Time’s Up

Well, Sister Y has had her chance.

As a note to future arguers: when you’re asked to justify a claim, replying with increasingly complex, abstract, and elaborate claims isn’t the way to go. It would be nice if you actually presented justification, as you were asked to, as well.

My high school chemistry teacher worked hard to convince us that we needed to delete decimal places in our results. The students always complained that it felt like throwing away information, but she would patiently point out that our final result couldn’t be more accurate than the least accurate measurement involved in the calculation. Eventually we recognized how right she was.

It’s a shame more people don’t recognize — or perhaps, refuse to — that their conclusions cannot be stronger than the weakest argument they present for it.

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9 Responses to “Time’s Up”

  1. their conclusions cannot be stronger than the weakest argument they present for it.
    That seems to conflict a bit with what you said here. An additional piece of evidence converging with previous ones shouldn’t make the conclusion weaker.

  2. tggp, agreed.

    I submit that one’s conclusion may be at least as strong as the strongest argument presented for it.

  3. His claim is true for series but not parallel

  4. Isak, agreed – good point.

    Regarding significant digits, they’re very arbitrary. For some reason powers of 10 are the magical numbers we round to – if we recorded our answers in binary, we’d properly round to significant digits there and get much more precise answers than using standard significant digits. Note arguments at http://en.wikipedia.org/wiki/Significant_figures#Importance

  5. Hmmm. I do need to restate that.

    The conclusion can’t be stronger than the weakest part of the strongest argument. If multiple valid arguments are possible, we could exclude the weaker ones and lose nothing.

    Is that better?

  6. Better, but still not right. If you’re just doing say, deductive logic, then perhaps you can exclude the weaker ones and lose nothing. But if your arguments are separately building up a preponderance of evidence, then excluding the weaker ones will lose something.

    Though perhaps you can sidestep this by claiming that this entire process constitutes one argument; in that case, though, it doesn’t make sense to speak of multiple arguments in the first place.

  7. There’s a difference between reaching a conclusion, and being confident in that conclusion.

    Bayesian reasoning, while correct in a limited way, doesn’t permit that distinction.

    Lots of weak arguments converging on a position are not equivalent to a few very strong arguments.

  8. There’s a difference between reaching a conclusion, and being confident in that conclusion.

    Bayesian reasoning, while correct in a limited way, doesn’t permit that distinction.

    But can’t ‘reaching a conclusion’ simply be thought of as reaching a threshold of confidence?

    Lots of weak arguments converging on a position are not equivalent to a few very strong arguments.

    Not equivalent in what sense? In that it is not conceivable that they can take you to the same confidence level?

  9. “Not equivalent in what sense?”

    If I have a single argument that is sufficient to justify a conclusion, and I learn that it’s wrong, what happens to my conclusion?

    If I have many weak arguments that lead me to a conclusion with the same confidence of the previous hypothetical, and I learn that one of them is wrong, what happens to my conclusion then?

    Bayesian methods don’t permit sophisticated forms of meta-thought well.

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