What is the proof of God through "Design theory" by William Dembski, stated in simple words? 

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Karen P.L. Hardison eNotes educator| Certified Educator

In the briefest and simplest terms, Dembski proves God by providing a new definition of information, as in the term "origin of information," which is what evolutionists and designists both seek to understand and what they disagree about. Evolutionists define information as "the transmission of signals across a communication channel." Dembski says that this definition defines the process, the "medium," of information communication but that it does not define information itself. Dembski redefines information as "the actualization of one possibility to the exclusion of others."

information in its most general sense can be defined as the actualization of one possibility to the exclusion of others (observe that this definition encompasses both syntactic and semantic information). (William A. Dembski, "Intelligent Design as a Theory of Information")

Simply put, Dembski says that:
(1) information is one possibility out of many possibilities that becomes actual (actualized).
(2) information is specified as a pattern before the pattern itself is actualized; e.g. a target drawn before an arrow is shot, not after it is shot, is a pattern displaying specified information.
(3) information is complex along a continuum of possible degrees of complication from very simple to very complicated.
(4) information can be both specified and complex; complex and specified information is labeled CSI.

Dembski says that CSI (complicated, pre-patterning information) has "intelligent origin." This intelligent origin can only be indirectly inferred through observation. He uses the example of a comparison between a spilled ink blotch on paper and words written in ink on paper. Comparison shows that intelligent origin lies behind the written words and accidental chance lies behind the ink blotch.

God is proved as intelligent origin (1) when specified information that is complex is seen in events or conditions and reveals the possibilities that were actualized and the excluded other possibilities in a pattern that cannot be attributed to chance and (2) when the possibility that was specified is so highly complex that it is also highly improbable as a random occurrence.

In other words, God is proved when CSI points to intelligent origin of information, intelligent causation of actualized possibilities, intelligent design of highly complex specified possibilities that excluded other possibilities.

In terms of probability, this means that the possibility that was specified is highly improbable. In terms of complexity, this means that the possibility that was specified is highly complex. All the elements in the general scheme for recognizing intelligent causation ... find their counterpart in complex specified information-CSI. (William A. Dembski, "Intelligent Design as a Theory of Information")