Irreducible Complexity:
Definition & Evaluation

by Craig Rusbult, Ph.D.

1. Definitions

      Defining by Analogy:  To illustrate the principle of irreducible complexity that is caused by functional interdependencies between parts in a system, Michael Behe asks us to think about a common mousetrap with five interacting parts: a base, hammer, spring, catch, and holding bar.  Each part is necessary, and there is no mouse-catching function unless all five parts are present.  A trap with only four parts doesn't just catch mice poorly, it doesn't catch them at all.

      Four Definitions of Irreducible Complexity
      1. Michael Behe's Original Definition — [an irreducibly complex system is] "a single system composed of several well-matched, interacting parts that contribute to the basic function of the system, wherein the removal of any one of the parts causes the system to effectively cease functioning." (Darwin's Black Box, page 39, 1996)
      2. William Dembski's Enhanced Definition — "A system performing a given basic function is irreducibly complex if it includes a set of well-matched, mutually interacting, nonarbitrarily individuated parts such that each part in the set is indispensable to maintaining the system's basic, and therefore original, function.  The set of these indispensable parts is known as the irreducible core of the system." (No Free Lunch, page 285, 2001)
      3. Michael Behe's "Evolutionary" Definition — "An irreducibly complex evolutionary pathway is one that contains one or more unselected steps (that is, one or more necessary-but-unselected mutations).  The degree of irreducible complexity is the number of unselected steps in the pathway."  (A Response to Critics of Darwin's Black Box, 2002)
      4. My Revision of Behe's Original Definition — A system is irreducibly complex if there is no function for any system that is missing one part, i.e. if all "subsystems with one less part" are functionless.    { This revision, suggested in 2001, corrects a minor error in Behe's original definition;  the error does not affect the logic of claims about irreducible complexity if we use Definitions 2, 3 or 4. }

      Irreducible Complexity is not just Complexity
      To understand the difference between complexity that is and isn't irreducible, imagine a system with 20 enzymes (1, 2, 3,..., 19, 20) that evolves because it can be assembled one enzyme at a time, and at each stage there is a useful function that can be selected for:  a 1-2 combination is functionally useful (so it offers an advantage and is selected for), but 1-2-3 is even better (so it is selected for), and then 1-2-3-4, and so on.  This process of gradually building complexity, in a step-by-step process guided by natural selection, continues until the whole system, 1-2-3-....19-20, has naturally evolved.  The 20-enzyme system is cumulatively complex but is not irreducibly complex.
      By contrast, a system with 5 enzymes (ABCDE) is much less complex, but is irreducibly complex — according to Definitions 2 and 4 — if every subsystem with 4 enzymes (ABCD, ABCE, ABDE, ACDE, and BCDE) is nonfunctional.  Because there is no functional 4-enzyme system, the evolution of ABCDE would require at least one unselected step in going from 3 to 4 enzymes, so ABCDE is also irreducibly complex according to the Evolutionary Definition (#3) which asks:  Would it be difficult, or even impossible, for evolution to produce the 5-enzyme system of ABCDE in a step-by-step process of Darwinian natural selection?

2. Evaluations

      Irreducible Complexity and Evolution

      According to Michael Behe, "an irreducibly complex biological system, if there is such a thing, would be a powerful challenge to Darwinian evolution."  This challenge has stimulated responses by many biologists, including Kenneth Miller who (in Answering the Biochemical Argument from Design) confidently concludes that anti-evolution arguments based on irreducible complexity are certainly wrong;  he argues for this conclusion by using a logical consequence of Behe's definition-based claim that "any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional."
      Miller states Behe's claim in a definition-corollary:  If a biochemical system is irreducibly complex, then (consistent with what Behe says) "individual parts are, by definition, without any selectable function."  He then uses this corollary to support his anti-design conclusion, by showing that "the premier example of irreducible complexity [the bacterial flagellum] contains individual parts that have selectable functions [so]... the hypothesis of irreducible complexity is falsified."  Miller is a skilled debater, and he trapped Behe with a "gotcha" argument that is logically valid, but is not scientifically conclusive in 2009 because pro-design arguments based on irreducible complexity have evolved since 1996.
      In 1996, Behe's challenge focused on direct evolution: "an irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system."  But to explain the evolution of systems that are (according to Behe) irreducibly complex, defenders of evolution typically propose scenarios with indirect evolution, which occurs when a system (or its eventual parts) change function as the system evolves.  They claim that Behe's focus on direct evolution is too narrow and restrictive because it excludes some of the most powerful ways that evolution can occur.  For example, Pete Dunkelberg (in Irreducible Complexity Demystified) describes three "major forms of molecular evolution observed by biologists, phrased in terms of [a system's] parts" — with an evolution of the parts or (by gene regulation) their deployment, or addition of new parts (formed by gene duplication followed by mutation of one copy of the duplicated gene) — plus the possibility, for a system that is now irreducibly complex, of "adding a part and then making it necessary" in a normal evolutionary scenario with a normal system (that was not irreducibly complex) originally using more parts than is now necessary for the function, followed by removal of one or more parts to produce the system in its current form which is irreducibly complex. {an example}
      But these evolutionary possibilities are now recognized by Behe and others.  Their thinking is not "stuck in 1996" and their arguments for irreducible complexity (IC) are evolving.  In addition to Behe's more recent arguments, William Dembski (in Irreducible Complexity Revisited) analyzes the wider range of proposed evolutionary scenarios, including Coevolution with Co-Option (this happens during an indirect evolutionary pathway in which function changes, e.g. if parts with their own initial functions combine to form a new system with a new function) and Scaffolding (if parts of an originally non-IC system were removed to produce a system that currently is IC);  and he frames his main claims for design in terms of probabilistic plausibility, not logical proof.  In a similar shift toward focusing on practical plausibility instead of technical proof, Michael Behe has added an Evolutionary Definition (#3) that asks scientists to think about the degree of challenge for evolution, which is partially determined by the degree of irreducible complexity that he defines as "the number of unselected steps in the [evolutionary] pathway" being proposed.  My imaginary example of ABCDE has only one unselected step, but Dembski argues that the flagellum would have many unselected steps if it evolved from a functional 10-part system (Type 3 Secretory System) into a functional flagellum with 40 to 50 parts.
      Logically Appropriate Humility: 
      Ken Miller claims that he has "answered the biochemical argument from design" even though he acknowledges that biologists "have not provided a detailed, step-by-step explanation of the evolution of the flagellum."  But he thinks this failure is temporary, and "is not much of an argument against Darwin; rather, it means that the field is still active, vital, and filled with scientific challenges."  By contrast, a scientist who is more cautiously humble (in predicting what will happen in the future of science) might think that although we eventually may learn enough to confidently conclude that this really was "not much of an argument," currently more humility is appropriate due to the current absence of detailed evolutionary explanations.  Miller's page to "answer the arguments" is not humble.  Instead it is filled with bold declarations that arguments for design are "disproved... falsified... invalidated... demonstrably false... collapsed... incorrect... fatally flawed... wrong."
      By contrast with these triumphalist proclamations, it seems more scientifically justifiable to admit that "we don't know for certain, so we need to collect and evaluate more evidence."  The pages cited in this section are from 2003-2004, and now in 2009 [and still in 2010] I think "the jury is still out" when we look for "proof beyond a reasonable doubt" on a verdict either for or against claims that irreducibly complex biological systems provide evidence for intelligent design.  We can also ask questions about the rate of evolution — for each step in an extrapolation from small-scale evolution to a large-scale natural production of all biological complexity, how many mutations and how much selection would be required to produce the changes we observe in DNA, how long would this take, and how probable is it? — and I think that in current science the answers are not certain, thus providing another reason for logically appropriate humility.  During a process of gradually learning more, the claims (and counter-claims) that seem logically justifiable will become more apparent, but until then some humility seems justifiable.

      Minimal Complexity for the Origin of Life
      For a nonliving system, questions about irreducible complexity are even more challenging for a totally natural non-design scenario, because natural selection — which is the main mechanism of Darwinian evolution — cannot exist until a system can reproduce.  For an origin of life we can think about the minimal complexity that would be required for reproduction and other basic life-functions.  Most scientists think this would require hundreds of biomolecular parts, not just the five parts in a simple mousetrap or in my imaginary LMNOP system.  And current science has no plausible theories to explain how the minimal complexity required for life (and the beginning of biological natural selection) could have been produced by natural process before the beginning of biological natural selection.



      The Evolutionary Implications of Irreducible Complexity
      In Darwin's Black Box: The Biochemical Challenge to Evolution (1996), Michael Behe claimed that some biochemical systems are irreducibly complex and therefore could not have been produced in a step-by-step process of natural selection.  Behe says, regarding the evolutionary implications, "An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional.  An irreducibly complex biological system, if there is such a thing, would be a powerful challenge to Darwinian evolution. (Darwin's Black Box, page 39)"   Darwin agrees, "If it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down. (Origin of Species, 6th edition, 1872)"

      Does one plausible evolutionary scenario disprove the claims of Behe?
      We should remember that the central question is NOT whether all claims — about particular systems being irreducibly complex (IC) and being impossible to produce by undirected natural evolution — are true.  This is not the proper question to ask.  Instead, a small-scale research question is whether a particular "possibly irreducibly complex system" (the one being investigated) could have evolved.  And a large-scale theoretical question is whether there is even one system that is IC (*) and whose natural evolution seems extremely improbable.  If such a system does exist, it would show that Behe's claim is justified.   * with IC that is relevant because it might make evolution difficult, not IC that is irrelevant for evolution, as explained below}
      Systems that currently seem irreducibly complex vary in the apparent difficulty, as estimated by scientists, of being produced by natural evolution.  Behe has made claims for only some of these currently-IC systems, those that he thinks would be especially unlikely to evolve.  Behe's critics could weaken his claims, and those of other advocates of intelligent design, by showing how one or more of the IC systems he has cited (the rotary flagellum,...) could have evolved by undirected natural process.  But if critics try to refute him by showing that other IC systems (those for which he has made no claims) could have evolved, this is less impressive and it does not directly refute his claims.  And if they explain how systems that are complex but not irreducibly complex could have evolved, this is not directly relevant, which is even less impressive.

      Critical Evaluation of Evolutionary Scenarios
      When we evaluate theoretical scenarios like those below (and others being proposed) we should supplement creative thinking with critical thinking.  Doing this will let us move beyond the easy question (is the proposed sequence of events possible in principle?) to ask the tough questions (is it plausible in reality, and did it probably occur in the actual history of nature?) that are scientifically interesting and logically justifiable.
      questions and responses:  In Darwin's Black Box, Behe describes some actual biochemical systems, and explains why each system seems to be irreducibly complex.  Are any of these systems actually irreducibly complex, and were any impossible to produce by natural selection?  Behe's challenge has stimulated creative thinking by scientists, who have proposed imaginative scenarios for a step-by-step evolutionary production of systems that are claimed to be irreducibly complex.
      For example, Allen Orr says "an irreducibly complex system can be built gradually by adding parts that, while initially just advantageous, become - because of later changes - essential."  A common illustration, in pages defending the creative power of evolution, is a Roman Arch that uses a temporary scaffold (during the process of construction) which later is removed to produce an irreducibly complex structure.  This possibility — of adding a part and then making it necessary — was described earlier.  In terms of a system with numbered components, a system with 12345 could be produced by "123 --> 1236 --> 12364 --> 123645 --[simplification]--> 12345" where — if all 4-part systems derived from 12345 are non-functional because they lack the 6 in 1236 (the 4-part system that was one step in the evolutionary development) — 12345 has become irreducibly complex;  originally (in 12364) 5 was not necessary, but now (in 12345) it is necessary.
      Or maybe it happened by "123 --> 1237 --> 12375 --> 12345" where enzyme-7 has mutated into enzyme-4 which helps produce the function of 12345.  But, unlike 1237, 1234 does not have this function (and neither does any other 4-part system) so 12345 is irreducibly complex even though it evolved.
      Or maybe sub-combinations were functional, so they were selected for, and then these parts combined to form a larger system;  this would occur, for example, if 123 (with a function) and 45 (with a function) combined to form 12345, with the same function (as 123 or 45) or a new function.

      Michael Behe's Original Definition from 1996 — Is it correct?
      No, it is not correct IF — as in the usual claim by advocates of intelligent design — irreducible complexity is an obstacle to Darwinian step-by-step evolution.  But this error is due to a minor oversight in the wording of his 1996 definition, and (after this has been corrected in Definitions 2, 3, or 4) it has no effect on a logical evaluation of Behe's claims about relationships between irreducible complexity and Darwinian natural selection during evolution.
      To see the evolutionary loophole in Behe's original definition, imagine a 5-part system which evolved in steps that were selected for because each step (LM, LMN, LMNO, and LMNOP) performed an increasingly useful function:
      According to Behe's original definition, LMNOP is irreducibly complex if "the removal of any one of the parts [after removal the 4-part subsystem could be either MNOP, LNOP, LMOP, LMNP, or LMNO] causes the system to effectively cease functioning."  Imagine that MNOP (or LNOP, LMOP, LMNP) is non-functional.  This makes the 5-part system (LMNOP) irreducibly complex, even though it did evolve by natural selection through the subsystem LMNO.
      Behe's original definition implies that Darwinian evolution is impossible if ANY one of the "subsystems missing one part" is nonfunctional.  But the actual requirement is that ALL of these subsystems must be nonfunctional.
      Is ABCDE irreducibly complex?  Behe's original definition (#1) says YES, but his evolutionary definition (#3) says NO because there are no "unselected steps in the pathway" to ABCDE.  Dembski's enhanced definition (#2) also says NO because it's not true that "each part in the set is indispensable" since E can be removed without loss of function, and my revised definition (#4) says NO because ABCD is a "subsystem with one less part" that is functional.  And when we ask whether ABCDE is a "challenge to Darwinian evolution" the answer is NO, consistent with Definitions 2, 3, and 4.

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Here are other related pages:

ideas from a variety of authors are in
IRREDUCIBLE COMPLEXITY — Design & Evolution, Behe & Critics
and, to get a wider "big picture" view of evolution, in
BIOLOGICAL EVOLUTION — Principles and Questions

This page, written by Craig Rusbult, is

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