A possible common rule of beauty would be that a thing is beautiful if it is appreciated by some sentient being that finds it beautiful. However, this is completely vacuous, defining no constraint on what a sentient being might find beautiful. It does not prohibit arbitrary concepts of beauty. It is also far from fundamental, as the sentient beings are made of complicated physical systems.
Do you have a concept of a common rule that actually implies that some concept of beauty is impossible?
A possible common rule of beauty would be that a thing is beautiful if it is appreciated by some sentient being that finds it beautiful. However, this is completely vacuous, defining no constraint on what a sentient being might find beautiful. It does not prohibit arbitrary concepts of beauty. It is also far from fundamental, as the sentient beings are made of complicated physical systems.
Do you have a concept of a common rule that actually implies that some concept of beauty is impossible?