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enbee comments on Open Thread, October 7 - October 12, 2013 - Less Wrong Discussion
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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.
I think the question is poorly formulated. If you say:
P: you have done something wrong
Q: you have a reason to hide something
P->Q: If you have done something wrong, then you have a reason to hide something
!Q->!P: If you do not have a reason to hide something, then you have not done something wrong
Which seems quite consistent to me, as it makes it possible to have a reason to hide something without having done something wrong. The negations of the original are throwing me, and I think the if-then phrase might be backwards as the causality should be doing something wrong causes you to have something to hide, rather than the reverse. My logic course was long enough ago that I can't pin it exactly.
Note the difference between "If you don't have a reason to hide something, then you have done nothing wrong" and "if you have done nothing wrong, then you don't have a reason to hide something." A person who is totally open has no skeletons in their closet- but the fetishist has something in his closet that isn't skeletons (unless it's skeletons).
Part of the problem turns out to be equivocation on "wrong". Consider the position of a chocolate-lover living in a hypothetical society where 1% of people are chocolate-lovers, 89% of people are not chocolate-lovers but are tolerant of people who are, and 10% of people think that anyone who eats chocolate should be shunned, persecuted, fired, exiled, tortured, or what-have-you.
Eating chocolate is not wrong according to our standards, nor by their own, nor by those of the majority of their society. However, many chocolate-eaters in this hypothetical society would prefer to cover up their actions, not out of shame but out of risk avoidance. They don't want to be mistreated by the anti-chocolate people who outnumber them ten to one. In the 1 in 10 chance that their boss is anti-chocolate, they don't want to be fired or mistreated on the job. And so on.
In effect, the saying should be, "If you haven't done anything that anyone anywhere disapproves of, you have nothing to hide."