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Koon's Cosmological Argument

Axioms and Definitions​

This argument is based on the following mereological axioms:

  1. A1: is a part of anything that overlaps overlaps .
  2. A2: If there is a thing of type , then there is an aggregate or sum of all such types.
  3. A3: is a part of and is a part of .
  4. A4: If a whole exists, so do all of its parts.
  5. A5: If all of the parts of a whole exist, so does the whole.

And the following definitions:

D. A wholly contingent thing is something that has no necessary parts.

Finally, the following principles of causation:

  1. C1: Only actual existent things can be causes or effects.
  2. C2: A cause and its effect must be distinct (i.e. a cause cannot overlap its effect).
  3. C3: Every wholly contingent thing has a cause.

Formulation​

  1. L1: All parts of a necessary thing are necessary. (A4, K)
  2. L2: Every contingent thing has a wholly contingent part. (A1, A2)
  3. Cdef: Let be the aggregate of all wholly contingent things.
  4. L3: If there are any contingent things, is a wholly contingent thing. (A1, A3, D, L1)
  5. L4: If there are any contingent things, has a cause. (L3, C3)
  6. L5: Every contingent thing overlaps . (L2, A2, Cdef)
  7. T: If there are any contingent things, then the cosmos (the sum of all wholly contingent things) has a cause that is a necessary thing. (L4, C2, L5, A1)

Simplified Formulation​

Below is a simplified and less formal formulation of the argument:

  1. There are contingent things. (Premise)
  2. Define the cosmos as the sum of all wholly contingent things.
  3. The sum of all wholly contingent things is a wholly contingent thing. (1, 2)
  4. So, the cosmos is a wholly contingent thing. (2, 3)
  5. Each wholly contingent thing has a cause. (Premise)
  6. So, the cosmos has a cause that is not contingent. (4, 5)

Discussion of the Axioms and Definitions​

The second mereological axiom A2 requires an existential quantification of aggregates and sums of types, hence a commitment to these sums. This requires more motivation; why would one ontologically commit to sums, such as the sum of Griffith's Electrodynamics, a cup of water, London, my computer mouse, and Saturn? One would not necessarily concieve this sum as a thing of its own right. In the most extreme case, mereological nihilism denies the existence of sums altogether. This is a radical position, but one would still have to defend this commitment to sums.

The fifth axiom A5 is also problematic. The milky way and the andromeda galaxy both exist, but their "whole", the Milkdromeda galaxy (which is when they eventually collide), does not exist. This is a counterexample to A5. To take another example, you can have a collection of parts of a car, but that does not mean that the car itself exists. One would have to defend A5 by invoking a statement of spatio-temporal arrangement of parts as a part itself, but that's not immediately obvious - when one lists the parts of a car individually, and miss their arrangement, someone else would not call them out and tell them that they are missing a part (the arrangement).

C3 is the most controversial of the three principles. The Principle of Sufficient Reasoning (PSR) does state that everything has a reason for its existence, but this fails for two reasons:

  1. The PSR cannot be applied to all things, as it would lead to an infinite regress.
  2. Even if we apply the PSR for all contingent things, that only means that all contingent things have an explanation, not a cause. The explanation could be a metaphysical grounding, a mathematical explanation, certain constraints, morals, etc., which are all noncausal explanations.

Commitment to C​

The argument, specifically Cdef, requires an ontological commitment to , defined as the sum of all wholly contingent things. There could be a problem with this, which can be shown b the following argument:

  1. Assume there exists the aggregate of all wholly contingent things, . That is, Cdef is valid and true.
  2. Assume that L3 holds. (If there are any contingent things, is a wholly contingent thing.)
  3. That means that is a wholly contingent thing. (2)
  4. But that means that is part of the aggregate of all wholly contingent things. (3)
  5. This means that is a part of itself. This is a contradiction. (1, 4)
  6. Therefore, the assumption that there exists the aggregate of all wholly contingent things is false.

While this argument does not completely disprove the existence of the aggregate of all wholly contingent things, it does show that there is a problem with the commitment to it - it leads to this infinite/recursive definition of .

One way to resolve this could be to, instead of treating as its own thing, make use of plural quantification, which, intuitively, is a way to "consider" all the wholly contingent things at once, without having to commit to the existence of the aggregate of all wholly contingent things.

The Conclusion​

The conclusion, T, uses the word "cosmos", which is a bit misleading. By using "cosmos", the argument seems to create a sense of transcendance or grandeur - timelessness, spacelessness, but it is really just the sum of all wholly contingent things. This definition of "cosmos" is different from the usual definition of the universe.