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Dembski argues that it is impossible for specified complexity to exist in patterns displayed by configurations formed by unguided processes. Therefore, Dembski argues, the fact that specified complex patterns can be found in living things indicates some kind of guidance in their formation, which is indicative of intelligence. Dembski further argues that one can show by applying [[No free lunch in search and optimization|no-free-lunch theorems]] the inability of evolutionary algorithms to select or generate configurations of high specified complexity. Dembski states that specified complexity is a reliable marker of design by an [[intelligent designer|intelligent agent]]—a central tenet to intelligent design, which Dembski argues for in opposition to [[evolution|modern evolutionary theory]]. Specified complexity is what Dembski terms an "explanatory filter": one can recognize design by detecting '''complex specified information''' ('''CSI'''). Dembski argues that the unguided emergence of CSI solely according to known [[physical laws]] and chance is highly improbable.<ref>Olofsson, P., "Intelligent design and mathematical statistics: a troubled alliance", ''Biology and Philosophy'', (2008) 23: 545. {{doi|10.1007/s10539-007-9078-6}} ([https://web.archive.org/web/20180120070714/https://pdfs.semanticscholar.org/8def/d6c4582d252e55d8b4a188ccdb9bff6453c3.pdf pdf], retrieved December 18, 2017)</ref>
The concept of specified complexity is widely regarded as mathematically unsound and has not been the basis for further independent work in [[information theory]], in the theory of [[complex systems]], or in [[biology]].<ref>{{cite web |url=http://www.talkorigins.org/faqs/information/dembski.html |title=Information Theory and Creationism: William Dembski |author=Rich Baldwin |year=2005 |publisher=[[TalkOrigins Archive]] |access-date=2010-05-10}}</ref><ref>Mark Perakh, (2005). ''[http://www.talkreason.org/articles/newmath.cfm Dembski "displaces Darwinism" mathematically -- or does he?]''</ref><ref>Jason Rosenhouse, (2001). ''[http://educ.jmu.edu/~rosenhjd/sewell.pdf How Anti-Evolutionists Abuse Mathematics]'' The Mathematical Intelligencer, Vol. 23, No. 4, Fall 2001, pp. 3–8.</ref> A study by [[Wesley R. Elsberry|Wesley Elsberry]] and [[Jeffrey Shallit]] states: "Dembski's work is riddled with inconsistencies, equivocation, flawed use of mathematics, poor scholarship, and misrepresentation of others' results."<ref>{{cite web|url=http://www.talkreason.org/articles/eandsdembski.pdf|last1=Elsberry|first1=Wesley|last2=Shallit|first2=Jeffrey|year=2003|title=Information Theory, Evolutionary Computation, and Dembski's 'Complex Specified Information|access-date=20 October 2017}}</ref> Another objection concerns Dembski's calculation of probabilities. According to [[Martin Nowak]], a Harvard professor of mathematics and evolutionary biology, "We cannot calculate the probability that an eye came about. We don't have the information to make the calculation."<ref name="
Wallis, Claudia (2005). [http://content.time.com/time/magazine/article/0,9171,1090909,00.html Time Magazine], printed 15 August 2005, page 32
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Dembski's calculations show how a simple [[smooth function]] cannot gain information. He therefore concludes that there must be a designer to obtain CSI. However, natural selection has a branching mapping from one to many (replication) followed by pruning mapping of the many back down to a few (selection). When information is replicated, some copies can be differently modified while others remain the same, allowing information to increase. These increasing and reductional mappings were not modeled by Dembski. In other words, Dembski's calculations do not model birth and death. This basic flaw in his modeling renders all of Dembski's subsequent calculations and reasoning in ''No Free Lunch'' irrelevant because his basic model does not reflect reality. Since the basis of ''No Free Lunch'' relies on this flawed argument, the entire thesis of the book collapses.<ref>Thomas D. Schneider. (2002) [http://www.lecb.ncifcrf.gov/~toms/paper/ev/dembski/specified.complexity.html Dissecting Dembski's "Complex Specified Information"] {{webarchive|url=https://web.archive.org/web/20051026135240/http://www.lecb.ncifcrf.gov/~toms/paper/ev/dembski/specified.complexity.html |date=2005-10-26 }}</ref>
According to Martin Nowak, a Harvard professor of mathematics and evolutionary biology "We cannot calculate the probability that an eye came about. We don't have the information to make the calculation".<ref name="
Dembski's critics note that specified complexity, as originally defined by Leslie Orgel, is precisely what Darwinian evolution is supposed to create. Critics maintain that Dembski uses "complex" as most people would use "absurdly improbable". They also claim that his argument is [[circular reasoning|circular]]: CSI cannot occur naturally because Dembski has defined it thus. They argue that to successfully demonstrate the existence of CSI, it would be necessary to show that some biological feature undoubtedly has an extremely low probability of occurring by any natural means whatsoever, something which Dembski and others have almost never attempted to do. Such calculations depend on the accurate assessment of numerous contributing probabilities, the determination of which is often necessarily subjective. Hence, CSI can at most provide a "very high probability", but not absolute certainty.
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