Kurt Gödel's Ontological Argument
Small (Christopher)
Source: Personal Website
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  1. Kurt Gödel 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 Gödel has sketched a revised version of Anselm's traditional ontological argument for the existence of God.
  2. A biographical sketch
  3. The Role of Modal1 Necessity
  4. Windows into Modal2 Worlds
    1. Necessary Falsehood: Penrose Triangle
    2. Contingent Falsehood
    3. Contingent Truth
    4. Necessary Truth: Mandelbrot set
  5. Counterfactual Argumentation
  6. Essential Properties
  7. Anselm's ontological argument
  8. Gödel's positivity operator
  9. The Basic Definitions
  10. The Rest of the Argument
  11. Conclusion:
    • I should remind the reader again that the version of Gödel's argument that I have presented is not Gödel's original argument. When I first read Gödel'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 Gödel'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 Gödel's Ontological Argument ("Small (Christopher) - Reflections on Gödel’s Ontological Argument"; Christopher G. Small - Reflections on Gödel’s Ontological Argument).
    • Finally, if you are looking for a different perspective on ontological arguments, I recommend that you explore Graham Oppy's work (Link (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 Gödel's argument or debate the point are encouraged to contact me.


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