Alia, i like your style. Very good reasoning, perhaps a bit over my head, but i'll try to manage.
I accept this last defenition as i can see no flaws in it. Unless someone else can perfect it even more i suggest we go on with that one.
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Do you think that maybe we should also agree on a definition of the mind, here, from the beginning, or leave it for the discussion of the topic, later? In any case, I think that definitions of terms used by the part of dualism which we will agree to explore will be also needed, as for example what mind means, can differ from one person to another.
Good thinking, we would be wise to define the mind first in this case.
I'll try something, its a rather different view on the mind.
The mind is the screen on wich everything we interact with is projected.
Now i realise that this defenition is a bit to general, so if we where to agree that this represents the mind, then we will have to choose a part of the mind to explore. Like only our thinking, or even more specific as you suggested.
I think it would be logical to accept Leibniz's Law of Identity. If we are to go by logical reasoning we have little choice.
Also, i think i should say were i want to go with this discussion. The point were i am trying to go to is to see wheter good and evil, hot and cold, high or low, pleasant or unpleasant. Are any different at all, or if the difference is an illusion.
However, i do not wich to discuss if black and white, liquid or solid, light or dark. Are different or not.
The second are things that are provable in the real world, thus valid states that can be seen by science. The first part is based in human logic and the mind.
Now the question is, are these first dualisms illusions or not.
Therefor we needed to define dualism first, and now we will have to see just how we can define it so that we stay in that first branch of the mind. Otherwise someone could say that it can be scientifically proven that black is black and white is white and so refute our whole reasoning by a simple fact. But it cannot be proven that something is 'hot' vs 'cold', a beer of 30° is hot, a bath of 30° is cold, etc... But the more interesting one is good vs evil. right vs wrong.
We will see were logic leads us for now...