Artists tended to draw horses as having at least one hoof on the ground while they were in a gallop. In fact, it was (and maybe still is) a popular belief that at least one hoof remained planted firmly on the ground when a horse is in a gallop. This is true even among non-artists. The popular belief was due to one's intuition that it would be impossible for a horse to gallop if all of its hooves were fully airborne.
The advent of high-speed time-lapse photography changed our misconceived intuition. In 1892, Leland Stanford paid Eadweard Muybridge to devise an apparatus with multiple trip wires attached to camera shutters. The photographs taken by Muybridge showed that the horse was fully airborne when in a gallop.
The moral of the story is that we can test our intuitions using empirically informed methods. In the gait analysis case, photography was the experimental tool used to test the hypothesis that at least one of the horse's hooves had to remain firmly planted when in a gallop. If the experiment shows that our pre-theoretic intuitions are true, then horses need at least one hoof on the ground while they are in a gallop. If the outcome of the test shows our pre-theoretic intuitions are false, then we should reject our intuitions. Once our intuitions are affirmed or rejected, we may form an argument that is consistent with the data.
This is how empirically informed arguments win the day. In the Muybridge case, our pre-theoretic intuitions are rejected because the high-speed photography shows that all of the horse's hooves are in the air when in a gallop.
The Muybridge issue also overlaps with my interest in talking about action individuation. If the horse's actions can be described as "the horse gallops" and "the horse gallops gracefully," then we have two designations of one and the same action. So, Davidson's minimising account wins the day. But an equally coherent interpretation could argue that the two act-tokens designate two act-types. Therefore, the action descriptions designate different actions. So, Goldman's maximising account wins the day.
Muybridge's accomplishments in high-speed photography can give action theorists some insight into how to identify actions. If we can identify actions successfully, then telling how many actions an agent performs becomes much easier.