Tuesday, May 10, 2005

Do Worry, Preserve Happiness

Maverick Philosopher advises, "Don't worry, be happy":
The dreaded event will either occur or it will not. If it occurs, then the worrier suffers twice, once from the event, and once from the worry. If it does not occur, then the person suffers from neither. Therefore, worry is irrational.

This is one of my favourite logic puzzles. It's obvious that concern can be rational. Whether you worry or not might influence whether the dreaded event occurs. But it's no mean feat to translate this intuitive objection into a logically rigorous one. (Which premise is false? Or is the inference invalid?) Find out by reading my past discussions of an analogous argument, here and here.

1. Er its not much of a paradox - you just with hte informtion available attempt to maximise the gain by improving the chance of solving a problem and the loss of worrying. I think most people probably over emphasise the worrying side and thus in that way MP is probably right - but it is possible to go too far the other way.

2. BTW I propose you reject the conclusion.
The fact that having a smaller army is better if you win and if you loose doesnt mean that it is always better. It is like those misleading intelligence puzzles - you may need to look at all the options and realise that sometimes winning the war with a big army is the alternative of not winning the war with a small army.
If you find it a paradox it is because you misinterpret the information, and make inappropriate assumptions.

3. hmm oh i see you said that sort of thing.. hmm gee I'm too impaitent. alathough maybe slightly different anyway fundimentally I reject the conclusion to that sort of logic in principle regardless of the example.

4. Of course we reject the conclusion, but the puzzle is in logically justifying this, as the argument *appears* to be a valid deduction from true premises. We must show precisely how the premises are false, or the logic invalid, as my linked posts do. Merely saying "I reject the conclusion" doesn't shed any light on anything.

5. > the argument *appears* to be a valid

my point is it should not even appear to be valid. It only seems valid because we make an assumption we shouldn't be making. ie all the logic isnt there. Its a more complex example of trying to examine why a person adds 1 and 1 and gets 3.

6. Well, as I discuss in the linked posts, the argument form sure looks like a case of OR-elimination. That is:

P or Q
if P then R
if Q then R
Therefore, R.

That's a logically valid inference. So the trick is showing why the argument doesn't really fit this form (or else why the premises aren't actually true).

For clarity, let me restate BV's argument as follows: Let D = "the dreaded event will occur"
1. D or not-D
2. if D, then you ought not worry (since worrying would just make you even more miserable)
3. if not-D, then you ought not worry (again, worrying would just make you sad)
Therefore, you ought not worry.

I hope that makes the puzzle more apparent. (It really is exactly the same as the battle and cliff-jumping arguments I discussed in the other posts.)

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