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Are there logical relations between colors? For instance, is it logically true that red and blue make purple?

Perceived color is a matter of retinal and neurological processing. People with full color vision see a variety of spectral inputs (from single frequency to mixed frequencies) as purple. Perhaps you are asking, could people who perceive red and blue normally see a mixture of red and blue as anything other than purple (in the same circumstances)? I don't think there are any cases of this kind of odd color perception, so it may well be that our 3-sensor color perception system will always perceive a mixture of red and blue as purple. Does that mean it is a "logical truth" that red and blue make purple? Only in the same sense that it is a logical truth that if you can hear the note A and hear the note C you will hear the combination as a minor third.