Proof That God Exists

William S. Hatcher applies his Minimalist philosophy to Avicenna's neglected ontological proof. Hatcher uses first-order relational logic, avoiding the existential pitfalls of modal logic (necessity, contingency, and manifold universes). Hatcher's proof, linked in the title above, lays an explicit foundation for the following excerpt.

We now have before us four empirically grounded, and therefore plausibly true, metaphysical principles (P.0-P.3). We list them together for easy reference in the ensuing text.

P.0. V is composite.
[V is reality entire: subjective, objective, abstract, and concrete.]

P.1. Every existing phenomenon B is either caused (other-caused) or uncaused (self-caused), and never both.
[The complete cause equals the initial phenomenon plus the efficient cause (CC=IP+EC). The straw that breaks the camel's back is the efficient cause. The complete cause also includes the rest of the straws, and maybe an affidavit from the camel's chiropractor.]

P.2. Suppose that A→B holds, where B is composite. Then A→E also holds where E is any part of B (i.e., where either E∈B or E⊂B).
[Signifiers: → causation, ∈ composition, and ⊂ containment.]

P.3. A→E cannot hold if E is a component of A.

Besides P.0, which is absolutely certain, none of the other principles makes any existence assertions whatever. P.1-P.3 are all universal conditional statements—propositions which affirm that, whenever and if ever certain conditions are obtained, then certain other conditions must be fulfilled. In other words, these statements in themselves have no existential import. However, in conjunction with P.0 (i.e., under the assumption that something exists), these principles have strong and somewhat surprising existential consequences.

Theorem. It follows from P.0-P.3 that there is one and only one self-caused phenomenon G. Further, this G is simple (non-composite) and is a (necessarily unique) universal cause (i.e., a cause of every existent phenomenon).

Proof. We begin by asking the question “What is the cause of the global phenomenon V?” By P.1, V is either self-caused or other-caused. Suppose for the moment that it is self-caused, V→V. By P.0, V is composite. Hence, there is some component E∈V. Therefore, by P.2, V→E. But this contradicts the limitation principle P.3 since E is a component of V. Thus, V cannot be self-caused. In fact this argument is applicable to any composite and establishes the general principle: that no composite phenomenon can be self-caused.

Applying P.1 to the above, we now conclude that V must be other-caused by some phenomenon G≠V, G→V. Now, every phenomenon is either a component or a subsystem of V (see above). We thus have G→V and G is a part of V. By P.2, we can thus immediately conclude that G→G (i.e., G is self-caused). This means that G is simple because if G had some component E, we could then conclude (by P.2) that G→E, contradicting P.3. Thus, G is self-caused and simple. The simplicity of G implies that G is an entity (and thus a component of V, G∈V).

Moreover, G→V and every phenomenon B is a part of V. Hence, by P.2, G→B where B is any phenomenon whatever. G is therefore a universal cause.

Finally, G is the unique uncaused entity. To see this, suppose that G'→G' for some phenomenon G'. Now, we have already established that G is a universal cause, so G→G' also holds. Thus, G' is both self-caused and caused by G. However, P.1 asserts that no self-caused phenomenon can also be other-caused. Thus, G cannot be other than G' (i.e., G=G'). Hence, the simple entity G is the only uncaused phenomenon in existence.

It is important to realize that, in the light of the minimalistic method we have employed, the above theorem is not an idle word game. We have showed that the existence of a unique, simple, universal, uncaused cause follows by pure logic from a few, broad, objective properties of reality. In more formal terms, the conjuction of P.0-P.3 logically implies that G exists: (P.0 & P.1 & P.2 & P.3)→(G exists). This proof is totally objective. In other words, it is literally impossible that P.0-P.3 be true and that G not exist.