William Dembski, in a number of works, including *The Design Inference* (1998), *No Free Lunch* (2002b), and “Specification: The Pattern that Signifies Intelligence” (2005), claims that there is a robust decision process that can determine when certain structures observed in the natural world are the product of Intelligent Design (ID) rather than natural processes. As defined by the Discovery Institute Web page (Discovery Institute 2012), the theory of ID “holds that certain features of the universe and of living things are best explained by an intelligent cause, not an undirected process such as natural selection. Through the study and analysis of a system's components, a design theorist is able to determine whether various natural structures are the product of chance, natural law, intelligent design, or some combination thereof.”

Dembski also introduces his fourth law of thermodynamics that effectively states that *information*, using his definition, cannot increase by natural processes (2002b, section 3.10). He then argues that structures that are high in information cannot emerge by chance.

The essence of the first of these claims is that a robust decision process can be used to determine whether an observed event, that is, a structure, such as the flagellum that provides motility to certain bacteria (see Behe 1996), is an outcome of evolutionary processes, or is the product of nonnatural design. The Dembski decision process considers first whether such a structure or event can be explained by natural laws. If not, a randomness test is devised based on identifying and specifying the event *E*. When the probability of such a specified event occurring by chance is low, it is said to exhibit *Complex Specified Information* (CSI). According to Dembski, this event can be deemed to be due to ID as chance is eliminated. For example, Dembski (2002b, xiii) would see a random set of Scrabble pieces as complex but not specified, while a simple word “the” is specified without being complex. In contrast, a Shakespearean sonnet is both complex and specified and would be unlikely to occur by chance.

In mathematical terms, if is the probability of the specified event, given the chance hypothesis *H*, Dembski defines the *information* embodied in the outcome by . Dembski has defined his information measure so that the lower the probability of an observed outcome, the higher is the information and order embodied in the structures and, in Dembski's terms, the higher the complexity. This measure is the converse of the usual mathematical definitions of information and here will be denoted by and termed *D-information*. As is shown later, the concept of D-information has much in common with Kolmogorov's *deficiency in randomness*, that is, just like the deficiency in randomness, outcomes with high D-information would exhibit low algorithmic information, low entropy, and low algorithmic complexity. Shallit and Elsberry (2004, 134–35) have noted the same point and have suggested that the term *anti-information* be used to distinguish the common understanding of information from what here is called D-information.

This article makes the following main points:

- As Shallit and Elsberry have suggested (2004, 134), Kolmogorov's deficiency in randomness provides a far more satisfactory measure for D-information than that proposed by Dembski.
- As the Dembski approach does not adequately define a randomness test that can be implemented in practice (Elsberry and Shallit 2011), it should be replaced by the agreed mathematical measure of randomness known as a universal Martin-Löf randomness test. The universal randomness test achieves Dembski's purpose and avoids all the confusion and argument around the Dembski approach.
- The clarity of the Martin-Löf approach shows that the Dembski decision process to identify ID is flawed, as the decision route eliminates natural explanations for surprise outcomes before it eliminates chance. The fundamental choice to be made, given the available information, is not whether chance provides a better explanation than design, but whether natural laws provide a better explanation than a design.
- Dembski's fourth law of thermodynamics, that is, his law of conservation of the information , is no more than the second law of thermodynamics in disguise. It is equivalent to the unsurprising statement that entropy can only be conserved or increase in a closed system. Given the initial state of the universe, there is no evidence that the injection of D-information or its equivalent, the injection of low entropy from a nonnatural source, is required to produce any known structure.
- Dembski's claim that his law of conservation of information proves that high D-information structures cannot emerge by chance is irrelevant in an open system, such as the earth.

Elsberry and Shallit (2011) and Shallit and Elsberry (2004) provide a detailed critique of the inconsistencies of Dembski's idea of CSI and his so-called proof of the Law of Conservation of Information. While they and a number of other authors (Miller 2004, Musgrave 2006) show the bacterial flagellum can plausibly be explained by natural processes, as the ID supporters are likely to find other examples that they claim exhibits ID, the framework of the ID argument needs to be critiqued. Here, the primary concern is to show the whole mathematical approach used by Dembski is flawed. The mathematically robust Martin-Löf universal randomness test is used to replace Dembski's approach in order to determine whether natural laws can explain surprise events. This is particularly important, as influential thinkers, such as William Lane Craig, have been seduced by the apparent sophistication of the Dembski argument (Elsberry and Shallit 2011, 2). No implementable test of randomness can do better than a universal Martin-Löf test (Li and Vitányi 2008, 137). If order is recognized, the lack of randomness can be measured by this test. As a robust universal test of randomness (and therefore of order) already exists, the scientific community should only engage in discussions on the possibilities of design interventions in nature that are articulated in terms of this universal test.