What Can We Learn from Lewis Caroll's Paradox?

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  • ルイス・キャロルのパラドックスから何を学びうるか
  • ルイス キャロル ノ パラドックス カラ ナニ オ マナビウル カ

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Lewis Carroll created an interesting paradox about logic in his paper titled "What the Tortoise said to Achilles". This paradox raises the following question: Where can we get the meaning of the principle of inference? (The principle of inference is "If p>q and p are true, you can assert q.") By investigating this paradox and several philosophers' views about it and the principle of inference (Russell, Frege. Dummett. Geach, Quine et al.), I showed the following four points: (1) Ultimately it is not the principle of inference itself but individual activities of inference that have the power of connecting the premises and the conclusion. (2) These activities follow implicit customs. (3) It is impossible to make these customs completely explicit. (4) But without our practical knowledge of these customs the principle of inference cannot work as such. And on the basis of these arguments I made it clear what the difference of object language and metalanguage really means.

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