Editing Gödel's ontological proof (section)

===Translation of full argument===

[[Possible world|Possible-worlds]] readings of modal terms have been added in parentheses, i.e., "in all possible worlds" for "necessarily" and "in at least one possible world" for "possibly". For completeness, "in the actual world" should be added to all sentences that were said ''without'' "necessarily" or "possibly", but this has been skipped since it might make the text difficult to read.

* '''Axiom 1:''' If <math>\varphi</math> is a positive property, and if it is necessarily true (true in all possible worlds) that every object with property <math>\varphi</math> also has property <math>\psi</math>, then <math>\psi</math> is also a positive property.
* '''Axiom 2:''' The negation of a property <math>\varphi</math> is positive if, and only if, <math>\varphi</math> is not positive.
* '''Theorem 1:''' If a property <math>\varphi</math> is positive, then it is possible that there exists an object <math>x</math> that has this property (in at least one possible world, there exists an object <math>x</math> that has this property).
* '''Definition 1:''' An object <math>x</math> is God-like if, and only if, <math>x</math> has all positive properties.
* '''Axiom 3:''' The property of being God-like is itself a positive property.
* '''Theorem 2:''' It is possible that there exists a God-like object <math>x</math> (in at least one possible world, there exists a God-like object <math>x</math>).
* '''Definition 2:''' A property <math>\varphi</math> is an essential property of an object <math>x</math> if, <math>x</math> has property <math>\varphi</math>, and every property <math>\psi</math> of <math>x</math> necessarily (in all possible worlds) and generally (for all objects) follows from <math>\varphi</math>.
* '''Axiom 4:''' If a property <math>\varphi</math> is positive, then it is necessarily positive (positive in all possible worlds).
* '''Theorem 3:''' If <math>x</math> is God-like, then being God-like is an essential property of <math>x</math>.
* '''Definition 3:''' An object <math>x</math> "exists necessarily" if each of its essential properties <math>\varphi</math> applies, in each possible world, to some object <math>y</math>.
* '''Axiom 5:''' "Necessary existence" is a positive property.
* '''Theorem 4:''' It is necessarily true (true in all possible worlds) that a God-like object exists.