“1) I say an apple is red, you say purple. The law of non-contradiction is of no help here but it is often evoked in an attempt to prove that one of us must be right and the other wrong”
Well, the law would say that each of us is entitled to the truth of their experience. But each of us cannot not have two experiences which are opposite. You could not say ‘I see red and at the same time see purple.’ Unless there are two colors. But if there is one color, the one color cannot be two. Only one of us at a time can experience and only one of us can make a statement that can be tested by the law of contradiction.
As Avicenna / ابن سينا said
“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”
One person doesn’t scream because the other is being tortured. He is not contradicting your experience, but he is expressing his own. They are definitely being tortured.
Conversely, red cannot be a truth over the purple and vice versa. Two subjective experiences by two people cannot be in a hierarchy of truth; even if both of them be truths, but about separate experiences. Because the statement also implies ‘human beings have separate consciousness and there is truth to their separate experience.’ This cannot be so for one and not for the other: this would bring a contradiction. Ergo, the same must be true for others. And in validating your own, you must also make other experiences themselves equally valid. But subject others to the same standard: that they must be consistent and not have two contradictory experiences. Neither you nor they can have contradictory subjective experiences. You both have a unified one experience each which doesn’t contradict itself. Whether you are talking about something like an object or mere things to do with an object.
Brainpolice: universal morality stands. Because while two people can disagree, what matters is if someone is contradicting their own system or not. Or a system (one system) which people follow is doing this or not. Whether in speech or in action. In a way, universal morality is necessary only because there are subjective moralities first. Not to battle them per se or ‘subjectivity’ at all, but because they each must be valid until proven invalid*. Anyone can create a system and some statements. Whether mathematics or anything else that can be stated or applied to something. But it must be tested for internal consistency in order to be a working system; the same way an object like a hammer is checked for its soundness as a tool. And this be done in so much as it is possible. So bad things are not stated or done. And good things are stated and done. Good and bad, in so far as a distinction can or should be made, being the domain of morality, and nothing else. Morality in that way is the same as our language about objects; as arbitrariness of signs being what they are. And the principle of non-contradiction is helpful to both.
*we could agree that you see ‘red’, until you say that the ‘red’ you see is actually a taste. Or that you see no apple at all, but see the redness or purpleness anyway. Or some other thing like that, which proves logically that you are trying to fool us about your own consciousness. Or at the very least, what you report about your consciousness doesn’t conform to the shared language we are both using to understand your consciousness. Though, this is built into what you are saying. That there is a shared language. It is not an excuse for contradiction. Being water and agua simultaneously is not a contradiction, but one person speaking English and the other Spanish.