If the two examined terms (x and y) can be reduced to the same source, then they are elements or properties or aspects of that one source and in such case we have monism (for cases at least like mind and matter, or good and evil), or they are elements (properties, aspects) of one term (z) that could be examined in connection to its opposite (w). In case of our interpretation (or experience) of hot and cold, for example, or high and low, (x & y) can’t be caused to a subject (a person), at the same moment (time t) by the same object (source, or origin), as it depends on the circumstances applied at that moment. Or, at least that is the dualistic perception. (Proving that this can be done, by the way, would be an approach to disprove dualism). Now, terms like right and wrong, or pleasant and unpleasant, depending completely on someone’s perception (at least at my opinion), while usually can be treated as the previous terms, I believe that at some cases could be caused at the same moment (time t) by the same source and exactly that (again I think) could, maybe, be proved to be a weak spot of dualism.
(I used in the above paragraph the terms that A Smoking Fox brought as examples of what he was thinking examining, with the Leibniz's Law of Identity, which we had said with A Smoking Fox to accept as a definition for cases that the two examined terms will be considered identical).
Each one of x & y, of course, could be caused by more than one source and that could be covered by “categories of elements”, (I didn’t had that in mind when I was choosing this description, because I was thinking mainly about mind-matter dualism at that moment, but it occurred to me that, it covers that case also).
I used the “categories of elements” expression to describe “collections (bundles) of properties”. I mean the x and y could be described as the properties that they posses (in case of mind and body, for example, mind is mental, it thinks - body is physical it acts, etc) and this two collection of properties could be seen as the two opposite categories (x & y), under examination. I thought at that point that “collections of properties” didn’t cover other cases like the cases in which one term is used to refer in general to a category of something (spiritual & material, for example).
I was also thinking (picking up this term) of good and evil, with its various representatives in different religions and also, uniting terms like physical evil, moral evil, evil spirits, evil gods, under one word “evil” in my mind. (Even if I didn’t suggest it as a subject, I was having it in my mind as an example when I was forming the proposed definition). So instead of “collections of properties” it turned out “categories of elements”, “elements” being a word that could have many meanings, from physical to spiritual.
Also Praxis, I would like to mention that the last definition about which A Smoking Fox and me had agreed, was
QUOTE
Dualism is the theory that considers some possible thought or thing or state, to consist of only two different and irreducible origins or categories of the element.
(It includes "state", also).