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Lumifer comments on Open Thread, October 7 - October 12, 2013 - Less Wrong Discussion

5 Post author: Thomas 07 October 2013 02:52PM

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Comment author: savanik 09 October 2013 07:47:13PM 3 points [-]

I've been thinking about this statement in particular: 'If you've done nothing wrong, you have nothing to hide.' People naturally seem to gravitate to the logical contraposition: If P, then Q. Therefore if !Q, then !P. If you have something to hide, then you MUST have done something wrong. Drawing from this logical statement, they infer that anyone who even tries to hide anything MUST be doing something wrong.

It seems obvious to me, however, that not all people who attempt to hide things have done something wrong. Where is the logical error? Is it in the inversion of 'nothing' and 'something'? It's been a long time since my symbolic logic courses involving the negation of universal quantification.

Comment author: Lumifer 09 October 2013 08:03:06PM *  2 points [-]

Um, the statement "If you've done nothing wrong, you have nothing to hide" is wrong to start with.

EDIT: Deleted the mistaken part of the post -- was reading too fast and screwed up the formal logic counter-example. Mea culpa

Comment author: Emile 09 October 2013 08:16:55PM 3 points [-]

If P, then Q. Therefore if !Q, then !P.

...this is quite wrong as well. E.g. If you are a man, you're a human. Therefore if you're not a man you're not a human :-P

No, it would be "Therefore if you're not a human you're not a man", which does follow. The formal logic is fine.