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So basically, I know the name for both sides of a coin, yet not the coin itself.
In other words, when you refer to a coin, you don't want to say 'this object with one side heads, and the other tails', you would want to say 'this coin'. What I want is a general term to refer to two ideas, that are the absolute opposite to each other. I can't really use the word 'concept', or 'idea', because such words are already assigned to the very concepts/ideas themselves.
polar opposites:
polar opposite (plural polar opposites):
The complete opposite, opposite in every way.
https://en.wiktionary.org/wiki/polar_opposite
"Polar opposites" might also refer to the scientific or technical definition of two things having exactly opposing or inverted polarity, sign, orientation, or some other property.
I'd suggest dichotomy:
a difference between two opposite things : a division into two opposite groups.
diametric
- in direct opposition; being at opposite extremes; complete: diametrical opposites; a diametrical difference. –dictionary.com
Two things which are absolute opposites of each other, are diametrically opposed or diametric. We often perceive coins as being diametric, while forgetting that they have a third side: the edge.
Try antipodes at dictionary.com
either or both of two opposite things. (from singular "exact or opposite things")
They both are antipodes.
The questioner wants a singular noun that denotes a pair of antithetical ideas. I say there is no such word. The professor of English to whom I have been married for fifty years can't think of any. "Antithesis" denotes each in relation to the other. "Dichotomy" denotes the relation between them. "Dilemma" from its Greek roots should mean "two propositions," but it also requires that one of them must be chosen. "Oxymoron" is a conflation of two inconsistent ideas creating an absurdity.
"Dyad" denotes a pair of anything. It's the best I can think of. It's too inclusive, but it does include what the questioner asked for. A dyad is not necessarily a pair of antithetical ideas, but pair of antithetical ideas is a dyad.
Perhaps polarities
The state of having two opposite or contradictory tendencies, opinions, or aspects:
the polarity between male and female
the Cold War’s neat polarities can hardly be carried on
Oxford Dictionaries Online
EDIT I think dual might be the best term. It is an object (in the most abstract sense) that may have two opposing, mirrored, states.
Thanks to @user2901512's answer below for a hint to this.
Previous answer (incorrect as I initially thought the question asked for the name for two concepts which are opposite to each other, which is not OP's intention, I believe):
How about antonyms? They are words with completely opposite meanings.
If what you mean is "something with two possible values which can be interpreted as exclusive from one another," binary might also work.
A binary oppostion
https://en.wikipedia.org/wiki/Binary_opposition
A binary opposition (also binary system) is a pair of related terms or concepts that are opposite in meaning. Binary opposition is the system by which, in language and thought, two theoretical opposites are strictly defined and set off against one another. It is the contrast between two mutually exclusive terms, such as on and off, up and down, left and right.
Antithesis will also work, although it's very formal. The OED Online's first definition for antithesis is
1. Rhetoric. An opposition or contrast of ideas, expressed by using as the corresponding members of two contiguous sentences or clauses, words which are the opposites of, or strongly contrasted with, each other; as ‘he must increase, but I must decrease,’ ‘in newness of spirit, not in the oldness of the letter’.
One of the examples under that definition is
"In an Antithesis, one contrary must be pronounced louder than the other." (John Mason An essay on elocution, or, pronunciation 1748)
The third definition is also apropos:
- By extension: Direct or striking opposition of character or functions (between two things); contrast. Const. of, between (with obs.).
And one of its illustrations:
"The antithesis of natural and revealed religion." (Charles Kingsley · Alton Locke, tailor and poet II. xvii. 262 · 1st edition, 1850)
Apparently the word is from an ancient Greek term, via Latin; it was associated with Logic and Rhetoric all the way through.
Editing to add the second OED definition and my own paraphrase of the definition, per @Mazura's suggestion. I would phrase it as
Antithesis: A pair of opposing or contrasting ideas or things.
As the word in English has gone from a term of art to more general usage it has shifted away from this meaning so that now it's almost always used to mean the distinction between two things, or the second of two opposing things: where once we would have said X is antithetical to Y now we can say X is the antithesis of Y, and we're somewhat less likely to talk about the antithesis of X and Y.
But it certainly can still be used to describe the pair, e.g. X and Y are very different, and this antithesis is at the heart of... etc.
Duality: ''An instance of opposition or contrast between two concepts or two aspects of something; a dualism.''
However, an instance of opposition between two ideas, isn't strictly the same as the ideas themselves.
Contra is the root as in contradiction.
Edit: I appologize I did not mean to post this I thought I cancelled out. I stopped writing when I re-read the question and thought that this is about what to call the coin, not the concept.
If you are talking about a coin with two opposite sides, the sides become a characteristic of the object in question.
Rather than describe the sides, you wish to specify the analogy to the coin itself.
As a coin has two sides, I present "argument" as the term for that which has two sides.
The side lables themselves are of little interest or consequence and can be Pro or Con, Soft or Hard, etc. so long as they appear to be mutually exclusive of the other.
Two antonyms, and a spectrum in between, perhaps?
antonym: a word with a meaning that is opposite to the meaning of another word
Dichotomy. =]
More generally, not limited to two ideas or opposing ones.
Abstract concept or meta concept.
In programming, we usually refer to it as a class, parent class, or abstract.
Note that Abstract concept or meta concept can refer to something with more than two species, and to things that aren't limited to opposing species either.
It's even more general / abstract ;)
