An argument for the existence of God

Metaphysics & Epistemology
308

There’s a sleight of hand involved in modal ontological arguments that can be demonstrated by presenting the argument more clearly.

At their most fundamental, their premises take the following form:

  1. X is God if and only if X necessarily exists and has properties A, B, and C1.
  1. It is possible that God exists.

To prevent equivocation, we must use (1) to unpack (2), reformulating the argument as such:

  1. X is God if and only if X necessarily exists and has properties A, B, and C.
  1. It is possible that there exists some X such that X necessarily exists and has properties A, B, and C.

The phrase “it is possible that there exists some X such that X necessarily exists” is somewhat ambiguous. To address this ambiguity, we should perhaps reformulate the argument as such:

  1. X is God if and only if X necessarily exists and has properties A, B, and C.
  1. It is possibly necessary that there exists some X such that X has properties A, B, and C.

We can then use S5’s axiom that ◊□p ⊢ □p to present the following modal ontological argument:

  1. X is God if and only if X necessarily exists and has properties A, B, and C.

  1. It is possibly necessary that there exists some X such that X has properties A, B, and C.

  2. Therefore, there necessarily exists some X such that X has properties A, B, and C.

This argument is valid under S5. However, (4) needs to be justified; it is not true a priori.

It may be claimed that if “there exists some X such that X has properties A, B, and C” is not necessarily false then it is possibly necessarily true.

However, consider these claims:

  1. There exists some X such that X is the only Y and is Z
  2. There exists some X such that X is the only Y and is ¬Z

Given that these cannot both be true, under S5 they cannot both be possibly necessarily true. But neither are they necessarily false.

And so, once more, (4) needs to be justified.

It may be countered that (3) and (4) are not equivalent. If they are not equivalent then prima facie one cannot derive (5) from (3), and so something other than S5 is required. This is where the sleight of hand occurs.

1 The particular properties differ across arguments (omnipotence, omniscience, etc.); we need not make them explicit here.

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