Detecting design or intent in nature

[Chas]

Then you are making a straw man of biological evolution by leaving out the elements that differentiate if from the other things that fit your set.

Biological evolution is not an argument therefore it cannot be a straw man.

But I understand what you are saying and your error(and Chas's) is quite clear to me. Your error is like saying that conclusions drawn about the set of all polygons cannot be applied to the subset of triangles because the definition of all polygons leaves out elements that differentiate triangles from the rest of the set. Of course this is rubbish.

Dead fucking wrong. We are saying that what you demonstrate about the rectangles cannot be applied to the triangles.
You still don't understand sets. Your Heywood set has two disjoint subsets and you keep talking about only one of them and claiming it must apply to the other.

Claiming that conclusions drawn about the set of all systems which contain the elements of Replication, Heritable Traits, Change, and Selection cannot be applied to the subset of biological evolution is the same kind of rubbish.

Yes, that would be rubbish. But you are not doing that. You are only drawing conclusions about the subset that is known to be created and trying to apply it the the subset of the not know to be created.

If something is true of the set I have defined, and if biological evolution is an element of the set I have defined. Then what is true of the set I have defined is also true of biological evolution in the same way that what is true of all polygons is also true of all triangles.

Yes, correct, but that is not what you are doing.