Induction is impossible

[Lord Mhoram]

In response to the suggestion that we have more hard, technical philosophic topics, I came up with this one, Hume's famous "scandal of philosophy": a proof that induction is impossible. If true, it would mean that the assumptions underlying an enormous deal of human beliefs - including most notably science - are untenable. So hopefully I can sum it up adequately.

Hume's problem of induction essentially concerns how one's beliefs about the present and past justify one's beliefs about the future. Beliefs about the present and past justify, in other words, beliefs about the future (predictions) and certain generalizations about reality.

So I can make a prediction: the sun will rise tomorrow (the classical philosophic example). My present observation might be: the sun is now rising; my past observations are: the sun has risen each day I've been able to observe. My present mental conditions might be that I seem to be seeing the sun rise right now, and that I seem to remember it coming up in the past.

So let's turn to another example.

Prediction: the next emerald I will see will be green.

Generalization: all emeralds are green.

Let me elaborate. Call the prediction (PRED) and generalization (GEN).

(PRED)
(Premise) I've seen thousands of emeralds and they are all green.
(Conclusion) The next emerald I see is going to be green.

(GEN)
(Premise) Same as above.
(Conclusion) All emeralds are green.

These extrapolations are not perfect, and upon examination (which we can do if you don't believe that), probably unjustifiable. They're iffy at least, I think we can agree. So we should tighten them some how. Hume proposes the Principle of the Uniformity of Nature. Call that (PUN). (PUN) states: The future will be like the past. Add (PUN) to (PRED) and (GEN) above and you have justifiable conclusions, no?

So we can formulate some theses.

(1) Every inductive argument requires (PUN) as a premise.
(2) If the conclusion of the inductive argument is rationally justified by the premises, then those premises must be justified, too.
(3) So, (PUN) must be rationally justifiable.
(4) If (PUN) is rationally justifiable, there must be either a good inductive argument or a good deductive argument for it.
(5) There is no such thing as a good inductive argument, for (PUN) specifically. Any such argument would be circular. See:

(Premise) (PUN)
(Premise) In the past the future has been like the past.
(Conclusion) A restatement of (PUN).
It's totally circular.
(6) There is no good deductive argument for (PUN) either, because (PUN) is not a priori true. We can certainly imagine the future not being like the past.
[So there's no deductive argument either, so (4) fails.]
(7) (PUN) is not rationally justifiable.
____
(Conclusion) Every conclusion of an inductive argument is not rationally justifiable.

We are all irrational in inductive matters.

[Avatar]

I don't think it falsifies the premises of science, so much as gives the a caveat. And that caveat is "as far as we know."

Of course inductive logic can lead us astray...because it relies on it's premise. With a false premise, inductive reasoning gives you an incorrect conclusion, with perfect logic.

It was once believed that all swans were white, because nobody (who counted scientifically) had ever seen a black one.

--A

[Lord Mhoram]

Avatar,

I don't think it falsifies the premises of science, so much as gives the a caveat. And that caveat is "as far as we know."

But that caveat fails too. Change (PUN) to Usually the future will be like the past and you still have the problem of circular logic. I'm not saying -- nor was Hume, obviously -- that science is undermined so much as we should reexamine what exactly it's saying when it offers observations and rules. It's different than we assume.

[lucimay]

i guess francis bacon's a little upset huh.

[Lord Mhoram]

Luci,

No kidding! And he wouldn't be alone. That's what strikes me as crazy about this. Philosophy of science as a field was practically invented after Hume, and this problem has not yet been solved. As far as I know. Hopefully we in the Close can fix that.

[Queeaqueg]

Prediction: the next emerald I will see will be green.

Generalization: all emeralds are green.

Don't we generalise that because the definition of an Emerald is green? The next Emerald we see will be green because we have defined Emerald as being green.
If we saw an Emerald that wasn't green... it is no longer an Emerald.

As for black swans
There is no evidence of black swans is not the same as there is evidence of no black swans.

No Evidence of black swans - means we can't see any black swans n cant prove them
Evidence of no black swans - Conclusive, there are no black swans

Something like that lol

[Lord Mhoram]

Queeaqueg,

Don't we generalise that because the definition of an Emerald is green? The next Emerald we see will be green because we have defined Emerald as being green.
If we saw an Emerald that wasn't green... it is no longer an Emerald.

Okay I can buy that. I don't necessarily believe it's true -- perhaps it's, say, the chemical composition of emeralds that defines "emerald" as a concept -- but let's assume it is. So assuming that, we can only generalize that "All emeralds are green" by deduction, because we cannot imagine a not-green emerald. It's an a priori truth. So in that case, we still haven't proven that induction is justified. Replace the emerald example with an undeniably inductive example -- like the rising sun, which I maintain is inductive -- and we still have a serious problem.

[Zarathustra]

. . . you still have the problem of circular logic. I'm not saying -- nor was Hume, obviously -- that science is undermined so much as we should reexamine what exactly it's saying when it offers observations and rules. It's different than we assume.

Exactly. Hume wasn't saying that science doesn't seem to work. In fact, it works remarkably well. He was saying something much deeper: we have no idea why it works. It shouldn't work. The foundations which most people assume root it in certainty (or even high probability) aren't foundations at all . . . they are like prejudices or psychological habits. Like seeing faces in the clouds.

You can either base science on observation, logic, or some combo of both. Let's take observation first. An observation is a finite, self-contained event. It can't tell you anything about something beyond that observation--not without an assumption that transfers whatever "fact" you glean from the observation to something currently unobserved. But that kind of defeats the entire purpose of rooting your conclusions about reality upon observation, because you can't observer this connective assumption. That's an idea, not a phenomenon. Most of the time, we just make those up (again, like a face in the cloud).

Now, logic. Logic is very good at helping you analyze the connections between ideas, but tells you absolutely nothing about phenomena. I'm serious. No logical rule can tell you how a phenomenon will work, no more than computer programming can tell you what you're going to have for dinner. There is nothing necessary in events. They follow one another contingently (opposite of necessarily). Event B may depend upon event A in order to occur, but this dependence isn't one of logical necessity. It doesn't happen because of the rule, "if A, then B." The logical rule doesn't make it happen. That's just a way we describe it after the fact. Take dropping a book. There is no law in logic that would tell you that the book would fall. That book falling depended upon circumstances, such as being within a gravitational field. Every event is relative (to conditions), not necessary.

Ok, so we can't observe the connective assumptions between phenomenon (because those are purely logical constructs, not phenomena themselves), and we have no basis to root our logical descriptions after the fact, because events are contingent upon other events, not logical rules. In fact, the very act of applying these logical rules as descriptions of past events (and then predictions of future events) is itself a logical fallacy (problem of induction). So even as we achieve a measure of practical success, we are violating the very rationale upon which the enterprise is seeing its success. Weird!

Something "magical" is going on.

[Fist and Faith]

I have no idea what you're talking about. I don't see the problem. Or contradiction. Or fallacy. Or whatever you see. We're observing things. We see that every time X happens, it is followed by Y. Every time, no matter how many times we see X. If X is a certain sound, and Y is a blast of flame, we learn to duck when we hear that sound. What's the problem? We've learned to survive X.

We might even go further. If X happens in the same physical location many times, we might watch that spot for a long time, and see if we can see where the flame comes from, and/or how it's produced.

[wayfriend]

( Doesn't Godel's Theorem predict that induction theory would encounter a paradox if it is used to analyze itself? )

[Lord Mhoram]

Malik,

Excellent post. But what do you think the "weird" thing is that's going on? How are these connections made?

Fist and Faith,

Who is your post directed at? You seemingly haven't addressed anyone's actual arguments before you dismissed them.

wayfriend,

Not familiar with that. I'll have to read up on it. Thank you.

[wayfriend]

Godel's Second Incompleteness Theorem, to be specific. Basically, you "cannot prove that a system is consistent without resorting to rules of inference that are not expressible in that system".

As I apply it here, this means that analyzing the rules of inference itself, using only the rules of inference to perform said analysis, cannot preclude apparent paradox.

However, by asserting rules of inference that are not expressible as rules of inference, we can prove that there are no paradoxes!

If only we could do that... its like trying to find an object outside the universe.

[Lord Mhoram]

wayfriend,

Very interesting. But I would point out that in this case, we are talking about induction, which is a process of gaining knowledge. So in principle if induction were possible, we should be able to gain the knowledge to prove that induction itself is possible. It is probable that we in fact cannot.

[Fist and Faith]

Fist and Faith,

Who is your post directed at? You seemingly haven't addressed anyone's actual arguments before you dismissed them.

I haven't "dismissed" anything. However, it was Malik's post I was mainly thinking of. I didn't address it to him, but I followed immediately after him...

Anyway, I just said what I think happens when we try to understand the world around us. If anybody sees any problems with my understanding, I'd appreciate knowing.

[The Dreaming]

There are a surprising amount of postulates in science.

What the hell, exactly, is time? Mathematically, both directions are indistinguishable. Einstein called it "something measured by a clock". The only way we "can" distinguish direction in time is that entropy seems to only move one way, but even then the math says that entropy *should* increase in the past. For some reason it doesn't, and that's one of the huge mysteries of the universe, that entropy decreases when we go back in time.

[Fist and Faith]

Darn! That sounds very interesting, but I know I'll never understand what the heck you're saying!

How do we know entropy doesn't increase in the past?

And why *should* it? Is the present moment supposed to be the moment of least entropy, and it is supposed to increase when we move through time in either direction? How did the present moment get that distinction? And what happens when the present moment is a million years from now? Or when it was a million years in the past?

[Lord Mhoram]

Fist and Faith,

If anybody sees any problems with my understanding, I'd appreciate knowing.

It's not really that anyone has "problems" with induction, it is just that it seems readily apparent that induction isn't quite what we think it is for the reasons I stated above. It is indeed a "scandal of Philosophy" (Hume's words) that we cannot prove that the sun will rise tomorrow.

[Zarathustra]

I have no idea what you're talking about. I don't see the problem. Or contradiction. Or fallacy.

You’ve stated the fallacy! Or at least implied it. You said:

“We see that every time X happens, it is followed by Y. Every time, no matter how many times we see X. We see that every time X happens, it is followed by Y. Every time, no matter how many times we see X. If X is a certain sound, and Y is a blast of flame, we learn to duck when we hear that sound. What's the problem? We've learned to survive X.”

Now I agree that this is a pretty useful observation to make, and that it can even lead to high degrees of accuracy over time. Science works. You’re right. But, the fallacy lies in the conclusion:

“this has happened a lot in the past” = “this will always happen in the future.”

It's a conclusion that can only be made by assuming the conclusion to begin with. The conclusion that the future will be like the past is developed by looking at events that happened in the past! Even when you're talking about examples where the future turned out to be predictable. That's circular reasoning. You can't say, "the future will *continue* to be like the past, because in the past, previous futures turned out to be like the past." That's just a more complicated way of saying what you were trying to prove. That's stating what you want to prove, (something about the past) as *evidence* for what you want to prove, and assuming it will keep on happening. Stating that some-sequence-of-the-past, X, justifies the conclusion that the the past will predict the future, Y, is exactly what you were trying to prove in the first place. Such evidence (X) is still only an observation about the past.

There is absolutely no reason why every single law of science couldn't stop working tomorrow. Every single regularity in the universe could be held together by one underlying principle, and maybe tomorrow is when that principle "flips poles" or something.

Even though our trust in regularity seems reasonable, that sense is built up out of repetition alone, like Pavlov’s bell. It’s a reaction ingrained into you psychologically, rather than deduced or inferred. And that’s because it can’t be deduced or inferred. If such these things already existed in logic, then we wouldn’t ever have to look at the world. We could just sit around and deduce the nature of reality from a handful of rules. Logic is a map that can lead to a dead end—or a new map—at any time. We toss maps out as reality presents itself as more complex than our logical pictures portrayed. They are always approximations.

Not only are maps “merely” approximations--much more: they they occupy different kinds of reality. Maps are in the “realm of ideas.” In your head. In terms of purely abstract objects like the concept “number.” On the other hand, reality is the “realm of facts.” Obviously, facts are not ideas. But we get so used to confusing our maps with reality (because we’ve got some damn useful maps) that we begin to think of ideas and facts as pretty much the same thing, and working by the same exact rules. But there’s nothing in rules that say they operate by the same rules! What rules would those be? That would take a set of “meta-rules” that describes both realms (realm of ideas and realm facts), and the way these two interact. But of course, that meta-description would be just as problematic as the first. What connects the meta-rules to the two sides? Another meta-meta-rule?

[Zarathustra]

FF, I thought of a much shorter way to say it: if the reliability of X is in question, you can't use "X" as proof of it its own reliability, because the original question of its uncertainty would undermine its status as evidence for itself.

[Fist and Faith]

I think my problem is with the word proof. Let's say it's my first visit to the Fire Swamp. I hear a pft pft noise. When I look to the ground where the noise seemed to come from, flames shoot out! Next time I hear pft pft, I'm moving away from the sound. If flames don't shoot out this time, I consider the possibility that it was just a coincidence last time. I'll still pay attention, though, just in case there are flames next time. But if there are flames again, I'm pretty happy I moved away, and I'm really gonna try to attune my ears to that noise.

What have I proven? Well... Maybe nothing. (Heck, it's never even been proven that the flames would have hurt me. Just because flames always hurt me in the past, eh?) But then, I wasn't trying to prove anything. I was just trying to figure out how to stay alive. Which is working out so far.

And, proof or not, I will continue to assume the flames will follow the noise, and the sun will rise every morning, until they don't. I mean, I'm not about to change my behavior just because I can't prove there isn't an underlying principle that's about to flip-flop.