Hello atheists,
I welcome critique on a proof of God (if you don’t know first predicate logic, just follow the text).
The proof is found below.
*** Please read the notes at the end of the proof which help establish the soundness of the premises ***
If the proof is valid (which it is) and sound, then God is proved!
I hope one day to offer a reward to anyone capable of dismissing the proof.
Thanks!
>>>>>
PROOF >>>
There are no uncaused things. : From Cosmological Arguments
The Universe is a thing.
The Universe is caused (be it internally [self-caused] or externally).
∀x[Tx → Cx], Tu: Cu
1. ∀x[Tx → Cx] P (Premise)
2. Tu P
Proof:
3. Tu → Cu 1 UI (Universal Instantiation)
4. Cu 2, 3 MP (Modus Ponens) [END OF PART I]
It follows that for all caused things, there is an explanation.
The Universe is caused.
The Universe has an explanation.
∀x[Cx → Ex], Cu: Eu
1. ∀x[Cx → Ex] P
2. Cu P
Proof:
3. Cu → Eu 1 UI
4. Eu 2,3 MP [END OF PART II]
By definition: an ultimate explanation of the Universe must be complete and consistent (i.e., fully explained either through natural self-causation [TOE (Theory of Everything)] or 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. : From Ontological Arguments
∀x[Gx ↔ Ĝx]
Therefore, the ultimate explanation of the Universe can only be God.
Eu ↔ Ĝx
Proving God in 20 statements:
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) Critics often refer to Quantum Theory to show the possibility of something from "nothing" but in fact, at a minimum, a Quantum Vacuum is needed along with scientific laws. Hardly "nothing" I would say.
(ii) The Cosmological Argument used here does not argue for an external cause but ONLY a causation - which is not contentious.
(iii) God is “first cause” by definition and therefore not needed to be caused; however, God still does not necessarily violate the premise that all things are caused because the premise allows for self-causation, which can be applied to God: God causes God to exist.
(iv) “Explanation” as sought in the proof refers to a mode of causation, not a metaphysical “why?”
(v) 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.
(vi) Infinity here is not an abstract concept as is sometimes proffered by opponents to Ontological Arguments but is necessitated 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.
(vii) The conclusion of this proof is consistent with the Big Bang Theory which is the leading theoretical description of our Universe’s beginning, supported by the Universe’s observed expansion and increasing entropy. However, even fringe theories of an “infinite” Universe could only be, in their limits, described as “transfinite” Universe theories, thus being innocuous to the proof’s conclusion.
(viii) Refutations of this proof invoking a multiverse are in the realm of science fiction and are not accorded further comment beyond noting their non-scientific characterization (they are not falsifiable). The irony is that such flights of fantasy actually force opponents to accept the possibility of God in a multiverse where anything is possible.
(ix) 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.
I welcome critique on a proof of God (if you don’t know first predicate logic, just follow the text).
The proof is found below.
*** Please read the notes at the end of the proof which help establish the soundness of the premises ***
If the proof is valid (which it is) and sound, then God is proved!
I hope one day to offer a reward to anyone capable of dismissing the proof.
Thanks!
>>>>>
PROOF >>>
There are no uncaused things. : From Cosmological Arguments
The Universe is a thing.
The Universe is caused (be it internally [self-caused] or externally).
∀x[Tx → Cx], Tu: Cu
1. ∀x[Tx → Cx] P (Premise)
2. Tu P
Proof:
3. Tu → Cu 1 UI (Universal Instantiation)
4. Cu 2, 3 MP (Modus Ponens) [END OF PART I]
It follows that for all caused things, there is an explanation.
The Universe is caused.
The Universe has an explanation.
∀x[Cx → Ex], Cu: Eu
1. ∀x[Cx → Ex] P
2. Cu P
Proof:
3. Cu → Eu 1 UI
4. Eu 2,3 MP [END OF PART II]
By definition: an ultimate explanation of the Universe must be complete and consistent (i.e., fully explained either through natural self-causation [TOE (Theory of Everything)] or 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. : From Ontological Arguments
∀x[Gx ↔ Ĝx]
Therefore, the ultimate explanation of the Universe can only be God.
Eu ↔ Ĝx
Proving God in 20 statements:
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) Critics often refer to Quantum Theory to show the possibility of something from "nothing" but in fact, at a minimum, a Quantum Vacuum is needed along with scientific laws. Hardly "nothing" I would say.
(ii) The Cosmological Argument used here does not argue for an external cause but ONLY a causation - which is not contentious.
(iii) God is “first cause” by definition and therefore not needed to be caused; however, God still does not necessarily violate the premise that all things are caused because the premise allows for self-causation, which can be applied to God: God causes God to exist.
(iv) “Explanation” as sought in the proof refers to a mode of causation, not a metaphysical “why?”
(v) 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.
(vi) Infinity here is not an abstract concept as is sometimes proffered by opponents to Ontological Arguments but is necessitated 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.
(vii) The conclusion of this proof is consistent with the Big Bang Theory which is the leading theoretical description of our Universe’s beginning, supported by the Universe’s observed expansion and increasing entropy. However, even fringe theories of an “infinite” Universe could only be, in their limits, described as “transfinite” Universe theories, thus being innocuous to the proof’s conclusion.
(viii) Refutations of this proof invoking a multiverse are in the realm of science fiction and are not accorded further comment beyond noting their non-scientific characterization (they are not falsifiable). The irony is that such flights of fantasy actually force opponents to accept the possibility of God in a multiverse where anything is possible.
(ix) 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.
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