The Problem of Induction - Need help understanding.
Induction depends on The Principle of Uniformity of Nature (PUN).
PUN: observed events are good guides to unobserved events.
How do we prove PUN to give a solid foundation to induction?
Note1: We only have access to observed events.
It can't be deductively derived because no amount of observations can justify the movement from ''some'' to ''all''.
So, it has to be induction. But, induction depends on PUN. Circularity. This is the Problem of Induction.
Have I got it right? Can you explain it in a simpler way?
PUN: observed events are good guides to unobserved events.
How do we prove PUN to give a solid foundation to induction?
Note1: We only have access to observed events.
It can't be deductively derived because no amount of observations can justify the movement from ''some'' to ''all''.
So, it has to be induction. But, induction depends on PUN. Circularity. This is the Problem of Induction.
Have I got it right? Can you explain it in a simpler way?
Comments (17)
That's pretty much it. Hume's argument isn't that complicated. How much simpler were you hoping to make it?
Knowledge of the future always seems problematic. But there seems to be a limit on what could happen to abruptly change a state of affairs.
Discovering a Black swan is the classic case but that is not a major difference from a white swan that would warrant a complete reappraisal of a law.
1) Experienced by us and others. (The belief).
2) Reached some consensus in a population (the brief that is regarded as a fact).
And then attempt to apply this regularity to some problem.
Well, I more or less copy-pasted the OP from the Stanford site.
I just didn't and don't get it.
After giving it some thought here's my version (the way I understand it):
Induction is predicated on the principle of the uniformity of nature (PUN)
PUN = unobserved events will resemble observed events
How do we proved PUN?
By observing events and checking if they resemble past observations.
But no number of observations will be enough to prove PUN because there's always the possibility that the next observation will disprove PUN.
So, PUN can only be proved if we assume it to be true. Circular argument.
Is my reading correct?
I think you can replace uniformity with regularity. Induction is seen as a problem because of among other things the problems you state.
I think degrees of freedom is a good model. What possible arrangements are there to follow for a starting position. Is there a good reason to believe after seeing White swans all over England a pink swan will appear. I think induction is pragmatic not truth bearing.
PUN = unobserved events will probably resemble observed events
Finding an exception does not deter from the principle, it just modifies the list of observed events. The principle cannot be used as hard proof of anything since it is merely a statement of probability.
"How do we prove PUN to give a solid foundation to induction?
Note1: We only have access to observed events."
Well yes this is 'the problem'. Inductive knowledge is as good as it continuance. When it looks wrong you throw it. Deduction has nothing new in it, so is basically of little use. Induction is all we have to move knowledge forwards.
But there is no "only" about access to observed events. Observed events are everything; if only we would keep to them rather than fill our world's with made up shit we'd be a lot better off.
? Paulo Coelho, The Alchemist
Am I off? Or can this be connected with:
"If a tree falls in the forest, and there’s nobody around to hear, does it make a sound?"
Or better explained:
"If a tree falls in the forest unobserved, does the behavior change when it is being observed"
1.) For many years now I have asked--a few times out loud--if any two observed events are in any way identical. Even if they are in some small ways identical, isn't it a giant, maybe inappropriate, leap in reasoning to say that any two or more observed events together tell us anything about reality other than their own individual selves? An experiment might be repeated exactly like another experiment, but they were conducted at different points in time and space. Are they really identical? One could have been done in North America and the other in Europe, but even if they were both done in the exact same lab, the lab is not in the same place both times (the Earth is not in exactly the same place in its orbit each time, even if it is the same month).
2.) More recently I have asked how do we know that the observations people make during observed events are in any way objective. It could be that only people who will report the same observations are drawn to observing a particular event. How do we know that the latter has not happened?
I think the answer to both is abstraction, and that language and mathematics both excel at this.
Yes, I believe that's one accepted point of view. I think it makes sense to be practical and just get on with it, so to speak.
Quoting charleton
I guess it's a human weakness/strength, depending on how you look at it, to want absolute certainty.
We begin with observed events and we see a trend - observed events are a good guide to unobserved events. This we call the principle of uniformity of nature (PUN).
It becomes the foundation of induction.
Note that it's not arrived at deductively. So, it's just an assumption.
Now we need to prove this assumption.
All we can do is observe events and check if they're a good guide to unobserved events.
But that's exactly how we arrived at the PUN in the first place AND we know that that's not adequate proof. So, the PUN can't be proved deductively.
Hume divides arguments into two types: deductive and inductive.
Deductive he disposes of directly by claiming that "The past is not a guide to the future" is not a contradiction, so "The past is a guide to the future" is not a logical truth.
So an argument that yields "The past is a guide to the future" as its conclusion would have to be inductive. But that's almost immediately circular.
So the conclusion is not only that "The past is a guide to the future" is not arrived at by reasoning, but that it cannot be.
You know how we know induction works?
It's always worked before.
You should also check out Goodman's new riddle of induction.
Also Carl Hempel's ravens.