Yes I know that's your point. I'm saying you can't enumerate algorithms without selecting an algorithm. One way of selecting an algorithm is to select a way to

Yes I know that's your point. I'm saying you can't enumerate algorithms without selecting an algorithm. One way of selecting an algorithm is to select a way to encode the algorithms. It's easy to see that this is true. You chose an arbitrary example above. Try to do the same without choosing anything arbitrary. You can't.