Redigerer Gödels ontologiske bevis for Gud (avsnitt)

== Aksiomene ==
<!-- We first assume the following [[axiom]]:

:'''Axiom 1''': It is possible to single out ''positive'' properties from among all properties. Gödel defines a positive property thus: "Positive means positive in the [[moral]] [[aesthetics|aesthetic]] sense (independently of the accidental structure of the world)... It may also mean pure ''attribution'' as opposed to ''privation'' (or containing privation)." (Gödel 1995)

:If a property ''A'' entails a property ''B'' (ie in every possible world if an object has property A it must also have property B), and if A is positive, B must also be positive.

We then assume that the following three conditions hold for all positive properties (which can be summarized by saying "the positive properties form a principal [[ultrafilter]]"):

:'''Axiom 2''': For all properties ''A'', either ''A'' is positive or "not A" is positive.  Never both.
:'''Axiom 3''': The property of "being God-like", ''G'' is a positive property.
:'''Axiom 4''': If a property ''A'' is positive, then it is so in every possible world.

Finally, we assume:

:'''Axiom 5''': Necessary existence is a positive property (''Pos(NE)''). This mirrors the key assumption in Anselm's argument.

Now we '''define''' a new property ''G'': if ''x'' is an object in some possible world, then ''G''(''x'') is true if and only if ''P''(''x'') is true in that same world ''for all'' positive properties ''P''. ''G'' is called the "God-like" property. An object ''x'' that has the God-like property is called God. -->
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==Criticisms of Ontological arguments in general==

[[St Thomas Aquinas]] rejected St. Anselm's ontological argument.<ref>[[Aquinas]], Thomas, Saint. [[Summa Theologica]], Part 1, Question 2, Article 1.</ref> Likewise, some Catholic theologians have rejected<ref>{{cite encyclopedia | first=P.J. | last=Toner | title=The Existence of God | encyclopedia=The Catholic Encyclopedia | url=http://www.newadvent.org/cathen/06608b.htm#IBf | accessdate=2007-01-19}}</ref> Gödel's revised version.<ref name="uwaterloo"/> [[Bertrand Russell]] noted: "The argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies."<ref>{{cite book | first=Bertrand | last=Russell | authorlink=Bertrand Russell | title=[[History of Western Philosophy (Russell)|History of Western Philosophy]] | publisher=[[Touchstone]] | year=1972 | isbn=0-671-20158-1 | page=536}} (Book 3, Part 1, Section 11)</ref> However, Russell was also known to say: "Great God in Boots! — the ontological argument is sound!" as a parody,<ref>Autobiography of Bertrand Russell, vol. 1, 1967.</ref> including many others that parodied it, such as [[Gaunilo_of_Marmoutiers#The_.22Lost_Island.22_refutation|Gaunilo's Island]]. In ''[[Critique of Pure Reason]]'', [[Immanuel Kant]] famously rejected existence as a [[property (philosophy)|property]].<ref>{{cite book | first=Immanuel | last=Kant | authorlink=Immanuel Kant | title=[[Critique of Pure Reason]] | year=1781/1787 | pages=A 592–602/B 620–630}}</ref>

In [[David Hume]]'s [[Dialogues Concerning Natural Religion]], the character Cleanthes argues that no being could ever be proven to exist through an ''a priori'' demonstration:<ref>{{cite web | url=http://www.philosophyofreligion.info/humeonaprioriproofs.html | first=Tim | last=Holt | title=The Ontological Argument: Hume on a priori Existential Proofs | accessdate=2012-10-05 | archiveurl=https://web.archive.org/web/20080410180808/http://www.philosophyofreligion.info/humeonaprioriproofs.html | url-status=dead }}</ref>

:[T]here is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments ''a priori''. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable.

There have been many other arguments against ontological proofs such as: [[Ontological argument#Criticism by .22existence precedes essence.22|Existence precedes essence]]; [[Ontological argument#Gaunilo|Gaunilo's island]]; [[Ontological argument#Necessary nonexistence|Necessary nonexistence]]; [[Ontological argument#Kant: existence is not a predicate|Existence is not a predicate]]; and [[Ontological argument#Problem of incoherence|Problem of incoherence]]. -->
Formelt sett så er argumentet, Gödels ontologiske bevis for Gud, gjerne gitt (nå) som logisk gyldig, men at man stiller spørsmål ved argumentets «soundness<ref>Bergmann, M., et al., 2004. ''The Logic Book'', New York, NY: McGraw-Hill, s. 248.</ref>», troverdighet. «Soundness» er her en logisk term som man må forstå.<br />

Logisk gyldighet får man hvis linjen ved «Definisjon 1» blir dedusert ved «bikondisjonal eliminasjon» og at man, gitt tiden  Gödel har skrevet dette på, behandler argumentet litt «grovt», som ved moderne Fitch-struktur, så er konklusjonen relativt grei, og som tidligere nevnt, altså ''gyldig'', ved teorem 3, nødvendigvis så er egenskapen ved et vesen som er «som-Gud» eksemplifisert, dvs. ''eksisterer i virkeligheten'', gitt altså bare logikken da.

<!--==Criticism of Gödel's==

[[C. Anthony Anderson]] has said:<ref>{{cite journal|last=Anderso|first=C A|title=Some emendations of Gödel’s ontological proof|journal=Faith and Philosophy|year=1990|volume=7|issue=3|pages=291–303}}</ref>

:Consideration of the axioms, especially ... [Axiom 2], may tend to dampen one's confidence in ... [Axiom 3] and ... [Axiom 4] — that is, if one harbors any real doubt about self-consistency. I don't say that the argument begs the questions of ... [God's possible existence]; the charge is too difficult to establish. but observe that one cannot just tell by scrutinizing a property what it entails; one might be surprised at a consequence.

==Derivation==
From axioms 1 through 4, Gödel argued that in ''some'' possible world there exists God. He used a sort of modal [[plenitude principle]] to argue this from the logical consistency of Godlikeness. Note that this property is itself positive, since it is the conjunction of the (infinitely many) positive properties.

Then, Gödel defined ''essences'': if ''x'' is an object in some world, then the property ''P'' is said to be an essence of ''x'' if ''P''(''x'') is true in that world and if ''P'' entails all other properties that ''x'' has in that world. We also say that ''x'' ''necessarily exists'' if for every essence ''P'' the following is true: in every possible world, there is an element ''y'' with ''P''(''y'').

Since necessary existence is positive, it must follow from Godlikeness. Moreover, Godlikeness is an essence of God, since it entails all positive properties, and any nonpositive property is the negation of some positive property, so God cannot have any nonpositive properties. Since any Godlike object is necessarily existent, it follows that any Godlike object in one world is a Godlike object in all worlds, by the definition of necessary existence. Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the [[identity of indiscernibles]]: two or more objects are identical (are one and the same) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness. This was more to preserve the logical precision of the argument than due to a penchant for polytheism. This uniqueness proof will only work if one supposes that the positiveness of a property is independent of the object to which it is applied, a claim which some have considered to be suspect. --> <!-- Jeg har ikke lyst til å bli "bannet" for dette. Jeg har bort-kommentert en del tekst. Dette kan også være kompromisset for å importere engelsk tekst i "stort tempo" for så å lage en betraktelig større Wikipedia (enn alle andres). -->