CPT : What about Gödel’s proof of the existence of God?
CPT : What about Gödel’s proof of the existence of God?
JYB: Proofs of existence of God have a long story, starting with Anselm of Canterbury in the 11th century. Gödel’s ontological proof is very interesting. From it, it is in fact possible to deduce proofs of consistency of set-theory and arithmetic, contradicting somehow Gödel’s own second incompleteness theorem. This was shown by Piergiorgio Odifreddi, who presented a talk about that at the 3rd World Congress on Logic and Religion we organized in Varanasi, India (city famous both for Hinduism and Buddhism) in November 2022.
JYB: Proofs of existence of God have a long story, starting with Anselm of Canterbury in the 11th century. Gödel’s ontological proof is very interesting. From it, it is in fact possible to deduce proofs of consistency of set-theory and arithmetic, contradicting somehow Gödel’s own second incompleteness theorem. This was shown by Piergiorgio Odifreddi, who presented a talk about that at the 3rd World Congress on Logic and Religion we organized in Varanasi, India (city famous both for Hinduism and Buddhism) in November 2022.
This result may seem strange, but the incompleteness result is not absolute. Shortly after Gödel’s proof, Gerhard Gentzen presented a relative proof of the consistency of arithmetic. And Gentzen was one of the Gödel’s preferred logicians. He studied his works in details. Based on that, Gödel proved his last important result in mathematical logic, a consistency proof of arithmetic, known as “Dialectica proof”, since it was published in 1958 in a special issue of the Swiss journal Dialectica in honor of the 70th birthday of the Swiss logician Paul Bernays (main collaborator of David Hilbert in the field of logic).
This result may seem strange, but the incompleteness result is not absolute. Shortly after Gödel’s proof, Gerhard Gentzen presented a relative proof of the consistency of arithmetic. And Gentzen was one of the Gödel’s preferred logicians. He studied his works in details. Based on that, Gödel proved his last important result in mathematical logic, a consistency proof of arithmetic, known as “Dialectica proof”, since it was published in 1958 in a special issue of the Swiss journal Dialectica in honor of the 70th birthday of the Swiss logician Paul Bernays (main collaborator of David Hilbert in the field of logic).
And, funny enough, Chistoph Benzmueller and Dov Gabbay have shown that the interaction with computer technology, not only enable the formal assessment of ontological arguments, but also is useful to sharpen the conceptual understanding of the notions and concepts involved. This work was presented at the 2nd World Congress on Logic and Religion in Warsaw, Poland, in 2017. In this congress we also had the participation of Saul Kripke (Schock Prize), Laurent Lafforgue (Fields Medal), Michał Heller (Templeton Prize).
And, funny enough, Chistoph Benzmueller and Dov Gabbay have shown that the interaction with computer technology, not only enable the formal assessment of ontological arguments, but also is useful to sharpen the conceptual understanding of the notions and concepts involved. This work was presented at the 2nd World Congress on Logic and Religion in Warsaw, Poland, in 2017. In this congress we also had the participation of Saul Kripke (Schock Prize), Laurent Lafforgue (Fields Medal), Michał Heller (Templeton Prize).