Can God be Proven with Logic Alone?

In the 11th century, St. Anselm, the bishop of Canterbury, released a bombshell of medieval philosophy, an idea so powerful, we are still discussing it today: The Ontological Argument for the Existence of God. Ontology means, “The Study of Being,” and the goal of Anselm’s argument is to demonstrate that the very idea of God is such that God must exist, by definition. The argument is as follows:

1. God is the greatest being imaginable
2. A being that necessarily exists [it cannot be possible for the being to not exist] is greater than a being that just so happens to exist
3. A being that exists in one’s imagination, but not in reality is not as great as the being that exists in both our imagination and reality necessarily
4. Thus, if we are imagining the greatest being imaginable, than we are imagining something that necessarily exists in both our imagination and reality
5. Therefore, God exists

Just about nobody is actually convinced by this argument, and yet, for hundreds of years, people have been trying to figure out what exactly is wrong with it. The strongest criticism would come in the 18th century by enlightenment philosophers David Hume and Immanuel Kant. While writing independently of each other, they both criticized two pieces of the argument: the notion of necessary existence, and the notion that existence is a predicate.

Problem of Necessity: David Hume would argue that there are two kinds of truths, truths about the relationship between ideas (which would be things like logic and mathematics), and truths about the relationships between facts (which includes science, geography, history, and most other fields of study). For something to be logically necessity is a truth found in the relationship between ideas, but not in terms of facts. It is necessary that all bachelors be unmarried men, that all mothers have children, that all veterans were in the military, but this is because of the definition, not because of facts. Meanwhile, facts like, “Pierre is the Capitol of South Dakota” is not a necessary truth, because it’s possible that Rapid City could have been selected to be the capitol, it is not true by definition. Thus, whether something exists is a matter of fact, and cannot be resolved by definition.

Existence is not a Predicate: Kant went even further, attacking the notion that existence can be a predicate of an subject. Predicates are the qualifying terms placed around a subject: ice is COLD, a SHORT BALD man ROBBED us. To say, “God is the GREATEST BEING IMAGINABLE” is to tag God with a predicate of “Greatest being imaginable,” but to add, “God, the greatest being imaginable, exists” does not add anything to the notion of God as the greatest being imaginable, it only indicate where the notion can be found (exclusively in our minds, or in reality, too?)

Many people would consider Kant’s response to be the final word on the matter, but in the 20th century, a new discovery was turning the world of logic upside down: Modality and Possible World Semantics. With new tools in his kit, philosopher of religion Alvin Plantinga set out to make the “Victorious” Ontological Argument, working this out:

1. God is a coherent, “maximally excellent” concept, and could exist in a possible world (All coherent concepts exist in a possible world, according to modal logic, even in they don’t exist in our “Actual” world)
2. The greatest possible being would be maximally excellent in all possible worlds
3. A maximally excellent being that exists in all possible worlds possibly exists
4. A necessary being is one that exists in all possible worlds, and it is possible that God exists in all possible worlds; it is possible that God is necessary
5. By Axiom S5 (a controversial axiom of modal logic which states that if something is possible, it is necessarily possible), God is necessary in at least one possible world, meaning that God must be necessary in all possible worlds
6. Therefore, God, the maximally excellent and maximally great being, exists in our world, necessarily

Once again, not many people are going to be convinced by this argument. While the logic is valid as long as one holds to Axiom S5, and accepts possible world semantics (not everybody does, WVO Quine is a good example of somebody who did not), you could run this argument in the negative, positing that it is possibly necessary that no God exists. Plantinga even acknoledges this, and recognizes that the force of his argument is to defend that the concept of God is a rationally acceptable, rather than that the Ontological Argument is a “Slam Dunk” proof.

In my observation, the greatest difficulty in any ontological argument that the concept of God is even coherent to begin with. For example, Christian Orthodoxy holds that God is Omniscience, Omnipotent, Omnipresent, and Omnibenevolent. However, some strands of Christian thought (Open Theism) have argued that either God does not have immediate knowledge of the future, or God self-restricts knowledge of the future. Some schools of Judaism have questioned if God is really omnipotent, or if omnipotence is even a coherent concept.

Ultimately, the legacy of the Ontological Argument is in how it leads logicians to consider how their skills can be used for devotional purposes.

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