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To start this off light, I was initially thinking about this with Oreos. There are fresh Oreos, and then there are two different ways they can go stale: dry/hard (in low humidity) and soft/mushy (in high humidity). To me, the dry/hard stale and the soft/mushy stale are opposites of each other, but they are also opposites of fresh as well.

Now to give another example is apathy. The opposite of apathy is to feel strongly. Which could be both love and hate, which are both opposites of each other. I could love stale Oreos, I could hate stale Oreos, or I could feel completely apathetic about stale Oreos. All three of these seem to be mutually opposite of the other.

But also think of something too with things like sexism and racism and other political correctness where it's possible to go so over-corrective that it becomes its own offensive antithesis to both PC and non-PC alike. (I can't really think of a way to lighten this one with Oreos...)

I found the term autoantonym which seems to help a little bit with the relationship. I also know that in art and design you would call it a color triad where three colors are as far from each other on the spectrum as possible. However this still seems to come up short in trying to solve my existential Oreo issue...

*EDIT Ah! So let me add one last element to the question. In each instance where I think this situation could apply, I think we go from two words, A and B which appear to be binary opposites. It can either be A or not A. But when you add word/concept C which is both not A and not B, you either have a natural transition where it's possible to smoothly take the conversation to a broader or narrower scope (like emotions with love, hate and apathy). OR you could have a more unnatural transition where there isn't a clearly defined word for C (as far as I can tell there really isn't a word for that humid kind of stale. And that sad state of affairs really should have its own word, right?). And at the end of all this, it seems like we're trying to find a Word C even now...

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marked as duplicate by Bradd Szonye, MετάEd, tchrist, choster, Kristina Lopez Jun 17 '13 at 17:23

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I don't think the examples are clear enough to see what you're asking for. –  John Lawler Jun 14 '13 at 13:17
    
So, B is the opposite of A, and C is the opposite of A, but B and C are antonyms, rather than synonyms. Now, you want to describe the relationship between B and C... is that it? It sounds like B and C are at opposite ends of a spectrum. –  J.R. Jun 14 '13 at 19:03
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You had me at Oreos. –  Mitch Jun 14 '13 at 23:18
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Good question. It shows some pretty neat thinking. (By the way, did you get this question from a textbook on logic and then adapt it for your purposes here?) Your question is interesting in that it involves logic, philosophy, linguistics, pragmatics, and English language usage in general. I think, however, you might be confounding your question with too many variables, each one of which requires additional "unpacking."

In order to compare apples with apples and oranges with oranges, we need to separate some key variables. You've laid out the variables for an Oreo's staleness quite well. On the traditional X/Y axes, on the X axis you've got soft/mushy and hard/dry at opposite ends. (Let's presume there are degrees of softness/mushiness and hardness/dryness as you travel along the axis.)

On the Y axis you've got humidity, low to high. Plot a graph and you've got a 45-degree angle sloping from the top left to the bottom right. With high humidity comes high softness/mushiness; with low humidity comes hardness/dryness. Simple. You could, however, complicate things by adding more variables.

This, then, may be at the heart of your "dilemma." I say: take things apart; work with just two variables at a time; play with them; attach antonyms to a given phenomenon one pair at a time. You'll find out pretty quickly that in working with feelings and attitudes, things get complicated very quickly!

Take your "political correctness-to-an-extreme" example. You have the opposites of political correctness and incorrectness, but can you graph them one at a time the way you would the staleness of an Oreo? Frankly, I can't think of what the Y axis would be if you were to do so.

Perhaps we should stick to two simple horizontal continua: 1) "political incorrectness," and 2) "political correctness." Let's take them one at a time.

Political incorrectness could be labeled "reactionary" on one side of the continuum and "radical" on the other side. In other words, at one extreme you have the person who believes in no form of political correctness, and at the other extreme is the person who goes overboard, or over-compensates. So far, your Oreo analogy is holding up pretty well, since there are varying degrees of political incorrectness, just as there are varying degrees of staleness for cookies.

Now do the same for political correctness. What do you come up with? It's tricky, is it not? Until someone comes up with the definitive list of criteria by which political correctness can be measured, we're left only to guess what the "ideal" and the "not so ideal" are. In other words, what comprises Aristotle's "golden mean"? Moreover, who is going to come up with a measurement, an objective standard, by which the phenomenon can be measured and evaluated?

I guess our country's founding documents, particularly the Declaration of Independence and the U.S. Constitution--particularly the Bill of Rights--might be a good place to start. Interpretations of these seminal documents do vary, of course, which is why we have Republicans and Democrats!

To wrap up, words are funny things, especially graded antonyms (stale/fresh, PC/non-PC, beautiful/ugly, unique/common, selfish/selfless, proud/humble,etc.). On the one hand, it's relatively easy to understand the staleness of an Oreo cookie by labeling it soft/mushy and hard/dry, but try doing that with something as complicated as political correctness. You might think at first blush it would be easy, but contraire mon frère!

Who is to be the final arbiter of what constitutes political correctness? What are the standards by which one measures its opposite? Are they truly opposites, or can political correctness be another term for "It's OK to do anything you want, as long as you don't hurt someone"? I wouldn't call that political correctness; I'd call that stupidity--or perhaps to use one of your terms, "apathy."

We all draw a line in the sand on various things and say, "Here is where I stand; I'll go no further, at least until someone can persuade me otherwise." (Some folks do not add the part about persuasion, because their minds are made up, period!) Even the person who refuses to draw a line in the sand has already done so by default, and that line to him is, ironically, "no line" at all. Hey, if you don't take a stand for something, you might just fall for anything!

Probably the only thing I have done in this "answer" is complicate and confuse things unnecessarily--muddy the waters, so to speak. Perhaps I have laid a foundation someone else can build upon. At this point, I'm a little ambivalent about what my feeling state is about my answer, but you and others are welcome to join in the fray.

By the way, you might want to check out Brad Syzone's unanswered question about half-graded antonyms.

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Excellent answer! I think this definitely helped me find what I was really after. See if that edit opens up any more thoughts on the issue. –  cchapman900 Jun 15 '13 at 17:22
    
@cchapman900: Thank you. I've completely revised my answer for better clarity. That's a real "can of worms" you've opened up, but it's well worth exploring. I hope many others weigh in on your question, with each person generating a little bit of clarity amidst the confusion. (Hey, you've got two more antonyms!) As for your edits, I'll need to let them percolate a bit before getting back to you. –  rhetorician Jun 15 '13 at 21:32
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You might consider inconsistent and conflicting.

In your Oreo example, each of the terms in these attribute combinations are inconsistent or conflicting with the other terms:

  • fresh, wet, dry
  • fresh, soft, hard

In you example with apathy, each of the terms in these attribute combinations is inconsistent with the other terms:

  • apathy, love, hate

A multi-word term would be mutually exclusive.

In your graphical metaphor, you have the concept of orthogality, which covers the independence of the attributes. So, for example, wetness (wet or dry) and hardness (hard or soft) are independent attributes.

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