IA Scholar Query: Gödel's God in Isabelle/HOL.
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Internet Archive Scholar query results feedeninfo@archive.orgFri, 08 Jul 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Mathematical Proof Between Generations
https://scholar.archive.org/work/u4cubbwedfgf7fqhmzbyrifci4
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into peril. Now may be the time to reconcile theory and practice, i.e. precision and intuition, through the advent of computer proof assistants. For the most time this has been a topic for experts in specialized communities. However, mathematical proofs have become increasingly sophisticated, stretching the boundaries of what is humanly comprehensible, so that leading mathematicians have asked for formal verification of their proofs. At the same time, major theorems in mathematics have recently been computer-verified by people from outside of these communities, even by beginning students. This article investigates the gap between the different definitions of a proof and possibilities to build bridges. It is written as a polemic or a collage by different members of the communities in mathematics and computer science at different stages of their careers, challenging well-known preconceptions and exploring new perspectives.Jonas Bayer, Christoph Benzmüller, Kevin Buzzard, Marco David, Leslie Lamport, Yuri Matiyasevich, Lawrence Paulson, Dierk Schleicher, Benedikt Stock, Efim Zelmanovwork_u4cubbwedfgf7fqhmzbyrifci4Fri, 08 Jul 2022 00:00:00 GMTA Simplified Variant of Gödel's Ontological Argument
https://scholar.archive.org/work/o2clb2baq5cedkqte7xqob65ke
A simplified variant of G\"odel's ontological argument is presented. The simplified argument is valid already in basic modal logics K or KT, it does not suffer from modal collapse, and it avoids the rather complex predicates of essence (Ess.) and necessary existence (NE) as used by G\"odel. The variant presented has been obtained as a side result of a series of theory simplification experiments conducted in interaction with a modern proof assistant system. The starting point for these experiments was the computer encoding of G\"odel's argument, and then automated reasoning techniques were systematically applied to arrive at the simplified variant presented. The presented work thus exemplifies a fruitful human-computer interaction in computational metaphysics. Whether the presented result increases or decreases the attractiveness and persuasiveness of the ontological argument is a question I would like to pass on to philosophy and theology.Christoph Benzmüllerwork_o2clb2baq5cedkqte7xqob65keFri, 24 Jun 2022 00:00:00 GMT