[Math Lair] Hintikka's Paradox

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Hintikka's paradox is a paradox in modal logic devised by Jaako Hintikka. It asserts that, contrary to most people's moral intuitions that things that are impossible have no moral value, anything that is impossible is wrong. The paradox goes as follows:

  1. Doing something that cannot be done without something wrong being done would in itself be wrong.
  2. Something that cannot be done at all cannot be done either with or without something wrong being done. So, for example, if X is impossible and Y is wrong, it is not possible to do either (X and Y) or (X and (not Y)).
  3. Assume that Y is wrong. We have shown in the previous step that (X and (not Y)) is impossible. In other words, it is impossible to do X without something wrong (Y) being done. By step 1, X must be wrong.
  4. Therefore, if it is impossible to do something, it is wrong to do it.

Sources used (see bibliography page for titles corresponding to numbers): 58.