Gödel's Ontological Proof of God - Strengths and Limitations of Mathematical Logic

Gödel's Ontological Proof of God

This work is very interesting both from a logical and a philosophical point of view.
First the necessary vocabular should be clarified.

Ontology
. . . is the philosophical study of the nature of being, becoming, existence, or reality, as well as the basic categories of being and their relations. It is traditionally listed as a part of the major branch of philosophy and also known as Metaphysics.
Ref. [2]

Entitiy
. . . is something. It can be existent as an subject, an object, actually or potentially, it can be physical or abstract, hence this term is not limited to material existence.
Ref. [2]

The Mathematical Proof

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Formally, this proof is correct, hence from a logical point it is valid for itself. The use of mathematical logic is one of the most powerful tools to tackle question which can not be investigated via empirism. - But how exactly does it work?

Here is an as simple as possible verbal explanation of the premises and conclusions, which is similar to the one in the figure above but with additional comments to make it easier to understand:

1. premise - Either a property or its negation is positive, but not both. What means, that if a property is positive its negation is negative and vice versa.

2. A property necessarily implied by a positive property is positive.
   (Otherwise, the initial positive property would necessarily imply a negative one and thus indirectly provide a negative property for the entity, which in the first place would not allow it to be defined as a positive property.)

3. Positive properties are possbily exemplified, hence there possibly may be entities, that show these properties.

4. definition - A God-like being possesses all positive properties.

5. The property of being God-like is therefore positive.
   (To come to this use the logic provided in Point 2.)

6. conclusion - Hence positive properties are possibly exemplified, possibly God exists.

7. axiom - Positive properties are necessarily positive.

8. definition - An essence of an individual is a property, that is possessed by this individual and what necessarily implies any other of it properties.

9. theorem - Being God-like is an essence of any God-like being.
   (This theorem rises from the previous established statements.)

10. definition - Necessary existence of an individual is the necessary exemplification of all its essences. This means, that an individual shows necessary existence, whenever all its properties (or overriding: essences) are necessarily exemplified.

11. axiom - Necessary existence is a positive property.

12. theorem - Necessarily, God exists. Based on the previous established statements, this is the only correct conclusion: God possesses all positive properties, hence he also possesses the property of necessary existence.

Limitations

From a philosophical point of view for every mathematically correct proof, the premises, on which it necessarily rests upon, can be attacked and debated. The fact that the premises and definitions used here are predominantly very basic and clearly worded is a strength of this ontological proof. Furthermore, it can be questioned whether the logic itself, which is used for the proof, provides meaningful results for the considered issue.

This article does not intend to offend anyone's feelings by presenting this ontological proof, but is so interesting from a purely intellectual and scientific point of view, that it should be read and enjoyed in an appropriate neutral scientific way.
A lot of points for and against the existence of God can be found in further literature. A fruitful treatment of this - probably most difficult - question is by no means directly connected with this article only and requires a comprehensive and open discussion.

About the original Philosopher

Kurt Friedrich Gödel was an Austrian-American mathematician and philosopher and one of the most important logicians of the 20th century!
He made significant contributions to the first-order logic, to the relations of intuitionistic logic to both classical logic and modal logic and to the theory of relativity in physics.

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