A Computationally-Discovered Simplification of the Ontological Argument

@article{Oppenheimer2011ACS,
  title={A Computationally-Discovered Simplification of the Ontological Argument},
  author={Paul E. Oppenheimer and Edward N. Zalta},
  journal={Australasian Journal of Philosophy},
  year={2011},
  volume={89},
  pages={333 - 349}
}
The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise… Expand
On the PROVER9 Ontological Argument
Oppenheimer & Zalta have re-formulated their non-modal version of the ontological argument, with the help of PROVER9, an automated reasoning engine. The authors end up rejecting the new argument;Expand
The Ontological Argument in PVS
The Ontological Argument, an 11th Century proof of the existence of God, is a good candidate for Fun With Formal Methods as nearly everyone finds the topic interesting. We formalize the Argument inExpand
Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus
TLDR
The first formal proof closely follows the hints in Scott's manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness, and the second formal proof improves the first, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. Expand
A Computationally Assisted Reconstruction of an Ontological Argument in Spinoza’s The Ethics
Abstract The comments accompanying Proposition (Prop.) 11 (“God ... necessarily exists”) in Part I of Spinoza’s The Ethics contain sketches of what appear to be at least three more or less distinctExpand
An Object-Logic Explanation for the Inconsistency in Gödel's Ontological Theory (Extended Abstract, Sister Conferences)
This paper discusses the inconsistency in Gödel’s ontological argument. Despite the popularity of Gödel’s argument, this inconsistency remained unnoticed until 2013, when it was detectedExpand
The Inconsistency in Gödel's Ontological Argument: A Success Story for AI in Metaphysics
TLDR
The discovery of the inconsistency in Godel's ontological argument as a success story for artificial intelligence and the development of an improved syntactical hiding for the utilized logic embedding technique allows the refutation to be presented in a human-friendly way, suitable for non-experts in the technicalities of higher-order theorem proving. Expand
Can Computers Help to Sharpen our Understanding of Ontological Arguments
TLDR
It is claimed that interreligious understanding may be fostered by means of formal argumentation and, in particular, formal logical analysis supported by modern interactive and automated theorem proving technology. Expand
Automating Gödel's Ontological Proof of God's Existence with Higher-order Automated Theorem Provers
TLDR
The background theory of the work presented here offers a novel perspective towards a computational theoretical philosophy in Kurt Godel's ontological argument for God's existence. Expand
A Case Study On Computational Hermeneutics: E. J. Lowe's Modal Ontological Argument
TLDR
This claim is defended by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. Lowe's modern variant of St. Anselm’s ontological argument for the existence of God. Expand
Mechanized analysis of Anselm’s modal ontological argument
We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizationsExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 21 REFERENCES
REFLECTIONS ON THE LOGIC OF THE ONTOLOGICAL ARRGUMENT
Our 1991 paper on the logic of the ontological argument contained an analysis of the structure of Anselm’s argument for the existence of God. We showed that there is a valid argument for God’sExpand
ON THE LOGIC OF THE ONTOLOGICAL ARGUMENT
Saint Anselm of Canterbury offered several arguments for the existence of God. We examine the famous ontological argument in Proslogium II. Many recent authors have interpreted this argument as aExpand
Steps Toward a Computational Metaphysics
TLDR
This paper describes what is discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter), and how prover 9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. Expand
Mace4 Reference Manual and Guide
  • W. McCune
  • Computer Science, Mathematics
  • ArXiv
  • 2003
TLDR
Mace4 is a program that searches for finite models of first-order formulas and performs better on equational problems than did the previous model-searching program Mace2. Expand
OTTER 3.3 Reference Manual
  • W. McCune
  • Computer Science, Mathematics
  • ArXiv
  • 2003
OTTER is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyperresolution, UR-resolution, and binaryExpand
Prover9 Manual, URL = <http://www.cs.unm.edu/ ̃mccune/mace4/manual/2009-11A/>
  • 2009
Steps Towards a Computational Metaphysics
  • Journal of Philosophical Logic
  • 2007
On denoting what?
2003b, Mace4 Reference Manual and Guide (Tech
  • Memo ANL/MCS-TM-264, Mathematics and Computer Science Division),
  • 2003
...
1
2
3
...