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.

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.

By Yujin Nagasawa, published in OUPblog, November 8th 2017.

Yujin Nagasawa is Professor of Philosophy and Co-Director of the John Hick Centre for Philosophy of Religion at the University of Birmingham. His books include God and Phenomenal Consciousness: A Novel Approach to Knowledge Arguments (CUP, 2008), The Existence of God: A Philosophical Introduction (Routledge, 2011) and Miracles: A Very Short Introduction (OUP, 2017). He is currently President of the British Society for the Philosophy of Religion, Philosophy of Religion Editor of Philosophy Compass, and a member of the editorial board of Religious Studies, the International Journal for Philosophy of Religion and the European Journal for Philosophy of Religion. He is also the author of Maximal God: A New Defence of Perfect Being Theism (OUP, 2017).