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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?

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@Autistic suerely binary would be better than digital -- and I have heard that used. – Chris H Mar 29 at 11:27
Thanks for all the answers. Categorical was the word I was looking for, and now there is a whole plethora to choose from. – simon Mar 29 at 12:03
Categorical does not mean two states only. For instance, a valiable marital status that can take the states never married, married, divorced, widowed, is categorical too. – Jacinto Mar 29 at 12:27
@simon in that case, you'd be better off with "distinct", "enumerated" or "discrete" instead of "absolute". – corsiKa Mar 29 at 18:02
No one else seems to have suggested boolean – robjwilkins Mar 30 at 12:32

21 Answers 21

up vote 96 down vote accepted

The OP decribes exhaustive and mutually exclusive cases, with two options or outcomes. In statistics, this segmentation of the possible outcomes is often called a categorical variable. When the variable only takes two values, it is generally termed:

  • binary (already proposed by @Malvolio), for "appearing in pairs" (not directly related to the binary or base-2 number system) or Bernoulli variables. The related categories are often denoted by values 0 and 1 (very "binary" in the logical or computer sense), or 1 and 2.


  • dichotomous variables (which was proposed by @plagueheart, and I did not see at the time of my answer), from greek dikhótomos, “cut in half” or "cut in two".

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 -tomy ("to cut", like in a-tome, 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:

enter image description here

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.?

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"Absolute" is also used when there's no grey area or middle ground, and like "categorical" it can be used with more than two options. – user568458 Mar 29 at 11:53
Thanks @user568458, that is also useful. – simon Mar 29 at 12:04
Dichotomous was suggested by @plagueheart fifty minutes earlier, and binary was proposed by Malvolio, which is your suggestion?? – Mari-Lou A Mar 29 at 12:13
I suggest bolding binary, even though it's already in Malvolio's answer, because yours has been accepted. – Dan Henderson Mar 29 at 12:44
In my experience binary variables are a special case of categorical variables, which are any discrete variables (e.g. "country of birth" where there are multiple possible answers, but no "in between" answers). – Paul Mar 29 at 13:57

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"...

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While this is correct, it's worth emphasising that "Boolean" is not widely used or known outside of technical fields. Binary is much more common, but still more common in formal, academic or educated contexts than in casual, everyday speech. – user568458 Mar 29 at 11:51
@EdwinAshworth -- evidence of what? – Malvolio Mar 29 at 16:24
@EdwinAshworth -- around here, you might get an argument about whether an itch would be better modeled as a Boolean or a scalar ("it itches or it doesn't" vs "how much does it itch on a scale of 1 to 100?"), but not about the word itself. Would a dictionary cite suffice, or a quote from a movie review? ("The final act offers a binary choice: love or hate, forgiveness or vengeance, truth or consequences.") – Malvolio Mar 29 at 17:43
The non-technical senses of binary, such as this, didn't need to leak out of "purely technical contexts". – Jon Hanna Mar 30 at 9:37
@Wildcard -- an analog device operates by having quantities represented by some other quantity: e.g., the weight of an object being represented represented by the voltage in a line or a needle on a scale. A digital device only has a fixed number of quantities (typically two), and information is represented by combinations of those fixed quantities. Analog and digital, whatever might have been told, are dichotomous in the sense that any primitive device is one or the other (any modern computer has analog components, of course, typically for I/O). No third model exists (yet). – Malvolio Mar 30 at 18:52

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.

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+1. This is the best nontechnical answer so far. – Færd Mar 29 at 10:41
@Fard, true, now I can use this to explain my situation to a non-technical person. – simon Mar 29 at 12:09
This is definitely how I would describe the situation to most people. – corsiKa Mar 29 at 17:52
Note that "black and white" often implies that there is a right and wrong, as in the Scotland Office example. That's not necessarily what is asked for in the question. – 200_success Mar 30 at 2:54
hadn't thought of it before, but it's a slightly odd phrase isn't it? there may be only two options from which to choose - black AND white - but one must pick black OR white. "The situation is black or white" makes more sense: if it's black AND white, it's grey! : ) – wazz Apr 4 at 1:17

You could also refer to such an attribute as being dichotomous:

[adj] 1. Divided or dividing into two parts or classifications.

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Two distinct parts, but not necessarily true and false. – Boaz Mar 29 at 8:21
@Boaz The original question didn't specify they had to be true or false, however--only that it could only assume two values. "Boolean" covers the only true-or-false case. – plagueheart Mar 29 at 8:32
I thought this was the best answer, but actually, the original question does specify they have to be true or false - dichotomous things are usually two separate things where you can only have one or the other. The question is asking for a state that is either on or off, never halfway. I think boolean is actually more correct now. – Nacht Apr 6 at 3:49
@Nacht I suppose it's the inclusion of the rash case that makes me think it's not just Boolean, though I suppose one could restate it as: "Are you itchy? Y/N." – plagueheart Apr 6 at 5:15

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.

Principle 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.

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as opposed to ambivalent. nice. – wazz Apr 4 at 1:20


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.

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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.

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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

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Discrete is often used in contrast of something that is continuous (having an infinite number of values), and is very relevant in statistics which deals often with probabilities (%s). I'm not quite sure it fits OP's intention, although he did mention %s and statistics. – Darthfett Mar 29 at 16:17
@Darthfett That contrast with continuous is part of what the OP is looking for. As a generic English term, it just needs to include the OP's intent squarely within its semantic range. For use in a specialist context where the term has an existing and different definition, you can consider disambiguating with context or keywords, or use another specialist term such as crisp. – Lawrence Mar 29 at 16:27
Agreed. I was thinking a bit too much about the probability aspect of it. It definitely applies here. – Darthfett Mar 29 at 17:29
discrete, like categorical is too broad : it fails to communicate that only two values are possible. IOW, all binary variables are discrete variables, but not all discrete variables are binary variables. – MSalters Mar 30 at 10:04
@MSalters Agreed, except that the important aspect conveyed in the OP's explanations isn't that there are only two values - it's that there isn't anything in between. – Lawrence Mar 30 at 11:17

Polarize - as in "Results indicate that opinions were polarized on this matter".


"to ​cause something, ​especially something that ​contains different ​people or ​opinions, to ​divide into two ​completely ​opposing ​groups"

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Polarized doesn't imply that there's no in-between options (or opinions), however--only that they're unusual. – plagueheart Mar 31 at 20:36

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'.

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Or, "expressing a choice between two mutually exclusive possibilities". +1 – Mazura Mar 29 at 19:59

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.

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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.

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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 http://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."

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Exclusive disjunction seems quite technical, but it is an interesting phrase and fits the intended meaning, I like it! Oh, and welcome to EL&U :-) – Lucky Mar 29 at 21:38
Thanks, @Lucky. I hope it will be useful to someone. – Dalton Bentley Mar 29 at 23:29

There's an old expression that captures a binary choice or binary outcome quite well:

You can't get half pregnant

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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).

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Curious why this might have been downvoted - all the words apply and the first one is literally tailored for this exact situation. – corsiKa Mar 30 at 14:31
I'm not downvoter but I think "vanilla" is not at all like "binary", and "enumerated" does not convey the dichotomy that is implicit in each of the three examples. – DWin Apr 3 at 6:36

I think absolute is exactly what he's looking for if he wants the technically correct but non-field specific answer.

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Another old expression for a binary outcome:

An inch is as good as a mile

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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.

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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'

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I disagree. "Qualitative" really does not imply discrete possibilities. It rather includes descriptors of .... qualities, i.e. color, flavor, sharp, dull, etc. – DWin Apr 3 at 6:38


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.

  1. Having or exhibiting a single clearly defined meaning
  2. Admitting of no doubt or misunderstanding; having only one meaning or interpretation and leading to only one conclusion


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One sided is how I would describe that condition.

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Why the downvotes? – Evan Carslake Apr 18 at 18:00
There are two sides to every coin. – Hot Licks Apr 18 at 19:05
@HotLicks isn't there 3 sides to a coin. Top, Bottom, Side. – Evan Carslake Apr 18 at 21:11
I never take sides. – Hot Licks Apr 18 at 21:55

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