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Is there definitive proof of the existence of God?

When Kurt Gödel, one of the greatest mathematicians of the 20th century, died in 1978 he left mysterious notes filled with logical symbols. Towards the end of his life a rumour circulated that this enigmatic genius was engaged in a secret project that was not directly relevant to his usual mathematical work. According to the rumour, he had tried to develop a logical proof of the existence of God. The notes that Gödel left, which were published a decade after his death, confirmed that the rumour was indeed correct. Gödel had invented a version of the so-called modal ontological argument for God’s existence.

The modal ontological argument purports to establish the astounding thesis that the mere possibility of the existence of God entails its actuality. That is, the argument says, once we agree that God can in principle exist we can’t but accept that God does actually exist. There are many distinct versions of the modal ontological argument but one of the most straightforward can be presented as follows.

According to ‘perfect being theism’, a form of theism most widely accepted among Judaeo-Christian-Islamic theists, God is a being that exists necessarily. Such a being is distinct from contingent beings like tables, cars, planets and people, which exist merely by chance. If God exists at all, there is no possible situation in which he fails to exist. Proponents of perfect being theism also typically say that God is all-powerful, all-knowing, and morally perfect because he is perfect in all respects. This observation suggests that the thesis ‘it is possible that God exists’ is equivalent to ‘it is possible that, necessarily, an all-powerful, all-knowing and morally perfect being exists.’ At this point the modal ontological argument appeals to a principle in modal logic that is widely accepted by logicians: If it is ‘possible’ that something is ‘necessary’, then that thing is simply ‘necessary.’ In other words, if we have the sentence ‘it is possible that something is necessary’ we can drop the phrase ‘it is possible that’ without changing the meaning. If we apply this logical principle to what we have derived so far, namely, the thesis ‘it is possible that, necessarily, an all-powerful, all-knowing and morally perfect being exists’, we can derive the thesis ‘it is necessary that an all-powerful, all-knowing and morally perfect being exists.’ This is equivalent to saying that God exists necessarily. If God exists necessarily, then God actually exists. Hence, the mere possibility of the existence of God logically entails its actuality.

Portrait of Kurt Gödel, one of the most significant logicians of the 20th century, as a student in Vienna by unknown. Public domain via Wikimedia Commons.

Theists’ attempts to demonstrate the possibility of God involve some of the most creative ideas in philosophy. Clement Dore and Alexander Pruss, for example, try to establish the possibility that God exists by appealing to the fact that many people have encountered God in religious experiences. Dore and Pruss do not assume that these religious experiences are veridical – they are willing to accept that some (or even all) of them are hallucinations. However, according to them, if the existence of God is impossible then God cannot even appear in hallucinations. The fact that people encounter God in religious experiences suggests that, even if they are hallucinations, the existence of God is at least possible.

To take another example, Carl Kordig tries to establish the possibility that God exists by appealing to the so-called ‘ought implies can’ principle. If we ought to rescue a drowning child we can rescue that child. Conversely, if we cannot for some reason rescue a drowning child, then it is not the case that we ought to rescue that child. Kordig says that God ought to exist because he is a perfect being. And given that God ought to exist we can infer with the ‘ought implies can’ principle that he can exist as well. Hence, it is possible that God exists.

How does Gödel try to show that God’s existence is possible? He argues that it is possible because God has only positive properties. If God were to have both positive and negative properties simultaneously it would seem impossible for him to exist because they would contradict each other. For example, it would seem impossible for God to exist if he were to have the property of being all knowing (a positive property) and the property of being ignorant (a negative property) simultaneously. Therefore God, as the greatest possible being, has only positive properties, such as the properties of being all knowing, all powerful and morally perfect, which, according to Gödel, do not contradict each other.

Whether the abovementioned arguments for the possibility of God succeed is disputed. Yet the modal ontological argument is important because it seems to reduce the burden of proof on theists dramatically. They no longer need to rely on traditional arguments for the actuality of the existence of God, which appeal to the origin of the universe, the source of morality, the apparent design in nature, testimonies of miracles, and so on. All they need to do is show that the existence of God is at least possible. If we can show that, we can simply plug it into the modal ontological argument and derive, as a matter of logic, that the existence of God is actual. Hence, the modal ontological argument places us only a half-step away from a definitive proof of the existence of God.

Featured image credit: sunlight sunrise sunset dawn by 5hashank. Public domain via Pixabay.

Recent Comments

  1. Brian

    I fail to understand the logic of something possibly necessary being surely necessary. I may just need to take a class in logic, but isn’t the purpose of the word “possible” just to mean “not surely”? If it is possibly necessary to bring an umbrella to stay dry, because it may or may not rain today, how does that imply it is now definitively necessary to bring an umbrella to stay dry?

  2. Michael Starke

    This article does a rather good job of mirroring the foundation of religion, namely the compounding of one absurd proposition on top of another. Simply laughable. Remind me again, how many ridiculous conjectures may fit on the head of a pin?

  3. George

    @Brian,
    Because in modal logic, ‘possible’ means, ‘obtains at at least one accessible world’. So if something is possibly necessary P, then at one particular world, that world has necessarily P. Since this world is accessible to our world, and necessarily P means that P obtains at all accessible worlds, then P obtains at our world. Ergo God exists at our world if there’s a world where he exists (if he possibly exists).

  4. Josh

    The argument may equally reduce the burden on atheists: just show that atheism is possible.

  5. Dr. Iftikhar Qayum

    It’s called convincing yourself against the facts, something that the human mind is capable of, and that has been exploited throughout history by all sorts of salesmen and their pitches, including those bent on selling their version of religion.

  6. Victor Cypert

    Fascinating. And if anyone could’ve proved the existence of God, it would’ve been Gödel.

    It’s also worth noting that, toward the end of his life, Gödel was also worried about people poisoning his food. He ultimately died from malnutrition as a result of mental illness.

    These proofs may be something akin to Newton’s work in alchemy and Biblical prophecy–the creative byproduct of a tormented mind.

    Still, the archetype of the man in search of God (or God’s name) presents itself in history, myth, and popular culture. From Buddha beneath the Bodhi tree to the Grail Knights of Arthurian Legend to Max Cohen in Aronofsky’s “Pi,” the image persists–man seeking a connection to the divine.

    So even if God isn’t real, the archetypal yearning for God is very real. Madness or no, Gödel’s work resembles the efforts of others on the quest and speak to a genuine drive shared by humanity.

  7. Carl

    Brian, you are right to say that the inference from the possibility necessity of an umbrella to the actual necessity of an umbrella does not follow, but the example is not analogous. It is not analogous because the necessity of the umbrella is able to be caused.

    God is not able to be caused. (There is not space to prove this point here). Therefore, since there is nothing that could cause God’s existence, if it is possible that God exist, it is necessary that God exist. It would be contradictory to say “it is possible that God exists” and “God does not exist.” If God does not exist, then he could never exist. If God could never exist, then it is not possible that God exist. Instead, the existence of God would be impossible, not possible. The inference is sound.

  8. Oziel

    His just a foolish mathematician that doesn’t have anything to work on. God does not need to be proven. Science only deals with physical proof, not foolish ideologies. God cannot be intellectualise, I can prove that God exist and I can also prove he doesn’t, it only comes down to what I want to prove.
    Science and God are not related.

  9. David

    Very interesting article, specially for those who want to explore ontological argument, not for real amateurs they might take it as a joke.

  10. David Voorthuyzen

    To answer Brian, I think what is understood in logic when you say something is necessary, is that it is always necessary. When something is necessary this means that it’s not possible that it is not necessary. So saying something is possibly necessary is logically unsound. It is necessary or it isn’t.
    Just the way I understand it.

  11. Sean P.

    Using the English gematria, where A=6, B=12, C=18, D=24,…..Z=156,
    GOD = 156, JESUS = 444, CHRIST = 462, and of course JESUS CHRIST = 906.

    Who is the Father? Search the KJV Bible NT for the words “The Father” and you will find them 156 times.
    Who is the Lord ? Search the KJV Bible NT for the words ” The Lord ” and you will find them 462 times.

    Let’s bring the advanced ELS (Equidistant Letter Sequences) word search method into the picture.
    Set your ELS from 1 to the One God (1,156). Search for the following words….
    “The Code” “of God”,
    “The Code” “of Jesus”,
    “The Code” “of Christ”.
    You will find these words a total of 906 times.
    These are a few examples of the hundreds more.

    Here is another fun one. Jesus is the Son, and he is the Lord.
    Jesus will also appear a 2nd time, thus he will return and complete the circle.

    JESUS = 444, SON = 288, and LORD = 294.

    GOOGLE the following. 4.44288294 / sqrt(2) =
    Answer = 3.14159265…..
    And, PI = 3.14159265…..

  12. Karl Young

    Clever Sean, but ultimately irrationally divided rationality, transcendence does not make.

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