I don’t understand your point about anticipated experience. If I believe some action is good, I anticipate that doing that action will produce evidence (experience) that is indicative of increased welfare. That is exactly not like believing something to be “blegg”. Regarding mathematical groups, whether or not we care about them for their usefulness in physics seems not relevant for “group” to have a specific meaning. Like, you may not care about horses, but you still anticipate a certain visual experience when someone tells you they bought you a horse, it’s right outside. And for a group you’d anticipate that it turns out to satisfy associativity etc.
I don’t understand your point about anticipated experience. If I believe some action is good, I anticipate that doing that action will produce evidence (experience) that is indicative of increased welfare. That is exactly not like believing something to be “blegg”. Regarding mathematical groups, whether or not we care about them for their usefulness in physics seems not relevant for “group” to have a specific meaning. Like, you may not care about horses, but you still anticipate a certain visual experience when someone tells you they bought you a horse, it’s right outside. And for a group you’d anticipate that it turns out to satisfy associativity etc.