## Curry's paradox |

**Curry's paradox** is a

The paradox is named after the logician **Löb's paradox** after ^{[1]} due to its relationship to

- in natural language
- formal proof
- discussion
- resolution
- see also
- references
- external links

Claims of the form "if A, then B" are called

- If this sentence is true, then Germany borders China.

Even though

- First, common natural-language proof techniques can be used to prove that the example sentence is true.
- Second, the truth of the example sentence can be used to prove that Germany borders China. Because Germany does not border China, this suggests that there has been an error in one of the proofs.

The claim "Germany borders China" could be replaced by any other claim, and the sentence would still be provable. Thus every sentence appears to be provable. Because the proof uses only well-accepted methods of deduction, and because none of these methods appears to be incorrect, this situation is paradoxical.^{[2]}

The standard method for proving

To produce Curry's paradox, as described in the two steps above, apply this method to the sentence "if this sentence is true, then Germany borders China". Here A, "this sentence is true", refers to the overall sentence, while B is "Germany borders China". So, assuming A is the same as assuming "If A, then B". Therefore, in assuming A, we have assumed both A and "If A, then B". Therefore B is true, by

Now, because we have proved "If this sentence is true, then 'Germany borders China' is true", then we can again apply modus ponens, because we know that the claim "this sentence is true" is correct. In this way, we can deduce that Germany borders China.

Other Languages

bosanski: Kurijev paradoks

català: Paradoxa de Curry

Deutsch: Currys Paradoxon

español: Paradoja de Curry

français: Paradoxe de Curry

italiano: Paradosso di Curry

עברית: הפרדוקס של קרי

magyar: Curry paradoxonja

日本語: カリーのパラドックス

polski: Paradoks Curry’ego

português: Paradoxo de Curry

русский: Парадокс Карри

suomi: Curryn paradoksi

українська: Парадокс Каррі