Provability, Mechanism, and the Diagonal Problem

Leach-Krouse, Graham

doi:10.1093/acprof:oso/9780198759591.003.0009

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Definition 318 ([89]) a Formula1

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2020

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“…Cieśliński and Urbaniak [27] conjecture that any two distinct instances Y R (m) and Y R (n) of a Rosser-type Yablo formula Y R (x) based on a standard proof predicate are not provably equivalent. Leach-Krouse [88] constructs a standard proof predicate, and a Rosser-type Yablo formula Y R (x) based on this proof predicate such that T ⊢ ∀x∀y(Y R (x) ↔ Y R (y)).…”

Section: Definition 318 ([89]) a Formulamentioning

confidence: 99%

Current research on Gödel's incompleteness theorems

Cheng

2020

Preprint

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Section: Definition 318 ([89]) a Formulamentioning

confidence: 99%

Current research on Gödel's incompleteness theorems

Cheng

2020

Preprint

View full text Add to dashboard Cite

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Mathematical Proofs and Scientific Discovery

Sterpetti

2020

Human Perspectives in Health Sciences and Technology

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The idea that science can be automated is so deeply related to the view that the method of mathematics is the axiomatic method, that confuting the claim that mathematical knowledge can be extended by means of the axiomatic method is almost equivalent to confuting the claim that science can be automated. I argue that the axiomatic view is inadequate as a view of the method of mathematics and that the analytic view is to be preferred. But, if the method of mathematics and natural sciences is the analytic method, then the advancement of knowledge cannot be mechanized, since non-deductive reasoning plays a crucial role in the analytic method, and non-deductive reasoning cannot be fully mechanized.

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Provability, Mechanism, and the Diagonal Problem

Cited by 2 publications

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Current research on Gödel's incompleteness theorems

Current research on Gödel's incompleteness theorems

Mathematical Proofs and Scientific Discovery

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