Several critical reviews of Dembski’s work were offered by Wesley L. Elsberry (see www.infidels.org/library/modern/science/creationism/dembski.htm  ). 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. Elsberry suggests his own explanatory filter, which has four rather than three steps in a decision-making procedure, and in which the order in which chance and regularity are eliminated in favor of design is opposite to that suggested by Dembski.

            One more paper arguing against Dembski was posted by Thomas D. Schneider (see www.lecb.ncifcrf.gov/~toms/paper/ev/dembski/rebuttal.html ).  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, http://website.lineone.net/~rwein/skeptic/whatswrong.htm . 2) Taner Edis, www.csicop.org/si/2001-03/intelligent-design.html . 3) Victor J.  Stenger, http://spot.colorado.edu/~vstenger/Found/04MessageW.pdf (this link seems to be dysfunctional);  4) Matt Young, www.pcts.org/journal/young2002a.html .
              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, Wein, Edis, Stenger, Young, 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 at www.baylor.edu/~William_Dembski/docs_critics/pennock.htm .  (Many of Dembski's posts seem to have habitually been either removed from the web or often moved to other sites). 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 at www.leaderu.com/offices/dembski/docs/bd_analyze.html  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.  

2. DESIGN WITHOUT A DESIGNER 

          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 

a) Description of the 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.                           

b) Specification according to Dembski 

            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. 

c) “Mathematism” as a tool of embellishment 

            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. 

             If a 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.  

d) Can probability be separated from the event's causal antecedents? 

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 http://members.cox.net/perakm/good_bad_science.htm . 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 http://members.cox.net/perakm/good_bad_science.hm , 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.