From ac98d67a2dd6bfee4077d6b3a2aa5ab307ef6e33 Mon Sep 17 00:00:00 2001 From: Joe Carstairs Date: Tue, 28 Jan 2025 19:58:44 +0000 Subject: [PATCH] should --- website/src/content/blog/28/paradox.md | 76 ++++++++++++++++++++++++++ 1 file changed, 76 insertions(+) create mode 100644 website/src/content/blog/28/paradox.md diff --git a/website/src/content/blog/28/paradox.md b/website/src/content/blog/28/paradox.md new file mode 100644 index 0000000..19ba34c --- /dev/null +++ b/website/src/content/blog/28/paradox.md @@ -0,0 +1,76 @@ +--- +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.