FUTO - The Intern Experience and a FUTO Fellowship

The FUTO Fellowship experience: James Torre on self-justifying axiom systems.


See the JSL paper Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles by Dan Willard. Also his 2013 preprint On the Significance of Self-Justifying Axiom Systems from the Perspective of Analytic Tableaux. The idea is that by choosing a less expressive model than PA you can avoid the consequences of Gödel's Second Incompleteness Theorem. I think the far more important point he makes (at 17:21) is that any judgement of correctness of a description system is ultimately based on actual knowledge of some (presumably observable) physical property. See Jenann Ismael - Laplace meets Godel: How Self reference Foils Prediction.

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This is an idea that can be applied to abstract vector spaces as well as the space of (descriptions of) the positions of physical objects: 

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