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. If I worry: X chance it will happen (cost = worry (W) + event (E))
1-X chance it won't (cost = W)

If I dont worry: Y chance it will happen (cost = E)
1-Y chance it won't (cost = 0)

One false assumption is that E = W. If this were the case, then the cost of worrying would be at least W, whereas if I dont worry the cost at most would be W. But if W is far less than E, then this is not true.

Even still, if you assume that X = Y, then the expected cost in the worry situation is obviously going to be higher than in the not worrying situation (unless W is negative!). Obviously X != Y, as has already been pointed out.

in order for the argument to fail, it seems that X != Y, and W != E.

As far as the worrier puzzle goes, everything after the 'therefore' is unjustified.

6. > 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.

7. Ive gotta agree. As far as the worry case goes, it doesn't even appear logically valid. The battle case, however, is slightly different - and less easy to figure out.

8. 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.)

9. I agree that the puzzle is analogous to the battle-tactics one, however, when you restate the argument, you change the logical form. The logical puzzle is in the argument, not in the worry quote. In the worry quote, it goes straight from an account of the facts to a claim that worrying is irrational. There isn't much of an argument. There is no logical puzzle. IF you provide an argument, such as the battle-tactics one, then there can be a puzzle. However, I could interpret the worry quote in a completely different way.

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