Leibniz’s Cosmological Argument

January 23, 2013

By Kevin Rogers

1         Introduction

Why does anything at all exist? Why is there something rather than nothing? These were the questions that Gottfried Wilhelm Leibniz (1646-1716) raised, and from them he developed an argument for the existence of God based on the Principle of Sufficient Reason (PSR). The PSR is one form of various cosmological arguments.

Gottfried Wilhelm Leibniz (1646-1716)

Leibniz was a German mathematician and philosopher. In mathematics, he was the co-inventor (with Isaac Newton) of calculus, the first inventor of a mechanical calculator and the inventor of the binary number system. In philosophy, he suggested that we live in the “best of all possible worlds”, he was a key thinker in the development of rationalism and also a forerunner of modern logic and analytic philosophy. In his latter years, he fell out of favour due to disputes with Newton on whether he had copied Newton’s ideas on calculus. His writings were largely forgotten, but were revived in the 20^th century, and he is now highly regarded.

2         The Argument

Leibniz’s argument consists of 3 premises and 2 conclusions, as follows:

• Premise 1: Everything that exists has an explanation of its existence
• Premise 2: If the universe has an explanation of its existence, that explanation is God
• Premise 3: The universe exists
• Conclusion 1: The universe has an explanation of its existence
• Conclusion 2: Therefore the explanation of the universe’s existence is God

However, is it a good argument? A good argument must satisfy the following criteria:

1. The premises must be true, and
2. The conclusions must follow logically from the premises.

In this article, I will work backwards. I will firstly discuss the logical structure of the argument (its validity) and then consider the premises. We will firstly assume that the premises are true and verify whether the conclusions follow from the premises.

3         Logical Structure

Conclusion 1 is justified by Premise 1 and 3 as follows:

• Premise 1: Everything that exists has an explanation of its existence
• Premise 3: The universe exists
• Conclusion 1: The universe has an explanation of its existence

Thus if everything that exists has an explanation of its existence and the universe exists, then it follows that the universe has an explanation of its existence.

Conclusion 2 follows from premise 2 and conclusion 1 as follows:

• Premises 2: If the universe has an explanation of its existence, that explanation is God
• Conclusion 1: The universe has an explanation of its existence
• Conclusion 2: Therefore the explanation of the universe’s existence is God

I think it is fairly self-evident that the logical structure of the argument is valid. Now we will look at the premises.

4         Are the Premises True?

4.1       Premise 3

Premise 3 states that the universe exists. I think this is fairly self-evident. I am sure that there have been extreme sceptics that have questioned this claim, but I will not concern myself with them.

4.2       Premise 1

4.2.1       Objection 1 – How do we explain God?

Premise 1 states that everything that exists has an explanation of its existence. This has prompted the following objection:

If premise 1 is true, then God must have an explanation of his existence. The explanation of God’s existence must be some other being greater than God. That’s impossible; therefore, premise 1 must be false.

However, this objection is a misunderstanding of what Leibniz meant by “explanation”. According to Leibniz, there are 2 kinds of explanations:

1. Beings that exist necessarily (necessary beings), or
2. Beings that are produced by an external cause (contingent beings).

Necessary beings are those that exist by a necessity of their own nature. In other words it is impossible for them not to exist. Some mathematicians believe that abstract mathematical objects, such as numbers, sets and shapes (e.g. circles and triangles) exist necessarily. Necessary beings are not caused to exist by an external entity and necessarily exist in all possible worlds.

On the other hand, contingent beings are caused to exist by something else. They do not exist necessarily and exist because something else produced them. This includes physical objects such as people, planets and galaxies. It is easy to imagine possible worlds in which these objects do not exist. Thus we could expand premise 1 as follows:

Premise 1: Everything that exists has an explanation of its existence, either due to the necessity of its own nature or due to an external cause.

It is impossible for God to have a cause. Thus Leibniz’s argument is really for a God who must be a necessary, uncaused being. Thus the argument helps to define and constrain what we mean by “God”.

4.2.2       Objection 2 – Does the Universe need explaining?

Some atheists have objected that premise 1 is true of everything in the universe, but not the universe itself. However, it is arbitrary to claim that the universe is an exception. After all, even Leibniz did not exclude God from premise 1.

4.2.3       Objection 3 – An Explanation of the Universe is Impossible

Some atheists have suggested that it is impossible for the universe to have an explanation of its existence. Their argument goes something like this:

The explanation of the universe would have to be a prior state of affairs in which the universe did not exist. This would be nothingness. Nothingness cannot cause anything, Therefore the universe exists inexplicably.

This objection assumes that the universe includes everything and that there is nothing outside the universe, including God. The objection has excluded the possibility of God by definition. However, an alternative definition is that the universe contains all physical things, but that God exists apart from the universe. This objection assumes that atheism is true and argues in a circle. It is clearly begging the question.

4.3       Premise 2

Premise 2 states that if the universe has an explanation of its existence, then that explanation is God. This appears controversial at first, but in fact it is not. This is because atheists typically argue that if atheism is true, then the universe has no explanation of its existence. Thus if there is an explanation of the universe, then atheism must be false (i.e., God is the explanation of the universe). This conclusion follows from the following rule of logic: If p => (implies) Q, then “not Q” => “not P”. An example is, “If it is raining, then there are clouds. Thus if there are no clouds, then it is not raining.”

One may object at this point that the word “explanation” is ambiguous. An explanation for something may be due to either an intelligent agent or a mindless, unintelligent prior event or cause. For example, suppose we have a rusty car. The existence of the car was due to intelligent agents, but the rusty degradation was due to mindless, unintelligent causes. If the ultimate explanation of the universe is mindless and unintelligent, then the argument does not take us very far. However, could the existence of the universe be ultimately due to mindless causes?

However, I don’t think that the LCA necessarily demands that the observable universe has an intelligent explanation of its existence. For example, suppose that this universe was birthed by some other universe. Well, that other universe would be the explanation of its existence. Of course, that would simply push the problem back one step further. Even if an atheist wants to appeal to an infinite past succession of universes, we can still ask of that infinite succession, “Why does it exist, rather than nothing and what is its explanation?” But at that point, what kind of explanation can there be other than some transcendent, necessary cause? So a rational atheist is forced to either concede the argument or claim that the cosmos exists inexplicably (without explanation).

4.4       Objection 4 – The Universe exists Necessarily

All atheistic alternatives now seem to be closed, but not quite. Some atheists have claimed that the universe exists necessarily (i.e., the universe is a necessary being). If that were the case, then the universe would not require an external cause. However, this proposal is generally not taken seriously for the following reason. None of the universe’s components seem to exist necessarily. They could all fail to exist. Other material configurations are possible, the elementary particles could have been different and the physical laws could have been different as well. Thus the universe cannot exist necessarily.

However, is it valid to resort to God as the explanation of the universe? Are there other possibilities? The universe consists of space, time, matter and energy. The cause of the universe must be something other than the universe. Thus the cause of the universe must be non-physical, immaterial and beyond space and time. Abstract objects are not possible candidates as they have no causal relationships. Thus it seems reasonable to conclude that the cause of the universe must be a transcendent, unembodied mind.

5         Conclusion

Leibniz’s argument from the Principle of sufficient reason is an interesting argument for the existence of God, but it goes beyond just God’s existence. It also constrains the attributes of God to be a transcendent, uncaused, unembodied mind, who necessarily exists. In other words, this being is what the major monotheistic religions traditionally refer to as “God”.