does God exist?’ as: ‘Is it possible to formally demonstrate the non-existence of God?’
According to Gödel, the answer to that is clearly no. Just like a formal proof of the consistency of a logic system, the proof must take place from within the system, and that is not possible.
Atheism is thus inherently and intractably unprovable. As it turns out, atheism requires more faith than theism. There is evidence that God’s existence is not impossible, while a proof of God’s non-existence is indeed impossible.
Faith and Reason
Our understanding of Gödel’s philosophy and ideas about God come primarily from private conversations and letters, not from academic papers. Nonetheless, his private efforts demonstrate his belief that his methodologies were applicable beyond formal logic and mathematics, even if others had doubts.
Indeed, one of Gödel’s doubters was his own mother, who agreed with Wittgenstein (of all people) that the utilization of one’s intellectual faculties was inappropriate for examining issues of faith.
Undaunted, Gödel offered his mother the following line of argument for why an afterlife exists.
- Order pervades the world, as demonstrated by observation, science, and mathematics;
- Order is evidence that the world has meaning;
- Human beings can only realize a very small part of the potential in this world;
- Given that the world has meaning and that we cannot realize our full potential in it, there must be an afterlife; and
- Science supports the belief that the world had a beginning and will have an end, and this allows for the possibility of another world, an afterlife.
It is unclear to what extent Gödel may have been exposed to St. Thomas Aquinas, but his statement about human beings never being able to actualize their full potentiality in this world bears a striking resemblance.
Wittgenstein stated his opinion of such proofs in no uncertain terms, saying:
“But I think what believers who have furnished such proofs have wanted to do is to give their ‘belief’ an intellectual analysis and foundation, although they themselves would never have come to believe as a result of such proofs.”
Hao Wang, A Logical Journey, p. 113
What Wittgenstein does not appreciate is that proofs like the existence of God, unlike the proofs in logic with which he was more familiar, do not have as their primary goal the convincing of the unconvinced. As such, Wittgenstein unwittingly ventures into territory with both Aquinas and Chesterton.
Aquinas held that there are things that God has revealed about Himself which could be known by reason alone, and there are things that are known only because He reveals them.
Thus, proofs of God are meant to both demonstrate that God’s existence is a rational proposition, and to explore what we can know about God’s nature by reason and by revelation.
Chesterton took another tact, remarking that we can increase our understanding by making use of what is not understood. In other words, even the unbeliever can use a proof of God to better understand and appreciate God’s design and God’s plan even prior to being convinced that there is a God.
In Summa-ry
Because Aquinas keeps popping up in our discussions, I would be remiss not to mention the five ways to demonstrate God’s existence and nature that he offers in his seminal work, the Summa Theologica. Contrary to Wittgenstein’s assumptions about why one would spend time on such demonstrations, Aquinas does not expect his arguments to convince the non-believer.
- By motion: Whatever moves is moved by something else, and consequently there must be a First Mover that creates the chain reaction of motions. This First Mover is God who sets all things in motion and gives them their potential.
- By efficient cause: Nothing can be its own cause, and therefore everything must have either a direct cause or indirect cause. Without a First Cause, there would be no others. This First Cause is God.
- By necessary being: Objects in the world come into existence and pass out of existence. Therefore, it is possible for objects to exist or not exist at any particular time. However, nothing can come from nothing. This means something must exist at all times and pre-exist all objects that come into and out of existence. This is God.
- By gradation: Created objects possess properties of goodness in greater and lesser degrees. Therefore, there must be some Perfect Being that possesses those properties in their maximal degrees. This Perfect Being is God.
- By design: All things have an order or arrangement that leads them to a particular goal. Because the order of the universe cannot be the result of chance, design and purpose must be at work. This implies divine intelligence on the part of a Designer. This Designer is God.
Compare Aquinas with the two-step argument for God’s existence proffered by Descartes (and similar to the proof by Leibniz that inspired Gödel). First, God is the subject of all perfections. Second, existence is a perfection. Therefore, God exists.
Or compare to my own effort at consolidating all of these approaches:
- By observation, the universe exists;
- Thus, the property called ‘existence’ is real and already present;
- Real properties don’t appear without applying to something (you can’t have a real property dissociated from everything);
- Thus, the property of ‘existence’ must have applied to ‘something,’ independent of the universe existing;
- The universe defines space and time;
- Thus the ‘something’ that exists independently of the universe is something that exists outside of space and time;
- Existing outside of space and time is a God-like quality, and therefore the ‘something’ could possibly be God;
- Per Gödel’s proof, if God is possible, then God is actual.
Quod erat demonstrandum (QED).
[1] G.K. Chesterton, The Everlasting Man, p. 157
[2] Palle Yourgrau, A World Without Time, pp. 104-105
[3] Palle Yourgrau, A World Without Time, p. 13
[4] See https://richarddawkins.net/2014/06/the-improbability-of-god/