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Author
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Topic: Responses to Criticisms of Specified Complexity
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Micah Sparacio
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Member # 6
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posted 01. May 2003 20:43
In the Cataloguing Criticisms of Specified Complexity thread, we listed several critiques of the utility and theory of Dembski's notion of specified complexity.
I'd like to see this new thread accomplish two things. First, I've set up a poll so that we can narrow down the most potent criticisms. Second, I'd like to see a discussion develop around these criticisms. How can they be developed, which are the most important, etc. For those who would like the challenge, feel free to offer up responses to various criticisms.
Below I've listed the critiques from the previous thread (without any editing to remove duplicates and summarize...sorry).
C1: Theoretically compelling but too stringent on the UPB to be scientific useful. Too much effort put into keeping out false positives. In order to be freely applied scientifically, some effort needs to be put in to testing a scientifically useful Probability Bound.
C2) Imprecision of definition. On the one hand, Dembski defines complexity as being the reciprocal of the probability of something occurring via natural processes. Irrespective of the problems with this definition itself (see below), complexity is also used, by both Dembski and others, as referring to a measure of a state of an entity or event that is is independent of its history. For definition 2, one should theoretically be able to just look at the intricacies of the parts and their relationships of something and decide that it exhibits complexity, but for definition #1 one needs to know the history of the object. This confusion, and arguments which slide between the two meanings, is a major problem.
C3) Lack of measurability. There are no empirically useful measures for either of the definitions above that are applicable to biology. As I and others have argued, measurable and reproducible methods for establishing biological complexity (in either sense) need to be established such that they can reliably be applied to a full spectrum of phenomena - from those things we feel certainly are not complex in either sense to those that might be complex in the designed sense. No such procedures have been offered.
C4) Over-reliance on analogy. Almost all the arguments and examples of specified complexity rely on analogies with non-biological things: mousetraps, combination locks, outboard motors, etc. Analogies may be useful for understanding or stimulating thought, but analogies prove nothing. Only when the analogous aspects are tested against the true nature of the object of the analogy can one decide whether the analogy is apt or not.
C5) Over reliance on philosophical arguments without empirical content. For instance, the many versions of the “nature can’t create new information” arguments fail to ground themselves in empirically useful definitions or provide empirically useable procedures. (This is a more general problem that encompasses both points a and b above.) Philosophy, metaphysics, and theology are important fields of thought, but for them to actually lead to scientific knowledge, they must eventually connect with empirical data.
C6 A similar set of concerns apply. There are no empirical, reproducible definitions or procedures for determining specificity in a biological context. Almost all arguments are based on things like throwing dice and scrabble pieces. Arguments from analogy abound - a flagellum is like an outboard motor, so its specified, but some reason the fact that a river system is like a plumbing system doesn’t lead to the same conclusion about the rivers. In general, specificity when applied to biology always looks to me like drawing the target around the arrow.
C7: Dembski's original formulation of the CSI (complex specified information, i.e. specified complexity) argument was to:
(1) rule out chance causes (which can only produce small amounts of "specified information" -- the definition of this is difficult but we can think of it as a e.g. "functional DNA changes with a probability of random occurence greater than 10^-150"),
(2) rule out regular causes (which can only transmit "specified information", not increase it), and
(3) If (1) and (2) were successful, conclude design.
However this failed to rule out the very important possiblity of variation + natural selection, a combination of chance & regularity, which could randomly generate small amounts of specified information via chance and then preserve them (on average) via selection. Thus even hundreds or thousands of bits of SI (at some point we pass the 10^-150 random-generation-probability limit and reach CSI) could be generated by gradual accumulation.
To patch this hole, Dembski turned to Behe's concept of Irreducible Complexity. The beginnings of this are seen in his book Intelligent Design and IC is emphasized further in No Free Lunch. IMO Dembski's SC argument is in fact entirely dependent on the IC argument.
So C7 is: Dembski's SC argument boils down to Behe's IC argument, thus the SC argument adds nothing to the debate.
C8 is that the IC argument has been subject to a number of severe criticisms, especially regarding indirect evolutionary pathways. In recent articles Dembski seems to have been hedging his bets by saying that even if convincing evolutionary pathways to IC/SC were found (to his satisfaction) that the SC would still somehow imply design via obscure means (front-loading the fitness function, but conceiving this in practical ecological terms is difficult).
Summary of C8: Dembski having an emergency backup design scenario in case it turns out that IC/SC can evolve removes the SC-->ID argument from being falsifiable even in principle.
C9: Misuse of an inductive argument by the assertion of no false positives.
As I understand it, specified complexity as used in the filter guarantees no false positives. But the argument is inductive in nature, i.e. it relies on the possibility of sweeping the field of all chance, regularity, and chance+regularity scenarios, without examining each in detail beyond what is required to assign a probability to the scenario. Nothing in this process guarantees that some highly unlikely natural scenario might not in fact, occur and be mis-identified by the filter.
C10: One thing that can be said in favour of the definition of "specified complexity" is that it is detailed. To check if the definition is satisfied, one must specify a sample space, the set of hypotheses to be eliminated, the event under study, the specification, the value of the rejection function everywhere on the sample space, and background knowledge which "explicitly and univocally" identifies the rejection function. In practice, Dembski does not take his own definition seriously and in none of his examples has he provided the details needed to verify that the definition is satisfied. It is symptomatic that Dembski failed to specify any of these details in his analysis of the flagellum.
C11: The term "specified complexity" is a redundant, obfuscatory middle-man that serves no non-rhetorical purpose (it is apparently the name of the state of affairs that someone has sucessfully eliminated a set of non-ID hypotheses using the Explanatory Filter). It adds nothing to the actual argument, but it invites equivocation with other concepts with the same name (e.g. Paul Davies's concept) and with intuitive concepts of "complexity" that lack any a priori connection to specified complexity. Dembski also seems to equivocate between specified complexity w.r.t. to a uniform probability assumption and specified complexity w.r.t. all known natural causes.
C12: I have not checked all the relevant publications, but to the best of my knowledge at most one person has been able to apply Dembski's concepts and methods to a real example, namely Dembski himself. It's been something like five years the methods were first formulated and only one real application (the flagellum calculation) has been published. That no one except its creator has been able to apply the method and concepts, not even to simpler non-trivial real-world cases than the origin of flagella, is clear testament to its lack of scientific utility in its current state.
C13: The form of the Explanatory Filter gives ID a free-ride by asking us to accept a general "ID hypothesis" without evaluating the merits, or lack thereof, of this hypothesis. It also assumes the existence of a sharp dividing line separating non-intelligence and intelligence. Hypotheses involving intelligence are to lumped into the general ID hypothesis and protected from being subject to critical evaluations of their merits. This assumption is made without a definition of "intelligence".
C14: The definition of the concept of "specification" is so subjective that specifications, like the appeal of painting, are in the eye of the beholder. To establish that something is a "specification" all you do (and can do!) is to assert that you have background knowledge that allows you to explicitly and univocally identify a superset of the event in question without recourse to the event, and hope that the rest of the world believes you.
C15: The Universal Probability Bound is a reasonable estimate iff the definitions are strictly adhered to and intelligence is not as magical as Dembski assumes. This means, among other things, that one must be sure to specify the rejection function on the entire sample space. Since the definitions are not strictly adhered to in practice, there is no reason to think that the UPB is an underestimate of the appropriate probability. In Dembski's terminology, vagueness translates to lots of specificational resources. Regarding intelligence, we must assume that the intelligent agent that applies Dembski's method is not sufficiently magical and creative to (e.g.) come up with a specification for every observed event, whatever it is. If intelligent agents can escape the implications of the NFL theorems for learning/inference and optimization, and do things that no natural causes can, then what prevents them from inventing a (non-trivial) specification for every event they investigate?
C16
In NFL, Dembski broke the calculation of the probability of a specified set by allowing the specificational resources to include only specifications that are both simpler and rarer than the observed outcome. This is simply wrong, but fortunately can be fixed, as I do here. The criticism stands for any computation done with the NFL method of computing specificational resources.
C17
The result also is not mathematically solid if the language that one uses to describe a specification is dependent on the objects that one is trying to describe. Unfortunately, language is useful precisely when it depends on what exists; with a short phrase such as "Presidential Election Campaign" or "Pentium IV", we can very simply describe an extremely complex process or object. There is thus a fundamental problem: how can we avoid making it too easy to specify complex and arbitrary objects because, in fact, we have hidden that complexity inside the definition of words in our language (words which are not independent of the phenomenon in question)? This topic is, at least, under-addressed to the point where one would have limited confidence in the accuracy of any results of a probability calculation.
C18
There are precisely zero fully-worked-out positive examples of the design hypothesis applied to a scenario where there is known to be design. All examples to date have been sketches used for illustrative purposes. The mathematical results apply only if the determination of SC is made rigorously. A sketch is not typically regarded as a substitute for a positive validation, although after a rigorous positive validation, sketches can allow one to skip over the tedious and uninformative parts of a proof.
C19
Take a case in which the prior probability is extremely low that a designer can effect the potential “design” being observed. (By this I do not mean that this is a generally usable method for evaluating cases, rather I am specifying that in this case that prior probability can be known. I do not mean that such prior probability can regularly be known.) Also assume that there is a rather high probability that something was missed in the steps of analyzing chance and necessity in the explanatory filter. (In other words that the “argument from ignorance” aspect actually may have an important case that the observer is ignorant of, and this is a high probability in this case.) In this case the Bayesean posterior probability that the “designer did it” is often lower than the posterior probability that the missed case is the explanation. Now considering cases in which the prior probability is unknown (a basic assumption of the normal application of the “explanatory filter”) the reasonableness of the EF is dependent on the actual prior probability, though unknown. If one has certain religious reasons, for example, of having differing views of that prior probability, then the result changes based on those views. The EF is not an objective methodology, and its “reliability” differs depending on precisely that prior probability.
C20: As I previously discussed with Paul Nelson [* on the thread cited at the end of the post], I pointed out that Dembski's own displacement thesis seems to hinder any form of meaningful testing. If all forms of data representation that are passed through Dembski's EF are inherently the result of some intelligent (human) post-processing, I don't see how to provide valid controls for a verification experiment that would provide a baseline measure of how much SI this post-processing introduces. That is to say, my concern is with the data encoding itself displacing information in some manner.
For instance, suppose I want to test if a Shakespearean play was intelligently designed. But, rather than encoding the contents using ASCII encoding, I encode the words in reference to their order of appearance in Webster's Unabridged dictionary. Or suppose, I want to test if Beethoven's last piano concerto was intelligently designed. Rather than encode the audio according to the frequency content in the audidble range of human beings, I encoded it according to the audible range of vampire bats. Or perhaps, I measure the neural electrical impulses that come out of cranial nerve VIII of a test subject.
C21: The true positive vs. all the rest (i.e. false positive/ false negative/ true negative) distinction used to constrain the utility of Dembski's EF is a bit weak. In the absence of, for instance, true negative references, I do not see how a true positive is meaningful in any absolute sense. In other words, to hear the claim that X is truly designed, I'd like to know what is truly not designed. Otherwise, there exists the logical possibility that every object is designed, in which case claiming X is designed does not present much additional knowledge about what it means to be designed. More to the point, it diminishes the objectivity of the notion of design employed by Dembski. For instance, if I were to discover another filter that explains more designed items (including the ones that Dembski's EF might label incorrectly as false negatives), would that then mean that my filter is a better description of design? Or does that mean I have simply happened upon a different class of designed objects?
In any case, at the moment, I see no effort in discriminating between a false positive, a true negative, or a false negative. Indeed, Dembski dismisses the significance of false negatives all together. This approach is particularly frustrating for me because I could potentially offer many design scenarios that are clearly designs in some sense other than Dembski's, but fails the EF consistently for whatever reason.
C22 The requirement that the items of knowledge determining the specification and the event to be specified must be statistically independent is either practically impossible to verify or ineffective at ensuring Dembski's claim of no false positives. It is possible to interpret the condition strictly so that it represents a condition that serves it theoretical purpose well. If the condition is interpreted in an objective fashion, so that (e.g.) Bob above (or the reader of Sobel's review) could be faulted if he applied the Explanatory Filter without having made sure that the numbers of LCD 1 and LCD 2 are uncorrelated before using the latter as a specification, then it is difficult verify the validity of specifications in practice. On the other hand, if the independence criterion is interpreted to be less demanding, then it does not ensure that false positives cannot occur (with a non-neglible frequency).
[ 02. May 2003, 08:56: Message edited by: Micah Sparacio ]
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Evan
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posted 01. May 2003 23:53
Micah, I commend you for your work in nurturing constructive conversation here.
However, I don't think much of the idea of "putting on Dembski's shoes." I think those that wish to respond to and perhaps counter the criticisms ought to do so - I don’t think a reverse Devil’s advocate approach of the critics pretending to answer their own criticisms is very worthwhile.
Trying to answer for Dembski would be difficult, not the least of reasons being that one of the most common criticisms is that Dembski is inconsistent and ambiguous about some of his concepts, so it's hard to know which of his shoes one ought to put on.
I believe supporters of Dembski (and Dembski himself) should be the ones to try to bring some clarity to the criticisms that have been offered.
I would like to point out that I have fairly consistently here at ISCID adhered to the Dembskian idea that complexity, and ultimately design, were to be detected through a filter that eliminated natural processes as the complete cause of some events on the basis of probability.
However, I have become increasingly discouraged about anyone actually taking that seriously as a scientific idea. The confusion over definitions, the lack of measurability, and the displacement of the problem from empirical detectability to negative philosophical arguments has made it seem to me that no progress whatsoever has been made on the crucial issues - that of empirically detecting design.
So I think someone other than the critics ought to respond to the criticisms.
My 2¢.
[ 01. May 2003, 23:54: Message edited by: Evan ]
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Pim van Meurs
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posted 02. May 2003 00:26
I agree with the previous poster that it may be more helpful to have supporters of Dembski, or better even, Dembski himself address some of these issues.
One of the ID supporters, Ratzsch seems to have looked at the design inference and found it wanting in several areas. My greatest objection is the claim that there are no false positives, since it is trivial to show that this is incorrect I was initially surprised by the argument and Dembski's defense thereof but I now believe that Dembski is not defending the usefulness of the design inference here but the mathematical accuracy. Indeed IFF all other scenarios of regularity and chance can be eliminated then there will be no false positives. But this ignores that in any practical application of the design inference, false positives are unavoidable and due to the inherent nature of the design inference of being eliminative, false positives seem to be a 'show stopper'.
Thus the addition of 'we don't know' as an additional category as proposed by Wilkins and Elsberry would save the design inference but would also remove most of the appeal of the argument.
I am looking forward to Del's discussion to find out if he has changed his mind on his criticisms.
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gedanken
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posted 02. May 2003 08:45
I agree with above that I am not interested in "putting on Dembski's shoes" or the like.
I am, however, willing to criticize the arguments on this list, because I think that a fair criticism of ID concepts is reasonable, so getting to the heart of the issues is also reasonable and casting off aspects that don't do so is helpful.
For example:
quote:
C1: Theoretically compelling but too stringent on the UPB to be scientific useful. Too much effort put into keeping out false positives. In order to be freely applied scientifically, some effort needs to be put in to testing a scientifically useful Probability Bound.
I disagree with this. The ID promoters have defined the UPB as their cutoff. If you look at my argument (I believe C19) I examine a Bayesean approach from the standpoint of if one knew the priors. (I understand Dembski's point that one can't know the priors and thus this approach per se is not useful for identifying the "design" in the sense he wants to do so, but I'll discuss that separately.) But the Bayesean approach I outlined will show that if one uses the UPB, and that the prior probability of the designer acting is sufficiently higher than the probability of mistakes in the EF analysis, then the EF will give a Bayesean result that shows that "design" was higher posterior probability.
That UPB being so low is part of that argument, because no matter what prior probabilities are used, anything reasonable worth considering will be above that UPB itself. Analysis with the Bayesean approach thus makes certain the reduction above, because the less than, greater than relationships don't change since none of the others cross over the probabilities of the UPB.
And furthermore having a stringent requirement would only make the EF more reliable in the terms claimed for the EF, that of reducing false positives only. (Remember the EF is demonstrably unreliable in terms of false negatives.) The IDists actually claim to have results in which meeting the UPB are found. So I don't agree with C1 because the IDists themselves are satisfied with the UPB as their cutoff.
And my C19 (if details are expanded out) show precisely that the EF is not "Theoretically compelling". So I disagree with C1.
(And by the way, that analysis can proceed on theoretical grounds, and thus the issue I find is not in finding an empiricaly useful cutoff, rather the theoretical grounds themselves will show what cutoff is useful. That useful cutoff is one that depends on the prior probability of a "designer" acting, and that is a case by case analysis. No experimental treatment can show what that prior probability will be in the next case to be tried. And no experimental treatment will show the probability of a mistake in the EF steps in the next case to be tried or claimed, thus no experimental treatment of finding the cutoff can be useful. That cutoff must be theoretically based, and for many values there is no useful cutoff, for others the cutoff depends upon the case -- yet another disagreement with C1.)
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Now if this thread is to be a true discussion of the pros and cons of the various arguments, I would be willing to engage the other listed arguments. Otherwise I can't see how I can help, as I can't reasonably put myself into making the mistakes that I see Dembski making and thus find it difficult to view from that veiwpoint.
[ 02. May 2003, 09:00: Message edited by: gedanken ]
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Micah Sparacio
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posted 02. May 2003 08:57
Per the request of Evan, Pim and gedanken, I've modified my original post to allow more flexibility in the theme of this thread.
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Cre8ionist
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posted 02. May 2003 09:11
I'd like to encourage IDers to respond to these criticisms, they aren't that difficult, and none are scientific refutations of SC. Nobody's provided a test to show that Dembski is wrong and SC arises naturally.
The criticisms themselves seem to be open to criticism.
Take C7 - C9 for example, basically unsubstantiated appeals to NDT's ratcheting to overcome SC. Of course the authors of these criticisms failed to address the SC involved in the OOL which appears prior to the Darwinian ratchet.
Further, nobody has even attempted to refute the notion of the UPB. Most people use an undefined UPB, take this quote from Paul Davies (Darwinist/quasi IDer) in his "The Fifth Miracle," after discussing his reasons for believing in a universal ancestor he states the oft heard:
quote:
It is too much to believe that all these complex and highly specific features arose independently many times.
I would ask the critics of SC to answer the question, "What's too much to believe,"? Specifically. Why not try to specify this elusive upper limit? Not to mention that this comment flys in the face of the semi-newly promoted notion that life is bound to appear whenever the conditions are right. One has to ask, if that's true, why must it have only arisen once?
But back to the topic at hand, EFs come in many forms, and to my knowledge, only Dembski's has been seriously attacked as unscientific. Bloomfield's plagiarism filter, Seti's filter, Nasa's biosignature filter, and Paul Davies' (undefined) universal ancestor filter all get a pass by the Darwinists without comment, but when a probability expert attaches numbers to a filter which can be used in both biological and non-biological instances there's an outcry of foul. I'm not going to address every comment specifially (although I have a streak of ball hoggishness in me), but there are enough IDers here that each one could be dismantled in its turn.
Let me try C4.
quote:
C4) Over-reliance on analogy. Almost all the arguments and examples of specified
complexity rely on analogies with non-biological things: mousetraps, combination locks,
outboard motors, etc. Analogies may be useful for understanding or stimulating thought,
but analogies prove nothing. Only when the analogous aspects are tested against the true
nature of the object of the analogy can one decide whether the analogy is apt or not.
I've read much of Dembski and am familiar with the criteria for the EF which is used in detecting intelligence. In it I find no appeal to analogy, now in other places, there are appeals to analogy, but that's not what's being discussed here. So this criticism is totally out of place in IMO and should be deleted. My challenge here is for the critic to provide an example of analogy used by Dembski as a way of making a determination of SC. In other words, where does Dembski say that analogy is part of the EF?
Really couldn't vote for similar reasons to those given by Evan, don't see any criticisms really that stand out as better than the others. I'm perfectly happy to let the critics make that determination...............................Cre8
[ 02. May 2003, 18:19: Message edited by: Cre8ionist ]
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gedanken
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posted 02. May 2003 11:01
Cre8tionist said:
quote:
Further, nobody has even attempted to refute the notion of the UPB.
Indeed, the basis of the UPB needed to be challenged. Dembski’s argument about the UPB being meaningful is mistaken. He arrives at the UPB by considering the number of elementary quantum transitions that could have occurred in all the history of the universe, assuming a certain size for the universe. (Of course that size is not known, but that is not important as I shall argue). The problem is that events discussed in ID are combinatorial patterns, and thus the number of patterns possible are greater than the UPB by almost unimaginably higher numbers. And furthermore, the UPB is useful in the sense that it is lower than most probabilities that anyone will make use of in any argument -- thus ordering the probabilities of various comparisons in a Bayesean argument and transforming Dembski’s Fisherian argument into a Bayesean argument in certain cases, but with different outcomes than Dembski’s EF predicts depending on other parameters. In the typical cases that are used as examples of the EF, the Bayesean priors are such as to make the EF appear to work. That said, Cre8 is correct that no one has challenged the UPB per se in the list.
quote:
I would ask the critics of SC to answer the question, "What's too much to believe,"? Specifically. Why not try to specify this elusive upper limit?
Ah, this gets to an important difference between the logical analysis that goes on in science as opposed to the logical analysis that goes on in religious discussion. The difference is not that religious studies in any way avoid the need to consider real-world observation. The difference is that religious argument can include a foundation of belief as premise in the argument. People who take different beliefs into the premises will therefore disagree on the implications -- precisely because they disagree on the premises.
But the basis of science is supposed to be one that can be accepted broadly, based only upon observation and a philosophical position requiring only acceptance of a naïve realism. This ability of those with varying religious positions to all get together and work in useful topics in scientific research allows for much good to be done in the world that depends strictly on the properties of the physical world and their understanding.
For example in a medical treatment, people find religious thinking to be very important in many cases. (E.g. for psychological reasons, or the actual belief in God’s help, whatever the reasons there is a great deal of acceptance of importance in religious involvement in healing.) However that does not affect the fact that medical science and the scientific methods that focuses on that which is observable has done wonders in medical treatment. While there is definitely an art to medical practice, one generally does not want the doctor to be basing his choice of treatment on a belief argument, rather on a history of observed success in the treatment.
Now let’s return to Cre8’s question. Specifically consider the case in which one believes that God makes many non-physically realizable changes in the physical world (or any other belief in a “designer” that works regularly in an unseen manner in the physical world). By that I mean changes that are not attributable to any physically limited causal relationships. If you believe that, it does not matter if descent with modification is regularly observed with great frequency. It does not matter how strong the evidence for such physical process -- there would still be a great many cases in which the unknown history would lead believers to attribute the cause to God’s (or other “designer’s”) action. But if you believe that such a God does not act in such a manner to make physical world events inconsistent with physical relationships (either because one is an atheist or agnostic, or because one believes that God intends a consistent physical reality as an important aspect of His will for example) then one will find the explanation of an unembodied designer as proximate cause of events to have very low prior probability.
So the answer to Cre8’s question depends on one’s belief. That’s just how he asked the question -- entirely appropriately “What’s too much to believe”?. The answer is that if the basis is belief it may be very important intellectually -- just it is not the topic of the study of science as science is regularly accepted around the world.
This is what is wrong with Dembski’s EF in this regard. Specified Complexity only becomes relevant if the prior probabilities of the unembodied designer acting are believed to be high when there is no reasonable evidence for an embodied designer having access to cause the events in question, or when the prior probability of an embodied designer acting are actually known to be high. (Example is Caputo case, high prior probability of politician fixing elections directly observable and not dependent on “belief”, but evolution over millions of years depending on unseen “designer” could be considered by many to be low prior probability.) The EF actually reduces to a Bayesean argument dependent on belief in the priors.
On this basis I would disagree with:
quote:
C15: The Universal Probability Bound is a reasonable estimate iff the definitions are strictly adhered to and intelligence is not as magical as Dembski assumes. …
Because there are other issues, and one simply can’t adhere to the definitions strictly due to lack of clarity thereof. And if one did, there are other arguments why the EF will fail. The importance of the UPB is that it is lower than other probabilities that will occur in the analysis, including the probability that the eliminative steps in the EF are in error and certain combinations of those factors. So it is “reasonable” only due to those factors, not on the basis stated in C15, and only in certain conditions of prior probabilities of the “designer” acting in relation to the other issues.
[ 02. May 2003, 11:55: Message edited by: gedanken ]
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kyle7
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posted 02. May 2003 14:13
Specified Complexity is a useful construct that may advance science in general. Here are my responses to the first three criticisms. Hopefully, I can develop more as time permits.
C1: I think that one has to look at the system under investigation and determine an appropriate probability bound. Usually, the first run of an analysis should not have a rigid 10E-150 set as the probability bound. Also, there may be several different analyses that result in a combined probability bound of 10E-150. False positives are not a real problem. These will force us to scientifically focus on possibilities. Remember, Dembski's method is a tool that can help us focus scientifically. Possibly, it may confirm Darwinism as a valid theory. On the other hand it may be the tool that will undo Darwinism. Scientifically, we should not be afraid of it because both friend and foe of Darwinism may use it. All scientific endeavors require work! So, we should not shy away from the method because it may require some effort. Oftentimes the most effort leads to the greatest results!
C2: Complexity does have a number of different definitions. This is not problematic for the concept of Specified Complexity. Actually, we would want the term to be open so the method may be applied to the greatest number of problems. Each time one uses the method, a clear definition needs to be stated for the given problem. Possibly, one could catalog different definitions used for different types of problems.
C3: I would disagree with this statement. Specified Complexity is measurable depending on how one defines it. For example, a satellite may orbit a planet searching for life. Dembski's method may be used to analyze data received from instruments encompassing the electromagnetic spectrum. One definition of complex may be any source emitting infared rays (suggesting elevated temperatures – life operates on a thermodynamic cycle). Another definition used in analyzing surface topography may be any specified structures (e.g. circles, long straight lines, perfect squares and rectangles, etc). Hundreds of definitions may be supplied and the whole electromagnetic spectrum covered. The program would have to weight the different definitions of complexity (user supplied) and analyze the data to determine the best areas to send a probe or human explorers. The method of analysis relating to biology may be different but similar methods may be used to define complexity. This is why a department of intelligent design is needed. Procedures and methods need to be developed and constructed that will enable Dembski's method (and others) to be applied to a number disciplines – not just biology and the question of Darwinism.
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RBH
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posted 02. May 2003 16:13
I have been avoiding this because I haven't had (and don't really now have) time to develop it fully. Nevertheless, Gedanken has raised the issue of Fisherian versus Bayesian approaches to decision-making in this context, and I think his remarks are important. C19 and his subsequent postings express it, and I'll expand just a bit.
To briefly review, the logic of the Explanatory Filter is that observed structures or processes must be due to Regularity OR Chance OR Design (R OR C OR D). In The Design Inference, IIRC, Dembski groups Regularity and Chance so the framework is ((R OR C) OR D).
Then he discards R on non-probabilistic grounds. In the NFL version R is discarded because, based on Behe's irreducible complexity notion, R is a non-starter for some structures, e.g. the infamous flagellum. It could not have evolved via the mechanisms and processes invoked by evolutionary theory. The question thus is reduced to (C OR D).
Structures that cannot have evolved and whose probability of Chance formation is less than the UPB are inferred to be D. The probability of Chance formation is estimated against a uniform probability distribution - it assumes that all combinations of the necessary elements are equally probable.
Thus this is a Fisherian hypothesis test: Given the null hypothesis C, if p(C) is less than some rejection value, infer not-C. However, since in Dembski's version there is but one alternative, D, the conclusion becomes "infer D." For Dembski, as we all know, "complexity" = "improbability." In fact, early in TDI, as I recall, he uses "specified improbability," but that later shifts to "specified complexity" with no change in meaning.
This Fisherian procedure allows the inference of Design without ever having considered the probability, plausibility, or evidence regarding the Design hypothesis.
In a Bayesian framework, the question is different. Given a set of hypotheses, a prior probability distribution over those hypotheses, and some data, a Bayesian analysis asks what the posterior (after the data are considered) probability distribution over the hypotheses should be. That is, instead of evaluating just one hypothesis, the null, in the Fisherian approach, Bayesian analysis asks specifically about all the available candidate hypotheses in the light of the available data.
The Fisherian and Bayesian approaches are not isomorphic. Given the same hypotheses and the same data, they can come to very different conclusions: quote:
While in some cases, the answers from a Bayesian approach and from sampling theory [Fisherian approach] are very similar, we can also find cases where there are significant differences. We have already seen such an example in exercise 3.15 (p.63), where a sampling theorist got a p-value smaller than 7%, and viewed this as strong evidence against the null hypothesis, whereas the data actually favoured the null hypothesis over the simplest alternative. On p.68, another example was given where the p-value was smaller than the mystical value of 5%, yet the data again favoured the null hypothesis. Thus in some cases, sampling theory can be trigger-happy, declaring results to be `suffciently improbable that the null hypothesis should be rejected', when those results actually weakly support the null hypothesis. As we will now see, there are also inference problems where sampling theory fails to detect `significant' evidence where a Bayesian approach and everyday intuition agree that the evidence is strong. Most telling of all are the inference problems where the `significance' assigned by sampling theory changes depending on irrelevant factors concerned with the design of the experiment. (Information Theory, Inference, and Learning Algorithms, David J. C. MacKay (Draft 4.1, April 18, 2003, p. 490)
For "trigger-happy" above, read "false positives," false rejections of the null. An important point is that the rejection region is not the only experimenter-controlled parameter that can determine whether the null is rejected. The sample size (in the flagellum case, the number of elements deemed necessary) is one such parameter. Choose a different set of elements (e.g., at the level of cilia, rotors, and shafts), and the estimated probability of chance assembly will be different. The notion of "complexity" as "improbable below the UPB" is a Fisherian hypothesis test, and suffers from the same ills as do all Fisherian hypothesis tests.
RBH
[ 02. May 2003, 16:17: Message edited by: RBH ]
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Rex Kerr
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posted 02. May 2003 18:11
Unlike some others who disagree with Dembski, I will attempt to put on his shoes for a little while. I think doing so can be instructive, even if I in many cases will have to plead ignorance as to how Dembski could or should or would respond.
I will refrain from commenting on my own criticisms, since if I saw a way around them, I wouldn't have proposed them in the first place. (Or, in one case, I already pointed a way around the problem.)
C1: We do not expect a tornado in a junkyard to assemble a working 747 by chance with a probability of 10^-150 or even 10^-15000. Objects which are truly designed typically fall far outside of what can be produced by chance. Hence, we may reasonably expect that design in biology will follow the same pattern, and can err on the side of caution when constructing a UPB.
C2: I can't speak for Dembski on this one, but I view the overloading of the word "complexity" to be unhelpful rhetorically but not much of an impediment to the utility or theory of specified complexity. With effort, from context, you can figure out for each case what sense of complexity is meant. Clearer terminology would help errors in application, however.
C3: This seems a fair criticism of utility to me.
C4: Analogies, if they are to be used at all, must be used on non-biological examples since the very question we are trying to address is whether or not biological systems are designed; to assume that there was or was not design would be begging the question. The analogies are only used to label the peculiar class of specified complex objects in biology [assuming that there are any!] as "designed", since we label non-biological specified complex objects as "designed". Since these objects cannot [assuming the theory and analysis is correct] be assembled by natural processes, they are interesting and surprising regardless of what label we give them.
C5: This seems a fair criticism of the theory to me, but it is a fairly minor point in the theory. The accuracy of these statements can be checked by experiment, so the philosophical statements are mostly expendible.
C6: The argument from analogy has already been answered; the procedures issue is covered by C3 and C10. This point is therefore redundant with others on the list.
C7: Specified complexity is [in theory] quantifiable while naive observation of irreducible complexity is not. Further, although IC systems are a natural place to look for exceedingly low probability, they need not be the only place it is found. Since SC generalizes and quantifies the intuitions used to analyze IC systems, it is not redundant.
C8: This seems like a fair criticism of the theory to me, to the extent that mechanistically mysterious front-loading is invoked. (I haven't seen it invoked much, though, so it may not be an issue.)
C9: Perhaps asserting no false positives is misleading. One should really predict the probability of getting a false positive based on the theory alone--and compare this to the probability of messing up your analysis. If the probability of erronious analysis vastly exceeds the probability of the theory producing a false positive if followed ideally, then we can use the theory as if it were true, subject to experimental verification, just like any other theory we use. This is the best that we can do with any theory (and I don't think SC is pretending to be anything more).
C10: Yes, this is a problem, as far as I can tell.
C11: Specified complexity refers to events that are both specified and complex; it highlights the fact that you need both low probability and an independent method of selecting out that low-probability event. It is much shorter than, "System where we have successfully eliminated a set of non-ID hypotheses using the Explanatory Filter." It is, therefore, both useful and reasonably accurate. Equivocation is obviously a problem (specified complexity is defined w.r.t. all known natural causes). I can't speak for Dembski on those, especially as no examples have been given.
C12: This criticism is fair, but redundant with C3 and C10.
C13: It's unclear to me how relevant or important this criticism is. I'd need to see it further developed to know.
C14: If problems C10 or C18 were fixed, C14 would also be fixed, most likely. So it may be a problem, but it's redundant with other problems.
C15: Specificational resources are supposed to take care of the problem of inventing specifications. However, since we haven't seen any in detail, this is hard to evaluate. Again, fixing C10 or C18 would likely fix this.
C16-C18: These are mine, so I will skip them.
C19: Evaluating prior probabilities of design is difficult to do from scratch without detailed knowledge of the designer, or a large sample of designed things. However, if specified complexity is observed, we may infer that the prior probabilities were not so low after all: Given the prior of a lack of design at high probability, we do not expect to be able to reliably predict extremely improbable events (by definition). If we can, in fact, do this (or infer this, using specified complexity), our model predicts itself to be wrong. Thus, the prior probability of something else must have been higher than we had anticipated, in order to bring the (im)probability to a reasonable level. If the only options for priors are design and not-design, we can infer both design and estimate the prior probability.
C20: This seems to be a serious problem. It might be solved by solving C8, C3, and C10. Or possibly not.
C21: More attention to all four possible classes, with examples, would be instructive. I'm not sure that the lack thereof is a fatal problem in the theory, given the lack of competing design classifiers. However, more information on the false positive, true negative, and false negative cases would be desirable.
C22: That it is difficult to evaluate correlations between specifications and observations seems a valid criticism of the theory and/or utility of specified complexity. This is essentially the same criticism as C10, and is related to C17.
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The most telling criticisms, from my perspective, seem to group into three classes:
Imprecision of what "specification" is and how to calculate it rigorously: C6, C10, C14, C17, C18, C22
Inability to properly calculate values needed to reject all relevant chance hypotheses: C3, C7/8 in part, C12, C15, C18
Metaphysical/philosophical issues about the presumptions of the theory or its application: C4, C5, C9, C13, C19, C20
The others may be important too (as noted above), but these three trends seem to emerge. Of these three, I would suggest that the metaphysical/philosophical issues are simultaneously the easiest, least useful, and least convincing issues to address, since there is much room for argument, interpretation, differing world-views, and the like.
Therefore, I would recommend that ID researchers concentrate on the first two points predominantly, while keeping the others in mind, and fixing any legitimate complaints.
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gedanken
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posted 02. May 2003 18:47
Rex, (Or should I say "Dembski-Rex"),
On C19, I did not intend to claim that it was generally possible to evaluate the priors. (So you are correct that Bayesean approach won't be very usable in many case that Dembski describes.)
But my proposal was not intended to suggest that a Bayesean approach was an alternatitive to Dembski's Fisherian approach.
Rather my Bayesean approach was designed to be an analysis of the Fisherian approach including specific aspects of Dembski's methods, in the EF.
I don't have time or space here to develop this theme in detail. But when the prior probability of the designer acting is known to be high in a relative sense (say very much higher than the probability of making a mistake in the eliminative steps of the EF), then the EF gives a similar answer to the Bayesean approach in the sense of no false positives as evaluated by the Bayesean approach.
However when the prior probability of a designer acting is known to be very low, and is in fact much lower than the probability of making a mistake in the eliminative steps of the EF, then the EF is not reliable in the sense of no false positive. This can be shown on purely theoretical grounds, by Bayesean analysis.
So this is not an alternative to the EF. Rather it is a demonstration of when the EF is reliable.
And since the prior probability of an unembodied designer cannot be known (I would say inherently) the EF becomes an issue of philosophical judgment that such a probability of a designer acting to effect the observed result is not substantially lower than the probabiltiy of making a mistake in the eliminative steps of the EF.
Thus those who think that God regularly acts to effect design, for example, could plug in a relatively high value to the prior of a designer acting into the Bayesean approach. Thus the prior is based on a belief, not a generally accepted observation. But in that case, based on that assumption, the Fisherian approach is "reliable" in producing no false positives in the sense of being consistent with a Bayesean analysis, given that assumption.
But if one believes the prior of a designer acting is much much lower than the prior probability of making a mistake in the eliminative steps of the EF, then it is not "reliable" when plugging those numbers into a Bayesean approach. (In essence it becomes an "argument from ignorance" and we have assigned a prior probability of making a mistake of "ignorance").
The UPB of 10^-150 allows the prior probabilities being compared to have an extremely wide range. (And that's its importance, not the number of elementary quantum transitions etc.) So if the Bayesean priors varied by several orders of magnitude it would make no difference in many cases in the resulting analysis of "reliability".
So my claim is not that the Bayesean approach is useful as an alternative, rather it is useful as a means of analysis of the Dembskian EF procedure itself.
I'm sure this supports some of the other criticisms, such as the "philosophical" based ones. So as such it is not really distinct in its implcations when they are drawn out.
Also
quote:
However, if specified complexity is observed, we may infer that the prior probabilities were not so low after all.
I think one has to be careful here. A "fabrication" as Dembski puts it is simply a case of describing the event not independently of the event. We have a problem in that if a process produces things that we regularly could describe independently of that process, then we could easily have fabrications of actually designed cases, or we could have a failure to have what Dembski calls "complexity" because "complexity" actually means generated by an extremely low probability source. These are separate problems (fabrication and actual lack of complexity), but both can be the case if one has failed to actually be able to know the facts that are described as the inputs to the EF, in both cases because of ignorance of facts needed for analysis.
So the problem is "observing" SC, that one must know all possible processes (or the actual process) of construction to actually know that it was a case of SC -- and this is not strictly a matter of "observation". Thus saying "if specified complexity is observed..." is problematic. And your comments to C2 would support that being a problem.
[ 02. May 2003, 20:10: Message edited by: gedanken ]
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Erik
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posted 02. May 2003 20:59
Gedanken, if you want to be a Bayesian, you should pay at least as much attention to the likelihoods as to the prior probabilities. In Dembski's less strict version of Fisherian hypothesis testing, decisions should be based only on the value of the likelihood
Pr(specification | not ID).
In the Bayesian approach, we would base decisions on only the values of
Pr(not ID | data) = Pr(data | not ID) / (Pr(data | not ID) Pr(not ID) + Pr(data | ID) Pr(ID)),
Pr(ID | data) = Pr(data | ID) / (Pr(data | not ID) Pr(not ID) + Pr(data | ID) Pr(ID)).
In cases where Dembski's decision criterion leads to the rejection of "not ID", the value of Pr(data | not ID) is extremely small (since the data is, by definition, a subset of the specification in such cases). Thus, we may expect the likelihoods to massively dominate over the priors in this case. However, as a Bayesian (or even as a non-Bayesian) you should be very concerned with the other likelihood, Pr(data | ID), which could well be lower than Pr(data | not ID). (If the designer is God, then presumably almost anything is possible and a Bayesian would interpret the theists' general reluctance of predicting God's actions as a fairly flat likelihood function Pr(data | ID), which means that the likelihood of God generating any particular data set is infinitesimal!)
Rex Kerr, regarding C11, if you want a reasonably accurate abbreviation of the phrase "an event for which we have successfully eliminated a set of non-ID hypotheses using the Explanatory Filter", you should go for "[intelligently] designed event", "ID event", "extremely improbable event", "specifed improbability", or something else that actually reflects what the abbreviation refers to. 50% of the term "specified complexity" has nothing at all to do with Dembski's ideas. Since we already have a word for improbability (namely "improbability") it is unnecessary to call it "complexity"/"information" (especially considering that these words are used so often and so differently that they have lost all meaning). If Dembski had been targeting an audience of experts, then this might be a trivial concern, but misleading terminology becomes an issue when the primary audience is the general public.
Regarding C13, consider a modified version of the Explanatory Filter (EF). Instead of trying to reject all available non-ID hypotheses and then automatically accept a general ID hypothesis, we could try to reject all ID hypotheses and then automatically accept a general non-ID hypothesis. Thus, if an event can be shown to fit a specification and be a very improbable consequence of all available ID hypotheses, we say that we have "swept the field clear of ID hypotheses" and conclude that the event must have been the result of "natural" processes. Let's call this the Dual Explanatory Filter (DEF). On what basis do we, as Dembski implictly encourages us to do, choose the EF in favour of the DEF? I suggest that the preference for the EF over the DEF is the result of ID advocates' mystical view of intelligence and a reluctance to subject the idea of an Intelligent Designer to the same standard as scientific hypotheses (because pondering the likelihood of the Intelligent Designer realizing a particular event is thought to amount to "telling God what to do"). Furthermore, if the choice between the EF and the DEF is to meaningful there must be a sharp dividing line between "non-ID" and "ID". But what if the concept of intelligence is like the concept of a heap? Perhaps a thermostat is intelligent to the same extent that a pile of three stones is a heap. And frog might be intelligent to the same extent that a pile of seven stones is a heap, etc. The EF (and the DEF) is useless if we can't draw a line between intelligence and non-intelligence.
Regarding C14, this problem would not be fixed automatically if C10 was fixed (i.e. if the relevant details were supplied). Even if detailed examples of "items of knowledge" and the rejection functions that Dembski thinks are explicitly and univocally identified were supplied, the problem of how to determine whether this is the case for other examples would likely remain. The problem is that the relation is a psychological relation that must be verified by introspection. C10 is a criticism of Dembski's application(s), while C14 is a criticism of the theoretical considerations behind the EF.
Finally, C22 is not the same as C10. C10 has to with the lack of necessary details. C22 has to do with the interpretation of the independence criterion and the dilemma of choosing between an interpretation that is theoretically OK but practically impossible to use or a practical interpretation that does not ensure the lack of false positives.
Erik
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Rex Kerr
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posted 03. May 2003 00:48
gedanken wrote:
quote:
So [the Bayesian approach of C19] is not an alternative to the EF. Rather it is a demonstration of when the EF is reliable.
Granted.
quote:
And since the prior probability of an unembodied designer cannot be known (I would say inherently) the EF becomes an issue of philosophical judgment that such a probability of a designer acting to effect the observed result is not substantially lower than the probabiltiy of making a mistake in the eliminative steps of the EF.
Well, maybe. In particular, I don't see this as an issue of philosophy so much as one of probability. We can potentially estimate the probability of making a mistake in the eliminative steps of the EF by measuring rates of mistake-making in other similarly structured arguments (or test-cases generated by one person and scored by another).
I do fully agree that many ID proponents and critics have taken exactly the approach you describe: evaluating the results of the filter based on their world-views and predispositions. However, since the disagreement can likely be substantially addressed by experiment, I don't think it's necessarily a critical flaw in the theory.
With respect to fabrications, I agree with your comments, but I will point out that my statement was conditional: "if specified complexity is observed". The determination of specified complexity includes avoiding fabrications. So I maintain that my statement was accurate, while sharing your concerns about the ability to observe specified complexity.
Erik, no fair, you're taxing my abilities to emulate Dembski!
With regard to C11, Dembski's hypothesis is that instances of specified complexity aren't cases of improbability at all, just apparent improbability. Thus, specified improbability is misleading. It would be like using the term "malevolent accident" to describe intentional murder. It wasn't an accident at all! Specified complexity may be a confusing term, but I haven't yet seen a superior alternative that is sufficiently short.
With your extended description of C13, it sounds like a fair criticism. It only need come into play in cases where we evaluate the products of intermediate levels of intelligence/design--but in that realm it's a very serious issue. (It reminds me of giving talks where I describe an experiment that I have "designed", when in fact what I mean is that I accidentally did something, and noticed an interesting consequence.)
I'm afraid I still fail to see how taking the definition of specification seriously, and working through it in rigorous detail, still allows one to assert that you have background knowledge that allows such-and-so and hope that people believe you. Any rigorous treatment would have to involve justifying the use and existence of background knowledge, wouldn't it?
With C22, I think that the lack of necessary details is caused precisely because the interpretation is practically impossible to use. If the details could be shown then the interpretation wouldn't be impossible to use and C22 would vanish; if not, C10 (giving details) wouldn't be solved. Thus C22 is a subset of what must be accomplished to really address C10. I didn't mean to imply that C22 was a trivial problem; on the contrary, I think it is at least mathematically very serious, and yet is only a small part of what must be solved to "provide the details needed to verify that the definition is satisfied".
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gedanken
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posted 03. May 2003 02:15
Erik said:
quote:
However, as a Bayesian (or even as a non-Bayesian) you should be very concerned with the other likelihood, Pr(data | ID), which could well be lower than Pr(data | not ID). (If the designer is God, then presumably almost anything is possible and a Bayesian would interpret the theists' general reluctance of predicting God's actions as a fairly flat likelihood function Pr(data | ID), which means that the likelihood of God generating any particular data set is infinitesimal!)
Ah, very interesting! I'd never thought about it that way.
Now if I were to put on an IDist hat (and I've watched a lot of ID presentations and discussions) here is what I would say to that:
[IDist hat]
First Dembski's EF characterizes a "rejection region" so an area of possible responses are incorporated. Then no matter how large, the range of possible ID actions is not infinite (or if it is, then possibly the "rejection region" has the same cardinality). Thus the Pr(data | ID) is not infinitesimal, even if it is small. ("data" really means falling within the "rejection region" specification.)
Also this looks like an "inflationary" argument. (For some reason IDists seem to like this criticism of an argument, it wins points somewhere).
[/IDist hat]
Actually for normal examples I'd always considered Pr(data | ID) to be rather high, and explicitly high because of the very nature of the "specification". That "specification" matching the pattern actually means that there is a frequency of observation of events already falling within the "specification" that is not empty or infinitesimal, precisely because to be meaningful language statement it must represent some observed events in other situations that were caused by "intelligent agent" behavior.
(I'm trying to avoid defining "intelligent", and put both "intelligent" and "specification" in quotes to put them on the same par, so we really don't need to deal with difficulties therein.)
Take for example the Caputo case. We have a low but still reasonable experience of behaviors of politicians fixing elections. Now note that we have some issues of the independence of the event from the specification, or of separating the considered action of the politician from knowledge of possible actions like cheating on the election. The issue of motive is important in court cases, for example, because it raises that conditional probability. But because of this (in fact precisely because of this knowledge) we can assume Pr(data | ID) to be reasonably high in relative terms, say 1 in a million or something in a few orders of magnitude arround that. A bayesean argument in the Caputo case supports the "caputo cheated" hypothesis over the "fair toss" hypothesis. These are not exactly the "ID" and "non-ID" cases, but they are close enough when we intuitively observe the example given that we tend to accept the argument as valid.
I'm seeing some notational difficulties, because we don't have a term for the prior probability of the designer having access to the event, which was my original issue. I'll have to think about this.
--
Ah, I figured out what is bothering me! The term "ID" is actually a statement that the "Designer did it". Now what is the probabilty that the data occurred if we know the "designer did it"? That is 1.0. There are more difficulties, so I must report back later.
[ 03. May 2003, 04:03: Message edited by: gedanken ]
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gedanken
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posted 03. May 2003 12:20
Update on Bayes methods:
As mentioned, I figured out what is bothering me. The term "ID" would be a statement that the "Designer did it" if we were trying to use the same terms as the EF. Now what is the probability that the data occurred if we know the "designer did it"? That is 1.0. So Pr(data | ID) is always 1.0 in that terminology (differing from Eric’s). "not ID" is simply the "designer didn't do it" or the chance event takes presedence according to that terminology (once again differing from Eric’s). But that’s the problem, we want to know probability that designer did it.
Remember we're not trying to ascertain the probability of the existence of the ID agent or even the posterior probability that the agent had access to the events in question, per se. Eric’s Pr(data | ID) is a little confusing in that context. If "ID" were "access" then we would be calculating P("access"|"data"), and that's not what we meant.
Let me rewrite differently:
In the EF, we are trying to determine if we can infer whether "designer-did-event" in terms of P("event"|"not-designer-did-event"). This latter term is the likelihood of event without the designer, or the "chance" case supposedly analyzed in the EF (and indeed presuming we have not missed anything important).
Considered in Bayesean framework:
We want to know P("designer-did-event "|"event") in terms of cases " designer-did-event " (the ID case), or "not-designer-did-event" the chance case. (Assuming the "chance" is inherently all encompassing, including any natural cause excluding the agent action.) So P("event"|"designer-did-event")=1.0 by definition, P("event"|”not-designer-did-event") is the probability of chance by the natural processes excluding designer action is the normal subject of the EF so let’s take that as the calculation thereof.
Note I am collapsing RBH’s "(R OR C)" terms in to “chance” case, because that is how Dembski treats it in NFL. ("Regularity" is simply "chance" of high probability in relative terms. While the steps missing the R case may be important in analyzing the "argument from ignorance" aspect, I would like to ignore this in the first pass analysis of the EF, as they are equivalent to missing a "probabilistic resource" in the chance case.)
Priors are P("designer-did-event") and P("not-designer-did-event"). The former is probability of both designer existing, and of having access or motivation, etc., to actually effect the event. Latter is simply complement or 1.0-former.
P("event") = P("event"|"designer-did-event")* P("designer-did-event") + P("event"|"not-designer-did-event")* P("not-designer-did-event").
This can be reduced to P("event") = P("designer-did-event") + P("event"|"not-designer-did-event")*(1.0-P("designer-did-event")).
To use a Bayesean method to determine P("designer-did-event "|"event") one does not even need to use Bayes rule, rather the simple rule of conditional probability:
P(A|B) = P(A and B) / P(B).
So P("designer-did-event "|"event") = P("designer-did-event " and "event") / P("event")
But "event" subsumes “designer-did-event ", so P("designer-did-event " and "event") = P("designer-did-event "), and we get:
P("designer-did-event "|"event") = P("designer-did-event ") / P("event")
Where P("event") is given up above:
P("designer-did-event "|"event") = P("designer-did-event ") / (P("designer-did-event") + P("event"|"not-designer-did-event")*(1.0-P("designer-did-event"))).
The only likelihood we need is P("event"|"not-designer-did-event"), which is the normal subject of the EF. As mentioned P("event"|"designer-did-event") is always 1.0, and P("event"|"not-designer-did-event") less than P("event"|"designer-did-event"). The missing prior we need for a Bayes method is simply P("designer-did-event ").
I would note that P("designer-did-event") could never be 1.0 if there was any chance at all of a natural process doing the event, because the "designer" could have arrived to do the event and discovered it was already done and thus could not do it. Or in reverse the "chance" case would have to be reduced to 0.0 since the designer had already accomplished the event. I think we can neglect this aspect for practical cases.
Note then that P("designer-did-event "|"event") is highly dependent on P("designer-did-event"). If P("designer-did-event") were 0.0, then no matter how small the probability of the event happening outside of "design", the inference is still not of "designer-did-event". And if P("designer-did-event") is relatively high (say P("designer-did-event") substantially higher than P("event"|"not-designer-did-event") ), then P("designer-did-event") approaches unity.
This is the importance, by the way, of the UPB being so small, because it makes P("event"|"not-designer-did-event") virtually always substantially smaller than P("designer-did-event"). This is why, if there is a relatively high chance that the designer did it that the EF "reliably" predicts that the Bayesean approach will give a high probability the designer did it, and this is true even if there were substantial errors of many orders of magnitude in the P("event"|"not-designer-did-event") term.
I don’t disagree with Eric’s analysis of Pr(ID | data), just we weren’t looking for Pr(ID | data) in the terms described.
(End of minor digression from topic!)
[ 03. May 2003, 13:03: Message edited by: gedanken ]
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