Redigerer Gödels ontologiske bevis for Gud (avsnitt)

== Beviset ==
Symbolsk:

<math>
\begin{array}{rl}

\text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall x[\varphi(x) \to \psi(x)]\right\} \to P(\psi) \\

\text{Ax. 2.} & P(\neg \varphi) \leftrightarrow \neg P(\varphi) \\

\text{Th. 1.} & P(\varphi) \to \Diamond \; \exists x[\varphi(x)] \\

\text{Df. 1.} & G(x) \iff \forall \varphi [P(\varphi) \to \varphi(x)] \\

\text{Ax. 3.} & P(G) \\

\text{Th. 2.} & \Diamond \; \exists x \; G(x) \\

\text{Df. 2.} & \varphi \text{ ess } x \iff \varphi(x) \wedge \forall \psi \left\{\psi(x) \to \Box \; \forall x[\varphi(x) \to \psi(x)]\right\} \\

\text{Ax. 4.} & P(\varphi) \to \Box \; P(\varphi) \\

\text{Th. 3.} & G(x) \to G \text{ ess } x \\
		
\text{Df. 3.} & E(x) \iff \forall \varphi[\varphi \text{ ess } x \to \Box \; \exists x \; \varphi(x)] \\
			
\text{Ax. 5.} & P(E) \\
			
\text{Th. 4.} & \Box \; \exists x \; G(x)
  
\end{array}
</math>
:
Eller:

UoD], engelsk, «Diskusjonsunivers», definerer det som skal «diskuteres» i det oppsatte logiske argumentet: Alt.<br />
Gx: x er som-Gud<br />
Ex: x har essensielle egenskaper.<br />
Ax: x er en essens av A.<br />
Bx: x er en egenskap av B.<br />
Px: egenskap x er positiv.<br />
Nx: x er en Generell egenskap.<br />
Xx: x er Positiv eksistens.<br />
Cx: x er konsistent.
:
Fra:

<!-- Jeg forstår ikke meningen med å la den være på engelsk! Dette er Wikipedia på bokmål. Det finnes en engelsk Wikipedia. -->
Engelsk tekst følger for Gödels logiske argumentasjon, i sin helhet og slik han har historisk sett satt dem opp:<br />
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive<br />
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<br />
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified<br />
Axiom 1: If a property is positive, then its negation is not positive.<br />
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive<br />
Axiom 3: The property of being God-like is positive<br />
Axiom 4: If a property is positive, then it is necessarily positive<br />
Axiom 5: Necessary existence is positive<br />
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.<br />
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.<br />
Corollary 1: The property of being God-like is consistent.<br />
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.<br />
Theorem 3: Necessarily, the property of being God-like is exemplified.

<!-- Engelsk oversettelse trengs og jeg er trett.
==Modal logic==
The proof uses [[modal logic]], which distinguishes between ''necessary'' truths and ''contingent'' truths.<br />

In the most common interpretation of modal logic, one considers "all possible worlds". A [[truth]] is ''necessary'' if its negation entails a contradiction, such as 2 + 2 = 3, and is true in all possible worlds. By contrast, a truth is ''contingent'' if it just happens to be the case, for instance, "more than half of the planet is covered by water". If a statement happens to be true in our world, but is false in some other worlds, then it is a contingent truth. A statement that is true in some world (not necessarily our own) is called a ''[[logically possible|possible]]'' truth.

A ''property'' assigns to each [[object (philosophy)|object]], in every possible world, a [[truth value]] (either true or false). Note that not all worlds have the same objects: some objects exist in some worlds and not in others. A property has only to assign truth values to those objects that exist in a particular world. As an example, consider the property
:''P''(''s'') = ''s'' is pink

and consider the object
:''s'' = my shirt

In our world, ''P''(''s'') is true because my shirt happens to be pink; in some other world, ''P''(''s'') is false, while in still some other world, ''P''(''s'') wouldn't make sense because my shirt doesn't exist there.

We say that the property ''P'' ''entails'' the property ''Q'', if any object in any world that has the property ''P'' in that world also has the property ''Q'' in that same world. For example, the property
:''P''(''x'') = ''x'' is taller than 2 meters

entails the property
:''Q''(''x'') = ''x'' is taller than 1 meter.

The proof can be summarized as:

:IF it is possible for a rational omniscient being to exist THEN necessarily a rational omniscient being exists.<ref name="uwaterloo">{{cite web |url=http://www.stats.uwaterloo.ca/~cgsmall/ontology.html |title=Kurt Gödel's Ontological Argument |first=Christopher  |last=Small |page=1 |location=[[University of Waterloo]]}}</ref> -->
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