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Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy


A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted in larger scale by philosophers.

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Correspondence to C. Benzmüller.

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This work was supported by German National Research Foundation (DFG) under Grants BE 2501/9-1 and BE 2501/11-1.

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Benzmüller, C., Weber, L. & Woltzenlogel Paleo, B. Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy. Log. Univers. 11, 139–151 (2017).

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  • Ontological argument
  • Universal reasoning
  • Shallow semantical embedding
  • Higher-order modal logic
  • Classical higher-order logic
  • Higher-order automated theorem proving

Mathematics Subject Classification

  • 03A10
  • 03B15
  • 03B45