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----
-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
----
-
-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.