For example:
1) In statistics, this attribute will always either be 0% or 100%, never in-between.
2) The boundary is either safe or destroyed, because there is never a state where it is only 'slightly leaking'.
3) The rash either itches or does not. It can't itch a little. That would still be an itch.
What word can we use to describe this attribute?
The OP describes exhaustive and mutually exclusive cases, with two options or outcomes. In statistics, this segmentation of the possible outcomes in a finite number of choices is often called a categorical variable. When the variable only takes two values, it is generally termed:
or
Sometimes, categorical variables are segmented into: nominal, ordinal or dichotomous. Sometimes, people use "categorical variables" only for cases of three or more possible outcomes (multi-way, n-ary or polytomous), as opposed to 2-ary case.
Binary and dichotomous are sometimes considered synonyms. They both contains the root 2 (di- or bi-). For some, binary variables form a sub-species of dichotomous variables, whose values are assigned either a 0 or 1 label or binary state. The suffix -tomy ("to cut", like in atom, with privative "a-", which cannot be cut) in dichotomy seems more precise than the concept of arity, that denotes two objects or operands ("binary stars", "binary operation"), without clear reference to the mutual exclusion.
With 0 or 1 binary labels, it remains possible to perform mathematical operations on variables (like averaging) and to quantize or dichotomize the result afterward, while it is more difficult to "average" red and not-red dichotomous categories.
[EDIT] After some comments, one can wonder about the correct use of "binary" vs "dichotomous", the latter being at first glance the correct one. However, the use of binary is widespread. I tend to consider "binary" as a metonymy for the dichotomous case, as illustrated in the Yin-Yang symbol:
There are two categories: the shady side (yin), and the non-shady or sunny side (yang). They are mutually exclusive (although intricated and dual). But one could describe them has black and white, with colors represented by 0 and 1. In other words, labels 0 and 1 somehow encode the two possible outcomes, and the 0 and 1 symbols inherit from the mutually exclusive nature of the binary numbers.
Additional details are provided in What is the difference between “dichotomous”, “binary”, “boolean”, etc.?
In engineering, a choice that can only be "yes" or "no" is called binary or Boolean (after the mathematician George Boole).
Edit: Apparently, the word binary has leaked out of purely technical contexts. From a review of a TV movie:
The final act offers a binary choice: love or hate, forgiveness or vengeance, truth or consequences.
And now there is non-binary sex. I guess that would be "analog sex"...
You could call this situation black and white.
Some might argue this isn't a single word, but it does get its own entry in some dictionaries. NOAD says:
black and white (adj.) (of a situation or debate) involving clearly defined opposing principles or issues: there is nothing black and white about these matters.
The website vocabulary.com lists this definition:
black and white (adj.) of a situation that is sharply divided into mutually exclusive categories
When something is black and white, we might also say, "There are no shades of gray."
Here's an instance from a news story:
A Scotland Office spokesman said: “The situation is black and white, the solution must come from outside government.”
Lastly, I enjoy this amusing quote about politics, attributed to Peter Thorneycroft:
The choice in politics isn't usually between black and white. It's between two horrible shades of gray.
You could also refer to such an attribute as being dichotomous:
[adj] 1. Divided or dividing into two parts or classifications.
The situation can be described as being bivalent.
[MASS NOUN] Logic The existence of only two states or truth values (e.g. true and false):
So we may represent the Aristotelian solution as one which rejects the law of bivalence.
In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic.
either-or
used to refer to a situation in which there is a choice between two different plans of action, but both together are not possible:
It's an either-or situation - we can buy a new car this year or we can go on holiday, but we can't do both.
— http://dictionary.cambridge.org/dictionary/english/either-or
Consider all or nothing:
having no middle position or compromise available.
"an all-or-nothing decision"
Wikipedia's page on All or Nothing lists an article on all-or-nothing thinking, which redirects to psychological splitting, and an article on all or nothing financial option, which redirects to binary option.
You can describe your attributes as discrete. That is, the attributes may take on values from a (limited) set of distinct values, and no other, not even those that appear to fall between adjacent valid values.
Discrete adjective Individually separate and distinct - ODO
Polarize - as in "Results indicate that opinions were polarized on this matter".
http://dictionary.cambridge.org/dictionary/english/polarize
"to cause something, especially something that contains different people or opinions, to divide into two completely opposing groups"
One non-scientific word would be "Manichean", meaning to divide everything into the categories of good or evil. Stemming from religion, it would be used when the context is religious, moral, philosophical, maybe psychological.
Manichaean (also Manichean): based on the belief that there are two opposites in everything, for example good and evil or light and dark
The situations described in the original question are examples of a 'disjunctive' (which can act as an adjective as well as a noun). The word comes from Latin, and it means 'to separate exactly into two disjoint parts'.
I'm surpised this wasn't brought up, but what about
yes-no question, n: a question calling for an answer of yes or no.
This is literally exactly what you're talking about, and according to dictionary.com, it's actually a word.
There are some broader terms you can use, although they might be a bit hit-or-miss among your audience. They apply to this situation and others.
enumerate, v: specify individually
In this case, your options are enumerated. This is also useful when the options are "Yes, No, or Maybe". For instance, you might not want "Yes, No, Probably, Possibly, Darned Sure, Booked The Ticket But Also Have A Big Meeting The Day Before So I Bought Ticket Insurance Just In Case"... just lump everything else into maybe.
vanilla, adj: plain and without any extras or adornments
In this case, you don't want any extras. This is handy in cases where you want to get down to basics (and, of course, yes or no is pretty much the MOST basic answer to a question).
As much as the other answers give more recognizable and relevant answers, serendipitously A Word A Day gave a word today for this:
constative - A statement that can be judged as true or false. adjective: Capable of being true or false.
If your evaluation of a person shifts only between admiring or loving them to despising or hating them you are said to be splitting. This is a common feature of personality disorders, but BPD or borderline personality disorder in particular (and usually includes the same kind of diametric shift in self-image as well, e.g., believing oneself to be superior, then feeling wortheless at another time). I just noticed @Kevin Workman already mentioned splitting, but I'll leave my elaboration (as possibly useful as a brief summary of the concept).
Logically, the requirement for two mutually exclusive states is described by the term exclusive disjuntion or XOR. See https://math.stackexchange.com/questions/1254415/use-of-either-or-in-maths.
Binary is probably the most generally used specific term for an either-or possibility, I agree (with @Malvolio). It is becoming fairly common outside strictly engineering applications, e.g., "a simple binary decision based on prior conduct eliminates consideration of the finer detail of history."
I think absolute is exactly what he's looking for if he wants the technically correct but non-field specific answer.
A better technical term than binary (which can too easily be misused) is satisfies a zero-one law. This is a standard term in probability, and (roughly speaking, actually very roughly speaking) means all or none.
There's an old expression that captures a binary choice or binary outcome quite well:
You can't get half pregnant
Another old expression for a binary outcome:
An inch is as good as a mile
Not a word, but a phrase: binary solution set. It's not quite the same as yes-no as it is not limited to just questions, but it is probably more common for statistics.
In statistics, the term qualitative (as opposed to quantitative) is often used. It is generally regarded as synonymous with 'discrete' and 'categorical', which have also been suggested. The term refers to the type of data being captured, in this case whether a quality is present (1) or absent (0). For example, in a collection of subjects in an analysis, one might measure the amount of vitamin C they consume over a period (quantitative), vs whether they contracted a cold at all (qualitative). Qualitative data need not be binary, e.g. sex/gender, age category. Hence the overlap with 'categorical'
Unambiguous
If something is unambiguous, there are no two ways to interpret it. If your girlfriend burns all your letters, texts you that she hates you, and moves a thousand miles away, the unambiguous message is that she’s finished with you.
- Having or exhibiting a single clearly defined meaning
- Admitting of no doubt or misunderstanding; having only one meaning or interpretation and leading to only one conclusion
