# How can I describe a "one or more" condition (one that has many options; a "non-boolean")?

Generally speaking a boolean condition is understood to be an "either/or" relationship; for example, something is hot or cold.

What's do you call a "one or more" condition, e.g. something that can have many colors?

To add a bit of clarification, in conversation most people understand Boolean to be an "either/or" proposition, whether there are two or more conditions, as when you ask someone to pick a single color of paint (red, green, or blue).

When discussing that with non-programmers, I find they perfectly understand that when I describe it as a boolean condition.

However, I don't seem to know what to call a "one or more" condition, for example, "pick any colors that you like: red, green, blue, yellow, orange, purple."

I find my self saying "non-boolean" which isn't all that useful.

-- EDIT --

Rubergly's answer gave me an interesting thought:

Boolean is similar to "dichotomous" and also similar to "binary" (1 or 0). Trinary means set of three... so is "polynary" a word, or is there something similar?

• Int, char, float or string. :-) Commented Jul 19, 2011 at 21:44
• lol, I actually am interested in this because of some programming, but I'd like to explain "many-to-many" relationships using a work that non programmers would understand. Commented Jul 19, 2011 at 21:45
• As to your edit, would it be unacceptable to say “you may pick multiple colours”? Commented Jul 19, 2011 at 22:03
• The opposite of `true` is `false`. The opposite of `false` is `true`. So the opposite of Boolean is still Boolean :-)
– Dan
Commented Jul 20, 2011 at 1:49
• Just a nitpick: the word is ternary, not trinary. Commented Jul 20, 2011 at 5:09

There are many existing terms for a number possible concepts that you might be using:

• if you are talking about a question/situation that has one outcome (functional) out of many distinct choices, like one out of many but a finite set of colors, then it is discrete or nominal (the latter technical for statistics).
• if you are considering a situation where you get many results at once, like red, blue, and green together from the rainbow, then it is multivalued, a subset, a tuple, or n-ary (the latter 3 are technical). 'n-ary' is probably not in any nontechnical dictionary but is in wide use in mathematical language.

There's a lot of technical math vocabulary that may or may not be appropriate in informal conversation; one can consider the kinds of values returned (as in computer programming the type like boolean, int, or real) and also the number of different values returned (for a person - height, eye color, handedness). Here is a small taxonomy:

• number of values returned
• single value = functional
• multiple value = relational (or multivalued)
• a given set number of values returned is fixed arity
• variable being n-ary or polyadic (multivariate for arguments, __multivalued for results),
• the range/possibilities of a given single value
• continuous
• discrete, and discrete has a number of words to describe variations (binary, boolean, dichotomous, nominal, integral, combinatorial)
• Discrete vs Multivalue is a winning combination I think, better than "boolean vs. non-boolean" by a mile :) Commented Jul 20, 2011 at 0:54
• To me, discrete doesn't imply "only one value out of many". It just means that the many possible values are countable. Something can be simultaneously discrete and multivalued. They are not opposites so much as orthogonal concepts. Commented Jul 20, 2011 at 2:15
• I often use binary/digital to mean boolean, and Analog(ue) to mean something that is one of infinitely many. Not directly related to the question, I know. Commented Jul 20, 2011 at 6:18
• @John: yes...I was misleading. The words are probably what will work for the OP, but the use and explanation was not particularly coherent. I think I've fixed that (and explained further). Commented Jul 20, 2011 at 19:06

What about multiple-valued as in multiple-valued logic?

Time is precious, so I quote:

In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. An obvious extension to classical two-valued logic is an n-valued logic for n greater than 2.

• You had me at 'multi-valued'. Commented Jul 19, 2011 at 23:51
• Except this just means one of many values. A traditional light switch is binary, or Boolean. Those three-way bulbs allow a lamp to have more than two settings, but such a multivalued setup still only has one active setting at a time. Commented Jul 20, 2011 at 2:21

If you mean, what do you call a variable that has a limited number of states, but more than two, that's usually called an enumeration.

I feel that `multiple-valued` and `enumeration` both express the desired meaning, but still do so from a very programming-oriented perspective. I think `nondichotomous` is more fitting, though I have found little evidence that it is truly a word; dictionary.com insists it is, but I can't find any other dictionaries referring to it.

• Dichotomous is indeed a word, but the prefix should be followed by a hyphen. Commented Jul 19, 2011 at 22:38
• WOW! You gave me a great idea: along the lines of "dichotomous" is "binary", which means very nearly the same thing as "boolean" (1 or 0). Is "polynary" a word?? Commented Jul 19, 2011 at 23:24
• @HarroldCavendish Wikipedia's hyphen page (and Wiktionary's non- page agrees) states that the hyphen is more of a UK/America issue. Commented Jul 19, 2011 at 23:34
• @Andrew unfortunately, I cannot find any record of a "many" form of "binary/trinary/etc." If you'd like, you could always use vigenary just to confuse people who don't know Latin. Commented Jul 19, 2011 at 23:47

This forum thread suggests polyvalent and multivalent.

• You know I think monovalent vs. polyvalent might actually be a great way to describe what I'm talking about, thanks!! Commented Jul 20, 2011 at 21:51

I kind of like plural. "A plural condition." Since boolean/binary is arguably about zero or one, a word for "more than one" makes some sense. Arguably ;)

`Multi-valued`, `enumeration`, and `discrete scalar` sound like supersets of boolean and supersets do not seem to have the stronger connotation of an opposite. `Many-valued` is similar to `discrete scalar` and is hyphenated so it might be avoided for the aesthetic. The original question says that `non-boolean` was not well received so perhaps `non-dichotomous` is going to fail in a similar way. Both aim to say what something is not, which truly might be the best answer strictly, but depending on the purpose not as good as describing what something is.

A `continuous scalar` value has a strong sense of being the opposite of a boolean value. Since a dichotomous scalar is a bit of an exception, and continuity might be assumed, in some contexts the qualification could safely be dropped.

A `scalar` is the opposite of a boolean when a more permissive usage is appropriate.

• I like how `scalar` sounds, but I'm not sure I understand how you mean it. Looking it up (merriam-webster.com/dictionary/scalar) it seems like a scalar is defined to be something having an "uninterrupted sequence of steps." Can you elaborate on why you feel that expresses the opposite idea of a binary or boolean choice? Thanks! Commented Jul 20, 2011 at 3:36
• You want to describe a many valued variable but you did not specifically suggest discrete values when you gave your "many colours" example. Scalars do not have to be discrete and that's why I suggested it. The quality of being an opposite can be subjective. It's probably better to decide if scalar is suitable rather than to decide if it really is opposite. Commented Jul 21, 2011 at 5:11