A Consistent Inconsistency

How Dr. Dembski infers intelligent design

By Mark Perakh

First posted on July 10, 2001. Updated August 10, 2003.

Contents

1. Introduction

2. Design without a designer

3. Dembski's explanatory filter

1. Description of the Explanatory Filter

2. Specification according to Dembski

3. “Mathematism” as a tool of embellishment

4. Can probability be separated from the event's causal antecedents?

5. Law vs either chance or design

6. "Unequivocal chance" vs "either chance or design"

7. The third "node" - Design vs chance

1. The criteria of design according to Dembski

2. False positives

3. Illusory patterns

4. The nature and role of specification

4. Probability according to Dembski

5. Complexity according to Dembski

1. Dembski’s definitions of complexity/difficulty

2. Other interpretations of complexity

6. Dembski's treatment of information

1. General discussion of information

2. Information as a tool in Dembski's theory; Dembski's "Law of Conservation of Information."

3. Information, probability, and Dembski's "specification"

7. Dembski's design inference

8. Conclusion

9. References

William A. Dembski is a very prolific writer whose literary production, while covering an extensive span of subjects, from history of philosophy to probability theory and from theology to information theory, seems to be all devoted to one idea – to prove that the universe in general and life in particular are the results of a design by an unnamed intelligent mind.

In this article I shall discuss two of Dembski's books [1,2] as well as a number of his papers [3,4,5].

It seems that Dembski is one of the most prominent participants in the "intelligent design movement." Indeed, whereas another prolific writer, Phillip E. Johnson, who is a lawyer, has been proclaimed the leader of the "movement" in question (see A Militant Dilettante in Judgement of Science), Dembski's writing is much more sophisticated than the often very superficial even if rather eloquent diatribes by Johnson, and this makes Dembski arguably the most revered figure among his supporters and colleagues. Their articles and books are full of praise for Dembski's "mathematically rigorous" discourse. Here is just one example.

Professor of philosophy at the University of Texas Rob Koons wrote (quoted from the blurb on Dembski's book "Intelligent Design"): "William Dembski is the Isaac Newton of information theory, and since this is the Age of Information, that makes Dembski one of the most important thinkers of our time. His 'law of conservation of information' represents a revolutionary breakthrough."

Similar praise for Dembski's work can be found in the blurbs of his books and in many papers and books written by his supporters.

Here is one more quotation. Professor of biochemistry Michael J. Behe, (see Irreducible Contradiction) also often referred to as a pioneer in the modern revival of the intelligent design, in his foreword to Dembski's "Intelligent Design" wrote: "I expect that in the decades ahead we will see the contingent aspects of nature steadily shrink. And through all of this work we will make our judgment about design and contingency on the theoretical foundation of Bill Dembski's work."

Although I could easily quote many more examples of high acclaim bestowed on Dembski's work by his colleagues, it seems obvious that Dembski is rather universally being held in high esteem by his colleagues, who all seem to agree that his work is a revolutionary step in science, on a par with achievements of Newton. Dembski's admirers often stress that his work is the most scientifically rigorous one.

While Dembski's colleagues so highly admire his contribution to the "design theory," there have also been heard critical voices.

For example, in a book [6] professor of philosophy Robert T. Pennock offered a critical discussion of certain parts of Dembski's work. Some of Pennock's critique is directed at the so-called "explanatory filter," which has been suggested by Dembski as a versatile tool for establishing design. Other critical comments by Pennock relate to Dembski's thesis about the so-called "specified complex information." Pennock did not, though, review Dembski's work in a comprehensive way since his analysis of Dembski's ideas is only one of many topics discussed in the mentioned book.

Another book, in which we find a more detailed and systematic criticism of Dembski's work was published [7] by the professor of philosophy Del Ratzsch. The entirety of Ratzsch's writing makes it clear that he himself belongs to the camp of "design theorists." However, unlike most of his co-travelers, Ratzsch is usually logical and meticulous in his discourse. In an appendix to the mentioned book, Ratzsch subjects some parts of Dembski's work to a strong critique. Ratzsch's critical remarks relate almost exclusively to Dembski's "explanatory filter." In particular, Ratzsch convincingly illustrates the fallacy of Dembski's assertion that his "filter" does not produce "false positives," which is in itself sufficient to render the entire concept of that "filter" largely useless.

In a paper [8] Ellery Eells offered a critical analysis of Dembski's "The Design Inference," mainly of the parts devoted to what Dembski calls "magic number" of 1/2 as a universal threshold separating "small" and "not small" probabilities. Eells concludes that Dembski's theory is "not on the mark."

A detailed critical analysis of Dembski's theory was offered in a paper [9] by professors of philosophy Branden Fitelson, Christopher Stephens and Elliott Sober. This review discusses Dembski's discourse (mainly his explanatory filter) from philosophical and Bayesian viewpoints. This review does not seem to be addressed to laymen in philosophy and probability theory, but provides a number of intricate arguments revealing inconsistencies in Dembski's analysis.

Highly critical reviews [10,11] of Dembski's work were published by professor of ecology Massimo Pigliucci. The first review is of a rather general character, where Pigliucci does not delve into the intricacies of Dembski's discourse, mainly limiting his discussion by pointing to the menace to the genuine science from Dembski and the latter's cohorts in the so-called "intelligent design movement." The second review is more detailed. Here Pigliucci repudiates Dembski's assertion that science had unduly abandoned some of the Aristotle's four "causes." Pigliucci offers a classification of various types of design, interpreting this term in a broad sense, so that it encompasses four different versions of design, including what he calls "non-intelligent natural design." The latter, according to Pigliucci, does not require action of a conscious intelligent agent but may be, for example, the result of natural selection.

Other critical reviews of Dembski's work appeared on the Internet.

One of the well substantiated critical reviews of Dembski's "Intelligent Design" was suggested by the biologist Gert Korthof (see Was Darwin Wrong?). Korthof mainly concentrated on Demski's treatment of biological structures but also criticized inconsistencies in Dembski's treatment of information.

A rather detailed review of Dembski' work was written by Dr. Eli Chiprout of the IBM Research (this essay is temporarily available at http://members.cox.net/chiprout/DesignInference/Demski.htm).

As Chiprout has indicated, he shares Dembski's belief that the universe was created by an "intelligent designer." However, he says, this fact alone is not sufficient to accept uncritically Dembski's theory. Chiprout finds many faults in Dembski's theory. He concentrates mainly on the analysis of Dembski's so-called "explanatory filter," which many reviewers, both supporting and criticizing Dembski, seem to view as the central part of Dembski's work.

Several critical reviews of Dembski's work were offered by Wesley L. Elsberry (see Critiques and Reviews of the Work of William Dembski). In one of these reviews Elsberry points to discrepancies between Dembski's book "The Design Inference," and some of his other publications. One of the points discussed by Elsberry is the lack of discrimination in Dembski's discourse between a direct design by an intelligent agent and the design "by proxy." In Elsberry's another critical review, one of Elsberry's assertions is that the concept of design as defined by Dembski can also encompass natural selection.

One more paper arguing against Dembski was posted by Thomas D. Schneider (see Rebuttal to William A. Dembski's Posting). In that paper Schneider convincingly refutes some particular points of disagreement with Dembski, related to Schneider's computer simulation of evolution.

In Elsberry's website indicated above, there are links to some other reviews of Dembski's work, including rejoinders to a few replies from Dembski to his critics.

(Comment on February 19, 2002: I have recently learned about some critical reviews of Dembski's publication of which I did not know. I am listing here the links to these postings without comments, although I found these four pieces very interesting and offering various strong arguments against Dembski's position. 1) Richard Wein, What's Wrong with the Design Inference?. 2) Taner Edis, Darwin in Mind . 3) Victor J. Stenger, Messages from Heaven. 4). Matt Young, How to Evolve Specified Complexity by Natural Means).

While there are in the above listed papers and books certain points common for more than one reviewer, who happened sometimes to have noticed the same shortcomings of Dembski's discourse, one also finds in those papers a variety of approaches and viewpoints, all of which agree though that Dembski's work contains many weaknesses and inconsistencies.

While I largely agree with the critical comments by Pennock, Ratzsch, Chiprout, Elsberry, Eells, Korthof, Pigliucci, Schneider, and Fitelson-Stephens-Sober (except for some minor points some of which will be discussed later) I intend to offer in this article my own, more or less systematic, critical analysis of Dembski's theory, including not only his explanatory filter, but also his theoretical treatment of probability, complexity, information, and design. I intend to suggest some critical points which view Dembski's discourse from angles not utilized by the mentioned reviewers. I will try to make my critical analysis of Dembski's work as simple as it is reasonably possible, thus making it more or less comprehensible for non-experts. In some instances such an approach requires substantial simplifications without which a person having no extensive educational background in certain fields will not be able to comprehend the gist of the dispute. Whenever it will be impossible to avoid using some concepts or terms with which unprepared readers may be not familiar, I will try to explain these concepts or terms in plain words.

Before starting the detailed analysis of Dembski's work, let us briefly discuss Dembski's reaction to criticism. In an article printed in November 2000 issue of "The American Spectator" another proponent of "intelligent design" Fred Heeren quotes Dembski as saying: "I always learn more from my critics than from people who think I'm wonderful." Also, on page 13 in [5] Dembski says: "How can a scientist keep from descending into dogmatism? The only way I know is to look oneself squarely in the mirror and continually affirm: 'I may be wrong...' – and mean it." This seems to be a good advice. However, reviewing Dembski's publications shows that the quoted statement as well as that quoted by Heeren must be taken with a grain of salt, because Dembski does not seem to follow his own advice. As mentioned, since his books were published, a number of highly critical reviews of them have appeared, including those from some people (like Ratzsch and Chiprout) who share Dembski's adherence to intelligent design.

The reaction from Dembski to the criticism seems to have been rather limited. From the material posted in the above mentioned Elsberry's website we can infer that Dembski has exchanged a few rejoinders with some of his opponents, including Schneider and Elsberry. He has posted a reply to Pennock. All that Dembski deigned to discuss in that brief piece, was Pennock's replacement of a single word ("evolutionists" instead of "evolution") in a quotation from Dembski, while ignoring the essence of Pennock's critical remarks regarding Dembski's publications. In a paper [5] Dembski allocated three full pages (pp 17-19) to an attack on Pennock. Almost all this criticism addressed a single paragraph in Pennock's book, in which Pennock did not mention either Dembski or the latter's writing. However, Dembski, again, ignored in his paper Pennock's criticism of Dembski's theory. In a posting, How Not to Analyze Design, Dembski replied to Eells, but his reply essentially boiled down to the assertion that Eells simply did not understand Dembski's fine theory. Dembski's public reply to Fitelson et al seems to have been limited to a single sentence at the end of his reply to Eells. (As indicated by Pigliucci and Fitelson et al, they received from Dembski private messages in reply to their criticism.) On the other hand, Dembski continues publishing the same arguments time and time again, often repeating verbatim his earlier publications, showing no sign of having paid any attention to and being seemingly unperturbed by the criticism from which he supposedly learns so much.

Dembski is obviously a well educated man of many talents, who, in my view, was led astray by his desire to promptly develop a neat theory of design, which would support his preconceived views and beliefs. Instead of following the logic of an objective analysis, he attempted to squeeze the enormous variability of real situations into the Procrustean couch of a one-dimensional theory. The real world however rarely fits a neat scheme.

Almost at the very beginning of "The Design Inference" [1] we discover a peculiar feature of Dembski's discourse. Its succinct expression is given in the following statement (page 9): "Design therefore constitutes a logical rather than causal category."

What is the meaning of that statement? If design is disconnected from any causal history, it seems to mean that Dembski's concept is that of a design without a designer.

Indeed, the quoted assertion is preceded (on page 8) by the following statement: "Although a design inference is often the occasion for inferring an intelligent agent... as a pattern of inference the design inference is not tied to any doctrine of intelligent agency." Note the word often in that quotation. Whatever interpretation of the quoted assertion one may prefer, often certainly does not mean always. It is hard to read that quotation other than an assertion that at least in some cases design does not imply a designer.

For centuries, the battle cry of the intelligent design proponents was "If there is design, there must be a designer." The proponents of the intelligent design viewed that slogan as logically unassailable. Now the new champion of intelligent design Dembski announces that the hypothesis of a designer is not necessary.

My interpretation of Dembski's assertion finds confirmation in his other statements. On the same page 9, he writes: "Thus, even though a design inference is frequently the first step toward identifying an intelligent agent, design as inferred from design inference does not entail an intelligent agent."

I submit that the design inference, whether according to Dembski, or by any other means, is aimed at distinguishing events that are designed by an intelligent agent from events that occurred without such an agent. Design inference is really interesting only if it is inference to a designer, either human, alien, or supernatural. (In order to stay within the framework of Dembski's concepts, I am not mentioning here the very interesting questions about "design" stemming either from artificial intelligence or from natural processes - as the latter was discussed by Pigliucci and Elsberry.)

The reason for Dembski's approach may be his desire to avoid accusations that "design theory" is just a disguised religion. However, to claim that design has meaning without a designer can hardly sound credible either to proponents or to opponents of the intelligent design hypothesis.

Having made his statement that separates design inference from inference to a designer, Dembski sometimes seems to forget about it. Here and there in his books and papers, he sometimes surreptitiously and sometimes quite openly squeezes in the idea of a designer who is behind the design. Actually, just two pages after Dembski's quoted claim that design does not necessarily imply an intelligent agent, Dembski seems to have forgotten this claim. He discusses an example of an election fraud committed by one Nicholas Caputo. As we will discuss later in detail, Dembski's method hinges on a triad of explanatory options which are, according to Dembski, regularity, chance and design. However, when discussing the Caputo case, Dembski presents this triad in the form regularity, chance and agency, i.e. replacing design with agency. The meaning of the term agency is unequivocally explained by Dembski in the next paragraph as an action "of a fully conscious intelligent agent" (page 11.) Hence, in Caputo's example, Dembski uses design and agency, as synonyms, where agency means actions of an intelligent agent.

This is just one example of inconsistencies found in many parts of Dembski's work.

3. Dembski's explanatory filter

Dembski suggests that his explanatory filter is a versatile tool for identifying design. He also maintains that the procedure encapsulated in his filter has been used routinely in many fields of human endeavors, without realizing it.

Dembski has published his description of the explanatory filter at least five times, in the above listed two books and three papers. The schematic presentations of his filter are slightly different in these five publications, but essentially they all are just variations of the same scheme.

There are several points underlying Dembski's scheme. One is that every event can be attributed to one of only three possible sources. The first such source Dembski calls necessity (in three of the published schemes of his filter) or regularity (in one of the published schemes) or law (in one more of the published schemes.) The second possible source of events is chance, and the third is design (sometimes also referred to as agency.) According to Dembski, these three possible sources of events cover all possibilities and are clearly distinguishable from each other. If, according to Dembski, an event can be attributed to law (regularity, necessity) then its causal connection to chance or design is unequivocally excluded. Likewise, if an event can be attributed to chance, a possibility of its causal connection to law and/or design is eliminated. Finally, if an event can be attributed to design, this automatically excludes its possible causal connection to chance and/or law. Indeed, here is a quotation from page 36 of Dembski's "The Design Inference": "To attribute an event to design is to say that it cannot reasonably be referred to either regularity or chance. Defining design as the set-theoretic complement of the disjunction regularity-or-chance guarantees that the three modes of explanation are mutually exclusive and exhaustive."

The second fundamental point of Dembski's scheme is the dominant role of probability of an event in the process of the filter's application.

The event to be analyzed is subjected to three tests, aimed at determining whether it can be attributed to regularity (law, necessity), chance, or design. Correspondingly, the filter comprises three so-called "nodes," i.e. three steps of testing. At each of the three steps there is a fork, whose one prong points out of the filter, and the other prong, to the next "node" or, in the case of the third "node," to the final conclusion about the causal antecedent of the event.

At the first "node" the choice is made between attributing the event in question either to law (regularity, necessity) or to absence of law. If law (regularity, necessity) is determined as the source of the event, the procedure stops at that step and the event is removed from the filter trough that prong of the fork leading out of the filter, while chance and design are eliminated as possible causal antecedents of that event. If, though, the law (regularity, necessity) is excluded as a causal antecedent, the event passes through the second prong of the fork, to the second "node."

At the second "node" the choice is made between either attributing the event unequivocally to chance, or, without eliminating the possibility of chance, also allowing for its possible attribution to design. If chance has been determined unequivocally as the causal antecedent, while the possibility of design is eliminated, the test stops at that step. If, though, neither chance nor design can be eliminated as possible causal antecedents, the event passes through the second prong of the fork to the third, ultimate "node." At this step, the final choice is made between attributing the event either to chance or to design, the two alternatives being, according to Dembski, mutually exclusive.

What are, according to Dembski, the criteria determining the choice between the two alternatives at each "node" of the filter? They are different for the first and the second "node," on the one hand, and for the third "node," on the other hand.

At the first and the second "nodes" there is, according to Dembski, one and only one criterion, which is the value of the event's probability. At the first "node," law (regularity, necessity) is determined as the causal antecedent of the event if, and only if the probability of that event is large. Dembski omits the question of what should be the lower bound on the probability in question in order for the event to qualify for being attributed to law (regularity, necessity.)

At the second "node," the only criterion for either unequivocally choosing chance as the causal antecedent of the event, or passing it to the third node, is again solely the value of the event's probability. If this probability is determined as being, in Dembski's terms, intermediate, the event is kicked out from the filter, being thus attributed to chance. Again, Dembski avoids indicating what is quantitatively the lower bound for the probability to be viewed as "intermediate." If, though, the probability of the event in question turns out to be "low" (whatever this term means quantitatively), the decision about the event's causal connection is postponed and the event passes through the second prong of the fork to the third "node."

The third "node" is the heart of Dembski's explanatory filter. Here the crucial choice is made between attributing the event to chance or to design. Unlike at the two preceding "nodes," where the sole criterion in use was the value of the event's probability, at the third node the criterion is two-fold. To qualify for being attributed to design, the event in question must: a) have a low probability and b) be "specified." Each of these two conditions is necessary, but neither of them alone is sufficient to attribute the event's origin to design. Only the two listed conditions together are both necessary and sufficient. If at least one of the two conditions is not met, the event is attributed to chance. If both conditions are met, the event is attributed to design.

Dembski's treatments of probability and of specification are different. In all five publications describing the explanatory filter, within the framework of that filter's scheme, probability is left without any detailed discussion (although probability is discussed in detail in a separate chapter in "The Design Inference," without explicit connection to the explanatory filter.) On the other hand, specification is discussed by Dembski in great detail.

As indicated in the preceding section, Dembski's criterion of design entails two necessary elements, one being the low probability of the event in question, and the other, the event's specification.

Dembski first explains that specification of an event means that it displays a pattern. One of the simple but telltale examples illustrating that concept is found in Michael Behe's foreword to Dembski's "Intelligent Design." Since Dembski never disowned the foreword in question, and, moreover, used himself elsewhere the same example, it seems safe to infer that he approves of Behe's presentation. Behe writes: "...we apprehend design in highly improbable (complex) events that also fit some independently identifiable pattern (specification.) For example, if we turned a corner and saw a couple of Scrabble letters on a table that spelled AN, we would not, just on that basis, be able to decide if they were purposely arranged... On the other hand, the probability of seeing some particular long sequence of Scrabble letters, such as NDEIRUABFDMOJHRINKE, is quite small (around one in a billion billion billion.) Nonetheless, if we saw that sequence lined up on a table, we would think little of it because it is not specified – it matches no recognizable pattern. But if we saw a sequence of letters that read, say, METHINKSITISLIKEAWEASEL, we would easily conclude that the letters were intentionally arranged that way... It is a product of intelligent design."

Hence, Dembski's criterion of design is the combination of a very low probability with an identifiable (recognizable, specified) pattern.

Dembski spends a considerable effort to elaborate his requirement of a recognizable pattern (specification.) In order to serve as a specification, the pattern, according to Dembski, must meet an additional condition of "detachability." While Dembski offers a rather convoluted analysis of "detachability," he also provides a simple example clarifying that concept. He writes (page 17 in "The Design Inference"): "...suppose I walk down a dirt road and find some stones lying around. The configuration of stones says nothing to me. Given my background knowledge I can discover no pattern in the configuration that I could have formulated on my own without actually seeing the stones lying about as they do. I cannot detach the pattern of stones from the configuration they assume. I therefore have no reason to attribute the configuration to anything other than chance. But suppose next an astronomer travels this same road and looks at the same stones only to find that the configuration precisely matches some highly complex constellation. Given the astronomer's background knowledge, this pattern now becomes detachable."

From that example is evident that by detachability Dembski's actually means a subjective "recognizability" of the pattern in question. In order to decide that the pattern discerned in a low probability event is detachable, and hence serves as specification, i.e. points to design, we must be able to recognize that pattern as matching some already familiar image. For that to happen, we must have a certain background knowledge.

While the concept, as exemplified in the above quotation, seems simple enough, Dembski also provides a much more convoluted elaboration of detachability accompanied by its representation in a mathematical symbolism.

In order for an event to be detachable, teaches us Dembski, it must meet several conditions.

The first condition is "conditional independence" of the background knowledge. This condition means that the background knowledge which we utilize to recognize the pattern must not affect the probability of the event in question estimated on the assumption of it being produced by chance. In other words, the background knowledge must have no probabilistic implications for the event in question. For Dembski, the probability of an event and its specification are two independent categories, not affecting each other.

The second condition is "tractability." This term means, in Dembski's words (page 149 in "The Design Inference") that "by using I it should be possible to reconstruct D," where I is the background information and D is the pattern in question.

While conditional independence and tractability are, according to Dembski, the constituent parts of detachability, to qualify for specification the pattern must meet one more condition, referred to by Dembski as "delimitation." That concept is explained by Dembski as follows (page 152 in the same book): "...to say that D delimits E (or equivalently that E conforms to D) means that E entails D* (i.e. that the occurrence of E guarantees the occurrence of D*.)" In that definition, E means an event, D means the pattern and D* means "the event described by D" (page 151 in that book.)

Dembski's main idea has been succinctly expressed under the label of "Law of Small Probability," (page 48 in "The Design Inference") as follows: "Specified events of low probability do not occur by chance."

Now, having briefly described Dembski's concept of the explanatory filter, we can turn to the discussion of its weaknesses and inconsistencies

Before discussing in detail the inconsistencies in Dembski's explanatory filter theory, I wish to first comment on one striking feature of Dembski's writing, especially pronounced in his highly technical monograph "The Design Inference."

If the quality of a mathematical treatise were evaluated by the number of mathematical symbols, Dembski's book "The Design Inference" would qualify as a great achievement in mathematics. This may be one of the reasons why many of Dembski's colleagues in the so-called "intelligent design movement" so much admire his opus. They commonly praise the supposed great rigor of Dembski's mathematical analysis. It is interesting to note, though, that most such accolades stem from the writers who themselves do not seem to be mathematicians.

Reviewing all these extensive collections of mathematical expressions in Dembski's book reveals that only a few of them are anything more than a simple illustration of whatever Dembski states in plain words. Except for a few cases (of which some are not quite relevant to Dembski's thesis) his mathematical exercise does not either prove any new mathematical theorem or derive any new formula. Actually the removal of 80% of those formulas would hardly make much difference except for depriving Dembski's book of its mathematical appearance.

The use of mathematical language in science is discussed in detail at Science In the Eyes Of a Scientist. When a new mathematical theorem is proven, it advances the mathematics itself, thus possibly opening new vistas for additional applications. If a mathematical formula is derived in physics, or some technical science, or engineering, it compresses into easily comprehensible form certain essential relations between various data, which otherwise would be much harder to review and manipulate. This immensely facilitates some useful procedure. If, though, mathematical symbolism is used for the sake of symbolism itself, it does not advance the understanding of a subject, at best simply saving some space and time in the discussion of a subject, and at worst making the matter more obscure because of esoteric symbolism which requires a lengthy deciphering.

Actually Dembski's book "The Design Inference" contains little of genuine mathematics, but is full of "mathematism," this term denoting the use of mathematical symbolism as embellishment, often possibly only to create an impression of a scientific rigor of the discourse.

To illustrate my point, consider the following example. On page 48 of "The Design Inference" Dembski offers the following argument:

Premise 1: E has occurred.

Premise 2: E is specified.

Premise 3: If E is due to chance, then E has small probability.

Premise 4: Specified events of small probability do not occur by chance.

Premise 5: E is not due to regularity.

Premise 6: E is due either to a regularity, chance or design.

Conclusion: E is due to design.

(I am not yet discussing either merits or drawbacks of the above argument, since my goal at this point is simply to illustrate the "mathematism" employed by Dembski throughout his book.)

Next Dembski writes (page 49): "The validity of the preceding argument becomes clear once we recast it in symbolic form (note that E is a fixed event and that in Premise 4, X is a bound variable ranging over events):

The above argument, now rendered in a mathematically symbolic form, exactly reiterates the preceding plain-word rendition of the same argument. A question is: in what way does representing the same argument in a symbolic form make its validity clear? I submit that reiterating the above argument in a symbolic form adds nothing to its interpretation and does not at all make its validity more clear. This symbolic rendition sheds no additional light on the argument in question, neither supporting nor negating its validity. Moreover, this rendition in itself does not even save space or time since the symbols used in it require explanation in plain words. In order to make the symbolic rendition understandable, its author had to provide a glossary of symbols. Dembski must explain to readers (I am quoting from page 49) that

As can be seen, the symbolic rendition not only does not add anything of substance, it actually has no advantages over the preceding plain-word rendition even from the viewpoint of brevity. It seems to me that its only purpose was to impart on the discourse a rigorously-mathematical appearance.

Moreover, still not satisfied with the above symbolic rendition of his "design inference," Dembski offers several modifications of that rendition, gradually making its appearance more and more complex.

Throughout his book "The Design Inference" Dembski saturates his text with numerous combinations of mathematical symbols thus creating an impression of a sophisticated mathematical treatise. In my view, most of those combinations could be left out without doing any harm to his explanations.

I can envision a possible suspicion that my criticism of Dembski's extensive use of mathematical symbolism stems from my own discomfort with mathematics. I don't think this is the case. While I am a physicist rather than a mathematician, I enjoy mathematical treatment of various problems. I have derived hundreds of formulas which have been published in several hundreds of articles and monographs. They cover a rather wide range of topics. (For those skeptical of assertions not supported by direct references, here are just two examples of my published articles chock-full of formulas: 1. Mark Perakh, "Slot-type Field-Shaping Cell: Theory, Experiment and Application." Surface and Coatings Technology, 31, 409-426, 1987; 2. Mark Perakh, "Calculation of Spontaneous Macrostress in Deposits From Deformation of Substrates and Restoring (or Restraining) Factors." Surface Technology, 8, 265-309, 1979.) I have no objections to Dembski's extensive use of mathematical symbolism, which is his right and often looks quite attractive, but I don't think this extensive mathematism justifies viewing his discourse as “mathematically rigorous.” Many parts of that mathematical symbolism seem to serve no useful purpose.

I will discuss now a point, which, in my view, entails a rather general fault of the approach embodied in Dembski's Explanatory Filter.

Suggesting his explanatory filter as a versatile tool for discrimination between law, chance and design, Dembski bases the process of such discrimination on the evaluation of probabilities of events. One moves from one "node" of the filter to the next one according to the estimated value of the event's probability.

Dembski's entire chain of arguments presumes that probability is an independent category which may be estimated by itself without accounting for the possible cause of the event in question.

For example, on page 38 of "The Design Inference" we read: "Thus, if E happens to be an HP event, we stop and attribute E to a regularity." In this sentence E stands for "event" and HP for "high probability."

Actually we can't assert that "E happens to be an HP event," if we have not first assumed that it is due to law (regularity, necessity.) In fact, probability does not exist by itself, as an abstract concept, and can only be estimated by accounting for various types of information about the event in question. Dembski seems to realize that fact when he discusses probability in a chapter about probability but seems to forget about it when he turns to his explanatory filter.

According to Dembski, at the first "node" of his filter we attribute events to law (regularity, necessity) because their probability is high. I believe that the common procedure is opposite to his scheme: we conclude that the probability of an event is high, because it is due to law (regularity, necessity.)

Possibly Dembski's reversal of the normal order of inference in this case stems from his confusion of two very different procedures – one of postulating a certain law (let us denote it procedure A) and the other of attributing a particular event to some law (procedure B.) Obviously, the procedure at the first "node" of Dembski's explanatory filter is of B type. Procedures of scientific induction (A type) which are common in scientific research are discussed in detail at Science In the Eyes Of a Scientist. The classical version of procedure A is conducted under the conditions of ceteris paribus (see the above reference).

Despite the superficial similarity between the procedure of scientific induction and Dembski's alleged attribution of an event to law because its probability is high, these two procedures are principally different. At the first "node" of Dembski's filter, we have to decide whether or not a particular event has to be attributed to a regularity, while in the procedure of a scientific induction we postulate a definite regularity after having observed multiple repetitions of occurrences of certain events. In the latter case the tentative conclusion of a researcher is that "under these particular conditions the probability of a certain event is very high." On the other hand, at the first "node" of Dembski's filter the conclusion, according to his scheme, has to be "the probability of that particular event is high, therefore it must be attributed to regularity."

However, we can't conclude that the probability of a particular event is high unless we know it is due to regularity. Assume that we observed a particular event – a piece of metal Gallium in a vessel melted when the temperature reached about 302.5 K. Observing that event does not provide any clue regarding its probability. Unless we already know the law - the transition from solid to liquid in the case of pure Gallium, at atmospheric pressure, always occurs at about 302.5 K - we cannot assert that the observed event has a high probability and therefore has to be attributed to law. On the other hand, if we know the law – pure Gallium under atmospheric pressure melts at about 302.5 K - then we can confidently attribute the observed event to a law, and hence to estimate its probability as being very high.

Even if an event has been observed many times, this in itself is not sufficient to assume that its probability is high. As discussed at Science In the Eyes Of a Scientist, there is a necessary intermediate step – postulating that the observed repetition of the event was a manifestation of a law. It is not an uncommon situation in a scientific research when a repetition of a certain event is observed but nevertheless no assumption is made that a new law is at work.

In order to assign to an event a high probability first a law has to be accepted.

Likewise, at the second "node," according to Dembski, we attribute an event to chance because its probability is "intermediate." Again, I believe that the common procedure is just the opposite: we estimate the probability of a particular event assuming first that it is due to chance (see an example with a raffle described a little later.) Note that at the third "node" of the filter, Dembski himself suggests to estimate the probability of an event by first assuming that it is due to chance, which is contrary to the procedure he suggests for the second "node."

As can be seen from Dembski's own definition of probability (which will be discussed in detail in one of the subsequent sections) he defines probability as being conditioned "with respect to the background information." I believe that if Dembski has adopted a certain definition, he is supposed to stick to it throughout his discourse. However, when Dembski turns to his explanatory filter he seems to forget his own concept of probability.

Imagine that we estimate the probability of John Doe's winning in a raffle. Let us assume that there are one million tickets distributed in that raffle, each with the same chance of winning. What is our estimate of John Doe's probability of winning? Can we say unconditionally that the probability in question is one in a million? If we adopt Dembski's definition of probability, we can't say that. Based on his definition, we must say instead: "John Doe's probability of winning is one in a million upon the assumption that the drawing is random." In other words, the estimation of probability incorporates an assumption regarding the nature of the event in question, namely its being the result of chance. Accounting for all the relevant background information is necessary if we want to meet Dembski's definition of probability.

Imagine, though, that we have information about John Doe being in cahoots with the organizers of the raffle who have a record of earlier frauds. This background information must be incorporated in our estimate of probability. Upon the assumption that the new information obtains, the new estimate of probability of John Doe's winning is immensely higher than before. Based on the new information, we assume that John Doe's win is due to design (in this case, fraud), and that new assumption leads to a drastically increased estimate of the probability of his win.

The situation is different for the third node of Dembski's filter where the probability is first estimated upon the assumption of chance as the cause of the event, and then the situation is reconsidered accounting for the side information. The latter is though assumed not to affect the probability. I will discuss this assumption in subsequent sections.

It does not matter for the estimation of probability whether background information is actually available or is assumed for the sake of estimation. We estimate probability on the basis of a certain background information, either actually available, or assumed for the sake of estimation. Consciously or subconsciously, the assumption about the cause of the event is incorporated into the estimate of probability.

In particular, to conclude that an event is due to law, we have, according to Dembski, to first find that its probability is high. However, if we do not assume a priori that the event is due to law, so that we estimate its probability upon the assumption that it is due to chance, we will often arrive at a small probability which, according to Dembski, would point to either chance or design rather than to law. Here seems to be a vicious circle and to break out of it, there seems to be the only way – to get out of the confines of Dembski's scheme.

In subsequent sections I will further elaborate on that thesis, both in a way of examples and through some more general notions.

Another weakness of Dembski's scheme seems to be that, while attributing each event to either law, or chance, or design, he fails to account for the taxonomy of events according to any other criteria. It seems rather obvious that there are whole classes of events for which it may be impossible to identify their causal antecedents as belonging to only one of the three distinctive categories.

Consider one of Dembski's favorite examples, that of an archery competition. If an archer shot an arrow and hit a target, it is, according to Dembski, a specified event which definitely must be attributed to design. In Dembski's scheme, design excludes both chance and law. Can we really exclude law as a causal antecedent of the event in question? I submit that the archer's success was the result not of design alone, but of a combination of design and law. Indeed, archer's skill manifests itself only in ensuring a certain velocity of the arrow at the moment it leaves the bow. This value of velocity is due to design. However, as soon as the arrow has separated from the bow, its further flight is governed by laws of mechanics. The specified event – the perfect hit – was due to both design and law. The arrow would not hit the target if any one of these two causal antecedents were absent. We simply cannot separate the design from law in this case, because in this case design operates through law and would be impossible without law. Therefore Dembski's scheme which artificially divorces law from design, viewing them as two completely independent explanatory categories, does not seem to jibe with reality. (Besides law, chance may also contribute to the occurrence of a hit; for example, an accidental gust of wind may affect the flight of the arrow.)

In the class of events exemplified by the archer's feat, law and design not only are not mutually exclusive but, on the contrary, are complementary causal factors.

Likewise, there is a whole class of events for which it is impossible to separate law from chance as causal antecedents. Here is an example. There is a machine used for training tennis players. It randomly hurls tennis balls toward a player. There may be a large number of balls flying every minute, and it is impossible to predict the exact direction of each next flying ball. Choose an area anywhere within the court, say, of one square meter. Assume a particular ball landed within that area. Is that event due to chance or law? If in the course of a certain period of time the total number of flying balls was, say, 1000, and, say, only 50 of those balls landed within the selected one square meter, I believe, in such a situation most of the observers will attribute the event in question to chance. In fact, though, chance only determines the initial velocity of each ball. Upon leaving the machine, the flight of the ball and hence the location of its landing are determined by laws of mechanics. In this case, chance operates through law, so the location of the ball's landing is determined by both chance and law. The event most reasonably has to be attributed to a combination of law and chance.

Hence, for certain classes of events Dembski's filter fails to deliver already at its first "node."

Furthermore, as statistical science shows, random events follow certain laws, therefore even if an event is viewed as random, it cannot be completely divorced from a (statistical) law which is instrumental in causing the event in question. For example, recall the so called Galton board which is a device demonstrating the normal (Gaussian) distribution of chance events. In this device, hundreds of small balls are placed in a hopper which has an opening in its bottom. Pulled by gravitation, the balls fall down one by one. On their way down, the balls encounter a grid of hexagonal baffles. At each baffle, each ball has the same probability of 1/2 to pass the baffle either on the latter's left or its right side. After passing several rows of baffles, the balls fall into a row of bins. Which ball happens to get into which bin, is determined by chance. However, regardless of the absolute sizes of the device or of its parts, the overall result is always the same: when a sufficiently large number of balls fill the bins, their distribution between the bins meets the normal (Gaussian) distribution. In this case, the situation is in a sense opposite to the case of the tennis balls: while for the tennis balls chance operated through law, now the law (Gaussian distribution) operates through chance.

In all those examples, law and chance or law and design are equally contributing causal antecedents of an event.

Moreover, if we review again the example with tennis balls, it easy to see that, since the machine that hurls the balls has been designed by a human intelligent agent (an engineer) the event in question may be viewed in a certain sense as a causal consequent of all three sources – design, chance and law, whose contributions to the occurrence of the event cannot be separated from each other since each of them is necessary for the event to occur.

There are enormously many situations wherein regularity, design and chance are intertwined in various combinations, each contributing to varying degrees to the occurrence of events. Moreover, more than half a century after the formulation of principles of cybernetics, Dembski's scheme seems to be too simplistic in that it views the causal history of events as a one-directional straightforward process, thus ignoring feedbacks, conditional causes, superimposition of multiple causes of events, etc.

Therefore, in my view, Dembski's scheme based on the uncompromising demarcation between law, chance and design which are viewed as clearly separate causal categories, being always completely independent from each other, seems to be rather off the mark.

Now review what happens if an event passed to the second "node" of Dembski's filter. At this step, the probability of the event, which was found to be "not large" at the preceding step, is re-evaluated, to determine whether it is "intermediate" or "small." We know already that Dembski does not offer a definite quantitative criterion for classifying probability as either "intermediate," or "small." Of course, without such a criterion the procedure becomes quite uncertain, since what seems to be small for John may seem very large for Mary.

The more important objection to Dembski's scheme is, though, that, according to the above analysis, attributing an event to law or chance is normally not based on a prior estimate of probability, as Dembski suggests, but, on the contrary, probability can be estimated only after either law or chance have been determined as the event's causal antecedents. Therefore I submit that the first and the second "nodes" of his filter offer an unrealistic scenario and hence play no useful role for the design inference.

If any meaningful design inference takes place, all of it can only occur within the framework of the third "node" of the filter.

Of course, if that is the case, the filter loses its impressive appearance of a triad so neatly matching the three supposedly independent causes of events.

Assume, though, that we follow Dembski's scheme and, having arrived at the second "node," have somehow determined that the probability of the event in question is not "intermediate" but "small," in which case we proceed to the third "node" of the filter.

At the third "node" of the filter, according to Dembski's scheme, the choice is made between design and chance. Before analyzing the details of Dembski's procedure for discrimination between design and chance, let us briefly discuss a few general points.

One such point is the nature of design, and another is what can be called "the degree of design."

Regarding the nature of design, it seems reasonable to distinguish between various types of design. Even if we omit the host of vexing questions related to the possible design by artificial intelligence, we still can imagine at least three different kinds of design, namely a human design, an extraterrestrial's design, and a supernatural design. This question has been very thoroughly analyzed by Ratzsch [7]. (I am omitting the discussion of the design by either artificial intelligence or by natural processes because these types of design are completely absent in Dembski's theory.)

Dembski does not seem to acknowledge the differences between these three versions of design. On the contrary, he seems to stress the features common for all types of design. Remember Dembski's statement that design is a logical rather than causal category and that design does not necessarily entail a designer?

When we are dealing with a human design, usually we recognize design quite easily. Neither a "design theorist" such as Dembski nor the opponents of that "theory" will argue about the source of a poem or a novel, both readily attributing it to design and rejecting chance as a possible source of the text in question.

In case of a hypothetical extraterrestrial design, the situation is more complex. Since we have no experience with such type of design, we may be at loss when encountering certain objects which may look for us as having emerged through some chain of chance events whereas they may be products of a mind whose mental processes can be immensely different from ours. Dembski's filter seems to be hardly of help in such a situation.

If we turn to supernatural design, the problem is both similar and different as compared with extraterrestrial design. In the case of aliens we can at least reasonably assume that their designing activity is constrained by the same laws of physics we are familiar with. If we assume, as it is commonly done, that the supernatural designer is omnipotent, i.e. is not constrained by natural laws and is capable of creating new laws at will or breaking the existing laws in any particular case, then the distinction between law and design, as applied to a supernatural design, becomes meaningless, since the natural laws themselves are assumed to have been created by the supernatural designer. Again, Dembski's filter does not seem to be of help in that situation either.

Because of Dembski's generalization of the supposed indications of design, without accounting for differences between human, alien and supernatural design, his filter is useless for the most interesting discrimination – between the three listed types of design.

In relation to Dembski's concept of specification, let us again take a look at Behe's example with Scrabble letters. In that example, whose versions have also been discussed by Dembski, two strings of letters are compared, one a meaningless combination and the other a phrase from Hamlet. According to the Dembski/Behe explanation, both strings have equally low probability of emergence by chance. We recognize design in the meaningful phrase because, according to Dembski's scheme, it is specified, i.e. conforms to a recognizable pattern, while the line of gibberish is not specified and therefore is attributed to chance.

I submit that the explanation by Dembski/Behe is not quite adequate. I believe it is more reasonable to conclude that if we see a string of Scrabble letters on a table, we attribute its occurrence to agency regardless of its being a quotation from Shakespeare or a piece of gibberish. Remember, that on page 11 of "The Design Inference" Dembski used the term agency as a synonym for design, although elsewhere he distinguishes between these two concepts.

(The readers familiar with Ratzsch's book [7] may notice that if design is used as a synonym for agency, this is different from Ratzsch's interpretation. The latter seems to interpret design as necessarily including a purpose on the part of the "designer." Since Dembski's approach entails separation of design inference from an inference to a designer, obviously the question of a designer's purpose becomes moot. Since this discussion is about Dembski's theory, I will assume that the only question we are really concerned with is whether an event occurred by chance or its causal antecedent can be traced to an intelligent agent, and that a purpose such an agent might or might not have, while may be of interest, will be a separate issue. Hence I will use the term "design" simply to mean that the event in question occurred because of an action by an intelligent agent, leaving out the question of purpose.)

Back to the example with the two strings of Scrabble letters, we do not think even for a minute that the letters in the gibberish sequence have lined up on the table by themselves, due to some chance process. Somebody had to make these letters, bring them to the room, place on the table and arrange along a straight line. We are confident all this was done by a human, i.e. the occurrence of that piece of gibberish was due to design (in the above defined sense) not any less than the occurrence of the phrase from Hamlet.

In one case the "designer" (or a group of "designers") made the letters, brought them to the room, placed them on a table, arranged them randomly along a straight line and stopped at that point of their "designing" actions. In the other case, a designer continued, taking care to arrange the letters in an order forming a meaningful phrase in English. It is possible to say that the meaningful string is more narrowly specified than the random string. The difference seems to be in the degree of specification but not in its presence in one string and absence in the other.

Review again the possible counter-argument that the difference between a meaningful text and a gibberish is in that the former entails a purpose, while the latter does not. We have to remember, though, that Dembski defines design simply as the only remaining option after law and chance have been eliminated. With such an interpretation, the question of purpose involved in design becomes moot.

Moreover, I believe that the common concept of purpose entails the concept of a conscious action. If an event resulted from a subconscious action it can hardly be attributed to a purpose even if the action was by an intelligent agent.

It is easy to imagine situations when a meaningful phrase resulted from a purposeless action, while a gibberish phrase has been created for a purpose. There are many examples of the former. Whoever has taken part in lengthy and boring meetings knows that very commonly the participants, while listening to the discussion, absentmindedly chew pencils, bend and unbend fingers, and often doodle and scribble on pieces of paper. The products of these subconscious actions are most often meaningless figures and nets of curves, but not too rarely they form some meaningful words and even phrases, created without consciously realizing that and which their creators would not be able to remember a minute after the meeting is over, not to mention explaining the purpose of those phrases.

Now turn to an example of a gibberish phrase created for a purpose. Look at the following line: "Epsel mopsel raisobes." This line is a quotation from a poem by a Russian poet A. Zakharenkov, printed in a collection "Strofy Veka" (Polifact Publishers, Moscow, 1997.) This sequence is gibberish, it has no meaning either in Russian or in any other language. Its author deliberately wrote this line as gibberish to create a certain comic effect. It was designed for a purpose.

Let us again review the question whether or not a string of letters must necessarily have an identifiable semantic meaning in order to be viewed as "specified."

Here is an example. Since 1912 many scholars all over the world have been investing a considerable effort trying to decipher the so-called Voynich manuscript (VMs.) A slightly magnified black-and-white photo of a segment of that manuscript is shown in fig.1.

Neither the language nor the alphabet of that manuscript are known. All attempts to decode it have so far been unsuccessful. Therefore some scholars suggested that it has no meaningful contents but is a hoax, just over 200 pages of gibberish. I am of the opinion, based on a statistical analysis of the VMs's text and shared by the majority of those who have tried deciphering VMs, that it is a meaningful text. On the other hand, my colleague in the effort to apply the Letter Serial Correlation test to VMs, Dr. Brendan McKay, as well as some other scholars, is inclined to think that it is gibberish. However, regardless of the choice between the two mentioned views, nobody has ever doubted that VMs was written by some medieval author, i.e. that it is a product of design.

A glance at the text in fig. 1 makes it immediately obvious that we deal with an artifact, designed by a human mind, even though it is unknown whether or not the text is meaningful. Contrary to Dembski's scheme, the design is identified in this case without having available any "detachable" pattern, which, according to Dembski, is a necessary condition for recognizing design.

Does the above discussion mean that there is no difference between a quotation from Hamlet and a line of gibberish? Of course, there is a difference. It is in what can be termed as "degree of design." To place on a table a string of Scrabble letters arranged along a straight line requires design. Making a meaningful phrase requires, I would say, "more" of a design. Both the string of gibberish and the quotation from Hamlet are specified, but to a different degree. To form a quotation from Hamlet requires an agent who is more intelligent than it is sufficient to simply place a meaningless string of Scrabble letters on a table. Indeed, in the first case the intelligent agent must be familiar with Shakespeare's plays, while in the second case the letters could be placed on a table by an illiterate peasant. The recognition of different degrees of specification is absent in Dembski's discourse.

Let us note that Dembski's view of the difference between the two strings of Scrabble letters seems to indicate that he considers meaningfulness of the string as the indication of design, while the absence of meaning as an indication of chance. We will remember that when discussing Dembski's treatment of information.

An important point seems to be also that all of the above discussion is relevant only to human design. In the case of an alien design, and even more of a supernatural design, not to mention design by artificial intelligence, we may not know what the signs of design really are. In the case of a supernatural design, the requirements of meaningfulness may indeed be legitimate for recognizing design.

Let us now discuss specification from another angle.

According to Dembski, to qualify as specification, the event must be "detachable" and meet the condition of delimitation. In its turn, to be "detachable," the event must meet the conditions of epistemic independence of the side information and of tractability. While this multi-step scheme looks rather complicated, especially when Dembski renders it in a heavily symbolic mathematical form, when we review examples provided by Dembski himself or by his colleague Behe, we see that actually the idea underlying the discrimination procedure is not very complicated at all. In one example an astronomer recognized the configuration of a constellation in a pile of stones. In another example, we recognize a quotation from Hamlet in a string of Scrabble letters.

Actually all those convoluted notions of detachability, tractability and delimitation seem to be superfluous and the criterion of specification seems to boil down to the simple requirement that can be expressed as: an event is specified if it displays a recognizable pattern. Of course, if Dembski limited his discourse to such a brief and easily comprehensible assertion, he would not be able to write a whole book with its seemingly sophisticated mathematical apparatus.

What does recognizability entail? To recognize a pattern we must have in mind some image, independent of the pattern actually observed, to which we compare the observed pattern. That is actually the idea of "detachability," stripped of its sophisticated embellishments.

In view of the above, we can discuss Dembski's criterion of design without delving into the intricacies of his convoluted mathematical discourse.

Dembski admits that intelligent agents can, in his words, "mimic" chance and that in such cases his filter produces "false negatives."

However, insists Dembski, his filter never produces "false positives." In other words, if at the third "node" of the filter the conclusion is that the event is due to design, this conclusion is reliable.

To support his assertion, Dembski suggests two lines of proof. The first proof of the filter's reliability, according to Dembski (page 107 in [3]) is a "straightforward inductive argument: in every instance where the explanatory filter attributes design and where the underlying causal history is known, it turns out design is present; therefore design actually is present whenever the explanatory filter attributes design."

While Dembski devotes several pages to the elaboration of this assertion, he does not substantiate it by providing any record which would indeed show his filter's impeccable reliability. How can he prove that, indeed, his filter correctly indicates design in every instance? At best, he may assert that in those few examples he has investigated, his scheme indeed correctly identified design, but how can he be sure that it is true for "every instance?" Indeed, he has reviewed in his publications only a few examples, thus hardly providing a basis for sweeping generalization (not to mention that we don't know whether or not his examples were deliberately selected to meet his requirements.)

Generally speaking, anecdotal evidence is not proof. However, when a categorical statement like that by Dembski is offered, anecdotal examples can legitimately serve as a rebuttal. In a few paragraphs, I will describe instances of "false positives," which, in my view, exemplify the lack of substantiation in Dembski's categorical assertion.

The second argument offered by Dembski to prove the immunity of his filter to false positives is (page 111 in [3]): "The explanatory filter is a reliable criterion for detecting design because it coincides with how we recognize intelligent causation generally."

In that statement Dembski seems to stand alone in knowing for sure how "we recognize the intelligent causation generally." I submit that such a statement is rather dubious. Dembski suggested his filter precisely as a better and more reliable tool for recognition of "intelligent causation." Now he justifies its alleged perfection by comparing it to how we do it without his filter. How exactly do we recognize intelligent causation? If we can do it without his filter, and we all know how we do it, what then is his filter for? If his filter, though, is indeed a hitherto unknown perfect tool for recognizing intelligent causation, which is superior to "how we do it generally," then how can the comparison to an inferior way "we do it generally" vouch for the filter's reliability?

Both arguments in favor of his filter's reliability only express Dembski's own personal view but hardly have evidentiary significance.

Let us see if indeed "false positive" are never produced by the explanatory filter.

I submit that Dembski's explanatory filter can and does produce false positives in many common situations. One example of a "false positive" produced by Dembski's filter was suggested by Ratzsch (the "tumbleweed case" in [3].)

Here is another example. This is a real story. I can easily imagine that many readers may disbelieve it and think that I have made it up. However unbelievable it may seem, it is true and I will tell it, trying to recall it as accurately as possible.

He was traveling with his wife and two daughters from Balkhash to his native city of Kharkov in the Ukraine for vacation. On the morning of that day, on his way from Balkhash to Kharkov, he arrived in Moscow, where he was to stay for only a few hours, and then depart for Kharkov in the afternoon. One of his daughters caught cold. He left his family at the railway station and took the subway to Okhotny Ryad to find a pharmacy.

It is obvious that the probability of a chance encounter with Kot in the described circumstances was minuscule.

It is easy to verify that the described event also met Dembski's conditions of detachability (which comprises conditional independence and tractability) and delimitation. Instead of delving into Dembski's detailed definitions of these concepts, let us simply recall his own example of an astronomer who recognized the configuration of a constellation in a pile of stones. The astronomer in that example recognized the pattern because he had the proper background knowledge – he had in his mind the image of that constellation. This image did not affect the probability that the configuration of stones happened by chance (i.e. conditional independence.) He could easily create in his mind the image of the constellation in question (i.e. tractability.) The configuration actually observed was among those he had in his mind (i.e. delimitation.) Likewise, I recognized my cousin because I already had in my mind the image of him, which knowledge did not affect the probability of our chance encounter (i.e. conditional independence). I could easily create in my mind the image of Kot (i.e. tractability.) The image of Kot was among all those images I had in my mind (i.e. delimitation). If, according to Dembski, the astronomer's recognition of the configuration of a constellation was a specified event of low probability, then so too was my encounter with Kot.

In Dembski's view, recognizing the configuration of a constellation in a pile of stone leads inevitably to inferring design, i.e. to the conclusion that somebody intentionally arranged the stones in the observed configuration. Hence, if we accept Dembski's scheme, we have to conclude that my encounter with Kot was designed. It was not. This is a clear case of a false positive.

The story, however, had a continuation. In 1969 I lived in the city of Tver, some 120 miles north-west of Moscow. In April of 1969, exactly twenty years after my amazing encounter with my cousin, one morning I took a train to Moscow where I planned to stay for just a few hours and return to Tver the same evening. Close to noon I was walking on the same block of the same Okhotny Ryad street where twenty years earlier I had met Kot. Suddenly somebody hugged me from behind. I turned and, to my amazement, recognized my old friend Karl F. (Karl is alive and well and now lives in Brisbane, Australia.) Our friendship started in the fall of 1952 when we both worked at the same institute in Dushanbe, Tajikistan. It was based on our shared love for mountains. We climbed many mountains together in Pamir and Tien-Shan. The last time I met him before that encounter in April 1969 was in Siberia in 1959. Since then, I did not know his whereabouts. Now, in April of 1969, I learned from Karl that at that time he lived, of all places, in the city of Balkhash! He wound up in that forlorn city due to peculiar circumstances which are irrelevant to this story. He came to Moscow for only a few days.

I leave it to the readers to estimate the probability of our encounter at exactly that minute at exactly that particular spot, exactly twenty years after a similar encounter at the same location, with my cousin, a man whose name also began with the letter K, each time ten years after my previous meeting with each of them, both having come from the same remote town. The precise calculation of probability for the described events is difficult because many details of the situation have to be assumed without a verifiable information (for example, I can't confidently assert what exactly were the frequency and durations of Kot's and Karl's visits to Moscow, how many streets there are in Moscow, etc.) Therefore I will not provide specific numbers for that probability (although, making a few assumptions, I could roughly estimate it as being about ten to the power of minus fifty.)

Regarding a detachable pattern which is necessary, according to Dembski's theory, to infer design, if Dembski identifies such a pattern in the case of an archer hitting a target, certainly a much more pronounced specified pattern can be seen in the above story.

Let us now apply Dembski's design inference scheme to the described event. To this end, let us copy the design inference argument from Dembski's book in its symbolic form (page 49 in "The Design Inference") and add to it the description of the event in plain words. In the following scheme, Dembski's argument in its mathematically symbolic form, which was shown in one of the preceding sections of this article and designated as set (A) of formulas, is on the left, while my addition of the particulars of the event in question is on the right in the double square brackets.

Indeed? Isn't this a false positive at its extreme? Contrary to Dembski's confidence in the reliability of his scheme, which allegedly never produces false positives, such false positives can be expected in many situations.

If my extremely improbable encounters with Kot and Karl can be viewed as a rare exception, a rather more common example that immediately comes to mind is a raffle. Imagine a raffle in which ten million tickets have been sold, each bearing a seven-digit number, from, say, 0000001 to 9999999. Sweepstakes in which up to thirty million and even more tickets are distributed, for example by magazine peddlers, are quite common in the USA. The winning number is usually predetermined in advance, say that in our example it is 9765328. The probability of winning for each individual player is of course the same - one in ten million provided fraud is excluded. While this probability is not as exceedingly small as those sometimes calculated, for example, for the spontaneous emergence of a protein molecule, it is small enough to exclude law as a cause of winning. If John Doe won in an honestly conducted raffle, it was due to chance. However the event – John Doe's winning - is clearly specified. Both the player and the winning number are specified. In particular, the winning number constitutes a recognizable pattern. The combination of small probability and recognizable pattern, according to Dembski's filter, determines design (in this case fraud) as the cause of that event. It seems to be a false positive.

Of course, Dembski might say that the probability in this case is not small enough to warrant the conclusion of design. Indeed, this is his argument when he discusses the case of Shoemaker-Levy comet (wherein he estimated the probability as being 10^-8 - page 228 in "The Design Inference") insisting that his filter does not yield design easily. The probability of an event, according to Dembski, must be very low indeed to infer design. However, on page 189 of "The Design Inference," where Dembski discusses what constitutes a sufficiently small probability, he characterizes probability of 10^-5which is 100 times larger than in our example, as sufficiently "small to eliminate chance in case the conditional independence and tractability conditions are also satisfied." The listed conditions are satisfied in our example. Anyway, the numbers in themselves are not crucial, it is the principle which is under discussion. Indeed, it can easily be shown that the absolute value of probability is of secondary significance, and one in ten million and sometimes much larger numbers, can in many instances be justifiably viewed as a sufficiently small probability for the purpose of design inference.

To this end, consider a small raffle in which only 100 tickets are sold, which, however, is played more than once. The probability of John Doe's winning once in that raffle, if it is conducted honestly, is, of course, 1/100. Assume now that John Doe won that raffle three times in a row. The probability of such a triple win is (1/100)³ which is one in a million. That is ten times larger than in the above mentioned sweepstakes where it was one in ten million. However, despite larger probability of the triple win in the latter case, we now suspect fraud, i.e. design, and justifiably so. In the latter case the probability of one in a million is obviously small enough to suspect fraud, while the smaller probability in the sweepstakes with ten million players is justifiably used for assuming chance. This shows that the meaning of a certain value of probability is not absolute but has to be viewed in relation to the specific circumstances of the event, which does not seem to be accounted for by Dembski's filter.

(A detailed discussion of the reasons for the different intuitive interpretation of the results in a large raffle played just once and small raffle played several times in a row, is given in Improbable Probabilities.

It should be stressed that the particular event to be analyzed is a specified player winning in the raffle/sweepstakes, not someone winning. If in the case of the large sweepstakes we decide that one in ten million is not small enough to warrant the design inference, then it should hold even more for the small raffle played three times, where the probability of the event in question is ten times larger. On the other hand, if we decide that the probability of one in a million is small enough to infer design in the case of a triple win, it should hold even more for the case of a large sweepstakes where the probability of the event is ten times smaller.

I believe the above examples show some of the deficiencies of Dembski's filter which can easily produce both false negatives and false positives. It can be expected that in many cases we will be unable to decide whether the probability of a specified event is small enough to infer design or is "intermediate" thus pointing to chance.

I believe that there are whole classes of situations in which Dembski's explanatory filter is fully expected to produce false positives.

One such situation is that of an illusory pattern.

To clarify the concept of an illusory pattern, consider the following example. The Caucasus mountain range extends for several hundred miles. It comprises thousands of peaks, passes, dales and valleys, gorges and chasms, glaciers and moraines, etc. All these relief elements have different shapes, most of them quite irregular, although here and there parts of a mountain may form some more or less regular geometric patterns. The particular shape of this or that relief's element depends on an enormously large number of accidental factors so when we observe a particular mountain we realize that its particular shape has an extremely small probability. If we apply Dembski's filter to find whether or not that particular mountain's shape is due to chance or design, it would easily pass the first two nodes of the filter and lead right to the third, the crucial test in which we will look for a recognizable pattern. For the overwhelming majority of the mountains no pattern will be recognized, so the emergence of the particular shape of any particular mountain will be justifiably attributed to chance.

(Of course, some proponents of intelligent design can insist that everything is the result of design by a supernatural mind, so the irregular or sometimes seemingly regular shapes of the hills and gorges were designed that way. There is no rational way to reject such a statement. If, though, such a claim were made, it would make Dembski's filter absolutely unnecessary, since that filter allows for chance events to occur, while the above claim denies their existence altogether. Our discussion is within the framework of an approach which allows for chance and deals with the question of how to rationally distinguish between chance and design, in particular using Dembski's criterion.)

There is, though, in the Dombai region of the Caucasus range a mountain named Sulakhat. This word is a woman's name in the local language. Anybody looking up at Sulakhat from the valley circling that mountain immediately understands the reason for that name. From the valley the mountain looks like the perfect profile of a woman on her back, with the clearly delineated features of a young pretty face, neatly combed hair, taut breasts, arms crossed over her stomach, and slim legs slightly bent at the knees. The contours of the woman's body display all the features of a fine work by an accomplished sculptor. Many first-time visitors to Dombai refuse to believe that all they are seeing is an accidental combination of rocks and ice fields. Indeed, if we apply Dembski's filter, we clearly see a combination of improbability (complexity) with a recognizable pattern, which, according to Dembski, indicates design.

If, having climbed the mountain and having accurately measured the "body" of Sulakhat, we discovered that it is indeed a figure carved from a giant slab of stone, we could reasonably decide that the filter provided good reason to conclude that we saw the product of design.

Actually, this is a clear example of an illusory pattern. Indeed, as mountain climbers walk up the slopes of Sulakhat, they gradually discover that the sculpture-like shape is an illusion. The part that from the valley looks like a head turns out to be a combination of various rocks, scattered over a wide plateau and separated from each other sometimes by hundreds of feet. The two protrusions that from the valley look like a pair of breasts turn out to be of quite different shape and of grossly different size. They are located far apart and accidentally project toward the valley as though they are next to each other, thus falsely appearing of about the same size and of a similar breast-like shape. In other words, at a closer look, the alleged sculpture breaks down into an incoherent conglomerate of unrelated pieces. The explanatory filter has produced a false positive. The very low probability of Sulakhat's emergence by chance is indisputable. A recognized pattern is there for all (from the valley!) to see. "Design!" announces Dembski's filter. "Illusion," is the correct answer.

The described example of an illusory pattern can also be viewed as one more manifestation of the subjectivity of Dembski's criterion. From the subjective viewpoint of an observer who looks at Sulakhat from the valley, there seems to be a recognizable pattern. From the subjective viewpoint of an observer who has climbed the mountain, there is no recognizable pattern in the shape of that mountain. The criterion in question is subjective in regard to both false negatives and false positives.

In Dembski's scheme, specification is explicitly viewed as a category independent of probability. Moreover, he specifically maintains that the side information utilized to establish specification must be conditionally independent of the probability, expressing it as P(E|H&I)=P(E|H), where E stands for event, H is in this case the assumption that the event is due to chance and I is the side information.

In my view, the described approach is faulty. I submit that the procedure of design inference is essentially an estimation of the probability of either design or chance. Therefore the real role of specification is only in enhancing the probability of design as compared with the alternatives.

In Dembski's scheme, when we reach the third node of the filter, we first estimate the probability of the event in question assuming that it occurred by chance. If it turns out to be small, then, according to Dembski, we look for specification, i.e. for a recognizable pattern. If we find such pattern, it leads to the design inference.

Time and time again, throughout his books and papers, Dembski states that small probability in itself is insufficient to infer design. To infer design, according to Dembski, small probability must be accompanied by a recognizable pattern. In my view, Dembski's formula for inferring design unnecessarily introduces an artificial dichotomy between probability and specification. In fact, specification (i.e. a recognizable pattern) is not a factor independent of probability but rather only one of many factors affecting the estimate of the probability of design as compared with chance.

I guess that my approach is rooted in my background in statistical physics. The latter is a magnificent science, developed by such intellectual giants as Boltzmann, Maxwell, Gibbs, Clausius, Gauss, and other inordinately powerful minds. It has been established as a highly reliable penetration into reality. One of its salient features is that it clarifies the laws of thermodynamics, revealing the actual statistical nature of the latter. For example, statistical physics asserts that the predictions of the 2nd law of thermodynamics are not absolute but only determine the most probable outcomes of natural processes. The predictions of that law practically are highly reliable only because of their overwhelmingly larger probability as compared with any alternative occurrences. The extremely low probability of alternative events is the sole reason the laws of thermodynamics work so well despite not being statements of absolute truth.

While events may be affected by a multitude of factors, statistical physics incorporates all of them in one ultimate criterion – the probability of the event in question.

Accounting for the great success of statistical physics, I see no reason why the same approach should not be utilized in discussing the probability of design vs. chance. There is no need to separate specification from probability as an independent factor. Following the proven approach of statistical physics, it seems more reasonable to view specification as just another factor contributing to the probability of design vs chance. Like in statistical physics, what really counts is the overall probability of either design or chance, regardless which components it comprises. One of these components may or may not be specification, i.e. a recognizable pattern. In some circumstances specification may be a more important contributor to probability than other factors, while in some other circumstances it may be a less important contributor. In certain situations specification may not be a contributor to the probability of design at all. In that, specification, i.e. a recognizable pattern, is not any different from many other factors contributing to the estimate of probability of design vs chance.

If we see a poem or a novel, we unequivocally recognize design because the probability of design is overwhelmingly larger that that of chance. In this particular case, specification, i.e. a detachable pattern, contributes to the large probability of design. However, it is by no means the only possible situation. We may encounter an item which does not look as any familiar image, and hence does not match any detachable pattern, but identify it as an obvious artifact, because many factors other than specification combine in an unequivocal indication of the overwhelming probability of design as compared with chance. The Voynich manuscript is just one example of such a situation.

Dembski's attribution of a special status to specification as compared with other factors does not seem to be justified by evidence.

The design inference is never absolute. It can only be made in probabilistic terms. If an event has a very small probability of occurring by chance, a hypothesis of design may be highly reasonable. Dembski asserts, however, that small probability is not in itself sufficient to infer design. If the event also displays a recognizable pattern, the probability of design becomes even larger. However, in principle it is still a hypothesis, albeit with a higher probability. If, as Dembski states time and time again, low probability in itself is not sufficient to unequivocally infer design, neither is the combination of low probability with specification, because all the latter does is simply decreasing the probability of chance. This in itself does not introduce a new quality into the inference procedure, but is only a quantitative step toward the hypothesis of design.

Indeed, as several examples discussed in preceding paragraphs have shown, sometimes design can be reliably inferred in the absence of a recognizable pattern, i.e. of specification (as in all cases of "false negatives" whose possibility Dembski admits) while in other cases specification does not ensure the reliability of the design inference (as in cases of "false positives" which have been shown to happen despite Dembski's assertion to the contrary.) Therefore the conclusion seems to be that the entire foundation of Dembski's scheme is built on sand.

Dembski is right when, unlike some of his colleagues in the "intelligent design movement," he asserts that low probability in itself is not sufficient to eliminate chance as the source of an event. Indeed, chance events of extremely small probability occur routinely every minute. However, this situation cannot be remedied by mechanically adding to the estimate of probability some other factor, be it specification in Dembski's sense or anything else. Whichever additional factor is taken into consideration, it may or may not change the estimate of the probability in question. Therefore the design inference is doomed to be probabilistic. This does not though prevent such an inference from sometimes being highly plausible, but this plausibility may be achieved both in cases when specification according to Dembski is present and in cases when no such specification is discovered. In the example of the Voynich manuscript, no Dembski-sense specification seems to be found, however the design inference is quite reasonable, although it is based solely on the overwhelmingly larger probability of design vs. chance.

Another comment in regard to Dembski's definition of specification can be made if we review his favorite example of archery. In that example, Dembski compares two situations. In one an archer hits a wide wall and afterwards paints a target around the arrow. This is, in Dembski's terms, fabrication. In the other situation, an archer hits a small target that was painted on the wall beforehand. This is specification, says Dembski.

Whereas the case of fabrication is simply not interesting, it is easy to see that the difference between the two situations is not that in the first case the event was not specified while in the second case it was. The event is obviously specified in both cases. The entire wall is just a larger target (i.e., constitutes a "recognizable pattern") than the small round target painted on that wall. The difference is in the size of the target, which, of course, is not a principal difference. The same difference exists between, say, a painted target which is 5 cm in diameter and a painted target which is 50 cm in diameter. In both cases the event is specified. The mere fact that in one case a target is painted while in the other case the entire wall is a target, does not distinguish the events in terms of specification. The difference is only in a different probability of a hit.

Later we will discuss Dembski's theory of complexity in which he ties together three concepts: complexity, probability and difficulty of solving a problem. According to that theory, the more difficult is it to achieve a certain result, the smaller is its probability (which seems to be a trivial observation; but let us wait until we discuss this theory in detail.) When discussing the archery example, Dembski seems to forget his own definitions of the triad of probability, complexity, and difficulty.

In the case of the entire wall serving as a target, the probability of hitting it by chance is much larger than in the case of a small painted target. The same can be said about two targets, one 5 cm in diameter and the other 50 cm in diameter. This example illustrates the artificial character of Dembski's separation of specification from probability.

Specification in itself plays no independent role in the discrimination between design and chance, but is just a constituent of probability.

Likewise, if we see a meaningful text, we conclude that its emergence by chance was highly unlikely. The fact that the text meets a recognizable pattern points to design not because it adds some independent argument in favor of design, but because it enhances the probability of design. Every factor works either for or against probability, and specification is just one more contributor to the estimation of probability rather than a factor independent of probability. It is not combined with low probability, as Dembski maintains, but is incorporated into probability as a part of the necessary background information.

Let us discuss once again Dembski's example with archery competition. If there is a target painted on a wall and the archer hits that target, this is, according to Dembski, a specified event of small probability which therefore must be attributed to design. This conclusion, according to Dembski, is made because the event (hitting the target) meets the conditions of detachability and delimitation. Detachability, it turn, incorporates conditional independence of the background knowledge and tractability. In relation to the archer's success, let us discuss the conditional independence of the background knowledge which, according to Dembski, is necessary for design inference. From Dembski's explanations and examples seems to follow that the background knowledge relevant to the problem at hand boils down to the recognizability of the target. The painted target is specified, i.e. recognizable. The recognizability of the target does not affect the probability of the hit (i.e. conditional independence is satisfied) therefore when the arrow hits the target, we conclude the event in question was due to design. Any side information which may affect the probability of the hit, is, according to Dembski's scheme, irrelevant for design inference. For the sake of discussion, let us accept Dembski's scheme which asserts that the successful hit must be unequivocally attributed to design. (In other words, ignore the contribution of laws of mechanics and such chance events as an accidental gust of wind or a small earthquake at the moment of the archer's action, and the like).

Imagine, though, that prior to the archers' competition, we watched the archers exercising for several days. Imagine that archer A is a world champion with a record of hitting the target 98% of the time, while archer B is a beginner who tried many times to hit the target as we watched him and failed to do so in all of his attempts. Thus we acquire knowledge about the two archers in question, which obviously affects our estimate of the probability of success for both archers at the competition. According to Dembski's scheme, this knowledge does not meet the condition of detachability because it is not conditionally independent. Hence, according to Dembski's scheme, the knowledge about the skills of the two archers in question has no bearing on design inference. Imagine, though, that on the day of the actual competition both A and B successfully hit the target. According to Dembski' scheme, design inference is equally justified in both cases. I think, though, that our conclusion will be different in the two cases. In the case of archer A with his record of 98% success, we will confidently attribute his success to his skill (i.e. to design). In the case of archer B we will justifiably attribute his success to his luck (i.e. to chance). In this example, the choice between chance and design is made based on the background information which, contrary to Dembski's scheme, is not conditionally independent.

Furthermore, in the case of archer A, despite the high probability (98%) of a perfect hit, when the archer in question indeed hits the target, we do not conclude it is due to law, as, according to Dembski, is to be done in the case of high probability (as Dembski's scheme prescribes for the first node of his filter). We conclude that it was due to design, and applaud the archer's skill, while in Dembski's scheme the design inference (see the third node of the explanatory filter) necessarily requires a very low probability of the event in question. (As was discussed earlier, the archer's success has to be attributed to a combination of design and law; Dembski's scheme, though, does not recognize such a double attribution, hence we do not need to account for it when discussing that example within the framework of Dembski's theory.)

One more comment about Dembski's analysis of specification/pattern seems to be in order. Recall again his example of an archer. If the archer hits the target, we identify, according to Dembski, specification. However, describing this situation, Dembski in some instances mentions just a single hit as being sufficient to qualify as specification (in particular such an interpretation follows from the definition of pattern, page 136 in "The Design Inference") while in some other instances (for example, on page 13) he mentions an archer hitting the target a hundred times in a row, and that repeated success is viewed as an indication of design (i.e. of the archer's skill.) He does not seem to see the difference between these two situations.

Indeed, besides the examples of archery, the definition of a pattern given by Dembski (page 136 in "The Design Inference") seems to make clear that in his scheme the repetition of an event is not considered a factor in determining a pattern.

I believe a repetition of an event is a very important factor in a design inference, and Dembski seems to have missed it. To see why the repetition is important, imagine two situations. In one case, an archer shoots from a certain distance of L meters and hits the target just once. In another case the archer shoots from a much shorter distance N<L but hits the target 10 times in a row. If we adopt Dembski's theory of probability – complexity – difficulty (which we will discuss later) we can assign a certain value of probability to the success in both cases. Since N is shorter than L, it is easier to hit the target from N meters. Assume that the difference between L and N is such that the probability of hitting the target 10 times in a row from N meters is exactly the same as hitting it just once from L meters. Despite the equal probabilities in these two situations, I believe our intuitive judgment will be different in the two cases. In the case of just one hit we will be uncertain whether to attribute the archer's success to his skill (i.e. to design) or to chance. Indeed, however small the probability of hitting the target by chance may seem to be, it is not zero. If the archer hit the target just once, it might well be attributed to luck, i.e. to chance. In the second case, we rather confidently attribute the archer's success repeated ten times in a row to his skill (i.e. to design) despite the probability of chance being in that case not less than in the previous case.

We have to acknowledge the substantial role of a repetition of an event in the procedure of attributing it to either chance or design. Dembski's definition of a pattern and hence of specification fails to recognize that factor.

From yet another angle, there are various classes of events regarding the discrimination between chance and design. On the basis of the same type of background information, some events are readily recognized as having been designed, while some can resist such discrimination. If we find a book of poems, we easily recognize it as a result of design. This discrimination is made on the basis of our background knowledge. In particular, our experience tells us that humans write poems and print books and we have seen many of them and know that they are the products of human design. The same relates to Paley's watch and a myriad of other objects which are familiar to us as a part of our ken. However, there are other classes of objects, and one example of such is any biological structure. A DNA molecule has a very complex structure and carries a lot of information (in the sense of information theory). However, our ken does not include any knowledge which would make us conclude that it is the product of deliberate design. The pattern seemingly present in a DNA strand, is not "detachable" using Dembski's term, as that pattern is not recognizable.

This would not matter if we had knowledge of some other factors which, if combined, would point to an overwhelming probability of design vs chance. Unfortunately, we have no such knowledge. Biological structures display enormous complexity, but this in itself does not indicate design because structures of unlimited complexity can emerge in any stochastic process. (More about this in the section on information.) We do not possess any relevant background knowledge which would enable us to discern design in biological structures.

I take the liberty of giving a peculiar example. The famous Russian anthropologist of the 19th century Nikolai Miklukho Maklai spent a long time among the aborigines of New Guinea studying the ways of life, the language, the habits and mores of those tribes. When the ship that brought Maklai to the island appeared in view, the aborigines who had never before seen such a big ship, decided that it came from heaven and that the crew members were gods. As a precaution, Maklai never tried to disabuse the villagers of their belief. Moreover, to reinforce their belief, he sometimes would remove his artificial teeth, to the villagers' amazement. Their ken did not include the knowledge of artificial teeth, so they viewed Maklai's action as a miracle effected by supernatural forces. Obviously, such an explanation was unjustified and similar to the interpretation of the DNA structure as the result of supernatural design.

It can be added that emergence of biological structures could occur without an intelligent designer, but still in a non-random way. Indeed, the Darwinian explanation of the origin of biological structures actually emphasizes the non-random factors in the evolution (see, for example, the popular book "The Blind Watchmaker" by the prominent biologist Richard Dawkins, W.W. Norton & Company, 1996). There are theories offering plausible mechanisms for such occurrences – one such mechanism is described, for example, at Jigsaw model of the origin of life).

My conclusion is that Dembski's discourse regarding his highly acclaimed explanatory filter shows that his filter is often not a reliable tool to identify design. It often seems to fail even in cases of human design. This seems to be especially true in regard to supposed supernatural design, which seems to be the most interesting case.

In "The Design Inference," Dembski devotes the whole of chapter 3 (pages 67-91) to the discussion of probability and likelihood, and offers many notions related to probability in other chapters throughout his books, as well as in his papers.

Probability and likelihood are by no means novel concepts. Both have been discussed many times before Dembski. (A discussion of the conventional concept of probability, which is designed for non-experts, is given at Improbable Probabilities).

In probability theory there are various definitions of probability, such as the classical definition, frequentist definition, geometric definition, statistical definition, and finally the axiomatic definition given by Kolmogorov. There is also the so-called Bayesian approach in which distinction is made between three versions of probability, referred to as prior probability, posterior probability, and likelihood.

On pages 78-79 of "The Design Inference" Dembski briefly discusses the frequentist and classical definitions, and on pages 67-69, the Bayesian approach. (With his rather typical lack of excessive modesty, Dembski claims on page 86 "a huge advantage" of his approach as compared to the Bayesian). He points to certain limitations of each of those approaches. However, he does not mention any other definitions of probability, including that by Kolmogorov. Kolmogorov's axiomatic definition of probability is the most rigorous and the most general, and, on the one hand, encompasses all other definitions as particular cases, and, on the other hand, overcomes the limitations of all other definitions.

Having discussed the limitations of the classical and frequentist definitions as well as of the Bayesian approach, Dembski offers his own definitions of probability and likelihood. Here is Dembski's definition of probability (page 70 in "The Design Inference"):

Definition. The probability of an event E with respect to background information H, denoted P(E|H) and called "the probability of E given H," is the best available estimate of how likely E is to occur under the assumption that H obtains.

On page 78 of "The Design Inference" we find the following definition of likelihood:

Definition. The likelihood of an event E with respect to the background information H, denoted (E|H) and called "the likelihood of E given H," is that number, or range of numbers in the unit interval [0,1] denoting how likely E is to occur under the assumption that H obtains and upon the condition that H is as effectively utilized as possible.

If Dembski offers his own definitions of these concepts, one may expect that such new definitions will shed new light on the matter, or at least reveal some new facets in those concepts, or maybe provide a more convenient or a shorter way to handle these concepts. In my view, they do none of the above.

Let us first look at the definition of probability. I submit that it is not a real definition and makes little sense.

On the one hand, this "definition" correctly lists two essential characteristics of probability. Indeed, probability is nothing more than an estimate of how likely is an event to occur, this estimate's cognitive value being only as good as the available information about the situation at hand. If that information changes, the estimate of probability changes as well. The more information about the situation is available, the better is the estimate of probability. However, while the characterization of probability as an estimate which is dependent on the available information is correct, it does not tell us anything new because it has been discussed many times before Dembski. Since his "definition" contains practically nothing beyond the quoted statement, the entire "definition" does not offer anything new.

On the other hand, Dembski's definition lacks a crucial element. This element may be expressed by the word "quantity." Probability is a quantity and makes sense only if it is assigned a numerical value. All existing definitions of probability, whatever their limitations, and whatever differences between them, include prescriptions of how exactly to assign to probability that numerical value. Dembski's "definition" provides no indication whatsoever that the "estimate" in question must actually be assigned a numerical value and even less of how to determine the latter. Therefore his definition of probability is not only inferior to those definition suggested hitherto, but is not really a proper mathematical definition.

The reference to "the best available estimate" by no means saves his "definition." How do we translate "the best available estimate," even if such has been reliably made, into a numerical value? Moreover, what are the criteria enabling one to distinguish "the best available estimate" from, say "the second best estimate," or from a poor estimate?

Dembski tries to clarify his idea by indicating that the determination of "the best available estimate" is to be made by "the community of discourse." While this assertion may have a nice sound, it is actually of little substance. What are the criteria enabling one to determine what the agreement within "the community of discourse" is?

On page 88 we read: "Within a community of discourse at a particular time probability is therefore uniquely determined."

Indeed? I wish this were true. Recall, for example, the ongoing dispute about the probability of appearance of a so-called "code" in the text of the Bible. (See, for example B-Codes Page). The dispute about this matter within the relevant "community of discourse," which included prominent mathematicians, reminded, in the words of one of its participants, Professor Barry Simon, of a street fight. Proponents and opponents of the "code" have offered vastly differing estimates of the probability in question, each side offering a host of arguments. While only one side of the dispute was correct, the dispute has not brought about a consensus.

Other examples of disputes among scientists in regard to the calculation of probabilities are given at Improbable Probabilities. No, Dr. Dembski, quite commonly there is no such thing as an agreement within the appropriate "community of discourse" regarding the probability of various events.

The vagueness of the concept of an estimate agreed upon by the "community of discourse," which may be handy in some philosophical treatise, seems to make it rather out of place in a supposedly rigorous mathematical discourse.

Let us now look at Dembski's definition of likelihood.

The concept of likelihood is commonly used in the Bayesian probabilistic approach, where it is rather simply and rigorously defined. This concept has also been used in information theory, the field in which Dembski, according to his admirers, is an expert.

Whereas an estimation of probability which is made assuming certain background information (a hypothesis) mathematically formalizes the logical procedure of deduction, the Bayesian approach mathematically formalizes the logical procedure of abduction (a brief discussion of that procedure can be seen at The Anthropic Principles – Reasonable and