78 lines
3.3 KiB
Markdown
78 lines
3.3 KiB
Markdown
---
|
|
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.
|