Mea inu paradox

Ua ʻike ʻia ka ʻōlelo ma lalo nei ʻo "ka mea inu ʻawaʻawa": "Aia kekahi i loko o ka hale pāpaʻi, no laila inā e inu ana ʻo ia, inu nā mea a pau o ka hale inu." ʻAʻole ia he mea nui inā hoʻoikaika kēlā kanaka i nā mea ʻē aʻe e inu a i ʻole kekahi puka hope ʻē aʻe, e like me kā mākou e ʻike ai i kahi manawa. He laʻana maikaʻi ia mai ka makemakika papa kuhikuhi mua.


Hoʻomaka mākou ma ka ʻōlelo ʻana ʻaʻole inu nā mea a pau i loko o ka hale pāpaʻa a i ʻole hoʻokahi kanaka i loko o ka pā hale inu ʻole. No laila ua kūpono ka hoʻokaʻawale ʻana o kēia hihia:

  1. Inu nā kānaka a pau. A laila, inā e inu ana kekahi i loko o ka hale pāpaʻi, inu nā mea a pau i loko o ka pā hale - no ka mea e inu ana nā mea a pau.
  2. ʻAʻole inu kekahi kanaka. No ka mea inu ʻole, he ʻoiaʻiʻo inā inu lākou, inu nā mea a pau i loko o ka hale pāpaʻi - no ka mea ʻaʻole inu ke kanaka ( \(A \Rightarrow B\) he ʻoiaʻiʻo mau inā he wahaheʻe ʻo \(A\) .

Ma ke 'ano ma'amau, hiki ke ho'okumu 'ia ka theorem penei no kekahi predicate \(D\) a me kahi ho'onohonoho 'ole 'ole \(P\):

$$\exists x\in P.\ [D(x) \Rightarrow \forall y\in P.\ D(y)]$$

Hope