should

website/src/content/blog/28/paradox.md

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+---
+title: A paradox about 'should'
+description: >-
+  I seem to have accidentally proven that 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.