In speculating on a character trait, I think it's very important to define ones terms.
Treating others the way you would like to be treated (commonly known as 'the golden rule') has to do with reciprocity and courtesy, but it's not integrity.
Integrity has to do with being totally consistent in ones beliefs, morality, ethics, paradigm and actions. To have all of these in alignment with no duplicity, internal or external. In my way of thinking this means to make your choices be in alignment with what you believe to be true or right. As was said before, MUCH easier to say than to do. In other words, to strive for integrity is to make your undestanding of right and wrong reflect directly in your choices and actions, consistently, without regard to other factors. (Wow....I get wordy after a few cups of coffee)
Treating others with courtesy, with a sense of reciprocity, ....if I feel that THAT is what is RIGHT to do........then it would demonstrate integrity when I DO that.
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I think that we can, as martial artists, simply give consideration to what we believe to be right or best and strive to make our actions line up.
again
simple
but
NOT easy.......
Your Brother
John