Induction is impossible

[Zarathustra]

FF, there is absolutely nothing wrong with continuing as you think, and only deal with science as a pragmatic enterprise. Most scientists do the same thing, and don't worry about induction. They get results, build technology, and have a real sense that they are closing in on the nature of reality. This doesn't undermine any of that, it merely makes the scope of the mystery more apparent. We're not done yet. Maybe we'll discover our way around it, or not. Or maybe it's an unending paradox hinted at by Wayfriend with Godel's Theorem.

This, of course, can be "explained" in terms of the Athropothic Principle. (Or at least accounted for plausibly.) Randomly existing universes could have any qualities whatsoever, but only in those universes that just happen to operate according to "rules" that follow things like logic--the type of relations intelligent beings could understand--only in those universes will intelligent beings evolve in the first place to wonder about them. That could at least account for the uncanny coincidence. But that still means that somewhere in the possibility of Being, it existed "first" as a potential state of reality. So perhaps on some deep level, logic *must* be embedded for it to exist at all.

Or perhaps it's a kind of illusion, something that happens when loops of consciousness evolve into the universe, like holding up a mirror in a mirror, and seeing this pattern that wouldn't exist if you weren't looking at yourself.

[Lord Mhoram]

Malik,

Interesting hypotheses. Here's what Hume himself thought, from A Treatise on Human Nature (1739): "Nature, by an absolute and uncontroulable necessity has determin'd us to judge as well as to breathe and feel." In other words, it's some sort of instinct ingrained in our very human nature.

[The Dreaming]

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?

That's what's so amazing about the big bang, how the hell did such a low entropy state occur? As far as random chance goes, it's FAR more statistically likely that the present state of the universe is a anomaly, a random fluctuation in a static universe, in which all of our memories and histories are just an illusion created by random chance.

[Fist and Faith]

Aren't statistical likelihoods determined by looking at as many occurrences of a certain event as we can, and seeing how many of them fall into category X, how many fall into category Y, etc?

-When both parents have brown eyes, what color eyes do their children have? Let's count them up and see. Turns out X% have brown; Y% have blue, etc.

Isn't that how statistics are determined?

[Lord Mhoram]

Fist,

But in the case that you just mentioned, as with the vast majority of statistics, the ultimate statistic that you arrive at is an extrapolation from a sample to a given population. Statistics in reality determine that with x% of certainty (a good statistic is somewhere between 75-95%) we can make a prediction. Almost never 100%, unless it's a really small population in whcih case the statistic is probably not all that interesting anyway. So, again, we encounter the problem of induction, because as I said to Avatar upthread, even if we say Usually the future will be like the past or The future will be like the past x% of the time, the "scandal of Philosophy" remains.

[Avatar]

That the future may not necessarily be like the past? (Or nothing can be proven beyond what we know?)

But LM, how is instinct engrained? Doesn't this come back to what Fist might have been suggesting earlier? Or ability, or drive, to judge must have arisen from far more primitive beginnings...the kind of beginnings that dealt with our ability to survive.

As Malik implied, we use induction because 95 times out of 100, it works. Maybe it's the five percent that are the anomaly. Maybe not. But the weakness of induction does not preclude the possibility of it being right. As Quee said upthread, No evidence for is not the same as evidence against.

--A

[Hyperception]

OK, so let us consider the conservative principle of induction (CPI):

"Consecutive states of a system will vary with a probability proportional to their degree of difference from one another."

This does not require that the past exactly condition the present, only that any change must require a cause sufficiently great as to produce the degree of significant difference observed. Determinism is avoided, and induction need not entail a fallacy.

The task of the scientist then becomes to:

(A) provide law-like generalizations of the phenomena, expressible to as great an extent as possible in mathematical terms, and
(B) note anomalies/violations for further research into the presumptive causes thereof, prioritizing investigating those changes that are either
(B1) small enough that they occur frequently and can be repeated through designed experiments or
(B2) so remarkable for rarity and extreme deviance that they require revising basic assumptions underlying generalizations derived from (A).

There are two traps we need to avoid: universalizing inductive conclusions (i.e., words like "always" or "never" in science) and resorting to unfalsifiable hypotheses to explain B1 conditions, although we may assign such hypotheses to B2 conditions provisionally, subject to future revision. Of course there is also the de-convolution problem, by which multiple small causes have a single large effect, but that's for later.

The thing about the universe is, stuff doesn't change so radically within the lifetime of a human observer as to render understanding impossible, except during rare and normally unsurvivable events. It is therefore not unreasonable to assign increased evolutionary value (thank you, evolutionary psychology) to an intelligence capable of pattern-recognition, and as a further conclusion to expect that only those patterns recognizable by such specific adaptations will appear at all under normal circumstances; the rest of the phenomena would be screened out as incomprehensible and/or unobservable, or simply mistakenly reassigned to different patterns.

By the way, there is more ill-conceived drivel floating around back there in my mind on time, memory, and perception, but it's time to post.

God, I love b-vitamins!

[Fist and Faith]

Fist,

But in the case that you just mentioned, as with the vast majority of statistics, the ultimate statistic that you arrive at is an extrapolation from a sample to a given population. Statistics in reality determine that with x% of certainty (a good statistic is somewhere between 75-95%) we can make a prediction. Almost never 100%, unless it's a really small population in whcih case the statistic is probably not all that interesting anyway. So, again, we encounter the problem of induction, because as I said to Avatar upthread, even if we say Usually the future will be like the past or The future will be like the past x% of the time, the "scandal of Philosophy" remains.

Indeed. I wasn't trying to say that statistics will tell us what will happen. The higher the population examined, the more sure we can be of where to put our money, but it's never 100%.

But I asked how statistics are arrived upon because TD was talking about the statistical likelihood of the universe. Since there's only one universe to examine, I'm wondering how a statistical likelihood can be determined.

[Lord Mhoram]

Hyperception,

"Consecutive states of a system will vary with a probability proportional to their degree of difference from one another."

This seems to me to be essentially a more technical restatement of the potential corollaries to (PUN) that I stated above. Namely, Usually the future will be like the past and The future will be like the past x% of the time. Effectively it seems to me to be the same. The problem of induction still remains because even probabilistic claims about reality fall into the circular trap. Because however we state (PUN) -- we now have three restatements-- it must be one of the premises for any given inductive prediction (PRED).

Let's call your restatement (PUN 1a). When we formulate an inductive argument (PRED) to prove (PUN 1a), (PUN 1a) must be a premise because otherwise certain assumptions about the future and the past that are central to induction remain unsaid. So the problem of circularity in induction remains because (PUN 1a) is proving itself, and that's no good.

That said, I thoroughly agree with all of your statements about the aim of the scientist.

I think Quine was onto something when he posited, to quote the Stanford Encyclopedia, that "the similarity or sameness of kinds between instances...permits an induction: two green emeralds are more similar than two grue emeralds when one of them is green and the other blue. It is the “dubious scientific standing of a general notion of similarity, or of kind” (1969, 116) that prompts the discussion alluded to above. An intuitive notion of similarity is used in our ordinary inductions." For the reasons I stated above (to Quee) I don't think this really solves it either (my main issue with Quine's argument is, again, that I think it's deductive because isn't knowledge of a "natural kind" by definition a priori?) but the approach seems to me to be a better one overall.

Fist and Faith,

I really don't know. Philosophy of mathematics and frankly mathematics aren't exactly my speciality.

[Hyperception]

I think Quine was onto something when he posited, to quote the Stanford Encyclopedia, that "the similarity or sameness of kinds between instances...permits an induction: two green emeralds are more similar than two grue emeralds when one of them is green and the other blue. It is the “dubious scientific standing of a general notion of similarity, or of kind” (1969, 116) that prompts the discussion alluded to above. An intuitive notion of similarity is used in our ordinary inductions." For the reasons I stated above (to Quee) I don't think this really solves it either (my main issue with Quine's argument is, again, that I think it's deductive because isn't knowledge of a "natural kind" by definition a priori?) but the approach seems to me to be a better one overall.

My point was, though, that we are not so much interested in classification of similarities as we are in investigating change. If seemingly identical causes give rise to varying effects, we assume hidden causes; if seemingly identical effects occur we assume a singular cause or finite set of causes. The (PUN) buttresses or corroborates these assumptions at the same time as it is intuitively/inductively derived from them, granted, but it is during the times when these assumptions appear unwarranted that the most interesting 'stuff' is going on.

I have occasionally speculated that we know only the models we create, not the world that they are supposed to represent. Correspondence of model to phenomenon in all known instances, for example, need not imply necessary correspondence to all possible instances. In practice, we become at least as concerned to preserve the coherence of the model as to incorporate ever greater sets of instances, at ever greater degrees of accuracy of correspondence. This is where Kuhn's point about theory articulation becomes valuable; at some point the degree of complexity of the theory must become so large to accommodate so many contradictions and exceptions that it begins to lose explanatory coherence regardless of its initial utility. Do we adopt a postmodern view that "anything goes" and deny the importance of the world we are trying to explain? No, but we need at some point to revise our definitions or groupings or assumptions to improve not only the elegance and precision of our theories, but to open new realms for productive inquiry. Induction under this view becomes a tool for hypothesis formation, not a path to certainty.

Back to the Stanford, damn your eyes...

[Lord Mhoram]

Hyperception,

The (PUN) buttresses or corroborates these assumptions at the same time as it is intuitively/inductively derived from them, granted, but it is during the times when these assumptions appear unwarranted that the most interesting 'stuff' is going on.

Fair enough, no argument there. I merely set out in this thread to show that while induction provides perfectly reasonable results, and should not be abandoned necessarily, it has underlying, hidden, and serious flaws.

Induction under this view becomes a tool for hypothesis formation, not a path to certainty.

Hasn't induction always been a tool for hypothesis formation, though? In other words, aren't generalizations about phenomena and predictions about the future themselves hypotheses? I would wager they are. And that by making those generalizations and predictions inductively, we may be committing ourselves to a fallacy, even, as I said above, when we make probabilistic claims. All we need to do is (1) commit ourselves to finding a way to solve the problem of induction (lots of philosophers of science, and others from disparate fields, have tried to do just this since Hume), and (2) continue using the inductive method while recognizing its flaws and awaiting its repair.

[Kinslaughterer]

I'd say, as a scientist, that everyone is inductive but also fundamentally aware of the problem. The scientific method essentially forces us to be deductive. It becomes about falsification but with a practical level of confirmation. Hempel and Popper are my Theory of Science guys.

[Lord Mhoram]

Kinslaughterer,

The scientific method essentially forces us to be deductive.

Actually, if I'm remembering correctly, that is exactly what Karl Popper's response to the problem of induction was. I don't think the scientific method is entirely deductive, though. Surely scientific discoveries that have already been proved, which then serve as premises for further discoveries, mandate the inclusion of induction in the scientific method. But Popper's answer is still a good one.