I don’t know anything about gauge transformations, but you might be right. The canonical (ha) example I had in mind was category theory, where universal objects are defined up to isomorphism. But where you can have many different realizations of that universal object. Like a vector space over [‘red’, ‘blue’, ‘orange’] is isomorphic to one spanned by [‘red’, ‘blue’, ‘green’], but they’re not literally the same object.
As for the reflected visual field example, its kind of an instance of what I’m talking about. But, it would have to be done at birth, else its not an automorphism of mental states, because you’re not flipping the other mental structures that relate to the visual field.
Like when I’m talking about a map from physical → phenomenal states, I’m talking about the map from all the stuff making up your body and entering your sense, to your mental states. Not just the part of the map thats determined by what enters your senses.
I don’t know anything about gauge transformations, but you might be right. The canonical (ha) example I had in mind was category theory, where universal objects are defined up to isomorphism. But where you can have many different realizations of that universal object. Like a vector space over [‘red’, ‘blue’, ‘orange’] is isomorphic to one spanned by [‘red’, ‘blue’, ‘green’], but they’re not literally the same object.
As for the reflected visual field example, its kind of an instance of what I’m talking about. But, it would have to be done at birth, else its not an automorphism of mental states, because you’re not flipping the other mental structures that relate to the visual field.
Like when I’m talking about a map from physical → phenomenal states, I’m talking about the map from all the stuff making up your body and entering your sense, to your mental states. Not just the part of the map thats determined by what enters your senses.