Editing Existence of God (section)

===== Ontological argument =====

{{Main|Ontological argument}}

The ontological argument has been formulated by philosophers including [[St. Anselm]] and [[René Descartes]]. The argument proposes that God's existence is self-evident. The logic, depending on the formulation, reads roughly as follows:<ref name="Nolan">{{Cite web |last=Nolan |first=Lawrence |title=Descartes' Ontological Argument |url=http://plato.stanford.edu/entries/descartes-ontological/ |url-status=live |archive-url=https://web.archive.org/web/20120513205040/http://plato.stanford.edu/entries/descartes-ontological/ |archive-date=2012-05-13 |access-date=2012-06-20 |publisher=Stanford}}</ref>

{{Blockquote|
Whatever is contained in a clear and distinct idea of a thing must be predicated of that thing; but a clear and distinct idea of an absolutely perfect Being contains the idea of actual existence; therefore since we have the idea of an absolutely perfect Being such a Being must really exist.<ref name="Nolan" />}}

Thomas Aquinas criticized the argument for proposing a definition of God which, if God is transcendent, should be impossible for humans.<ref>{{Cite book |last=Aquinas |first=Thomas |url=http://www.newadvent.org/summa/ |title=Summa Theologica |year=1274 |at=Part 1, Question 2 |access-date=2012-06-20 |archive-url=https://web.archive.org/web/20120615112233/http://www.newadvent.org/summa/ |archive-date=2012-06-15 |url-status=live}}</ref> Immanuel Kant criticized the proof from a logical standpoint: he stated that the term "God" really signifies two different terms: both idea of God, and God. Kant concluded that the proof is equivocation, based on the ambiguity of the word God.<ref>{{Cite book |last=Kreeft |first=Peter |title=Socrates Meets Kant |publisher=Ignatius Press |year=2009 |isbn=9781586173487}}</ref> Kant also challenged the argument's assumption that existence is a predicate (of perfection) because it does not add anything to the essence of a being. If existence is not a predicate, then it is not [[Logical truth|necessarily true]] that the greatest possible being exists.<ref>{{Cite encyclopedia |title=Ontological Argument |encyclopedia=Internet Encyclopedia of Philosophy |url=http://www.iep.utm.edu/ont-arg |access-date=October 12, 2011 |last=Himma |first=Kenneth Einar |date=27 April 2005 |archive-url=https://web.archive.org/web/20121027042158/http://www.iep.utm.edu/ont-arg/ |archive-date=27 October 2012 |url-status=live}}</ref> A common rebuttal to Kant's critique is that, although "existence" does add something to both the concept and the reality of God, the concept would be vastly different if its referent is an unreal Being.{{Citation needed|date=August 2013}} Another response to Kant is attributed to Alvin Plantinga, who says that even if one were to grant that existence is not a real predicate, ''necessary existence'', which is the correct formulation of an understanding of God, ''is'' a real predicate.<ref>{{Cite web |title=Plantinga 'The Ontological Argument' Text |url=http://mind.ucsd.edu/syllabi/02-03/01w/readings/plantinga.html |url-status=dead |archive-url=https://web.archive.org/web/20130314123846/http://mind.ucsd.edu/syllabi/02-03/01w/readings/plantinga.html |archive-date=2013-03-14 |access-date=2013-05-14 |publisher=Mind.ucsd.edu}}</ref>

====== Gödel's ontological proof======
{{Excerpt|Gödel's ontological proof}}
The proof<ref>Gödel's proof is reprinted on pp. 403–404, 429–437 of: {{cite book |author=Gödel |first=Kurt |url=https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf |title=Unpublished Essays and Lectures |date=March 1995 |publisher=Oxford University Press |isbn=0-19-507255-3 |editor=Feferman |editor-first=Solomon |edition=1st |series=Collected Works |volume=III |location=Oxford, England |editor-last2=Dawson Jr. |editor-first2=John W. |editor-last3=Goldfarb |editor-first3=Warren |editor-last4=Parsons |editor-first4=Charles |editor-last5=Solovay |editor-first5=Robert M.}}</ref>{{#tag:ref |The presentation below follows that in Koons (2005),<ref name="Koons.2005"/> p.3-7.}} uses [[modal logic]], which distinguishes between [[logical truth|''necessary'' truths]] and [[Contingency (philosophy)|''contingent'' truths]]. In the most common semantics for modal logic, many "[[Modal logic#Semantics|possible worlds]]" are considered. A [[truth]] is ''necessary'' if it is true in all possible worlds. By contrast, if a statement happens to be true in our world, but is false in another world, 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.

Furthermore, the proof uses [[higher-order logic|higher-order]] (modal) logic because the definition of God employs an explicit quantification over properties.<ref>Fitting, 2002, p. 139</ref>

First, Gödel axiomatizes the notion of a "positive property":<ref group=note>It assumes that it is possible to single out ''positive'' properties from among all properties. Gödel comments that "Positive means positive in the [[morality|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), see also manuscript in (Gawlick 2012).</ref> for each property ''φ'', either ''φ'' or its [[negation]] ¬''φ'' must be positive, but not both (axiom 2). If a positive property ''φ'' implies a property ''ψ'' in each possible world, then ''ψ'' is positive, too (axiom 1).<ref group=note>As a profane example, if the property of being green is positive, that of not being red is, too (by axiom 1), hence that of being red is negative (by axiom 2). More generally, at most one color can be considered positive.</ref> Gödel then argues that each positive property is "possibly exemplified", i.e. applies at least to some object in some world (theorem 1). Defining an object to be Godlike if it has all positive properties (definition 1),<ref group=note>Continuing the color example, a godlike object must have the unique color that is considered positive, or no color at all; both alternatives may seem counter-intuitive.</ref> and requiring that property to be positive itself (axiom 3),<ref group=note>If one considers the [[partial order]] <math> \preceq </math> defined by <math> \varphi \preceq \psi </math> if <math> \square \forall y (\varphi(y) \to \psi(y)) </math>, then Axioms 1-3 can be summarized by saying that positive properties form an [[ultrafilter]] on this ordering. Definition 1 and Axiom 4 are needed to establish the ''Godlike'' property as principal element of the ultrafilter.</ref> Gödel shows that in ''some'' possible world a Godlike object exists (theorem 2), called "God" in the following.<ref group=note>By removing all modal operators from axioms, definitions, proofs, and theorems, a modified version of theorem 2 is obtained saying "∃''x'' ''G''(''x'')", i.e. "There exists an object which has all positive, but no negative properties". Nothing more than axioms 1-3, definition 1, and theorems 1-2 needs to be considered for this result.</ref> Gödel proceeds to prove that a Godlike object exists in ''every'' possible world.

====== Meinongian argument ======
{{Excerpt|Meinongian argument}}

====== Trademark argument ======
{{Excerpt|Trademark argument}}