Detecting design or intent in nature

[Heywood]

There exist a set...two-wheeled vehicles that are powered by a motor and have no pedals.

A motorcycle is not a Segway, but both are members of the set, two-wheeled vehicles that are powered by a motor and have no pedals.

Now if I make a point about the set, say....every element contains two wheels made of rubber, you don't refute the point about the set by claiming a motorcycle is not a Segway. You refute the point by providing an example of a two wheeled vehicle powered by a motor that does not have wheels made of rubber.

But if you prove something only using Segways it says nothing about proving it for motorcycles, and vice versa.

They are disjoint subsets of your set.

First, I am not proving anything. Every observation of a photon traveling through a vacuum at 299,792,458 meter per second doesn't prove that all photons which have ever traveled through a vacuum traveled at that speed. It only suggest that they all traveled at that speed.

Second, by looking at elements of a set, I can draw conclusions about the entire set. I conclude that all photons travel in a vacuum at 299,792,458 meters per second by looking at some of them and never finding one that doesn't. My conclusion is not proof. But I will rely on it anyways.

Third disjoint subsets does not invalidate the parent set. Just because a Toyota car is not in the set of Fiat cars, does not mean the set of all cars doesn't exist. If every time I observe that a car in the set of all cars has a steering wheel, and never observe a car in the set of all cars that does not have a steering, I can safely conclude that all cars have steering wheels. A Trabant is a car, I have never seen one, but I bet it has a steering wheel even though it is not a Fiat or Toyota and I have seen plenty of those. Why? Becuase the set of all cars seems to follow a rule that all the elements contain steering wheels.

The set of all systems which have the elements of replication, heritable traits, change, and selection all seem to follow a rule that they require intellects to come into existences.

The only reason people deny this rule exists is because their atheistic belief demands it. Sorry but that is not a good enough reason for me to pretend this rule does not exist. You will have to show me a system which contains replication, heritable traits, change and selection which does not follow this rule....then I will believe you.