Gödel's ontological proof

[Aetixintro]

Gödel's ontological proof can be questioned, however I've contributed with a version that makes it stand out as splendid and at the same time being accepted without a question outside the logical soundness objections to a "necessary God".

Here is:

UoD: Everything.

Gx: x is God-like
Ex: x has essential properties.
Ax: x is an essence of A.
Bx: x is a property of B.
Px: property x is positive.
Nx: x is a General property.
Xx: x is Positive existence.
Cx: x is consistent.

The final argument by my interpretation is presented below in 4 parts:

1.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ≡ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ≡E
------------------
7 │ □Gx 5, 6 ≡E

...

4.

1 │ □Bx ≡ □Gx A (A is Assumption)
2 │ ◊Ax ≡ □Bx ≡ (◊Ax ⊃ □Bx) A
3 │ ◊Ax A
------------------
4 │ □Bx 3, 2 ≡E
------------------
5 │ □Gx 4, 1 ≡E

Note for the 4th part: Consider (◊Ax ⊃ □Bx) as “added explanation�!
Also, line 2 of the 4th part is Definition 2 from the original argument of Gödel.
Note2: The following lines are taken out for having no use in this interpretation of the argument.
8 │ □Gx ⊃ □Px A
16│ □Gx ⊃ □Cx A
17│ □Gx ⊃ □Ax A.

From:
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 2: If a property is positive, then its negation is not positive.
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.

http://en.wikipedia.org/wiki/G%C3%B6del ... ical_proof
http://en.wikipedia.org/wiki/Universe_of_Discourse - UoD from above.
http://en.wikipedia.org/wiki/Logical_consequence - "Entailment"/"entails".

Some of the text is from http://whatiswritten777.blogspot.no/201 ... on-of.html.

[Aetixintro]

UoD: Everything.

Gx: x is God-like
Ex: x has essential properties.
Ax: x is an essence of A.
Bx: x is a property of B.
Px: property x is positive.
Nx: x is a General property.
Xx: x is Positive existence.
Cx: x is consistent.

The final argument by my interpretation is presented below in 4 parts:

1.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ≡ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ≡E
------------------
7 │ □Gx 5, 6 ≡E

Alt. 1, 1st.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ⊃ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ⊃E
------------------
7 │ □Gx 5, 6 ≡E

Alt. 1, 2nd.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ (□Px ⊃ □Nx) ⊃ □Px A
3 │ □Px ⊃ □Nx A
4 │ □Ex A
------------------
5 │ □Px 2, 3 ⊃E
6 │ □Px ≡ □Gx 1, 2 ≡E
------------------
7 │ □Gx 6, 5 ≡E

This alternative, nr. 2, takes care of the former line �6 │ (□Px ⊃ □Nx) ⊃ □Px A� and adds overall description by this!

2.

1 │ □Px ≡ □Gx A (A is Assumption)
2 │ □Xx ⊃ □Px A
3 │ □Xx A
------------------
4 │ □Px 2, 3 ⊃E
------------------
5 │ □Gx 1, 4 ≡E

3.

1 │ ◊Cx ≡ □Gx A (A is Assumption)
2 │ □Px ∨ ~□Px A
3 │ □Px ⊃ ◊Cx A
------------------
4 ││ □Px A
0 ││-----------------
5 ││ □Px 6 R

6 ││ ~□Px A
0 ││-----------------
7 ││ □Px 6 R
8 │ □Px 4, 6-9 ∨E
9 │ ◊Cx 8, 3 ⊃E
------------------
10│ □Gx 9, 1 ≡E

4.

1 │ □Bx ≡ □Gx A (A is Assumption)
2 │ ◊Ax ≡ □Bx ≡ (◊Ax ⊃ □Bx) A
3 │ ◊Ax A
------------------
4 │ □Bx 3, 2 ≡E
------------------
5 │ □Gx 4, 1 ≡E

Note for the 4th part: Consider (◊Ax ⊃ □Bx) as “added explanation�!
Also, line 2 of the 4th part is Definition 2 from the original argument of Gödel.
Note2: The following lines are taken out for having no use in this interpretation of the argument.
8 │ □Gx ⊃ □Px A
16│ □Gx ⊃ □Cx A
17│ □Gx ⊃ □Ax A.

[Goat]

This is the classic case of obscurantism. Let's take the classic argument, and make it all science like to try to make it more convincing.

As a theorem , it basically assumes god and god-like properties to show that god and god-like properties are possible, but it provides no evidence for this assumption.

So, you got a very complicated therom that assumes the possibility of what it is trying to show the possibility of, and you get what is known as 'circular reasoning'.

It also makes the assumption that 'God and God-like' is a positive property, yet can not demonstrate this is so.

So, it all boils down to relying on assumptions that can not be tested or shown to be true.

[Nickman]

You will have to dumb this down for us "more philosophically and theologically inclined" on the forum.

[Goat]

You will have to dumb this down for us "more philosophically and theologically inclined" on the forum.

IF you want a nice analysis of it from a skeptic point of view.

http://skepticsplay.blogspot.com/2009/0 ... ument.html

In my opinion, .. it's just the same old same old, but using the technique to tryign to baffle them with being all science like.

[Nilloc James]

Using formal logic doesnt make your premises right. It just helps avoid errors that common language can induce.

So please justify your premises.

[Aetixintro]

Nobody is attacked here, so please, relax. Just some Gödel pedagogics.

Let's start. Given the premises of Gödel - to prove God, more technically expressed with him.

Please, bother to educate yourself a bit, by looking up resources for logics and so on...

Goat, you fail on circularity:
Circularity is God implies God, that premise gets repeated as conclusion. This is not the case here, most evidently and by the World of logics today, 2013!

So, to help you on a bit, Gödel's argument here, in its logical beauty, is the DESCRIPTION, that he adds to the description for "necessary-God" in the tradition of the other "Ontological Arguments", see fx. St. Anselm etc., please.

Finally,
To Nilloc James. These are not my premises, they are Gödel's premises. I'm merely restating his deduction for better logical defences so that the criticism of his Argument can STOP!

Alright, all? Take care!

[Goat]

Nobody is attacked here, so please, relax. Just some Gödel pedagogics.

Let's start. Given the premises of Gödel - to prove God, more technically expressed with him.

Please, bother to educate yourself a bit, by looking up resources for logics and so on...

Goat, you fail on circularity:
Circularity is God implies God, that premise gets repeated as conclusion. This is not the case here, most evidently and by the World of logics today, 2013!

So, to help you on a bit, Gödel's argument here, in its logical beauty, is the DESCRIPTION, that he adds to the description for "necessary-God" in the tradition of the other "Ontological Arguments", see fx. St. Anselm etc., please.

Finally,
To Nilloc James. These are not my premises, they are Gödel's premises. I'm merely restating his deduction for better logical defences so that the criticism of his Argument can STOP!

Alright, all? Take care!

You are not being clear and concise here, as a matter of fact, you are being the opposite.

And, yes, that is exactly what Godel is doing, fancied up in modal logic, saying 'God implies god'.

[Nilloc James]

Nobody is attacked here, so please, relax. Just some Gödel pedagogics.

Let's start. Given the premises of Gödel - to prove God, more technically expressed with him.

Please, bother to educate yourself a bit, by looking up resources for logics and so on...

Goat, you fail on circularity:
Circularity is God implies God, that premise gets repeated as conclusion. This is not the case here, most evidently and by the World of logics today, 2013!

So, to help you on a bit, Gödel's argument here, in its logical beauty, is the DESCRIPTION, that he adds to the description for "necessary-God" in the tradition of the other "Ontological Arguments", see fx. St. Anselm etc., please.

Finally,
To Nilloc James. These are not my premises, they are Gödel's premises. I'm merely restating his deduction for better logical defences so that the criticism of his Argument can STOP!

Alright, all? Take care!

Im sorry, I dont unserstand.

Could you clarify please?

[Aetixintro]

Nobody is attacked here, so please, relax. ... Gödel's argument here, in its logical beauty, is the DESCRIPTION, that he adds to the description for "necessary-God" in the tradition of the other "Ontological Arguments", see fx. St. Anselm etc., please.

Finally,
To Nilloc James. These are not my premises, they are Gödel's premises. I'm merely restating his deduction for better logical defences so that the criticism of his Argument can STOP!

Alright, all? Take care!

You are not being clear and concise here, as a matter of fact, you are being the opposite.

And, yes, that is exactly what Godel is doing, fancied up in modal logic, saying 'God implies god'.

No. This is wrong, directly. Accounting 1 - 4 plus 2 alt. to 1st part, 'God implies god', '□Gx → □Gx', = Zero results! Correct?

Cheers!