Curry’s Paradox

Metadata

• Author: plato.stanford.edu
• Title: Curry’s Paradox

Page Notes

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Highlights

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• A theory is said to be trivial, or absolutely inconsistent, when it affirms every claim that is expressible in the language of the theory. — Updated on 2024-04-07 16:54:36
  • Is this a good solution to the problem? There may be issues where we just Curry sentences with clauses that require certain consequences to be false.

If we look at the issue, descriptively, it is is that any proposition can be “proved” by the reasoning. If we simply forbid this kind of reasoning that proves everything, it might be resolved. Perhaps we can be more specific (since ability to prove anything might be difficult to prove) and say that we shouldn’t accept reasoning that leads to immediate contradiction through logical steps. For example, I can show both $p$ and $notp$ through Curry sentences. Since this is contradictory, we say that the reasoning to reach there is incorrect.

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to-process

• A theory is said to be trivial, or absolutely inconsistent, when it affirms every claim that is expressible in the language of the theory. — Updated on 2024-04-07 16:54:36
  • Is this a good solution to the problem? There may be issues where we just Curry sentences with clauses that require certain consequences to be false.

If we look at the issue, descriptively, it is is that any proposition can be “proved” by the reasoning. If we simply forbid this kind of reasoning that proves everything, it might be resolved. Perhaps we can be more specific (since ability to prove anything might be difficult to prove) and say that we shouldn’t accept reasoning that leads to immediate contradiction through logical steps. For example, I can show both $p$ and $notp$ through Curry sentences. Since this is contradictory, we say that the reasoning to reach there is incorrect.