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Leibniz's Cosmological Argument

Leibniz was a German philosopher and mathematician who lived in the 17th and 18th centuries. He invented a form of calculus independently of Newton, and is known for his contributions to metaphysics and philosophy of mind.

Formulation​

  1. Anything that exists has a sufficient reason for its existence, either in a contingent being or in a necessary being.
  2. The universe exists.
  3. Therefore, the universe has a sufficient reason for its existence, either in a contingent being or in a necessary being. (1, 2)
  4. The sufficient reason for the universe's existence cannot be found in a contingent being because:
    1. The universe is a collection of contingent beings.
    2. The collection of contingent beings cannot explain the existence of the collection.
  5. Therefore, the sufficient reason for the universe's existence must be found in a necessary being outside of the world. (3, 4)
  6. Therefore, there is a necessary being outside of the world that explains the existence of the universe (God). (5)

Principle of Sufficient Reason​

Leibniz is known for his Principle of Sufficient Reason (PSR), which states that everything that exists has a sufficient reason for its existence. This principle is the foundation of his cosmological argument.

Consider the first premise of the argument, and more specifically, what it means for a reason to "explain" the existence of something:

  1. As a removal of doubt - the reason removes doubt about why something exists. This is a more epistemic interpretation.
  2. As a relation - this could be causation, or a realization, or a grounding relation. For example, the structure of transistors grounds the structure of a circuit.

An object cannot be its own reason for existence, because that would imply that it is prior and posterior to itself. Even in an epistemic sense, it would not make any sense to say " is true because is true". This means that must be explained by , and must be explained by , and so on ad infinitum. One way to stop this infinite regress is to construct a causal loop, but this leads to circular reasoning, which is, to a certain extent, a type of self explanation.

The next logical question is to ask why the infinite chain exists in the first place. This cannot be explained by any constituent elements in the chain, because the chain itself is the object of explanation. It would not make sense to say "there are fish in the sea because there is a fish in the sea".

One could posit an explanation for the chain, but that would itself be then part of the chain. As such, teh PSR does not really allow for this, and has to be restricted.

The first premise states that "anything" that exists has a sufficient reason for its existence. This is a universal quantification, and it is not clear why this should be the case.

Definition of the Universe​

In the second premise, Leibniz states that the universe exists.

In premise 4.1, the argument provides a definition of the universe as a collection of contingent beings. Substituting this definition into the argument, we get:

"The collection of contingent beings exists."

Why is that? A collection is not an abstract set, but a concrete thing. The collection of my book, my pen, the Statue of Liberty, and the Eiffel Tower does not exist, for example.

The Conclusion​

The conclusion of the argument is that there is a necessary being outside of the world that explains the existence of the universe. Many cosmological arguments end with conclusions like this, which do not necessarily entail the traditional conception of God. However, this conclusion specifically is quite misleading.

By stating that it is "outside of the universe", the argument creates a sense of transcendance, spacelessness, timelessness, and immateriality. In reality, since the argument defined the universe as a collection of contingent beings, it simply means that it is not contingent. Then, the argument's conclusion is:

"There is a necessary being that is not contingent."

This is tautological and the "outside of the universe" part should really be removed.