AE BB DB Explorer


Action:
Author:
Search Terms (separate with commas, no spaces):


form_srcid: Missing Shade of Blue

form_srcid: Missing Shade of Blue

form_cmd: view_author

Your IP address is 54.81.80.46

View Author detected.

view author posts with search matches:

Retrieve source record and display it.

form_author:

form_srcid: Missing Shade of Blue

q: SELECT AUTHOR, MEMBER_NAME, IP_ADDR, POST_DATE, TOPIC_ID, t1.FORUM_ID, POST, POST_ID, FORUM_VIEW_THREADS from ib_forum_posts AS t1 LEFT JOIN (ib_member_profiles AS t2, ib_forum_info AS t3) ON (t1.forum_id = t3.forum_id AND t1.author = t2.member_id) WHERE MEMBER_NAME like 'Missing Shade of Blue%' and forum_view_threads LIKE '*' ORDER BY POST_DATE ASC

DB_err:

DB_result: Resource id #4

Date: 2008/12/19 23:56:46, Link
Author: Missing Shade of Blue
Hi all,

I've been lurking here and at UD for a little while because I'm very interested in the evolution/ID debate. I'm fairly convinced that you guys are on the right side of pretty much all the specific arguments that get discussed here. The level of discourse at UD is distressingly juvenile (that's also often true of the discourse here, but at least you guys do it intentionally). But I am still not convinced that evolutionary theory can fully explain all the apparent design in the biological world. Believe me, I want to be convinced. I'm not hubristic enough to think that the entire scientific establishment is wrong and I'm right. Any questions I have are most probably misunderstandings on my part. Still, I haven't yet seen those questions adequately addressed.

What I'm getting to in a roundabout way is that I was wondering if it would be kosher for me to post a couple of questions I have in the hope that some of you could help me answer them. I don't want to derail the UD discussion, so I'm not going to post them here, but I don't really know which is the appropriate forum. I can't start a new thread because I just registered. Is there an existing thread for stuff like this?

Thanks.

Date: 2008/12/20 01:25:12, Link
Author: Missing Shade of Blue
Thanks, OA.

The thing that bothers me most is inductive bias. We are physiologically set up to carve the world up in certain ways, and to consider certain predicates natural and projectible. The worry is basically the same as in Nelson Goodman's 'New Riddle of Induction', so I'll use his example (and apologies for rehashing this if you're familiar with the example).

Consider the predicate grue, which translated into our language, means "green if discovered before 2012, and blue afterwards", and the corresponding predicate bleen, "blue if discovered before 2012, and green afterwards." To us, this is an extremely unnatural predicate, and it is definitely not projectible. All emeralds we've found so far are green, and we think this licenses the inductive inference "All emeralds are green." All the emeralds we've found so far are also grue, but, crucially, we don't think this licenses the inference "All emeralds are grue." Our inductive bias is for blue-green rather than grue-bleen predicates. Now, Goodman's insight is that any attempt to justify this preference by appealing to the simplicity of green over grue, or the way green rather than grue integrates with the rest of science, is bound to be circular. If we encountered an alien species that was physiologically set up to consider grue and bleen natural, then there would be no way to rationally convince them they were wrong. Well, there would be one way. We could wait till 2012 and show them that their predictions have failed and ours haven't. Short of that, though, there's nothing we could do.

Now, natural selection can't see the future, so until 2012 creatures with green-blue predilections have no obvious selective advantage over the grue-bleeners. And of course, this holds not just for grue-bleen but a zillion other gruesome predicates. So from an evolutionary standpoint, it seems to me like we'd have to say that our particular inductive biases don't stand out uniquely in search space. There's a whole host of different biases that, ceteris paribus, would have been just as fit as the actual one in the environments in which we evolved. The surprising thing, then, is that our particular biases have worked so incredibly well.

I guess one way to bring this out is to modify grue so that the change occurs in 1912 rather than in 2012. If grue and bleen (modified in this way) had been the actual predicates that fit the world, then we would have been thrown into a tizzy in 1912. But it turned out that they weren't. We dodged that bullet. We also dodged a bullet in 1712, and in 1612. In fact, we've dodged an infinite number of bullets. So far, out of the many ways in which the world could have radically bucked our inductive expectations, none have come to pass. It looks like our inductive biases fit the structure of the world pretty well. This is apparent design.

Now what confuses me is that it seems that it is basically impossible to come up with an evolutionary explanation for this apparent design. Like I said, the environment in which we evolved these biases was just as compatible with a number of other biases (an infinity, basically) which would have failed by now, such as the 1912 grue-bleen bias. And yet we ended up with the bias that works. And its not like there was some population of 1912 grue-bleeners who went extinct when 1912 came around, leaving us top dogs.

I guess it seems to me that this example is distinct from the usual god-of-the-gaps nonsense because it's not just that we are ignorant of the mechanism by which natural selection hit upon the right (at least, right so far) inductive bias. It's more like we have principled reasons to think there could be no such mechanism. For natural selection to choose blue-greenism over grue-bleenism it would need information about the future that is unavailable to it.

Anyway, that's my longwinded question. I hope I've explained it adequately. Any answers or references to literature that discusses this problem would be greatly appreciated.

Date: 2008/12/20 04:34:55, Link
Author: Missing Shade of Blue
Keith,

Your five premises are accurate, but I think you're missing the full force of Goodman's reasoning. Let me play the role of a Keith counterpart on a planet with grue-bleen inductive biases. Here are my five premises, which are collectively equivalent to yours, but rephrased so that green and blue sound like absurd gerrymandered predicates:

1. If we see a grue object before 2012, we put it in the category 'green'.
2. If we see a grue object afterwards, we put it in the category 'blue'.
3. If we see a bleen object before 2012, we put it in the category 'blue'.
4. If we see a bleen object afterwards, we put it in the category 'green'.
5. For the purposes of this discussion, the appearance of objects does not change.  Once bleen, always bleen, etc.

I hope it's obvious that if your five premises are true, then these five must also be true. So far, the blue-green and grue-bleen situations are symmetric. Everything else you said in your post can also be completely symmetrically translated into grue-bleen language. For instance, you say natural selection is betting on blue and green because the sky has always been blue and the grass has always been green. But of course, given my definitions of grue and bleen, it is also the case that the sky has always been bleen and the grass has always been grue. So why would natural selection bet on blue-green over grue-bleen? It seems you're surreptitiously relying on some notion that blue and green are more natural or simpler than grue and bleen, but of course, this is just your inductive bias speaking.

I agree with you that a species that latched on to non-projectible predicates would eventually be selected against. But the point I was trying to make is that this selective story can't be the explanation for our preference for blue-green over grue-bleen, because selection could only kick in when the difference in predicates makes an significant material difference in the behavior of the organism, and that's only in 2012. Natural selection figures out whether blue-green or grue-bleen is right at the same time that we do. It has no special prospective access to the fact of the matter.

Now you may say, "Yes, you're right. Natural selection doesn't know whether blue-green or grue-bleen will turn out to be right. It has contingently bet on blue-green and we'll have to wait and see in 2012 whether it wins the bet." My point is that it has already won a stupendous series of bets. I don't know how far back trichromatic color vision stretches, but I know chimps have a visual system that's pretty much like ours, so our blue-green inductive bias stretches at least as far back as 5 million years. Some of our more basic inductive biases stretch back much further than that. Any time between then and now our inductive biases could have failed us, but they didn't. For five million years, evolution's bet on blue-green has been vindicated. And it's not like we started out five million years ago with populations with all different kinds of color biases, and they went extinct one by one until we are the only ones who remain. If that were the case, then the sort of anthropic reasoning Nerull suggested would render our success unsurprising. But as far as I know, in the last five million years, no known species has gone extinct due to incorrect color inductive bias. What we have, and what I'm having trouble explaining, is natural selection guessing five million years ago that a particular set of predicates would be projectible, and even though this guess was vastly underdetermined by the information available at the time, it has been borne out for five million years.

I chose color as an example due to Goodman, but I could have chosen any number of other, much more fundamental inductive biases. Something constrained the evolution of inductive preferences to ones that have worked fairly consistently. It couldn't have been natural selection, because given he environment up to time t, there is a literally infinite choice among predicates that agree up to t, but disagree later. Somehow the predicates chosen for us at t have worked all the way up to t + 5*10^6 yrs. This is mysterious to me.

Date: 2008/12/20 05:14:56, Link
Author: Missing Shade of Blue
Wesley,

I'm not claiming our inductive biases are perfect, especially when it comes to highly theoretical predicates like "phlogiston" or "caloric". But our folk inductive assumptions about medium-sized dry goods (stuff like shape, sensory properties, causal properties, etc.) works well enough to allow us (and all kinds of other animals) to get by pretty well. And that in itself is surprising to me.

The radical Humean skeptic about induction: "Hey, why do you think nature will continue to be so stable and uniform? How do you know Planck's constant won't change tomorrow? Or that your cat won't turn into some kind of evil fire-breathing demon?" This is the kind of thing people make fun of philosophers for.

Goodman's skepticism is subtly different, and to me far more troubling. It's not "Why do you think nature is, to a large extent, uniform across time?" It's "Granted that nature is uniform, what does that mean?" And the answer is that it depends on your choice of vocabulary. What it would be for nature to be uniform is different for creatures with blue-green vs. grue-bleen predilections. Now we were endowed with certain predilections in the distant past, and it turns out that so far, nature has actually been pretty uniform on our preferred descriptions.
Our biases haven't been perfect, sure, but our inductive expectations are very rarely shattered by everyday macroscopic phenomena millions of years after they evolved. And that fact in itself, I suspect, puts them in a set of measure zero in the space of all possible biases.

Quote
As yet unobserved conditions or stimuli (as in the "ue" of "grue") are also unavailable to natural selection; why would anybody imagine that natural selection could develop systems corresponding to "grue-bleenism" prospectively?


It seems like the lack of clarity in my initial post has claimed another victim. I hope the response I wrote to Keith makes things a little clearer. The point I was trying to make was that "grue" and "green" are really on the same footing evolutionarily. In particular, "grue" does not involve unobserved conditions or stimuli any more than "green" does. To suppose otherwise is to assume an asymmetry between the predicates that can only be justified by our inductive bias. And it is the emergence of that very bias that we're trying to explain. Note that the temporally disjunctive aspect of grue and bleen is merely an artifact of their representation in our blue-green basis. If we try to represent blue or green in a grue-bleen basis, then they would appear temporally disjunctive.

Date: 2008/12/20 05:29:16, Link
Author: Missing Shade of Blue
Nerull,

I wasn't denying that there are species with different color perception than humans. What I was saying is that the continued success of specifically hominid trichromatic color vision millions of years after it emerged can't be explained away by an anthropic argument. We didn't start out with a vast number of different hominid species with different inductive biases which were gradually pruned away until we (and chimps, gorillas and orangutans) were the only ones left. What happened was that hominid color biases were fixed millions of years ago, and then they continued to be successful. What I am asking is how evolution knew which biases to pick (out of the infinite number of choices) all those years ago.

Also, the question about the designer. I want to assure you that I'm not coming into this with any intent to vindicate ID. While I probably have less of a distaste for ID-type hypotheses than a lot of the posters here, I still see it as a position of last resort. Even if it turns out that this particular case of apparent design cannot be explained evolutionarily, I would look for other non-teleological explanations before turning to some kind of design hypothesis.

Date: 2008/12/20 05:59:28, Link
Author: Missing Shade of Blue
Keith,

I don't think talking about wavelengths ameliorates the problem. All you're doing there is justifying the idea that one of predicates is projectible by appealing to the projectivity of another of our predicates (in this case, a far more theoretical predicate). Anyway, I have a minor and a major response to your argument.

Minor response: It's inaccurate to think that our perceptual system responds in a simple way to any fundamental physical property such as wavelength. In actual fact, we are not the kinds of systems that respond in a simple manner to wavelength or surface reflectance. There are all kinds of phenomena in color science that demonstrate this. Metamers have different surface reflectance properties but they appear to be of the same color. Conversely, patches with identical reflectance properties can look differently colored depending on the environment in which they are placed, as a number of awesome optical illusions illustrate. Certain colors (brown, for instance) only exist as contrast colors. There is no such thing as a pure saturated brown stimulus. All of this goes to show that color perception is already quite a complex phenomenon and does not obviously track any fundamental physical property. So the assumption that evolution will tend to produce creatures that respond simply and directly to fundamental physical properties is questionable.

Major response: Let's say I accept that the perception of green and blue is a direct response to wavelength. I never said the grue-bleeners respond to wavelengths any differently than we do. I merely said that their natural dispositions to classify stimuli are different. They might agree that light of 500 nm wavelength is green and 450 nm light is blue. But this supports the projectibility of blue and green only if you make the prior assumption that wavelength measured in nm is projectible. The grue-bleeners deny this. For them, of course, the projectible predicate is "500 nm wavelength before 2012 and 450 nm after 2012".

The larger point here is that justifying the projectibility of our predicates with reference to our best science can't take us where we want to go. It only works if we assume that our scientific theories are projectible, which only works if we assume the predicates involved in those those theories are projectible. And ultimately, the assumed projectibility of scientific predicates is grounded on the assumed projectibility of certain macroscopic observational predicates (the kind that are used in measurement and experiment). And really we have no justification for these other than our inductive biases. We can't collectively vindicate our entire vocabulary as the simplest or most natural choice.

Date: 2008/12/20 13:38:56, Link
Author: Missing Shade of Blue
Sweet. My own thread.

Thanks for all the responses, guys. A lot to think about, so you'll forgive me if I don't address every point made just yet. But I do think there's still a hint of circularity in some of the arguments I'm seeing.

To boil it down a little, my initial point was that it's hard to come up with an objective notion of simplicity on which blue-green is a simpler set of predicates than grue-bleen. The obvious suggestion would be that grue-bleen is computationally more complex than grue-bleen. To put it crudely, a fully consistent grue-bleen program (one that also gruified other relevant scientific predicates, such as wavelength) would be a lot longer than a blue-green program.

But of course, the algorithmic complexity of a particular problem depends crucially on the structure of the computer. One could construct computers for which the string 1010101010101010.... is simple and predictable. In fact, we ourselves are such computers. But we could also construct weird computers for which this string is quite complex, and the string 110001001000110101011.... is simple. It all depends on what the "natural language" is for the computer, and that depends on how the computer is constructed. Similarly for blue-green and grue-bleen. We happen to be blue-green computers. For us, these are natural and projectible predicates. The world will be simple if blue things stay blue; it will be less simple if blue things change to green at some arbitrary time. But grue-bleen computers, for which the exact opposite is true, are not inconceivable. So a syntactic notion of simplicity doesn't settle the matter.

[I should note here that I tend to prefer an ecological/embodied approach to cognition, so when I refer to humans as computers, I'm not just referring to what goes on in the head, but to a whole host of bodily mechanisms.]

It seems that some of you (keith, Bill, Zachriel) want to move the discussion up a level and talk about the complexity of the computer itself. You argue that while a grue-bleen computer may be possible, it would be far more complex than a blue-green computer and therefore more expensive to construct. Here is where I smell the vicious circle (or its slightly less dreadful cousin, the infinite regress).

If we describe things using our own natural predicates, then it is only to be expected that blue-green computers will turn out to be simpler than grue-bleen computers. After all, we ourselves are blue-green computers. The question is whether there's an objective sense in which blue-green computers are simpler than grue-bleen ones. Here's one suggestion: It takes fewer resources for a Universal Turing Machine to emulate a blue-green computer than a grue-bleen computer. Unfortunately, this doesn't work for the same reasons as before: it depends on the construction of the UTM. We can construct UTMs for which grue-bleen is more natural (and more easily emulated) than blue-green. Again it depends on our choice of description language.

It seems to me that every problem that arises when trying to adjudicate the complexity of the predicates themselves also arises when we move up a level to consider the computers that use the predicates. I hear you saying that grue-bleen systems are complex and more expensive because they require multi-year timers. But of course that is only under the assumptions that our inductive biases are right, that blue/green really are the natural and simplest predicates, that the giant evolutionary UTM is set up to more easily emulate blue-green computers than grue-bleen ones. From a grue-bleen perspective, none of these statements are true. According to them, it is us, the blue-greeners, who require multi-year timers to detect when grue switches to bleen. We are the ones who are more complex.

What I think is needed is a way to break this symmetry without surreptitiously sneaking in our own inductive biases in describing the situation.

Date: 2008/12/20 13:58:05, Link
Author: Missing Shade of Blue
One small correction:

In describing the two binary strings, I shouldn't have put ellipses at the end suggesting they're infinitely long. If they were, then it might well be the case that there is no UTM for which the second string is algorithmically simpler than the first one. Imagine the ellipses merely indicate that the strings are a billion digits long.

Date: 2008/12/20 14:11:22, Link
Author: Missing Shade of Blue
Wesley,

Thanks for referring me to the Solomonoff stuff. This may be the kind I'm looking for. Excuse me for a little while I look through it.

Date: 2008/12/20 14:12:08, Link
Author: Missing Shade of Blue
And by "kind" I mean "kind of thing".

Date: 2008/12/20 15:02:34, Link
Author: Missing Shade of Blue
Wesley,

Based on a preliminary review, I dont think Solomonoff induction addresses my concern here. If I'm correct, Solomonoff induction begins by assuming a particular description language for sequences. It then applies Occam's razor based on this description language: programs with lower algorithmic complexity when written in the chosen language are assigned a higher prior probability. In general, I think approaches that are based on Kolmogorov complexity will have to start with an assumption about the description language. They don't provide a language-independent notion of simplicity.

The question I had is logically prior to this whole process. Which is the appropriate language according to which we conduct our judgments of simplicity? Presumably there is at least one such language that is "natural". This would be the language according to which Occam's razor actually works, i.e. the simplest hypothesis in this language will actually be projectible. [Incidentally, this is what I meant by the uniformity of nature: Not that every single one of predicates is projectible, which would be equivalent to saying that nothing changes, but that a large cluster of our most basic observational and theoretical predicates are projectible, at least in our immediate environment, thus allowing for a myriad of successful inductions.] Now it might turn out that our predicates aren't actually the most natural ones. Come 2012 we might discover that the universe actually prefers grue-bleen.

While I admit this as a theoretical possibility, I am confident this will not happen. What is bothering me (and I guess I'm not able to communicate this concern adequately, but I'll try again) is that I can't give a non-question-begging justification for why I am confident the grue-bleeners will be proved wrong. And by the same token, evolution has no non-question-begging justification (apologies for the excessive anthropomorphization) for its choice of blue-green over grue-bleen or 1912 grue-bleen or 1812 grue-bleen or an infinite number of other possible inductive biases.

I see two sorts of responses here:

1) There is such a non-question-begging justification that involves the greater simplicity of blue-green, or of blue-green computers (humans) or of blue-green computer computers (the evolutionary process itself). In a previous post I said why I don't think this is satisfactory.

2) Our inductive biases are not particularly successful, and in so far as they are, it's just a lucky accident. Think of all the other species that went extinct due to bad inductive biases (the dodo, for instance). I don't find this satisfactory either. While evolution has no doubt sampled a large number of different sorts of inductive biases, and many have proved unsuccessful, it is also true that the number of biases sampled is an infinitesimally small proportion of the total number of possible biases. And yet it managed to hit on ones that have allowed a number of species to survive for millions of years after the respective biases evolved. This seems too improbable to be explicable as a lucky accident. So we should expect that the sampling wasn't random. There was some kind of search mechanism that looked for biases that more or less match the natural structure of the world. What I have been arguing is that this search mechanism could not have been natural selection, because when you lack information beyond a certain point in time, it radically underdetermines your judgments about which predicates are natural.

Date: 2008/12/20 15:25:54, Link
Author: Missing Shade of Blue
Zachriel,

Quote
In science, the way we test for bias is by making empirical predictions that are entailed in our hypothesis. If the predictions for a blue universe and a bleen universe are identical, then your claim is scientifically vacuous. If they are not, then you can make empirical predictions to distinguish between the two views.


I agree. Grue and green universes are not empirically equivalent. They are just empirically equivalent up to 2012. But gruers and greeners will make different predictions about what happens after that. Greeners will predict that emeralds discovered post-2012 will be green, which means they will not be grue. Gruers will predict that these emeralds will be grue, which means they will not be grue.

Quote
Otherwise, your argument has nothing to do with the Theory of Evolution except that it's an argument about scientific induction. If you want to make that argument, then you should first dispense with the distraction about biology.


Ultimately, my argument is about scientific induction, viz. that our inductive biases are to a certain degree arbitrary and unjustifiable. But I don't think biology is a distraction here. Our inductive biases serve a certain purpose. They allow us to make inductive inferences well enough to get by. There are many other biases which would, at some point or another, fail at this task. A vast number of them would have failed before now. So here we have a crucial functional aspect of our biology, and usually I look for adaptive explanations for such features of our biology. But for the same sorts of reasons that I think the biases are arbitrary and unjustifiable, I can't see that any adaptive explanation could account for the continued functionality of this bias. I think natural selection is a beautiful theory that accounts (or can potentially account) for every other apparently designed feature of our biology, so this one holdout bothers me.

Date: 2008/12/20 16:25:51, Link
Author: Missing Shade of Blue
Keith,

A few thoughts:

1. You'll forgive me if I occasionally continue to use "predicate" and "Turing Machine". It makes things clearer for me to follow. This might be one of the reasons I'm having trouble seeing the arguments here. I might be a bit too inured to thinking in terms of language and representation.

2. Your wavelength detector example is useful. The suggestion seems to be that a blue-green computer is simpler than a grue-bleen computer not on some syntactic notion of simplicity, but according to a simple physical notion of simplicity. A blue-green detector can be constructed with fewer physical parts than a grue-bleen one. Maybe not just fewer. Maybe it's the case that for any grue-bleen detector, one could construct a blue-green detector using a proper subset of the grue-bleen's physical parts.

Here's my response. I'll have to think about the issue some more to figure out what I really think, but here's what I'm thinking right now:

Let's say you describe the physically simplest color discrimination device, say a pigment in a box, and claim its a blue-green detector. The grue-bleener might agree that this device is the simplest, but disagree that it's a blue-green detector. They say it must be a grue-bleen detector. Recall that you and the grue-bleener have different theories of the world, and that's going to affect how you predict this detector will behave post-2012. The blue-greener claims the pigment distinguishes grue and bleen, not blue and green. Now you can use all sorts of physical arguments to try to convince the grue-bleener that the pigment detects blue and green. The grue-bleener will just claim that your arguments are tainted by your use of bizarrely gerrymandered concepts (such as wavelength in nm). He has exactly symmetrical arguments for why the pigment detects grue. Both of your scientific theories are empirically equivalent up to 2012, but they disagree after that. Before 2012 there is no way to decide who's right without reference to our inductive bias.

Now comes the crucial part. We have the detector but we can't establish in a non-question-begging way whether it detects blue-green or grue-bleen. Your choice in this matter will affect how you think the device ought to behave once it has made the detection. If you think blue and green are the natural predicates, you set up the device to say "blue" when it detects 450 nm light. But if you're a grue-bleener you set up the device to say "bleen" under the same circumstances. Importantly, the detection part of these devices are identical. The only thing that differs is the response. Now one of these devices will get things wrong after 2012, depending on which set of predicates is projectible. But until 2012, we cannot say (without consulting our biases) which device is going to get things wrong. If we had a choice between setting up the blue response or the bleen response, we would have no non-biased rational basis to make it.

This is roughly the situation evolution was a long long time ago. Let's say the simplest sort of wavelength (or possible grue-wavelength) detecting machine has been constructed. There is a further decision to be made about the machine's response to these detection events, and this is where the inductive bias of the machine is set. Evolution chose (seemingly arbitrarily) for the responses to be blue-type rather than bleen-type, and this has worked pretty well so far. This is the puzzle.

In the previous discussion physical simplicity is not even a factor, because there is no difference in the detection mechanism. Inductive bias becomes relevant when constructing the response mechanism, and it is not at all obvious to me that blue-type response systems are more easily constructed than bleen-type systems.

Date: 2008/12/20 16:32:14, Link
Author: Missing Shade of Blue
Zachriel,

While I agree that the worry is a general one about inductive learning, I focus on evolution because it is, in our world at least, the mother of all inductive learning systems.

When I construct a learning machine, I endow it with a certain inductive bias. When asked to justify this decision, I can refer back to my own inductive biases. When asked to justify those, I can refer back to evolution's inductive bias. When asked to justify that, I can...?

Date: 2008/12/20 16:44:32, Link
Author: Missing Shade of Blue
On further reflection on keith's argument, it might be the case that there are systems with blue-type responses that are physically simpler than any bleen-type response system. So maybe evolution's particular inductive bias is attributable to the fact that it is easier (given, say, how organic chemistry works) to construct blue-type response systems. But of course, this is not a search strategy, so prima facie it provides no explanation for why the inductive biases embedded in these responses actually match the world into the future.

BTW, it seems like some people still harbor the suspicion that I'm some sort of ID fifth columnist. Maybe I should make it clear that even if my concern is valid and unanswerable (a huge if), this would not mean evolutionary biology should be consigned to the scrapheap of history. It would not affect the fact that natural selection is the best explanation for the majority of our functional traits. It would, however, suggest that the evolutionary story is incomplete if one of our most functional traits, our ability to make more or less accurate inductive inferences, lacks explanation.

Perhaps this is just one of those places where explanation bottoms out, but to me it's a peculiarly unsatisfactory bottom...

Date: 2008/12/20 17:04:34, Link
Author: Missing Shade of Blue
Zachriel,

Quote

Or the year 2525. Or 3535. Or 6565. There are an infinitude of equivalent claims. In other words, it is scientifically vacuous.


Hold on. I agree that the difference between two theories is scientifically vacuous if that difference has no observable consequences. But that doesn't seem to be the notion of vacuity you're using here. What you're doing here is saying that if there are an infinity of empirically distinguishable theories that are all produced using the same sort of schema, then the difference between them is scientifically vacuous. This I don't agree with at all.

The theories make radically different predictions. They are not "equivalent claims" and I don't see why their infinitude matters. What notion of scientific vacuity are you using here?

I will say this. I agree that it is perfectly acceptable for scientists to use their inductive biases to eliminate hypotheses. I'm not challenging the use of Occam's razor in science. Without it, we would constantly be confronted with an infinitude of equally successful hypotheses. I am definitely not attacking this aspect of the scientific method. I agree: "All emeralds are green" is a good theory and "All emeralds are grue" is a bad one.

But there is one area of inquiry in which scientists cannot take their inductive biases as granted. This is when they consider themselves as cognitive systems and attempt to explain their own inductive predilections. It is only in this peculiarly reflexive case that I'm questioning the straightforward use of Occam's razor.

Date: 2008/12/20 17:26:29, Link
Author: Missing Shade of Blue
Quote

Science assumes basic induction. You can't discuss the nature of biological evolution without agreeing to the axioms of induction.

There is no absolute foundation for induction. The world may simply end tomorrow. But if you accept the existence of memory (or that we can make and read records), then we can define inductive learning axiomatically. We can even provide a level of "confidence" based in statistics.

You don't have to really think induction is meaningful. Just that when we talk, we agree to the meanings of our words. So, if I say the Sun rises every day in the East, you understand this is a generalization with a high level of confidence (even if you think to yourself that we don't know with certainty that it will continue to do so in the future).

The rest is merely details.


Fair enough. I was hoping my question was a bit more localized than the problem of induction, but on reflection maybe it isn't. Doesn't that leave you with a deep and unsatisfying worry, though? After all, we are just contingent products of a gradual evolutionary process. In so far as we display ostensibly purposive or functional behavior it should be traceable to non-teleological causes. And when I say "it" I mean not just the behavior itself but its apparent purposiveness (excepting exaptations for the moment). In the case of inductive inference the behavior itself may have a non-teleological causal explanation (basically just a record of the particular series of biological changes that led to this set of inductive biases), but the apparent purposivity of the behavior has (and can have) no such explanation. To think otherwise would be tantamount to solving the problem of induction.

This is a troubling state of affairs for me. I guess ultimately we must think our continued ability to make inductive inferences is an exaptation, not an adaptation. If that's the case, what a whopper of a spandrel it is...

Date: 2008/12/20 17:32:48, Link
Author: Missing Shade of Blue
Quote

Naïve induction may sometimes have that problem. That's why we have developed the scientific method. But as far as I can tell, we're still stuck on simple induction.


Wait what? Are you suggesting that there is some scientific notion of induction that doesn't suffer from the same sorts of foundational problems as naive induction? Or are you just saying (a la Popper) that the scientific method isn't inductive at all?

In both cases, I disagree. I think the best formalization of scientific belief revision would be along Bayesian lines, rather than Popper's hypothetico-deductive approach. And Bayesian reasoning has foundational issues regarding the choice of priors that are basically just technical versions of the problem of induction.

Date: 2008/12/20 17:42:17, Link
Author: Missing Shade of Blue
Quote
Nothing you have said would indicate that the evolutionary story is incomplete. If we somehow knew that the world was going to bleen tomorrow, it wouldn't change the Theory of Evolution. Unless you could show that organisms had somehow anticipated this one time event. I mentioned this above too.

Do you accept induction?


What you regard as a relevant "event" that needs anticipation is conditioned by your inductive bias. Incidentally, the fact that you talk about the world "going to bleen" suggests a minor misunderstanding. The sky is either bleen or blue. If it is bleen it will go from blue to green. If it is blue it will go from bleen to grue. But in the particular example I used it makes no sense to talk of the world going from blue to bleen.

Anyway, here's a way to rephrase your point. I haven't showed that evolution anticipated a switch (or lack thereof) in 2012. True enough. It might not have. What I'm pointing out is that evolution has aparently anticipated an infinitude of events that occurred prior to the present. These events are the lack of switch in color properties at times before now. You may not think a lack of switch is an event, but of course this is only a lack of switch when considered in a particular basis. The fact remains that evolution prepared us not to expect a switch in 1912 or 1812 or 1712... And in each of these cases the evolutionary prediction has panned out.

Date: 2008/12/20 17:52:55, Link
Author: Missing Shade of Blue
Quote

No problem, William Dembski Missing Shade of Blue.


Curses. Foiled again.

In all seriousness though, I am definitely not Dembski, and I hope my rhetorical style has not been Dembskiesque (trans: arrogant, dishonest, dismissive and liberally sprinkled with fart jokes). I get the sense that I'm getting on peoples' nerves here. If that is the case, please let me know and I'll stop it. I don't want to be a troll.

I have an honest problem wrapping my head around the origin of inductive bias. My experience talking to theists in the past has been that many of them have explanatory itches that atheists just do not feel compelled to scratch. For instance, "Why is there something rather than nothing?" I just don't see that as something that needs explanation.

Maybe the line of inquiry I'm pursuing here is a similar phenomenon. Maybe there's an explanatory itch here that I find annoying, but this is just an idiosyncratic feature of my psychology.

And in a further pathetic attempt to bolster my non-ID credentials, you should check out my comments at UD. I've been posting there (sparsely) under the pseudonym Sotto Voce. You will notice that all my comments there have been critical. If I am a Dembski sockpuppet, this is quite an elaborate ruse I've got going.

Date: 2008/12/20 19:28:34, Link
Author: Missing Shade of Blue
Zachriel,

The concern I'm raising here is not epistemological. I'm not asking how we can justify inductive inference. I'm perfectly willing to grant that induction works. To put it another way, I'm not disputing that our inductive biases are the right ones. What I'm asking is how we ended up with the right inductive biases.

So let's take it for granted in this argument that our inductive biases match the world. It is true that all emeralds are (and will be) green. It is false that all emeralds are grue.

Hope this makes things less murky.

Date: 2008/12/20 19:43:11, Link
Author: Missing Shade of Blue
Quote
No, I'm saying the scientific method was developed to minimize the role of bias, such as through the use of multiple observers and other objective measures.


Oh, no doubt the scientific method is set up to minimize (and ideally, perhaps, eliminate) all sorts of biases. And perhaps to some degree scientists try to remove certain types of inductive bias. But inductive bias is unlike many other types of systematic bias in that eliminating it altogether is undesirable. After all, without an inductive bias, learning is impossible.

In fact, specific inductive biases are integral elements of the scientific method. Occam's razor and it's technical statistical counterparts, for instance. Without these tools for deciding which hypotheses are simple, every dataset would be compatible with an infinity of hypotheses with no means of deciding between them. Thank god for inductive bias.

But of course, the fact that we couldn't do science without an inductive bias means the sort of foundational issues raised by the problem of induction are ineliminable. So I question your claim that the problem of induction is more of a problem for naive induction than for the scientific method. It is, in fact, a problem for any learning algorithm.

Still, I am with you that the epistemological issues aren't important here and should be set aside.

Date: 2008/12/20 20:00:30, Link
Author: Missing Shade of Blue
Quote

If the inductive biases of our early hominid ancestors gave them an advantage, it was because those biases in some way reflected the real world. In a relatively consistent universe, it follows that their successful descendants would tend to inherent biases that reflected the real world they lived in.


But what does it mean to say that their biases "reflected the real world." What it is for an inductive bias to reflect the real world is for the bias to allow predictions that match the real world. So the way to check whether a bias reflects the real world or not is to let the organism make a prediction and then wait to see whether the prediction comes true or not. Then maybe eliminate all the organisms whose predictions were false and repeat the process again with the remaining ones, and so on.

Now this explicitly did not happen with homonids. A very small number of possible biases were sampled. One of them was basically selected over the others something like 5 million years ago, and there has been no further selection along this parameter since then. But the one that was selected has worked throughout those 5 million years.

Now I agree with you that this would work if we assumed that the pace of change in the environment would be slow, and maybe evolution had some reason for making that assumption (apologies again for the anthropomorphization). But actually we need to know more than that. A change that is gradual or non-existent under a blue-green representation is radical and discontinuous under a grue-bleen basis. So we need to assume not just that the pace of change is slow, but that the pace of change under this representation rather than that one is slow. And this just returns us to the problem of selecting the appropriate inductive bias.

Date: 2008/12/20 20:20:10, Link
Author: Missing Shade of Blue
Reed,

Picture yourself in the role of evolution. You are presented with a particular phenotype, you look at it, look at the environment in which it lives and decide how fit it's going to be. Its 5 million BC and you're presented with six different types of hominids: blue-green, 1612 grue-bleen, 1712 grue-bleen, 1812 grue-bleen, 1912 grue-bleen and 2012 grue-bleen. Now you look at their environment and assign fitness values to them. You think, "Ah, blue-green should be pretty fit because its picking up on a stable set of properties." Then you look at 1612 grue-bleen and you go, "Oh crap, this looks like a stable set of properties too. At least, given the information I have right now. I'd have to wait till 1612 to figure out which one of them is right. So I guess given what I know now, I should assign this guy the same fitness as blue-green." And exactly similarly for all the others. Of course, successfully approximating the future helps you reproduce, and effects your fitness, but all of these different inductive agents are equally good at successfully approximating the future in their immediate environment. You have no basis for considering one fitter than the other right now.

Come 1612, of course, you say "Ah, now I know 1612 grue-bleen isn't a stable set of properties, so I can reduce the fitness of this guy." But you can only say that in 1612.

But of course, this didn't actually happen. What actually happened is that evolution chose blue-green 5 mya and stuck with it. But if the story I've told above is on the right track, then there is something arbitrary about this choice. It could just as well have chosen 1612 grue-bleen or 1712 grue-bleen or... (if these variations had been available, of course, which they weren't, but that's beside the point). And if it had chosen any of those other traits, that particular lineage of homonids would have been screwed by now. But no, evolution fortuitously bet on the phenotype that has remained unscrewed for all these years.

Date: 2008/12/20 21:02:01, Link
Author: Missing Shade of Blue
How does my parable represent selection as forward-looking? I was trying to deliberately avoid that. In fact my whole point is that the success of our inductive bias cannot be explained adaptively because selection is not forward-looking.

Date: 2008/12/20 23:56:42, Link
Author: Missing Shade of Blue
Quote
This is a terrible way of thinking about it. Evolution doesn't think, doesn't plan, doesn't care how many species go extinct. It's not striving toward some specific goal. It just tinkers and kills. Your burden, if you are going to claim that this is insufficient, is to come up with a specific case where it is demonstrably insufficient. Not a contrived example with no connection to the real world.


OK, I'll admit that I should try to avoid using language that suggests natural selection is an intentional agent. But the point I was trying to make didn't rely on those ill-advised rhetorical flourishes. I really don't understand what you mean when you ask for a specific case where evolution is demonstrably insufficient. I think there is only a specific case where this is true - inductive bias. As far as I'm aware, natural selection is perfectly capable of explaining all other functional traits.

The example I used may be a bit simplified, but is a real world example. The fact that you think otherwise suggests to me that there is something about the example you do not understand. So let me try one more time:

1. Humans have certain inductive biases (in the real world, not some contrived hypothetical world). A particular example is the tendency to think of the color properties of many sorts of surfaces observed under normal circumstances as projectible. My jacket is blue and I confidently project that my jacket will be blue tomorrow. I also confidently project that the next emerald to be found will be green.

2. These biases, considered collectively, are highly functional. They support inferences which allow us to plan and learn about the world successfully.

3. These traits were selected a long long time ago and have remained more or less fixed in humans for at least, say, the past 100,000 years. There have not been significant selective forces altering our most basic inductive biases for at least that long.

4. So biases that were selected for their immediate projectibility over 100,000 years ago remain projectible today. This is by no means unsurprising. There are a vast number of other potential inductive biases that would have been just as fit as the current one 100,000 years ago, but would not continue to track the structure of the world for the ensuing 100,000 years. Somehow, humans ended up with a set of biases that are quite extraordinarily functional.

5. Here are some hypotheses about why we ended up with biases that work today:
(a) Natural Selection. This can't be the answer. By 3, there has not been significant selection for these traits (because there has not been significant variation) in at least the past 100,000 years. So if there was selection for the biases, it happened more than 100,000 years ago. But, like I said, there are a vast number of possible biases that would have been just as fit 100,000 years ago as our actual biases, but would not have been as successful over the next 100,000 years. Natural selection cannot account for why we ended up with our particular bias rather than one of these less functional biases.
But perhaps you disagree that these alternate biases would have been as fit 100,000 years ago. Even though they were as predictively successful as the blue-green bias in that environment, perhaps the argument is that they were not as simple as the blue-green bias, and so imposed extra resource costs on organisms that adhered to them. This is the sort of argument keith was making earlier. See my responses to him and to Wesley on the previous page about how such judgments of simplicity already presume a certain inductive bias. There is, as far as I know, no bias-independent conception of simplicity on which blue-green is the simplest bias. In fact, there is no bias-independent conception of simplicity at all.
Finally, one could respond (as you did) that natural selection selected for the inductive biases that reflect the structure of the world. But selection could only have used information about the environment at that particular time, viz. 100,000 years ago (plus information about past environments stored in the organism's genome). And, like I said, there were a vast number of different biases which reflected the structure of the world at that time but would not have continued to reflect that structure as time went on. None of these biases were selected. The one that was selected is the one that continued to work reliably for the next 100,000 years.
(b) Morphological/Developmental Constraints. Perhaps biochemistry sets constraints on the sorts of inductive agents that can develop, and that explains why we ended up with this particular set of inductive biases rather than some other set. This might well be true, but it does not answer the question. The question is "Why do our inductive biases work so well today?" The answer can't be "Because they are one of the few sets of morphologically feasible biases." That doesn't address the question at all.
© Trivial. This is the response that basically rejects that the question is problematic at all. It's along the lines of "The world is blue and green, damnit, not grue and bleen like in your fantasy scenario. The organisms that evolve will be the ones who see things in blue and green." I hope it's clear now why this sort of response doesn't get to the issue I'm concerned with. I'm not questioning the fact that blue and green are natural predicates. I'm not postulating (as you suggest) some bizarre hypothetical world in which colors change. I'm saying, granted that blue and green are natural projectible predicates, what explains the evolution of organisms (like us) that know this, that have by and large the right sorts of inductive biases. It's a question about the evolution of an actual observable trait in the actual world, accompanied by an argument as to why this question is particularly problematic.

Date: 2008/12/21 00:00:49, Link
Author: Missing Shade of Blue
Nerull,

Quote
Given the way color vision works, blue-green would almost be required to evolve before grue-breen. The eye works by filtering light through different colored pigments, much in the same way digital cameras work - consumer grade cameras have built in filters, like our eyes, scientific grade cameras usually place filters in front of the entire sensor, but still work in a similar manner.

Too add in a timer that swaps around colors at a certain date requires adding on to the existing color vision mechanism. This means that, in order to spread through the population, there needs to be some reason why grue-breen is selected over blue-green. The more complicated something is, the easier it is to break, so this seems unlikely.


I think this is basically the same sort of worry keith had. I wrote a response to him here. Look it over and see if it works.

Date: 2008/12/21 00:21:38, Link
Author: Missing Shade of Blue
Quote

BTW, I don't see that perceptual inductive biases are different in kind than other adaptations. How did embryological bird wings come to anticipate the aerodynamic demands of the current atmosphere? How is it that avian flight evolved tens of millions of years ago in such a way that it anticipated the demands of current atmospheric systems? The answer is that neither did either. I don't see that the evolution of inductive biases, and their success over long periods of time, present a challenge differing in kind from these adaptations.


Hmmm... I see what you are saying. This is sort of like the No Free Lunch stuff. (Hey, maybe I am Dembski!) For natural selection to be a successful search strategy, we already assume that the fitness landscape has certain features, specifically the sort of features that enable NS's own inductive bias to work fairly well (and one of the requisites is probably some sort of cross-temporal smoothness). The case of the evolution of our own inductive bias is really no different. Yes, we have to appeal to evolution's bias to justify our own bias, but that's true for every single adaptation.

That's really helpful. Thanks Bill. I guess I was making a pretty simple mistake. When you put it that way, the explanatory itch kind of goes away. I see nothing problematic about assuming a certain structure to the fitness landscape when discussing other traits, so why this one?

Anyway, I'll have to think about it some more, but for the moment I'm satisfied. Apologies for any aggravation, people.

Date: 2008/12/21 22:53:32, Link
Author: Missing Shade of Blue
Wesley,

1. I am aware of the invariance theorem. You will note that on page 1 I made a post specifically mentioning that if we have two infinite strings, there may well be a language-independent sense in which one is simpler than the other. However, I think it's true that for any two finite strings there is no language-independent way to make qualitative comparisons of algorithmic complexity between them. And that is perfectly consistent with the invariance theorem. Is that wrong?

Perhaps I should not have written the sloppy sentence you quote, suggesting that there is no language-independent sense of simplicity simpliciter, but I do think if you had read my other contributions to the discussion you would have recognized that I wasn't making the specific mistake you charge.

I will look at that universal distribution paper you mention.

2. Also, I don't think my argument was inconsistent (at least, not in that regard). I agreed that our inductive biases are not optimal, but I maintained that it is surprising enough that they are as functional as they are. The fact that you think they have been selected suggests that you agree that they are functional enough to require some sort of explanation

I didn't just dismiss the point about extinction. I mentioned (in a number of posts) that a superexponentially vast number of possible inductive biases were never even sampled. Sure, a large number of species have gone extinct due to bad inductive biases. But that number is still miniscule in comparison to the number of possible biases. In the absence of a plausible search strategy like NS (at least that's what I thought at the time, but see below) I suggested it was very unlikely to hit upon functional biases in so few tries (relatively speaking).

3. We don't have to agree to disagree. At least, not about the larger point of whether or not our inductive biases could be selected. I have already conceded that my question was misguided. This discussion has cleared up the issue for me and I no longer have a problem with evolutionary explanations of our biases. I suspect you haven't been reading all my posts. I don't blame you, considering how garrulous I am. But still, I would hope you would have read everything I wrote before saying, for instance, that I am long on assertion but short on argument.

Date: 2008/12/21 22:59:34, Link
Author: Missing Shade of Blue
Quote
However, I think it's true that for any two finite strings there is no language-independent way to make qualitative comparisons of algorithmic complexity between them. And that is perfectly consistent with the invariance theorem. Is that wrong?


I should qualify this. I haven't yet read the universal distribution paper, and maybe it's the case that it shows that my claim is false. If that's the case I'd be very surprised, though. Don't think I'll get the chance to read it tonight, but I'll definitely look at it tomorrow.

However, I do think that my claim is consistent with the invariance theorem.

Date: 2008/12/22 02:02:33, Link
Author: Missing Shade of Blue
Wesley,

Thanks for pointing me to the universal distribution. It sounds very interesting and I will certainly look into it. I don't want to pretend to have more than a layperson's familiarity with algorithmic information theory. I was aware of the invariance theorem, but I had not heard of the universal distribution before.

I still don't think I've been inconsistent, at least not in a dishonest way. I am probably guilty of qualifying statements I've made in one post in some other post, and also of being sloppy on occasion. I was trying to rapidly respond to a number of different people, and unfortunately rigor was a casualty.

I hesitate to carry this discussion further because (a) I feel like my initial question has been adequately answered and (b) you would undoubtedly mop the floor with me if we argued about information theory. But I do take issue with your response to one of my points:

Quote
The argument that different computers can reduce the size of input data needed to emit a bit string doesn't comport with familiarity with algorithmic information theory, where the computational complexity is defined as the minimal size of input and program that emits a particular string. In the case of the two example strings, a computer program that privileges the second string will be longer than the minimal computer program to emit the first string. That dog won't hunt, in other words. Shifting the complexity from the input to the program (or "computer structure") doesn't -- and can't -- make the complexity go away.


By "computer" I didn't mean the program but the UTM on which the program is run. For any particular pair of finite strings A and B, I can construct a UTM for which the minimal program to output A will be shorter than the program to output B, and I can construct another UTM for which the B program will be shorter than the A program. This is what I was claiming and I still think it must be true. Now maybe one of these UTMs is far more unlikely than the other (assuming some sort of probability measure over the ensemble of all UTMs). But for any two finite strings one could in principle construct a UTM that favored either one of them. Is this wrong?

Date: 2008/12/22 02:05:04, Link
Author: Missing Shade of Blue
Sloppy again. Instead of "Maybe one of these UTMs..." read "Maybe one of these types of UTMs..."

Date: 2008/12/22 12:54:24, Link
Author: Missing Shade of Blue
Quote

It's true that no search algorithm is better than any other, on average, on an arbitrary landscape. But we're not talking about an arbitrarily chaotic universe.


Zachriel, you're right. Bill helped me realize that my question was much broader than I initially thought. It's something along the lines of "Why does the evolutionary learning algorithm have the sorts of inductive biases that allow it to be an efficient search strategy over the sorts of fitness landscapes we see in this world?"

And while that question is interesting and may be worth pursuing, it's not the sort of showstopper I thought it was. What troubled me earlier was that one particular functional trait was apparently not explicable by selection. But that's just because I was perversely refusing to allow, in this particular case, that we could assume that our fitness landscape has certain properties that enable natural selection to perform better than say random search.

I now recognize my perversity, and I'm in full agreement with everything you said in your post.

Date: 2008/12/22 13:20:06, Link
Author: Missing Shade of Blue
Zachriel,

The idea that the search algorithm and the landscape are matched because ultimately they're made of the same stuff following the same fundamental laws is interesting. I hadn't thought about it that way before.

Date: 2008/12/22 13:29:52, Link
Author: Missing Shade of Blue
The speculation about my secret identity is amusing. I don't know whether to be flattered or insulted. I guess I should be flattered that the prime suspects are Dembski and Mike Gene and not, say, Denyse O'Leary or bornagain77.

So thanks for the compliments, and have a great Christmas!

Date: 2008/12/22 13:51:48, Link
Author: Missing Shade of Blue
And to allay your curiosity a little bit, I am but a humble grad student with a non-professional interest in both the scientific and cultural aspects of the evolution/ID debate. My degree is in physics, so I admit I am not even close to an expert on evolution, machine learning or information theory. I have studied philosophy of science quite a bit, so I feel slightly more comfortable pontificating in that area.

I'm an atheist. I think common descent and evolution via natural selection are the best explanations for the origin, diversity and apparent design of species (and, thanks to you guys, that includes inductive biases ;) ). I think all ID hypotheses offered so far are untenable, but I don't think the ID project is deserving of the blanket scorn I sometimes see on this forum (although given the behavior of some of the ID adherents, I can see why one would be scornful).

I like Thai food, mountain biking and noise music. Turn-offs include rudeness and scabies.

Date: 2008/12/22 14:51:03, Link
Author: Missing Shade of Blue
Quote
Yes, but what is your shoe size?


There is a reason I didn't mention this. I'm ashamed. I'm a size 18, which means I can only wear clown shoes.

On the bright side, though, you know what they say about guys with big feet... That's right, if our arms fall off, we can still pick our noses.

Date: 2008/12/22 18:41:52, Link
Author: Missing Shade of Blue
Wesley,

I read the paper you cited. Thanks for pointing me to it. It was clear and informative. But I still don't see how the universal distribution shows I am wrong.

I said that for any two finite strings, there is no language-independent means of determining which has the greater Kolmogorov complexity. Let's take strings s1 = 1010101010.... and s2 = 1000110111.... (where the ellipses indicate the strings are a billion digits long). I can construct a UTM for which the program to produce s1 will be shorter than the program to produce s2. In fact, my laptop is one such UTM.

But I can also construct a UTM for which s2 can be produced by a shorter program. I merely make it part of the UTMs hardware that if the input begins with a 0, it immediately prints out s2 and halts. If its input begins with a 1 it moves on to the next symbol on the tape and proceeds to responds to the rest of the input the same way my laptop does. For this UTM s2 is less complex than s1.

This is a completely general scheme. I can do it with any two finite strings. And it doesn't violate the Invariance Theorem.

Now you suggested that the Universal Distribution would actually provide a language-independent way of deciding whether s1 is simpler than s2 or vice versa. But I don't see how this can be true. According to the paper you cited, the Universal Distribution assigns higher probabilities to strings with lower Kolmogorov complexities. So prior to figuring out what the Distribution will look like, we need to figure out what the complexities of the individual strings are. And there's no language-independent way to do that.

Depending on what UTM we use to make our judgments about complexity, the Universal Distribution will look different. If we use my laptop, s1 will have a higher probability than s2. If we use the baroque computer I constructed, s2 will have a higher probability.

Isn't this right? How does the Universal Distribution help me figure out whether s1 is simpler than s2 independent of the UTM used? I guess I was imagining some way of assigning a distribution not over the strings, but over the ensemble of all possible UTMs. Maybe if we moved up to that level, we can come up with some sense in which one of the strings is simpler (because its complexity is lower on "more" UTMs as determined by our measure). But that's not what the Universal Distribution is.

Anyway, it strikes me that the correct way to approach this problem is not to attempt to articulate a language-independent notion of simplicity but to acknowledge that the particular inductive bias of the evolutionary process sets a natural language. It happens to be a language that works well for the kinds of fitness landscapes we see in nature. Maybe we can come up with a deeper reason for this match between learning algorithm and fitness landscape (I think Zachriel was suggesting that it has something to do with them being made of the same stuff) but I don't even know if that's the kind of thing that needs special explanation. I feel the same way about this phenomenon as I do about the alleged fine tuning of our fundamental constants: "What are the alternatives and how in the world did you get a probability measure over them?" So, as I said before, I'm satisfied.

Date: 2008/12/22 20:35:02, Link
Author: Missing Shade of Blue
Quote
Then you haven't reduced the complexity, you've simply shifted it from the software to the hardware.


But this just begs the question. In what sense is the second UTM more complex than the first one? Is this sense language-independent?

Quote
How do you think this helps you, particularly if you're trying to establish an analogy with natural selection?


I wasn't trying to argue from analogy here. I was trying to argue that in principle there is no description language-independent notion of simplicity. This was supposed to be an argument against those who were saying that green really is simpler than grue in some objective sense.

I moved the discussion up to the complexity of the computers themselves in the first post I made on this thread. This was in response to those who were suggesting that although green may not be simpler than grue in purely linguistic terms, green-computers would be simpler than grue-computers.

Date: 2008/12/22 22:43:06, Link
Author: Missing Shade of Blue
Quote
In terms of the number of two-input NAND expressions required to describe a minimal Boolean implementation.


OK, what you've done there is chosen a specific description language. I agree that once you do that you can straightforwardly quantify the complexity of your computer/string/whatever. But then this quantification isn't language-independent. It's relative to a choice of natural predicates.

Maybe this is leading back to what you were initially arguing: we shouldn't be restricting ourselves to purely syntactic notions of complexity because there's a natural physical notion of simplicity when we're considering material objects. I offered a response to that on the first page and I still stand by most of that response more or less.

Just to be clear though, I'm no longer interested in defending my argument about how inductive biases couldn't evolve. That argument is flawed. In so far as it's valid, I think it just collapses into a general Humean inductive skepticism, and that way leads to pointlessness. So yeah, nothing I say here from now on should be construed as a criticism of evolutionary biology.

I do still stand by the claims I was making about the lack of a language-independent syntactic notion of simplicity. Wesley apparently disagrees. He suggested that the Universal Distribution provides such a notion. I don't see how that can work. Appealing to a measure of simplicity that relies upon a particular way of describing a UTM (the number of NAND expressions, in your case) is no help.

Date: 2008/12/22 23:01:02, Link
Author: Missing Shade of Blue
Keith,

I made it sound in the last post that there is no workable notion of physical simplicity. But I don't think that's true. I think some things are made out of more basic parts (and types of parts) than other things. But whether or not the syntactic simplicity of our descriptions tracks the physical simplicity of objects depends on whether our language (more generally, our set of inductive biases) carves nature at the joints. While I'm usually happy to assume that it does, I was resisting the idea that we can make this assumption when we're trying to account for the origin of those biases themselves. This was why I thought your physical simplicity proposal was question-begging. Since then, I have come to accept that there's no special problem with assuming our inductive biases are accurate when attempting to explain them. So I no longer think your proposal is question-begging.

However, the context of this discussion with Wesley is different. Here I'm responding specifically to his charge that I was wrong when I said that algorithmic information theory does not have the resources to adjudicate the relative simplicity of two finite strings without first assuming a natural language (which amounts to assuming a particular construction for the UTM). Appealing to the actual physical structure of the world we live in in order to privilege one sort of UTM over the other transcends algorithmic information theory, which is a purely syntactic measure of complexity.

Date: 2008/12/22 23:13:04, Link
Author: Missing Shade of Blue
Nerull,

If you look at my response to Keith here, you'll notice that I am not arguing that:

Quote
a color filter and a photon detector is not simpler than a color filter, a photon detector, a biological timer that is set to go off at some distant point in the future, and an input inverter


What I was arguing in that post was that to assume that a grue detector would need that more elaborate construction is already to assume the correctness of your inductive biases. Without appealing to those biases, you do not know if a simple device made up of a filter and a photon detector detects green or grue.

So the enhanced physical complexity of a grue detector is a red herring. A grue detector would only need to be more physically complex if grue were not a projectible predicate. But that is just to assume what needs to be proved.

I find myself in the oddly schizophrenic position of going back and defending the few valid pieces of my argument which I now recognize is globally invalid. I think I still agree with most of what I wrote above except the last bit: "But that is just to assume what needs to be proved." In the context of the inductive bias discussion, I no longer think its out of bounds to begin with the assumption that green is projectible and grue isn't.

I do however still object to the notion (if anybody is defending it) that one can show green to be projectible without taking for granted our (or, more appropriately, evolution's) inductive biases.

Date: 2008/12/23 13:11:54, Link
Author: Missing Shade of Blue
Bill,

Your argument already assumes a particular inductive bias. You say that the grue-bleen perceptual system would have to have at least two components: one that allows it to detect blue-green in the current environment and another that somehow anticipates a switch in 2012. The first component would be subject to normalizing selection before 2012 but the second wouldn't and so it would become non-functional, leaving regular blue-green systems with no switch mechanism.

The assumption here is that grue-bleen has to have this multi-component structure but blue-green does not. Why? Because grue-bleen involves a switch to different properties but blue-green does not. But that is only true in the blue-green basis. If you represent the situation using grue and bleen as natural predicates, then it is the blue-green system that is preparing for a switch. Prior to 2012 both systems are subject to normalizing selection to ensure that they can adequately track grue and bleen (and remember, in this basis, grue and bleen are not weird cross-temporal disjunctive properties but merely the properties things have at a particular time), but the blue-green system has an extra component that anticipates the switch in 2012 from grue to bleen and vice versa. This component is not subject to selection and will deteriorate.

So the idea that grue-bleen is temporally disjunctive while blue-green isn't (which lead to the idea that grue-bleen requires multiple components, including some kind of timer) assumes that prior to 2012 evolution naturally works in the blue-green rather than the grue-bleen basis. And this is an appeal to a particular inductive bias. But again, I no longer thing appealing to evolution's own inductive bias in this matter is problematic, so your analysis does work. However, it would not work if we were actually refraining from privileging any particular inductive bias.

Date: 2008/12/23 13:33:30, Link
Author: Missing Shade of Blue
Quote
My metric -- the number of two-input NAND expressions required for a minimal implementation of a particular UTM -- does not depend on the physical structure of the world.  It depends only on Boolean logic.

Please tell me you're not asking us to consider worlds where Boolean logic doesn't hold.


You misunderstand me. I was not suggesting that you needed to refer to the physical world to justify your appeal to Boolean logic. But you chose a specific basis in which to express Boolean expressions: the NAND basis. On this basis computer 1 will turn out to be simpler than computer 2. However, the NAND basis is not the only one that spans Boolean space. Or, to put it differently, the NAND gate is not the only universal logic gate. Trivially, there's also the NOR gate. So your choice to represent the implementation in terms of NAND rather than NOR (or for that matter, in terms of AND, OR and NOT) is a choice of description language.

You might say, "So what? Computer 1 will be simpler on these other representations as well." But NAND and NOR are not the only two universal gates. They are merely the simplest ones (relative to our inductive biases). One could construct universal gates (or sets of non-universal gates that collectively span Boolean space) that would look extremely elaborate when translated into NAND representation. Can you guarantee that computer 1 is simpler in every one of these bases? I would be very surprised if it were. For instance, consider the entire Boolean description of computer 2. It might turn out that this whole description is a universal gate (unlikely, maybe, but not impossible). If that were the case, then on that representation computer 2 would be simpler than computer 1. So the choice of NAND as the preferred representation is a choice of a particular language.

I assumed you were trying to justify the choice of NAND over NOR or the even more grotesque universal gates by appealing to the physical simplicity of constructing a NAND gate as opposed to one of these others. That's why I brought physical simplicity into the discussion. But as long as we're talking purely formally, I don't see why one should prefer NAND to one of the many other possible Boolean representations.

Date: 2008/12/23 14:03:38, Link
Author: Missing Shade of Blue
Quote

I've only a moment, but think about what you have predicted:

You've predicted that just one of these variants will be evident.  

Not because of evolutionary prescience, but because of the action of selection.


I'm really not sure what you're saying here. But let me try to clarify my view. In crude terms, there are two aspects to the blue-green (or grue-bleen) inductive system. There's the detection system and there's the response system. Now the supposition is that the detection system is identical for blue-green and grue-bleen creatures. It's not that one of them has a more elaborate system made up of multiple filters and timers or whatever. No, they both have the same detection system.

Now if we are being truly neutral with respect to these inductive biases, we must concede that we do not know if this detection system detects grue or green (i.e. we do not know whether the detector gives stable output when presented with grue or green input). Given its performance so far, it could be either one. We'll only find out for sure in 2012.

Now where the creatures differ is in their response systems. The blue-green creatures respond to particular detections with green-type expectations about the future. The grue-bleen creatures respond to the same detections with grue type expectations about the future. Given that their detection systems are identical, one of these creatures is going to be surprised come 2012 because its expectation system does not match its detection system. Its expectations will diverge from its detections. Again, without assuming an inductive bias ourselves, we cannot predict which creature will be surprised.

Now my claims were that: (a) These creatures are, ceteris paribus, equally fit prior to 2012. (b) There's no obvious sense in which one creature has all the components of the other plus some more. They have the same detection system and different response systems. Both of these systems will be subject to selection (against other such systems) prior to 2012, but they remain neutral relative to each other until 2012. There is no exploitable asymmetry here until 2012.

So given this description, in what sense have I predicted that "just one of these variants will be evident"?

Date: 2008/12/23 14:21:55, Link
Author: Missing Shade of Blue
Quote

First you asked us how it was possible for natural selection to settle on a blue/green inductive bias when, according to you, a grue/bleen bias would have been equally valid.

Now you're telling us that the choice of inductive bias makes no difference.  In a grue/bleen world, a grue/bleen detector has exactly the same structure as a blue/green detector in a blue/green world.  Natural selection gets it right either way by producing the simpler design.


Keith,

See my response to Bill. I think the crucial point here is that there is a difference between inductive biases and the perceptual system. These are two different cognitive capacities. Saying the detectors have the same structure is to say that the perceptual system is the same. But the inductive biases can still be difference. So the choice of inductive bias makes a difference, but it makes a difference to what the organism expects/predicts, not to what it detects.

Date: 2008/12/23 17:28:52, Link
Author: Missing Shade of Blue
Keith and Bill,

My understanding of Bill's point is that he thinks the grue-bleen inductive agent must have all the same components as the blue-green agent plus something extra. This extra something is not subject to normative selection, so it will eventually deteriorate, leaving a regular blue-green agent. If we redescribe the situation in grue-bleen terms, then the verdict just reverses. Now it is the blue-green agent who has the something extra, and so she will eventually be whittled down to the grue-bleen agent (well, not literally her, but her descendants).

In either case, we will end up with the same sort of agent. Anything that could distinguish blue-green agents from grue-bleen ones must be some kind of idle non-adaptive dangler prior to 2012, so its going to disappear. Is this an accurate paraphrase of your argument, Bill? Now I hope you'll bear with me. The next section is kind of long, but I wanted to make sure the issues involved are clear. I feel like all of us are talking past each other a little bit.

--

Now I think that there is no reason to think the response systems of the two agents must be additively related in this way. Let me give an example of a really simple blue-green inductive agent. When it sees a bunch of emeralds (pre-2012) it forms the belief "Emeralds are green." What I mean by "forms a belief" in this context is cashed out completely in terms of the following stimulus-response behavior.

The agent can bet a certain amount of resources for or against certain questions posed to it by some external tester (a proxy for the environment). Here are the responses to some questions:

"Will emerald x be green?" - Bet on yes.
"Will emerald x be blue?" - Bet on no.
"Will emerald x be grue?" - If x is discovered prior to 2012 bet on yes, else bet on no.
"Will emerald x be bleen?" - If x is discovered prior to 2012 bet on no, else bet on yes.

Now we have a grue-bleen agent. When faced with the exact same initial set of data as the first agent it forms the belief "Emeralds are grue," cashed out in terms of this response table:

"Will emerald x be grue?" - Bet on yes.
"Will emerald x be bleen?" - Bet on no.
"Will emerald x be green?" - If x is discovered prior to 2012 bet on yes, else bet on no.
"Will emerald x be blue?" - If x is discovered prior to 2012 bet on no, else bet on yes.

Note that both these agents are formally identical, but they differ in their semantic properties: they respond differently to different external stimuli. One of them will start losing resources in 2012.

Now if Bill is right, one/both of these agents has an idle dangler in its response system that will deteriorate before 2012. In this case, the formal identity of both agents means that if one of them has this dangler the other will too (there's no reasonable sense in which the response system of one of these agents is a proper sub-part of the response system of the other). And the plausible candidate for the dangler is the difference in their responses to grue and green questions. This difference will only manifest after 2012, so prior to that it is not subject to normative selection (on Bill's story). This difference in the responses will be whittled away until we are left with creatures who are neutral with respect to these inductive biases, which means they either: (a) make inconsistent bets post-2012 (betting yes on both green and grue for instance), (b) refuse to bet on post-2012 emeralds, or © develop some sort of probabilistic betting strategy that weighs both biases equally (so maybe half the population bets on green and the other half on grue).

But all of this relies on a premise: The part of the inductive bias that has to do with grue/green differences is purely additive. Removing it doesn't affect the functioning of the rest of the system. This is a big big assumption, though. It is quite possible that the cheapest sort of response system does distinguish grue and green. In other words, the cheapest way to buy inductive success in the present might involve committing the system to one particular inductive bias in the future. And it might be the case that while the cost of both the blue-green and grue-bleen inductive systems is equivalent prior to 2012 (by hypothesis), they are both cheaper than the sort of inductive system that does not choose between the biases.

Now even if you accept all this, you might say, "OK, so maybe it is possible that it's cheaper to have an post-2012 inductive bias rather than none at all. But it's still going to be the case that only one of these biases will survive. By hypothesis, the grue-bleen trait is neutral relative to the blue-green one, so we expect one of them to go to fixation just by random drift." But this is only relevant if the blue-green and grue-bleen populations interbreed. I agree that we should expect a uniform inductive bias within a breeding sub-population.

Date: 2008/12/23 17:32:08, Link
Author: Missing Shade of Blue
A quick correction: In the previous post when I was considering the two simple agents I said that the difference between them will only be manifest post-2012. I should have said that the difference between them will only have adaptive consequences post-2012. There will be observable differences between them before then. They'll both make different predictions about what will happen after 2012, for instance.

Date: 2008/12/23 17:57:53, Link
Author: Missing Shade of Blue
BTW, I apologize to all the people I haven't yet responded to. It's not that I'm ignoring your posts because I think they're stupid (or, conversely, unanswerable). I'm posting stuff on here in between bouts of trying to get a chapter of my dissertation ready. I'm already spending way more time on here than I probably should, so you'll excuse me for shying away from becoming embroiled in more than one discussion at a time. Although so far I haven't done such a great job in the shying away department.

Date: 2008/12/23 21:57:32, Link
Author: Missing Shade of Blue
Quote

The simplest possible blue-green system shaped by "experience" (selection) in an exclusively blue-green world would lack the facilities to make the "if date < 2012 then predict green else predict blue" decisions you describe. Hence it is not formally equivalent to the grue-bleen system you subsequently describe, does does need something equivalent to an if-then-else decision logic that tests the date prior to every prediction. Which facilities are the very "dangler" you describe, features that must be lost even in a grue-bleen world because invisible to normalizing selection prior to 2012.


This is the part I disagree with. You think that there is something about the world being blue-green that will make blue-green inductive agents simpler than grue-bleen ones, prior to 2012 (grue-bleen agents would need an extra dangler). Presumably you also agree that if the world were actually grue-bleen then grue-bleen agents would be simpler than blue-green ones prior to 2012.

But what does it mean for the world to be blue-green vs. grue-bleen? It just means that "blue" remains a stable and lawlike predicate (and mutatis mutandis for grue). Things that are naturally blue do not change their color discontinuously and without cause. But if this is all it means for a world to be blue-green, then we could change a blue-green world to a grue-bleen world without changing anything that happens before 2012. Just switching the colors of objects post-2012 without touching anything before 2012 should give us a grue-bleen world. In other words, we can have a grue-bleen world and a blue-green world that look just like each other up to 2012 and only differ afterwards. Right? Seems right to me. But you say it's wrong.

According to you, you can't change a blue-green world to a grue-bleen one without changing some stuff prior to 2012. Namely, you have to change the construction of inductive agents, because you don't think we could end up with simpler grue-bleen creatures in a blue-green world and vice versa. Which means you think that information about the natural structure of the world (whether its blue-green or grue-bleen) is available prior to 2012. I don't see how this could be the case (if we don't assume the correctness of our or evolution's inductive biases).

Properties don't come tagged with labels reading "this is natural". The naturalness (at least, the projectibility) of green vs. grue consists solely in how objects behave after 2012. In a naturally green world they stay green, while in a grue world they switch to blue. So it seems to me that you must either maintain that green creatures must be simpler than grue ones independently of the structure of the world (its blue-greenness or grue-bleenness), in which case we're back to the question of a language-independent notion of simplicity. Or you should agree that there is no obvious reason to think that blue-green creatures will be simpler even in an exclusively blue-green world.

[Here's where I go schizophrenic again. While I think its wrong to say that blue-green creatures will be favored in a naturally blue-green world, it is correct to say blue-green creatures will be favored in a world where the evolutionary algorithm has a blue-green inductive bias. There's no non-biased reason to thing the bias of the algorithm must track the structure of the world, but that's just the general Humean problem of induction, which is why I abandoned that line of inquiry.]

Date: 2008/12/23 22:09:46, Link
Author: Missing Shade of Blue
I note with dismay that we've crossed 100 posts on this thread. I've really been posting way too much so I'm going to try to cut back and get some actual work done. I'm going to read what people have to say and I might be irresistibly drawn to respond, but this is my official request not to be offended if I don't reply for a while. Discussing this has certainly been illuminating and enjoyable for me, and I appreciate y'all being gentle. I came in to this deeply puzzled and I leave significantly less puzzled. That's a lot more than you can reasonably expect from your usual internet forum discussion. Have a great holiday season, everybody. I hope baby Jesus brings you lots of presents.

Date: 2008/12/24 14:19:47, Link
Author: Missing Shade of Blue
Keith and Bill,

Yeah, I see the point about the quasi-grue/bleen world. If we change the properties of the external world and the structure of the agents at the same time we're creating a world that is not detectably different from our own. In fact, it's basically just redescribing our own world using a different set of predicates.

I should have been tipped off by the formal equivalence of the two inductive agents I described. If they're truly formally equivalent then the best way of describing the situation is not that theyre picking out different properties but that they're using different languages (which are grue/green inverts of each other) to pick out the same properties.

So yeah, I accept that true grue-bleen agents, ones who make materially different predictions post-2012, would have to be structurally quite different from blue-green ones. Would they have to be more complex? This is the tricky part for me. Whatever their construction, there will be some representation in which it will be simpler to describe the grue-bleen agent. There is no purely syntactic sense in which this representation is unnatural. But maybe there is a physical sense in which it would be unnatural. Possibly such a representation would carve up physical objects in ways that are just objectively complex. I'll think about it.

But yeah, I was on the wrong track, so thanks for pointing that out and being patient.

Date: 2008/12/24 17:58:37, Link
Author: Missing Shade of Blue
Keith,

I don't know if I want to go into too much detail about it, but I would be happy to give a broad description of my work. The dissertation is in the foundations of statistical mechanics. Slightly more specifically, I'm investigating the physical grounds for the success of phase averaging (the process by which thermodynamic quantities are calculated by averaging over functions on phase space under some probability distribution). The textbook justification for this is ergodicity (crudely, the idea that thermodynamic systems follow a trajectory that passes arbitrarily close to every point in phase space), but that is unsatisfactory for a number of reasons, so I'm exploring the possibility of a non-ergodic approach to the foundations of the theory.

Date: 2008/12/25 14:36:52, Link
Author: Missing Shade of Blue
Oleg,

I absolutely agree that phase averaging works very well. But I don't think the ergodic hypothesis is an adequate rationale for the procedure. We can only prove ergodicity for certain special systems (hard spheres in a box, geodesic motion on a manifold with negative curvature). We don't have proofs of ergodicity for virtually all the systems to which we usually apply classical stat. mech. In fact, there's good reason to think many of these systems are not ergodic. The KAM Theorem leads us to expect that a typical Hamiltonian system with finite degrees of freedom will contain islands of non-ergodic flow. Less abstractly, phase averaging works for a number of systems that we know contain KAM tori. The explanation for the success of the procedure in this case cannot be explained by the ergodic theory as traditionally conceived.

There are also conceptual problems with the way ergodicity is used to justify phase averaging. We need an explanation for why our macrosopic measurements of thermodynamic quantities match the phase average. The traditional justification for this is that our macroscopic observation times are so long relative to characteristic microscopic time scales that we might as well consider our macroscopic observations as infinite time averages which, for ergodic systems, are just phase averages. To my eyes, at least, this sort of justification is almost laughably ad hoc. One obvious problem: if macroscopic measurements really approximate infinite time averages, how could we ever observe a system going into equilibrium?

There is a more plausible (although, mysteriously, less widely quoted) justification. One can prove, using Birkhoff's theorem, that if a system is ergodic then the only invariant probability measure over the phase space (meeting some further trivial criteria) is the microcanonical measure. And, if the system is large enough, then in equilibrium there is an overwhelmingly large probability (under this measure) that the system is at a phase point where thermodynamic quantities are very very close to phase averages. No appeal to time averages at all. Unfortunately, this argument doesn't work at all if there are any non-ergodic regions in phase space that are greater than measure zero. Even if the phase space contains a really really tiny non-ergodic island, one can no longer prove that the microcanonical measure is the unique invariant measure. So again, this justification, which is quite elegant, unfortunately only works for a very very restricted set of systems.

So yeah those are some of the reasons I think ergodicity is a red herring.

Date: 2008/12/25 14:49:02, Link
Author: Missing Shade of Blue
Cubist,

Perhaps this sort of speculation is just mental masturbation. But since there was more than one person involved in the discussion, doesn't it qualify as mental sex? Or at least a mental circle-jerk.

Date: 2008/12/26 03:39:07, Link
Author: Missing Shade of Blue
Oleg,

I certainly don't want to argue that ergodic theory is useless in physics. I am merely criticizing its use in one particular area: the justification of the phase averaging procedure.

I do have a slight quibble with the notion that glass "becomes non-ergodic" at low temperatures. The phrase suggests that the system in its high-temperature equilibrium state is ergodic, and that it loses this ergodicity when it freezes into a glass state. But there is no reason to believe that the equilibrium state is ergodic if you reject the standard stat. mech. assumption that thermodynamic equilibrium implies ergodicity.

No doubt the low-temperature state is in some sense "more non-ergodic" than the high-temperature state. Regions of phase space that were mutually accessible become separated as the glass cools, and the final frozen state is conspicuously path-dependent. So "ergodicity breaking" is an important phenomenon. But calling it that might give the false impression that the original state was ergodic in the full technical sense, and this need not be true (and probably isn't true for most real glass transitions). The relevant transition is not from ergodicity to non-ergodicity, but from a stable global equilibrium to a metastable local equilibrium.

Date: 2008/12/26 04:23:27, Link
Author: Missing Shade of Blue
Oleg,

I'm assuming you're a physicist. What area do you work on, if you don't me asking?

Date: 2009/10/18 18:05:35, Link
Author: Missing Shade of Blue
Quote
Does Jaynes really think that observing one hard diamond after another doesn't strengthen the hypothesis that all diamonds are hard?


I haven't really posted here in a while, but I cannot resist the opportunity to defend Jaynes' honor. The idea is that whether or not a particular instance of a generalization confirms the generalization depends on background knowledge. Good's two worlds example illustrates this, but here's a simpler example.

A chemist friend of mind is out in the field investigating whether all diamonds are hard. He agrees to inform me about the result of his investigations using the following code: if he discovers a diamond that is not hard, he will send me a hard diamond in the mail. I get a hard diamond from him in the mail, and (appropriately) take that as strong evidence against the generalization 'all diamonds are hard'. An instance of the generalization disconfirms the generalization.

The example might seem silly, but the point being made isn't. The degree of confirmation of a particular hypothesis by some evidence is always relative to a set of auxiliary hypotheses about the world. In Hempel's raven paradox, a black raven is more confirmatory than a yellow banana only given a number of auxiliary hypotheses, including the assumption that the sampling procedure is random and the base rate of ravens in the population of interest is smaller than the base rate of non-black objects. You can always find auxiliary hypotheses relative to which a yellow banana would actually be more confirmatory. You could even find auxiliaries relative to which a black raven would be disconfirmatory.

Date: 2009/10/19 00:31:54, Link
Author: Missing Shade of Blue
The dissertation is nearing completion, thank god. Hopefully just another few months, and I'll be the proud (and probably unemployed) holder of a doctoral degree.

I mostly agree with what you're saying here, Keith. The example I gave was merely in response to your claim that it is absurd to think that an instance of a hypothesis does not in general confirm the hypothesis. Under certain auxiliary assumptions, an instance can disconfirm the generalization.

As for the rest, I'm with you. It is in fact a straightforward consequence of Bayes' theorem that a yellow banana confirms the hypothesis "All ravens are black" given natural assumptions about sampling. And you're right, I shouldn't have said the sampling procedure has to be completely random. But there are constraints on sampling, and this is partly what I meant by auxiliary assumptions being essential. Here's another example: Suppose my lab assistant is collecting samples for me, and I know she's a bit scientifically dishonest. She will never collect a sample which falsifies the hypothesis. Out of all the samples that don't falsify the hypothesis she picks randomly. Suppose she goes into a room that I know contains a million ravens and two bananas, in order to pick a sample for me. She comes out carrying a yellow banana. Given my auxiliary assumptions about her sampling procedure, I should actually drastically reduce my credence in the hypothesis. She probably would not have brought me a banana unless almost all the ravens in the room were not black. So yeah, while the assumption of random sampling is unnecessarily, some constraint on sampling is necessary in order for any evidence to count as genuinely confirmatory.

Date: 2009/10/19 00:48:50, Link
Author: Missing Shade of Blue
Keith:

Quote
Any potentially falsifying observation that turns out not to falsify the hypothesis has strengthened it, because there is now one less opportunity for it to be falsified.

As far as I can tell, the only necessary background assumptions are these:

1. Valid falsifying observations are possible in principle (though they won't be possible in practice if the hypothesis turns out to be true).
2. Nothing (including our own behavior) is systematically preventing such valid falsifying observations from taking place.


These are not the only necessary background assumptions needed for your general claim to be true. Think of Good's example again, except make it slightly less fanciful. Suppose my background theory tells me that if there is any species where all the organisms are black, then for some reason it cannot grow beyond 500 organisms. On the other hand, if some but not all the members of a species are black, it will grow to at least a million organisms. I also know that there are at least 100 million birds in the world, and they are randomly distributed (i.e. species are not geographically localized).

I decide to test the hypothesis "All ravens are black." I step out of the house and the first bird I see is a black raven. What does this do to my hypothesis? Plausibly (given some further natural assumptions) it disconfirms my hypothesis. If all ravens were indeed black, then it would be incredibly unlikely that a randomly sampled bird is a raven. On the other hand, if some ravens are black but all of them are not, then it's not that unlikely. Given my background theory, the observation of the black raven, a potentially falsifying observation, neither falsifies nor strengthens my hypothesis. It weakens my hypothesis. And this is the case even though I have not violated either of the two background assumptions you regard as sufficient.

Date: 2009/10/19 01:12:50, Link
Author: Missing Shade of Blue
Quote
I agree. That's why I specified the following in my reply to Erasmus above:

2. Nothing (including our own behavior) is systematically preventing such valid falsifying observations from taking place.

The case of the dishonest lab assistant clearly violates this stipulation.


Agreed. I made that post before I read your response to Erasmus. But what do you think about the example in my next post?

Date: 2009/10/19 01:50:09, Link
Author: Missing Shade of Blue
Quote

So to my two conditions you would have to add a third:

3. You possess no background information whereby certain non-falsifying observations would actually weaken the hypothesis more than they strengthen it.


And with that third condition, you and I (and Jaynes) are in agreement. That's all I was trying to say really, that for instance confirmation to work, the background information (or, as I put it, auxiliary assumptions) need to cooperate.

Of course, once you have a condition as broad as 3, I begin to wonder whether you're not approaching triviality. Isn't 3 pretty close to "Observations of this type strengthen your hypothesis unless they don't"?

I think the way to go is to abandon Hempelian instance confirmation entirely and just be a straight-up Bayesian. With Bayes' rule you're guaranteed to be updating your beliefs rationally without having to make all sorts of caveats.

BTW, to anyone interested in this sort of stuff I highly recommend Jaynes' "Probability Theory: The Logic of Science". Not easy going, but the most subtle and enlightening text on probability/statistics I've ever read. I recommend it especially to Fisherians. Hypothesis testing, like instance confirmation, works well enough for most of the purposes to which it's applied, but conceptually it's a mess.

 

 

 

=====