title: A paradox about 'should'
description: >-
  I seem to have accidentally proven that drinking wine both is and is not a
  thing you should do. Let's hope that wine doesn't disappear in a puff of
  logical smoke.
pubDate: 2025-01-28

content: |
  We're pretty familiar with the idea that there can be reasons for doing
  something, and reasons against. Drinking wine is bad for your liver, but good
  for your social life.
  
  But look what happens if we express this in this way:
  
  1. Drinking wine is bad for your liver.
  2. You shouldn't do things which are bad for your liver.
  3. All things you shouldn't do aren't things you should do.
  4. Therefore, drinking wine isn't a thing you should do.
  
  In contrast to this:
  
  5. Drinking wine is a good social activity.
  6. You should do things which are good social activities.
  7. Therefore, drinking wine is a thing you should do.
  
  Now both 1-4 and 5-7 seem like logically valid arguments with true premises,
  but 4 and 7 are contradictory!
  
  I don't think there's any use in complaining about premise 3. All that gives us
  is the possibility that wine is both a thing you should do, and a thing you
  shouldn't do. But that's an absurdity. Something can't be both obligatory and
  forbidden at the same time. It's scarcely any better than a contradiction: it
  is inconsistent with any useful concept of obligation.
  
  Remember that we would quite like to know, at the end of all our argument,
  whether we should drink wine or whether we shouldn't. 'Both' is not an adequate
  answer, because it's not a useful guide for action: we can't both drink wine and
  not drink wine. So if 'should' is to function as we need it to, 3 must be true.
  
  I think a more profitable way forward is this. Let's re-write premise 2:
  
  2. All things which are bad for your liver are things such that the fact that
     that thing is bad for your liver is a reason not to do it.
  
  We can similarly re-write premise 6:
  
  6. All things which are good social activites are things such that the fact that
     they are good social activities is a reason to do them.
  
  Then premise 3, if it's to play the same logical role in the argument, would
  have to read:
  
  3. All things such that the fact that that thing is bad for your liver is a
     reason not to do it is not a thing such that the fact that that thing is a
     good social activity is a reason to do it.
  
  Our re-written 2 and 6 seem to adequately capture the sense of the original,
  but 3 is now obviously false. With our re-written sentences, we can avoid
  generating a contradiction without doing any fatal damage to our concept of
  'should'.
  
  OK. Grant for the sake of argument that that was a good move. What have we
  achieved? Have we actually solved the problem?
  
  We started out with a pair of arguments which generate a contradiction. Our
  move generated a new pair of arguments which don't generate a contradiction. So
  what? Isn't the first contradiction still there?
  
  Perhaps you could say that our re-written version of 2 (and so on) are more
  accurate elaborations of the originals. Fine. But what about those originals,
  then? You've still either got to say that they're true, false, or gibberish.
  Producing your second argument hasn't convinced me to move my opinion about the
  originals. The original premises seem just as true, and the original arguments
  just as valid, as when we began.
  
  What gives? Answers on a postcard as usual please.
