Hartshorne's Modal Proof.

Using the Modal operators N(x) and P(x) for "x is logically necessary" (i.e. correct) and "x is logically possible" respectively we immediately have ¬P(x) = N(¬x) and ¬N(¬x) = P(x).

1) G => N(G)

Anselm's principle.

2) N(G) v ¬N(G)

The Existence Of God is necessary, or not necessary, (excluded middle).

3) N(G) v N¬N(G)

Becker's postulate: Modal status is always necessary. The status of something necessary is always necessary.

4) N(G) v N(¬G)   =>   N(G) v ¬P(G)

Contrapositive of (1) applied.

5) P(G)  =  ¬N(¬G)

Our postulate, the existence of perfection is not impossible.

6) N(G)

Our result. (the left side of the "or" statement.)

7) N(G) => G

Modal axiom

8) G

God, a perfect being exists.

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