Because of our back country riding we prefer horses that do the running walk, rather than trotting. Thus we have Tennessee walkers and rocky mountain horses, and here an interesting difference arises. The rockies can either trot or gait and have to be made to do the running walk. The walkers never trot, including when they are in the field unsaddled. Much follows from this.
So far as I know the walkers are physically capable of trotting. Physically they are almost indistinguishable from the rockies. If so then the fact that they do not trot is a mental condition, not a physical one. This suggests that the walkers either do not know how to trot or they choose not to. My conjecture is that they simply do not know how to trot. In terms of the theory of cognition being developed here, they lack the concept of trotting.
Concepts are bodies of basic knowledge, which can be acquired either by learning or by instinct. Breeding for behavior is the manipulation of instinct. The walkers have been bred not to trot which means they have been bred not to know how to trot.