`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.`

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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
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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
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`UPDATE:`

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Elsewhere, an author claims this argument shows ID is committed to substance dualism.

http://www.jackscanlan.com/2011/08/homologous-legs-now-has-a-facebook-page-its-2011-right/

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.

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