Descartes’ Cosmological Proof for the Existence of God
Philosophy ·Cogito ergo sum (I think therefore I am) - René Descartes.
In this post, I will explain Descartes’ cosmological proof of the existence of God, albeit with a twist. Since Descartes was a mathematician, I will present his proof in a mathematical style. There are obviously several flaws in the proof. Finding a flaw in the argument is left as an exercise for the reader. Before we can begin understanding Descartes’ proof of the the existence of God, we need to recall a few definitions and examples.
The first step is to classify our beliefs as probably true and certainly true. We want to find atleast one example of a belief which is in the second category, that is, something which is certainly true. Descartes proposes the following solution: get rid of everything that is not true or probably true and then the thing that remains must be true. Before we begin categorising beliefs into these categories we need working definition of these terms. This comes from Descartes Principal of Doubt.
Descartes Principal of Doubt. If a given belief can be doubted then it is in the probably true category.
Example 1. The statement “The height of Mount Everest is 8848 m” can be doubted. We can either doubt the scientists who measured the height or the instruments which were used. Thus by Descartes’ principal of doubt, this statement is probably true.
The above example in essence shows that our entire knowledge of the external universe can be doubted and hence is probably true according to Descartes. Even the fact that we have bodies and minds can be doubted. The famous example that Descartes gives is that of a dream. In a dream, one thinks of him/herself as having bodies and experiences but the moment we wake up, we find that it was all a mental construct and hence false. Note that this does not mean that we can doubt the existence of mind, since you need the mind to dream in the first place.
We can record this conclusion as a theorem.
Theorem 1. The statement “The external universe exist” is probably true.
Remark 1. Note that Descartes is very careful in choosing his terminology. He does not call something which can be doubted as “false”. He knows that the existence of God can be and is doubted. So at first glance, God exists is probably true.
Remark 2. I must admit that the analysis of waking, dreaming and deep-sleep to argue about the nature of reality predates Descartes by atleast 2000 to 3000 years and is found in the ancient Hindu text called the Mandukya Upanishad.
After discarding all statements about the existence of external objects, Descartes makes the following profound discovery.
Theorem 2. “I exist” is a certainly true statement.
Proof. The statement “I exist” cannot be doubted. Indeed, even to doubt this statement, I must exist first and then only can I doubt this statement. $\blacksquare$
Note that Descartes is not telling us that we exist as bodies or minds. All he is claiming is that we are some sort of “thinking things” behind the veil of ideas and perception. By “veil”, Descartes means that if there is anything other than a thinking mind that exists, there is no way of knowing its existence, that is there is a veil between a thinking mind and anything else, if it exists, distinct from the mind.
We now make the following definition.
Definition 1. Ideas are mental images of things and the thing the idea is about is called the object of the idea.
Example 2. The mental image of a “red apple” is an idea and the red apple as a thing is the object of the idea.
Remark 3. It follows from the definition that ideas cannot exist independently, it is always about “something”. It is also clear that most of the things in the universe are not ideas, they are not about anything. For example, the moon is not about something, it exists (if we assume that it exists since it is in probably true category) independent of any idea in our minds. On the other hand the idea of the moon cannot exist without first conceiving of the thing called moon.
Remark 4. Note that Descartes is not saying that the thing has to exist for its idea to exist. For example, the idea of a unicorn exists even though unicorns don’t!
This motivates the following definition.
Definition 2. A substance is a bearer of properties and needs nothing else to exist. A mode is a property or modification of a substance and its existence is contingent on the existence of the substance.
Example 3. A red apple is a substance while the redness of the apple is a mode. The apple first has to exist for it to be red.
Example 4. A crucial example that Descartes gives is that of the mind and ideas. A mind is a substance while ideas in the mind are its modes. In fact that is what Descartes concludes from Theorem 2 that the only statement which is certainly true is that mind exists. From neuroscience point of view, this makes sense. Ideas or more generally, thoughts, emotions, feelings and so on are certain neuronal pathways in the brain while the mind can be thought of as a background. So ideas are really modifications of the mind.
Descartes then assigns degree of reality to substances.
Definition 3. Infinite substances are said to have maximal degree of reality, finite substances are said to have medium degree of reality and modes of a substance are said to have minimum degree of reality.
Example 5. God has maximal degree of reality, the Earth, Moon, Sun etc have medium degree of reality and ideas have minimum degree of reality.
Remark 5. The reason for such a distinction of degree is that Descartes wants to distinguish between substances which might depend on God, if it exists, for their existence. For example, if God exists, it must not depend on any other substance for its existence, while the existence of every other substance depends on God since God, by definition, is the creator of the universe.
The next step is to define levels of reality. There are two of them that Descartes introduces: formal or actual reality and objective reality. Let us define these terms.
Definition 4. The level of formal reality of a thing or idea is its degree of reality defined in Definition 3. The level of objective reality of an idea is the level of formal reality of its object.
Remark 6. Note that only ideas have any degree of objective reality since only ideas have objects. This also means that ideas always have minimum level of formal reality since ideas are always modes of substances.
Example 6. The idea of color green has level minimum level of of formal reality and minimum level of objective reality since the object of the idea is the color green which is a mode. We give several examples in the form of a table. The reasoning is left as an exercise for the reader.
| Thing | Formal reality | Objective reality |
|---|---|---|
| Idea of a cat | Minimum | Medium |
| Moon | Medium | NA |
| Color Green | Minimum | NA |
| Idea of sweet taste | Minimum | Minimum |
| God | Maximum | NA |
| Idea of God | Minimum | Maximum |
We are now ready to prove the existence of God. Before we proceed, we need the following axioms/assumptions/premises that Descartes puts forward:
- Everything has a cause.
- Level of reality of the cause $\geq$ level of reality of effect.
- Level of formal reality of the cause is $\geq$ level of objective reality of effect.
The first two assumptions seem intuitive. We live in a universe which follows causality and it is intuitive to assume that the cause must be somewhat more real that its effect. For example, the liquid which is green in color is more real than the color green itself. A good argument is that the cause can exist by itself but the effect can never exist without its cause. The third assumption is highly controversial as there is no good way of arguing for it. Let us now prove the existence of God.
Main Theorem 3. God exists.
Proof. We begin by observing that the idea of God exists in our mind. Thus it must have a cause. Moreover, the objective reality of idea of God is maximum and hence the cause of the idea of God must have maximum formal reality. Thus there must exist something with maximal level of formal reality. Since the level of formal reality of the mind is medium, there must exist something other than the mind with maximal level of formal reality. Since God is the only thing with maximal formal reality, God exists. $\blacksquare$
Note that when Descartes concludes that there must exist a thing distinct from mind with maximal level of formal reality, he has already broken through the veil of ideas and perceptions. So now Descartes concludes that atleast two statements are certainly true: I exist and God exists. In his 6 part series called “Meditations”, Descartes then proves the existence of all physical universe and experiences.
There are several loopholes in this proof. First, premise number three, as already pointed out does not stand against rigorous scrutiny. The entire proof then falls apart. Other loopholes are left for the reader to find out. The argumentation also reveals that Descartes is a dualist, who believes that the mind and body are two separate entities. So not only has Descartes put himself in the enmity of atheists, he has also made dualists his enemy.