Problem of Induction
Posted on: October 14, 2010 - 9:26am
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Problem of Induction
Hi all, I'm back again.
I am looking for a very specific answer to the problem of induction as proposed by David Hume.
Why is there no a priori justification for the inference from the observed to the unobserved?
Quote:
That there are no demonstrative {a priori} arguments in the case {for induction} seems evident; since it implies no contradiction that the course of nature may change...- David Hume
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Can other people post on this thread or have I inadvertently locked them out?
Thread is open for posting. You might want to give it more than six minutes before wondering why you don't have an answer.
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Maybe a lot of posters are like me - I see your question, but there isn't enough there for me to have an answer for you. Not that my answer would be worth much of anything, but there are a few people on the forums who are interested in this sort of question. Maybe one of them will be willing to respond.
I'm not a philosopher, not even particularly interested in philosophy, but what I have read of Hume, he seems to be sensible.
This is from the Wiki article on inductive reasoning:
Which gives me enough information to say that Hume has a point. There are times when inductive reasoning works and times when it doesn't and times when that is all you have.
If you are looking for some sort of discussion for a paper for your philosophy class, you will have to find someone other than me to assist. If you are looking to argue about inductive reasoning and religion, you will have to find someone other than me to engage in that argument. Pink unicorns don't exist, invisible dragons don't exist, god/s/dess doesn't exist. But Uranus does exist even if I can't go walk around on the surface.
-- I feel so much better since I stopped trying to believe.
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The kind of justification Hume is talking about is logical deductive justification, not simply everyday notions of 'good reasons to believe'.
In essence, he's saying (and he's right) that you cannot use the system of logic to justify conclusions about the real world which are based on the idea that "it worked in the past", because there is no guarantee that "it will work in the future".
He then goes on to say, essentially, that even though this is the case, in our practical experience, induction does very often work in the real world, and so we have 'good reasons', practically speaking, to keep using induction, even if we cannot prove induction using the system of logic.
For example, imagine that there's an object which has always been seen to be green. Every time we've looked in the past, the object was green. We might postulate a logical hypothesis Green(X). However, unbeknownst to us, at some time in the near future, there will be a cataclysmic change in the laws of the universe, such that the object X will thenceforth forever appear to be blue, i.e. Blue(X).
Logic alone cannot make the conclusion about the *real* world, Green(x) --> Green(X), since things can change in the real world which are not accurately represented in a system of logic. And we can't be sure ahead of time what those changes might be, because again, our knowledge based on the past might turn out to be wrong in the future.
However, two things: First, Green(X) --> Green(X) is valid and true *within* the system of logic, cuz that's just how the axioms work out. Like in a game of chess, Rooks move in horizontal and vertical lines, cuz that's just how the rules of the game are.
Second, Green(X) --> Green(X) *usually* works in the real world, except when it doesn't. Although it can't be defended with logic alone, it is defensible because it is very useful and works a lot of the time (this is a pragmatic defense, rather than a strictly deductive, logical defense).
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I should also mention that in the modern day, we have advanced a long ways, and our advancements in probability theory and statistics give us very solid justifications of why we would *expect* induction to work, in a practical sense, in the real world.
Essentially, statistics shows that even in 'random' systems, there are patterns which arise simply because an immense number of random events tend toward an 'average' that is stable. Mathematically speaking, the number of 'average' permutations hugely outnumbers the number of 'extreme' permutations.
Try rolling a million 6-sided dice and adding them all together. I can't tell you exactly what the sum will be, but I can tell you with great certainty that it will be very close to 3.5 million. I can also tell you it will almost certainly not equal exactly 1 million, because there's only one permutation which would allow that sum, namely that every single one of the million dice rolled a 1, which is an extremely unlikely event, even though it is actually possible.
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Bertrand Russell has an awesome metaphor about this:
«On a farm, there was a flock of chickens. One chicken started talking with another, remarking "How good our farmer has been to us. I think he is an awfully nice man, because he comes every morning to feed us." The other chicken nodded in agreement, adding "and he has been feeding each and everyone of us here every day like clockwork, every day without fail since we were all just little baby chicks." Indeed, when queried, most of the other chickens clucked in agreement about how benevolent their farmer was.
But there was one chicken, intelligent but eccentric, who countered saying "How do you know he is all that good? I remember, not too long ago, that there were some older chickens who were taken away, and I haven't seen them since. What ever happened to them?"
Some of the chickens may have slept a little uneasy that night, but in the morning the farmer came as usual, this time scattering even more corn around. The chickens ate this with gusto, and this dispelled any remaining doubts about the benevolence of the farmer. "You see, there is nothing to worry about. Our farmer had a little extra food, so he gave it to us because he likes us! He is a good man," remarked one chicken to the others, and they all nodded in agreement, all of them, that is, except one.
The intelligent but eccentric chicken became even more agitated. "He is just fattening us up! We are going to be slaughtered in a weeks time!" he squawked in alarm. But nobody listened. All the other chickens just thought he was a troublemaker.
A week later, all the chickens were placed into cages, loaded onto a truck, and driven to the slaughterhouse.»
The End
Yeah, I just saw the n/a in the replies column and thought I might have closed it, so I posted to see if I could reply.
I thought so.
I'm just finishing a paper on Hume's account of induction.
Natural pointed out that's it's largely statistical.... But if one is looking for deductive certainty from induction, you'll never get it without exhaustive knowledge. For that reason, one can only have statistical certainty from induction, and in steps Baye's theorm.
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