From Gödel to God

God as the Ultimate Explanation of the Universe - First Predicate Logic Proof

(aka, "Proving God in 20 Steps")

​​By definition: an Ultimate Explanation of the Universe must be complete and consistent (i.e., either fully explained either through natural demonstration [a TOE (Theory of Everything)] or metaphysically otherwise).

​Eu ↔ Ku

A formal system of explanation (basically, any scientifically compatible explanation) is complete and consistent only in the infinite (recall that higher type formal systems can always be formulated into the transfinite). : From Gödel’s Second Incompleteness Theorem. This rules out a TOE and leads to the rest of this proof.

​∀x[Kx ↔ Ix]

An infinite formal system of explanation is logically equivalent with the “Greatest” one imaginable.

Ix ↔ Gx

The last two premises mean that our Universe is ultimately only explainable by an infinitely great power. It is also easy to see that...

Any characteristic “Greatest” refers to God. 

∀x[Gx ↔ Ĝx]

Therefore, the ultimate explanation of the Universe can only be God.

Eu ↔ Ĝx

Proof:
Eu ↔ Ku, ∀x[Kx ↔ Ix], Ix ↔ Gx, ∀x[Gx ↔ Ĝx]: Eu ↔ Ĝx 

1.   Eu ↔ Ku                                   P

2.   ∀x[Kx ↔ Ix]                             P

3.   Ix ↔ Gx                                    P

4.   ∀x[Gx ↔ Ĝx]                           P

5.   (Eu → Ku) & (Ku → Eu)           1 Equiv (Equivalence)

6.   Eu → Ku                                   5 Simp (Simplification)

7.   Ku → Eu                                   5 Simp

8.   (Kx → Ix) & (Ix → Kx)             2  Equiv

9.   Kx → Ix                                    8 Simp 

10. Ix → Kx                                    8 Simp

11. (Ix ↔ Gx) & (Gx → Ix)              3 Equiv 

12. Ix → Gx                                    11 Simp 

13. Gx → Ix                                    11 Simp 

14. (Gx → Ĝx) & (Ĝx → Gx)           4 Equiv 

15. Gx → Ĝx                                   14 Simp

16. Ĝx → Gx                                   14 Simp

17. Eu → Ĝx                                   6, 9, 12, 15 UI, HS (Hypothetical Syllogism)   

18. Ĝx → Eu                                   16, 13, 10, 7 UI, HS 

19. (Eu → Ĝx) & (Ĝx → Eu)            17, 18 Conj (Conjunction) 

20. Eu ↔ Ĝx                                   19 Equiv [END OF PROOF] 

Notes

​(i) Problems with including causation and existence as predicates are avoided with a conclusion of God as rather, an ultimate explanation.

(ii) “Explanation” as sought in the proof refers to an understanding of the underlying laws and forces in the universe, not an answer to the “why?” of its existence.

(iii) It is important that any invocation of Gödel’s Theorem outside of mathematics maintains a sure link between formal systems with a certain amount of arithmetic and any extra-mathematical conclusions. In this proof, such a link is maintained for the soundness of the premises.

(iv) Infinity here is not an abstract concept as is sometimes countered by opponents to ontological arguments but is logically necessary for an ultimate explanation of the Universe. In other words, it cannot be abstract here because it is demonstrably necessary for the Universe’s existence.

(v) Given that logic entails a certain amount of arithmetic, it is not itself both complete and consistent; however, that does not mean that we can't trust logical conclusions, such as presented here. All that is necessary is that the logical system that we use is founded on true axioms.

​(vi) For more, see FAQ