Here is a first order predicate logic proof which shows ID implies a supernatural causal agent. The agent is properly called "supernatural" because it possess an ability that is above nature.
Legend ------ V x p : universal quantification - for all x proposition p holds ~p : not p p1 ^ p2 : conjunction p1 v p2 : disjunction p1 -> p2 : implication The following is how new universal propositions are introduced using temporary variables. The | indicates that the corresponding line is part of a subproof. The numbers on the right indicate which prior lines, and laws/identities, are used to generate the current line. 1. | x0 ^ y0 x0, y0 -- 2. | x0 1 3. V x, y ( x ^ y -> x ) 1-2 Proof ----- P(x): x is an entity that is entirely controlled by physical laws C&N(x): x is an entity that operates by events entirely describable by chance and necessity C&NO(x): x is an entity whose origin can be explained by proximate chance and necessity causes CSI(x): x contains CSI C(x, y): x is the proximate cause of y Goal: V x, y ( C(x, y) ^ CSI(y) -> ~P(x) ) 1. V x ( P(x) -> C&N(x) ) 2. V x ( CSI(x) -> ~C&NO(x) ) 3. V x, y ( C&N(x) ^ C(x, y) -> C&NO(y) ) 4. | C&N(x0) ^ C(x0, y0) ^ CSI(y0) x0, y0 -- 5. | CSI(y0) 4 6. | ~C&NO(y0) 2, 5 7. | C&NO(y0) 3, 4 8. | _|_ 6, 7 9. V x, y ( ~(C&N(x) ^ C(x, y) ^ CSI(y)) ) 4-8 10. V x, y ( ~C&N(x) v ~C(x, y) v ~CSI(y) ) 9 & De Morgan's Law 11. | C(x0, y0) ^ CSI(y0) x0, y0 -- 12. | ~C&N(x0) 10, 11 13. | ~P(x0) 1 & Modus Tollens, 12 14. V x, y ( C(x, y) ^ CSI(y) -> ~P(x) ) 11-13
Elsewhere, an author claims this argument shows ID is committed to substance dualism.
While I agree substance dualism is the easiest way to make sense of this argument, it is still not a necessary conclusion. For example, Mormon theology maintains there is a way for matter to be intelligent and possess free will. Such a claim is not logically incoherent (as far as I know), so here we have a materialistic theory of intelligence that is compatible with my argument above.
However, a materialistic theory of intelligence would still be supernatural, since intelligent matter is beyond the physical laws of chance and necessity.