ID Implies the Supernatural

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

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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

UPDATE:

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.