<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Small (Christopher) - Kurt Gdel's Ontological Argument (Theo Todman's Book Collection - Paper Abstracts) </title> <link href="../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../TT_ICO.png" /></head> <BODY> <CENTER> <div id="header"><HR><h1>Theo Todman's Web Page - Paper Abstracts</h1><HR></div><A name="Top"></A> <TABLE class = "Bridge" WIDTH=950> <tr><th><A HREF = "../../PaperSummaries/PaperSummary_16/PaperSummary_16502.htm">Kurt Gdel's Ontological Argument</A></th></tr> <tr><th><A HREF = "../../Authors/S/Author_Small (Christopher).htm">Small (Christopher)</a></th></tr> <tr><th>Source: Personal Website</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=600><tr><td><A HREF = "../../PaperSummaries/PaperSummary_16/PaperSummary_16502.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_16/PapersToNotes_16502.htm">Notes Citing this Paper</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Excerpts / Contents</U><FONT COLOR = "800080"><ol type="1"><li>Kurt Gdel is best known to mathematicians and the general public for his celebrated incompleteness theorems. Physicists also know his famous cosmological model in which time-like lines close back on themselves so that the distance past and the distant future are one and the same. What is less well known is the fact that Gdel has sketched a revised version of Anselm's traditional ontological argument for the existence of God.</li><li>A biographical sketch</li><li>The Role of <a name="1"></a><A HREF="../../Notes/Notes_1/Notes_121.htm">Modal</A><SUP>1</SUP> Necessity</li><li>Windows into <a name="2"></a><A HREF="../../Notes/Notes_1/Notes_121.htm">Modal</A><SUP>2</SUP> Worlds <ol type="I"><li>Necessary Falsehood: Penrose Triangle</li><li>Contingent Falsehood</li><li>Contingent Truth</li><li>Necessary Truth: Mandelbrot set</ol></li><li>Counterfactual Argumentation</li><li>Essential Properties</li><li>Anselm's ontological argument</li><li>Gdel's positivity operator</li><li>The Basic Definitions</li><li>The Rest of the Argument</li><li>Conclusion: <ul type="disc"><li>I should remind the reader again that the version of Gdel's argument that I have presented is <B>not</B> Gdel's original argument. When I first read Gdel's notes on his ontological argument, I, like many others, found the axioms confusing and difficult to accept. So I turned to the emended version of the argument due to Anderson. This version has now been widely discussed. But the more I fuss around with this version the more uncomfortable I become with it. I went back to Gdel's original version and found that it was far better than I had originally understood. If you are interested in studying this argument, and the reasons why I prefer it to Anderson's emendation, you can click to obtain a PDF file entitled Reflections on Gdel's Ontological Argument (<a name="3"></a>"<A HREF = "../../Abstracts/Abstract_16/Abstract_16503.htm">Small (Christopher) - Reflections on Gdel s Ontological Argument</A>"; <a name="W220W"></a><A HREF = "http://www.stats.uwaterloo.ca/~cgsmall/Godel.final.revision.PDF" TARGET = "_top">Link</A>). </li><li>Finally, if you are looking for a different perspective on ontological arguments, I recommend that you explore Graham Oppy's work (<a name="W1400W"></a><A HREF = "http://www.arts.monash.edu.au/phil/department/Oppy/" TARGET = "_top">Link</A> (Defunct)). Graham Oppy raises some important objections to ontological arguments which are well worth mulling over. I would strongly agree with Graham Oppy that the argument has enough uncertainty attached to it as to leave its conclusion in doubt. Readers of this essay who wish to raise objections to Gdel's argument or debate the point are encouraged to contact me. </li></ul></li></ol></FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="W219W"></a><A HREF = "http://www.stats.uwaterloo.ca/~cgsmall/ontology.html" TARGET = "_top">Link</A>.<BR><FONT COLOR = "0000FF"><HR></P><a name="ColourConventions"></a><p><b>Text Colour Conventions (see <A HREF="../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</b></p><OL TYPE="1"><LI><FONT COLOR = "0000FF">Blue</FONT>: Text by me; &copy; Theo Todman, 2018</li><LI><FONT COLOR = "800080">Mauve</FONT>: Text by correspondent(s) or other author(s); &copy; the author(s)</li></OL> <BR><HR><BR><CENTER> <TABLE class = "Bridge" WIDTH=950> <TR><TD WIDTH="30%">&copy; Theo Todman, June 2007 - August 2018.</TD> <TD WIDTH="40%">Please address any comments on this page to <A HREF="mailto:theo@theotodman.com">theo@theotodman.com</A>.</TD> <TD WIDTH="30%">File output: <time datetime="2018-08-03T00:13" pubdate>03/08/2018 00:13:55</time> <br><A HREF="../../Notes/Notes_10/Notes_1010.htm">Website Maintenance Dashboard</A></TD></TR> <TD WIDTH="30%"><A HREF="#Top">Return to Top of this Page</A></TD> <TD WIDTH="40%"><A HREF="../../Notes/Notes_11/Notes_1140.htm">Return to Theo Todman's Philosophy Page</A></TD> <TD WIDTH="30%"><A HREF="../../index.htm">Return to Theo Todman's Home Page</A></TD> </TR></TABLE></CENTER><HR> </BODY> </HTML>