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Saturday, May 05, 2012

Popperians Rely on the Truth of Conservative Induction All the Time

without realizing it.

I recall a humorous instance when one of my Popperian friends in London chastised me for moving to Hackney. "Don't you realize how high the crime rate is there?"

"[INSERT NAME HERE]," I replied, "you're not suggesting that, because the crime rate was high there until today, it will continue to be high there tomorrow, are you? Because that sounds a lot like an inductive inference."

Of course, no one could make it through the day without making continual inductive inferences, so of course Popperians make them all of the time... even when trying to refute the idea that inductive inference is necessary. Take Lee Kelly, responding to my previous post on Popper:
(1) A theory which is falsified by some observation-statement today is still falsified by it tomorrow, next week, a month later, and forever after. This is not induction. The falsifying relation is deductive and timeless–to say that it will continue to hold in the future is to be merely logically consistent.

A mathematician is not inducing when he concludes that ‘1 + 1 = 2’, which is true today, will continue to be true tomorrow. If there is no pretense of having derived the future from the past, then there is no attempted induction. The mathematician concludes that ‘1 + 1 = 2’ will continue to be true tomorrow because its negation is inconsistent–a deductive inference.

The falsifying relations between statements are analogous to the above equation. If a theory is falsified by some statement today, then it will continue to be falsified by it tomorrow.
Kelly muddies the water here, because the issue of induction is only of concern for empirical theories, but he presents us with a deductive theory in his example. Of course, if I am trying to prove a timeless, mathematical truth, and it is false at any point in time, that means it is false forever. But things are very different with empirical theories. They are true if they describe reality accurately, and false if they do not.

So, consider the theory, "On earth, feathered, flying bipeds evolved from dinosaurs." If this theory was put forward by an alien scientist visiting earth 200 million years ago, it would be false. No such thing had happened. But if we put it forward today, it is true. On a simpler level, let us imagine that, in 2008, I said, "The US has combat troops in Iraq." Can Kelly come forward now, and say, "Well, I checked that today, and the US doesn't have such troops in Iraq: and so, since a statement falsified by an observation today is falsified by it for all time, your theory was wrong."

Thus, it should be obvious that an empirical theory can be false if put forward at time T, but become true at some other point T + x. "Ah," but Kelly may respond, "but you are talking about historically contingent theories now, and that's cheating. You know I meant things like the laws of physics, which we expect to hold at all times."

And this point is very telling. When Newton put forward his theory of gravity, he didn't mean to say that gravity worked this way in the 1600s, but hadn't in 600, and won't again in 2600. He meant this as a timeless law.

However, he meant it as a timeless law that because he assumed conservative induction to be the right principal to use in formulating scientific theories. As Kelly unwittingly did in making his complaint about my example. For, if revolutionary induction (Time for a change!) is the right principle, then the fact that my law of gravitation was falsified today is no reason at all to think it has been falsified for all time, just like the fact that "Mitt Romney is president of the United States" is a false theory today says nothing about whether it will also be a false theory in six months. If revolutionary induction is based on an accurate view of the world, then the fact my theory was falsified today gives me great hope that it will become true tomorrow: today, it can be shown that masses attract each other with an inverse square law, while my theory says the attraction follows in inverse cube law. If tomorrow, the laws of physics all change, and gravity, in fact, obeys an inverse cube law, then my theory becomes true in just the same way "Mitt  Romney is president of the US" becomes true if he is elected, in fact, in the only way empirical theories are ever true: it will correctly describe reality. So what, it doesn't do so today? From tomorrow on, it will!

And what leads all of us to reject my new theory of gravity based on revolutionary induction, and theories like "grue and bleen," as being valid scientific theories, is that we all, even Popperians, quite sensibly employ conservative induction in confronting the world.

SYNOPSIS OF THE ARGUMENT:
1) A theory being falsified once only means it is falsified for all time if it is a time-independent theory.
2) But scientific laws are time-independent theories only if we assume the principle of conservative induction.
3) QED: Kelly unwittingly assumes conservative induction in his complaint above.

7 comments:

  1. Gene, I really get nervous that you are slipping around all over the place on this. The main thing is, didn't Popper start out his book by saying, "I believe I have solved the problem of induction"? And yet, you think if you catch a Popperian using induction, that somehow falsifies (again, note the irony of that verb!) Popper. I don't think it does. I thought Popper was taking the--perfectly valid to this day--observation that what we seem to do in the natural sciences isn't logically valid, and reconciling it with the apparent reality that induction in the empirical sciences is quite useful. So maybe Popper is wrong, but the way you keep trying to knock him/his fans down, just seems off to me.

    More specifically, I thought Lee Kelly did a perfectly adequate job showing why your last "aha" was goofy. Then you come back with this:

    "So, consider the theory, "On earth, feathered, flying bipeds evolved from dinosaurs." If this theory was put forward by an alien scientist visiting earth 200 million years ago, it would be false. No such thing had happened. But if we put it forward today, it is true. "

    Sure OK, but what you've just done here is the equivalent of the schoolboy joke:

    Q: What was the president's name in 1970?
    A: Richard Nixon?
    Q: Nope! Barack Obama!

    If someone deployed the above in a discussion of US presidential history, at best it would provide levity. You are doing the opposite trick with your observation. Nobody when talking about empirical theories is referring to things that can change over time. Indeed, when some scientists recently (like in the last 10 years) suggested that maybe the charge on an electron or other universal constants might have changed over billions of years, people freaked out because that was so unorthodox.

    I'm claiming that in a discussion of Popper, nobody (except now Gene Callahan) ever has in mind a claim that is time specific, like, "The amount of rain today was ___ inches." No, they are always referring to "laws of nature" that are eternal, and the question is, why do we feel comfortable and "scientific" doing this, when we know logically speaking what we are doing is invalid?

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    Replies
    1. "No, they are always referring to "laws of nature" that are eternal"

      Right you are, Bob. And in so referring, they are assuming conservative induction. So here you confirm what I have been noting.

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    2. "Nobody when talking about empirical theories is referring to things that can change over time."

      Exactly! So they are assuming conservative induction! You confirm my point.

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    3. "I may be mistaken; but I think that I have solved a major philosophical problem: the problem of induction." -- Karl Popper

      "I thought Popper was taking the--perfectly valid to this day--observation that what we seem to do in the natural sciences isn't logically valid"

      It is not deductive logic.

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  2. Lee, very sorry, I have learned through experience that there is no point arguing with critical rationalists -- you will simply keep saying the exact same things as if I had never written anything. So no, I won't be posting your remarks, not because they were rude or anything -- they certainly weren't -- but because it would lead to what might appear to be discussion but wouldn't actually be discussion at all.

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  3. I don't think Popper was exactly wrong, his idea just wasn't that big of a deal in fields where it could be safely applied (without much affect). He went way wrong when he started applying it where it didn't belong, in philosophy and political science. If you think about it, what is liberalism but the rigid application of the idea that truth is continually discovered at the intersection of individualism and utilitarianism, the twin cults of modernity?

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    Replies
    1. Gabe, Popper was a bright fellow, who made a bold attempt at trying to save the positivist project. But Hume was right: once one rejects formal and final causes, any remaining faith in empirical science is just a matter of habit.

      Luckily, there is no reason we have to reject formal and final causes!

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