Ambiguity

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Ambiguity is the property of being ambiguous, where a word, term, notation, sign, symbol, phrase, sentence, or any other form used for communication, is called ambiguous if it can be interpreted in more than one way. Ambiguity is distinct from vagueness, which arises when the boundaries of meaning are indistinct. Ambiguity is context-dependent: the same communication may be ambiguous in one context and unambiguous in another context. For a word, ambiguity typically refers to an unclear choice between different definitions as may be found in a dictionary. A sentence may be ambiguous due to different ways of parsing the same sequence of words.

Linguistic forms

Lexical ambiguity arises when context is insufficient to determine the sense of a single word that has more than one meaning. For example, the word “bank” has several distinct definitions, including “financial institution” and “edge of a river,” but if someone says “I deposited $100 in the bank,” most people would not think you used a shovel to dig in the mud. The word "run" has 130 ambiguous definitions in some lexicons. "Biweekly" can mean "fortnightly" (once every two weeks - 26 times a year), OR "twice a week" (104 times a year). Stating a specific context like "meeting schedule" does NOT disambiguate "biweekly." Many people believe that such lexically-ambiguous, miscommunication-prone words should be avoided altogether, since the user generally has to waste time, effort, and attention span to define what is meant when they are used.

The use of multi-defined words requires the author or speaker to clarify their context, and sometimes elaborate on their specific intended meaning (in which case, a less ambiguous term should have been used). The goal of clear concise communication is that the receiver(s) have no misunderstanding about what was meant to be conveyed. An exception to this could include a politician whose "wiggle words" and obfuscation are necessary to gain support from multiple constituent (politics) with mutually exclusive conflicting desires from their candidate of choice. Ambiguity is a powerful tool of political science.

More problematic are words whose senses express closely-related concepts. “Good,” for example, can mean “useful” or “functional” (That’s a good hammer), “exemplary” (She’s a good student), “pleasing” (This is good soup), “moral” (a good person versus the lesson to be learned from a story), "righteous", etc. “I have a good daughter” is not clear about which sense is intended. The various ways to apply prefixes and suffixes can also create ambiguity (“unlockable” can mean “capable of being unlocked” or “impossible to lock”, and therefore should not be used).

Syntactic ambiguity arises when a sentence can be parsed in more than one way. “He ate the cookies on the couch,” for example, could mean that he ate those cookies which were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies.

Spoken language can contain many more types of ambiguities, where there is more than one way to compose a set of sounds into words, for example “ice cream” and “I scream.” Such ambiguity is generally resolved based on the context. A mishearing of such, based on incorrectly-resolved ambiguity, is called a mondegreen.

Semantic ambiguity arises when a word or concept has an inherently diffuse meaning based on widespread or informal usage. This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion.

For example, “You could do with a new automobile. How about a test drive?” The clause “You could do with” presents a statement with such wide possible interpretation as to be essentially meaningless. Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning. This form of ambiguity is closely related to vagueness.

Ambiguity at the translation

Semantic ambiguity reveals usually in funny forms at the translation to other languages; and especially at the multiple translations, for example, from language A to language B and then from language B to language C. (The resulting C-code is unlikely to run well!). Words "run", "flesh", "file", "archieve" provide rich filed for ambiguity. Imagine, how can sound the sentence about electric cirquits in railroads: "the naked conductor runs along the wagon".

The non-complete overlapping of meanings of words in various languages is rather rule than exception. Such ambiguity is main difficulty of the automatic translation; in general, the correct translation without semantic context is impossible

Intentional application of ambiguity

Philosophers (and other users of logic) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments, because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments. For example, a politician might say “I oppose taxes that hinder economic growth.” Some will think he opposes taxes in general, because they hinder economic growth. Others may think he opposes only those taxes that he believes will hinder economic growth (although in writing, the correct insertion or omission of a comma after “taxes” and the use of "which" can help reduce ambiguity here. For the first meaning, “, which” is properly used in place of “that”), or restructure the sentence to completely eliminate possible misinterpretation. The devious politician hopes that each constituent (politics) will interpret the above statement in the most desirable way, and think the politician supports everyone's opinion. However, the opposite can also be true - An opponent can turn a positive statement into a bad one, if the speaker uses ambiguity (intentionally or not). The logical fallacies of amphiboly and equivocation rely heavily on the use of ambiguous words and phrases.

In literature and rhetoric, on the other hand, ambiguity can be a useful tool. Groucho Marx’s classic joke depends on a grammatical ambiguity for its humor, for example: “Last night I shot an elephant in my pajamas. What he was doing in my pajamas I’ll never know.” Ambiguity can also be used as a comic device through a genuine intention to confuse, as does Magic: The Gathering's Unhinged © Ambiguity, which makes puns with homophones, mispunctuation, and run-ons: “Whenever a player plays a spell that counters a spell that has been played[,] or a player plays a spell that comes into play with counters, that player may counter the next spell played[,] or put an additional counter on a permanent that has already been played, but not countered.” Songs and poetry often rely on ambiguous words for artistic effect, as in the song title “Don’t It Make My Brown Eyes Blue” (where “blue” can refer to the color, or to sadness).

In narrative, ambiguity can be introduced in several ways: motive, plot, character. F. Scott Fitzgerald uses the latter type of ambiguity with notable effect in his novel The Great Gatsby.

All religions debate the orthodoxy or heterodoxy of ambiguity. Christianity and Judaism employ the concept of paradox synonymously with 'ambiguity'. Ambiguity within Christianity (and other religions) is resisted by the conservatives and fundamentalists, who regard the concept as equating with 'contradiction'. Non-fundamentalist Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans.

Ambiguity in abbreviations and jargon

Abbreviations form one of the richest sources of ambiguity, see List of classical abbreviations, (which is still far from complete). For example, AU may mean Atomic Unit, Astronomical unit, as well as Arbitrary Unit, American University, and a lot of other things. Simple transmutation of the same two letters gives University of Arizona (which is 200 km away from the Arizona State University), United Airlines, Unidad Administrativa (Spanish) and so on.

Many cryptic acronyms spell words that also have a different meaning, such as the "Rental Update Notification," "Research Unit in Networking," or "Resource Utilization Number" (RUN), which also has 130 other formally-defined meanings. Common words like "RUN" make very-poor miscommunition-prone acronyms, and therefore should generally be avoided. The "IBM" TLA is very well known in most contexts, but Acronym Finder has over 200 definitions for IBM.

Sometimes, an abbreviation that seems innocent enough in one language (e.g. Exxon), but has a profane interpretation in another language, or in street jargon. This is often true if an abbreviation constructed from several run-together lowercase words is used, such is the case in many web URLs. A person defining, or trying to interpret, ambiguous abbreviations must be very careful. The abbreviation may have several distinct but ambiguous interpretations. Examples:

• http://www.therapistfinder.com; One might be led to think that this link leads to a list of sexual offenders, when in fact it is a means of finding a therapist in the state of California
• http://www.opticsexpress.org; An automatic filter cannot tell if this link refers to some editorial publishing materials about 'optic sex'
• http://xxx.lanl.gov; (A system manager condemned one "investigator" for intents to access this URL, certain that thesite referred to adult material. He failed to check the site or ask the researcher.)

One of the humorous statements is: "All TLAs are ambiguous." TLA may mean Two-Letter Acronym, Three-Letter Acronym, etc., either one of which is true. BUT, the unique airport code for Teller Alaska (TLA) is not ambiguous (within an airplane navigation system database).

Metonymy involves the use of the name of a subcomponent part as an abbreviation, or jargon, for the name of the whole object (for example "wheels" to refer to a car, or "flowers" to refer to beautiful offspring, an entire plant, or a collection of blooming plants). In modern vocabulary critical semiotics, metonymy encompasses any potentially-ambiguous word substitution that is based on contextual contiguity (located close together), or a function or process that an object performs, such as "sweet ride" to refer to a nice car. Metonym miscommunication is considered a primary mechanism of linguistic humour., but ambiguity has often led to serious/expensive/deadly mistakes.

Disambiguating enterprise miscommunication

In enterprise modelling, ambiguity often occurs in two ways:

(1) Autonomous departments can have many different meanings for the same word: i.e., different point of view (view (database), model-view-controller), levels of abstraction / context-specific detail, or homonyms (like "2", "two", "to", and "too"; "your" and "you're"). Spell checkers can misinterpret these ambiguities, contractions, and improper usage. Computer-automated voice dictation systems (like NaturallySpeaking) require sophisticated context-analysis algorithms with user-specific usage customization preferences, and they still make some mistakes.

(2) The same concept (object, process, or thing) may have two-or-more very-different synonym names within the enterprise, industry and government.

These types of ambiguity are further compounded by the common use of departmental abbreviations, jargon, or acronyms that are quite context-specific. Familiar abbreviations accelerate communication within a well-known context (department), but they INCREASE critical enterprise miscommunication between departments.

An Enterprise Architecture glossary must disambiguate such miscommunication, specify context for every important definition (and possibly hyperlink to more-detailed documentation, or the named system, process, or form itself). The Internet / Intranet now makes this much easier to do, and enterprise internal-and-external communication quality. Enterprise application integration and inter-departmental metadata management are therefore improving greatly. The enterprise disambiguation glossary acts somewhat like a vocabulary-based search engine, to help improve reuse of previously-developed concepts. The glossary is also reducing redundancy and reinventing the wheel, to cut costs, and improve quality, consistency and productivity.

Clearly documenting existing ambiguity for everyone to see can also encourage people to:

(1) Stop coining new terms that are already very ambiguous (like "RUN"), and

(2) Eliminate the need for each piece of internal documentation to develop its own unique context-specific glossary attachment (saving even more time, effort, and redundant, inconsistent, voluminous, information storage space, publication fees, access time, and data-retrieval transportation cost).

Psychology and Management

An increasing amount of research is concentrating on how people react and respond to ambiguous and uncertain situations. Much of this focuses on ambiguity tolerance. A number of correlations have been found between an individual’s reaction and tolerance to ambiguity and a range of factors.

Apter and Desselles (2001) for example, found a strong correlation with such attributes and factors like a greater preference for safe as opposed to risk based sports, a preference for endurance type activities as opposed to explosive activities, a more organised and less casual lifestyle, greater care and precision in descriptions, a lower sensitivity to emotional and unpleasant words, a less acute sense of humour, engaging a smaller variety of sexual practices than their more risk comfortable colleagues, a lower likelihood of the use of drugs, pornography and drink, a greater likelihood of displaying obsessional behaviour.

In the field of leadership Wilkinson (2006) found strong correlations between an individual leaders reaction to ambiguous situations and the Modes of Leadership they use, the type of creativity (Kirton (2003) and how they relate to others.

Ambiguity in Music

In music, pieces or sections which confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some polytonality, polymeter, other ambiguous meters or rhythms, and ambiguous phrasing, or (Stein 2005, p.79) any aspect of music. The music of Africa is often purposely ambiguous. To quote Sir Donald Francis Tovey (1935, p.195), “Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value.”

Ambiguity in Law

Ambiguity, in law, is of two kinds, patent and latent.

Patent ambiguity is that ambiguity which is apparent on the face of an instrument to any one perusing it, even if he be unacquainted with the circumstances of the parties. In the case of a patent ambiguity parol evidence is admissible to explain only what has been written, not what it was intended to write. For example, in Saunderson v. Piper, 18 39, 5 B.N.C. 425, where a bill was cdrawn in figures for X245 and in words for two hundred pounds, evidence that "and forty-five" had been omitted by mistake was rejected. But where it appears from the general context of the instrument what the parties really meant, the instrument will be construed as if there was no ambiguity, as in Saye and Sele's case, io Mod. 46, where the name of the grantor had been omitted in the operative part of a grant, but, as it was clear from another part of the grant who he was, the deed was held to be valid.

Latent ambiguity is where the wording of an instrument is on the face of it clear and intelligible, but may, at the same time, apply equally to two different things or subject matters, as where a legacy is given "to my nephew, John," and the testator is shown to have two nephews of that name. A latent ambiguity may be explained by parol evidence, for, as the ambiguity has been brought about by circumstances extraneous to the instrument, the explanation must necessarily be sought for from such circumstances.

Constructed language

Some languages have been created with the intention of avoiding ambiguity, especially lexical ambiguity. Lojban and Loglan are two related languages which have been created with this in mind. The languages can be both spoken and written. These languages are intended to provide a greater technical precision over natural languages, although historically, such attempts at language improvement have been criticized. Languages composed from many diverse sources contain much ambiguity and inconsistity. The many exceptions to syntax and semantic rules are time-consuming and difficult to learn.

Ambiguity in mathematics and physics

Mathematical notation, widely used in physics and other sciences, avoids many ambiguities compared to expression in natural language. However, for various reasons, several lexical, syntactic and semantic ambiguities remain.

Ambiguity in concepts

Argument.
The concept of mathematical functions uses the term argument, it is independent variable; and the dependent variable is experessed as function of argument.
Also, dealing with complex numbers, various representations are used: $z=a+b\{rm\; i\}=r\; exp(\{rm\; i\}\; varphi)$. Real numbers $~a~$ and $~b~$ are called real part and imaginary part. Real numbers $~r~$ and $~varphi~$ are called amplitude and phase, but also may be called modulus and argument. In the scientific literature and algorithmic languages, notation arg is used: $~varphi=arg(z)~$.
In argumentation using funcitons $~f(z)~$, "the argument" may refer to $~z~$, or $~argBig(f(z)Big)~$, or $~arg(z)~$, causing confusions.

Ambiguity in names of functions

The ambiguity in the style of writing a function should not be confused with a multivalued function, which can (and should) be defined in a deterministic and unambiguous way. Several special functions still do not have established notations. Usually, the conversion to another notation requres to scale the argument and/or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:

• Sinc function
• Elliptic integral of the Third Kind; translating elliptic integral form MAPLE to Mathematica, one should replace the second argument to its square, see ; dealing with complex values, this may cause problems.
• Exponential integral, , page 228 http://www.math.sfu.ca/~cbm/aands/page_228.htm
• Hermite polynomial, , page 775 http://www.math.sfu.ca/~cbm/aands/page_775.htm

Ambiguity in expressions

Ambiguous espressions often appear in physical and mathematical texts. It is common practice to omit multiplication signs in mathematical expressions. Also, it is common, to give the same name to a variable and a function, for example, $~f=f(x)~$. Then, if one sees $~g=f(y+1)~$, there is no way to distinguish, does it mean $~f=f(x)~$ multiplied by $~(y+1)~$, or function $~f~$ evaluated at argument equal to $~(y+1)~$. In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.

Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages (C++, MATLAB, Fortran, Maple) require the character * as symbol of multiplication. The language Mathematica allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions. Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression f=f(x) is qualified as an error.

The order of operations may depend on the context. In most programming languages, the operations of division and multiplication have equal priority and are executed from left to right. Until the last century, many editorials assumed that multiplication is performed first, for example, $~a/bc~$ is interpreted as $~a/(bc)~$; in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language. In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity. Sometimes, one uses italics letters to denote elementary functions. In the scientific journal style, the expression $~\; s\; i\; n\; alpha~$ means product of variables $~s~$, $~i~$, $~n~$ and $~alpha~$, although in a slideshow, it may mean $~sin[alpha]~$.

Comma in subscripts and superscripts sometimes is omitted; it is also ambiguous notation. If it is written $~T\_\{mnk\}~$, the reader should guess from the context, does it mean a single-index object, evaluated while the subscript is equal to product of variables $~m~$, $~n~$ and $~k~$, or it is indication to a three-valent tensor. The writing of $~T\_\{mnk\}~$ instead of $~T\_\{m,n,k\}~$ may mean that the writer either is stretched in space (for example, to reduce the publication fees, or aims to increase number of publications without considering readers. The same may apply to any other use of ambiguous notations.

Examples of potentially confusing ambiguous mathematical expressions

$sin^2alpha/2,$, which could be understood to mean either $(sin(alpha/2))^2,$ or $(sin(alpha))^2/2,$.

$~sin^\{-1\}\; alpha$, which by convention means $~arcsin(alpha)\; ~$, though it might be thought to mean $(sin(alpha))^\{-1\},$ since $~sin^\{n\}\; alpha$ means $(sin(alpha))^\{n\},$.

$a/2b,$, which arguably should mean $(a/2)b,$ but would commonly be understood to mean $a/(2b),$

Ambiguity of notations in quantum optics and quantum mechanics

It is common to define the coherent states in quantum optics with $~|alpharangle~$ and states with fixed number of photons with $~|nrangle~$. Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and $~n~$photon state if the Latin characters dominate. The ambiguity becomes even worse, if $~|xrangle~$ is used for the states with certain value of the coordinate, and $~|prangle~$ means the state with certain value of the momentum, which may be used in books on quantum mechanics. Such ambiguities easy lead to confusions, especially if some normalized adimensional, dimensionless variables are used.

Examples of ambiguous terms in physics

Some physical quantities do not yet have established notations; their value (and sometimes even dimension, as in the case of the Einstein coefficients) depends on the system of notations.

A highly confusing term is gain. For example, the sentence "the gain of a system should be doubled", without context, means close to nothing.
It may mean that the ratio of the output voltage of an electric circuit to the input voltage should be doubled.
It may mean that the ratio of the output power of an electric or optical circuit to the input power should be doubled.
It may mean that the gain of the laser medium should be doubled, for example, doubling the population of the upper laser level in a quasi-two level system (assuming negligible absorption of the ground-state).

Also, confusions may be related with the use of atomic percent as measure of concentration of a dopant, or resolution of an imaging system, as measure of the size of the smallest detail which still can be resolved at the background of statistical noise. See also Accuracy and precision and its talk.

Many terms are ambiguous. Each use of an ambiguous term should be preceded by the definition, suitable for a specific case.

The Berry paradox arises as a result of systematic ambiguity. In various formulations of the Berry paradox, such as one that reads: The number not nameable in less than eleven syllables the term nameable is one that has this systematic ambiguity. Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, definable, true, false, function, property, class, relation, cardinal, and ordinal.

Pedagogic use of ambiguous expressions

Ambiguity can be used as a pedagogical trick, to force students to reproduce the deduction by themselves. Some textbooks give the same name to the function and to its Fourier transform:

$~f(omega)=int\; f(t)\; exp(iomega\; t)\; \{rm\; d\}t$.

Rigorously speaking, such an expression requires that $~\; f=0\; ~$; even if function $~\; f\; ~$ is a self-Fourier function, the expression should be written as $~f(omega)=frac\{1\}\{sqrt\{2pi\}\}int\; f(t)\; exp(iomega\; t)\; \{rm\; d\}t$; however, it is assumed that the shape of the function (and even its norm $int\; |f(x)|^2\; \{rm\; d\}x$) depend on the character used to denote its argument. If the Greek letter is used, it is assumed to be a Fourier transform of another function, The first function is assumed, if the expression in the argument contains more characters $~t~$ or $~tau~$, than characters $~omega~$, and the second function is assumed in the opposite case. Expressions like $~f(omega\; t)~$ or $~f(y)~$ contain symbols $~t~$ and $~omega~$ in equal amounts; they are ambiguous and should be avoided in serious deduction.

Ambiguity in citations

Some scientific journals required that the references are marked as if they would be exponential functions, for example: ..number of partial lasers does not exceed 10¹⁰.... (Can you guess that it is reference , which states that practically only 10 laser can be combined; not 10000000000 lasers?). Recently, OSA journals improved the style to avoid such ambiguity; since 2007, the cites appear in squared parentheses.

References

See also

• Abbreviation
• Amphibology
• Double entendre
• Imprecise language
• Fallacy

* Formal fallacy

* Informal fallacy

• Semantics
• Ambiguity tolerance
• Essentially contested concept
• Self reference
• Uncertainty
• Disambiguation
• Decision problem

External links

• Collection of Ambiguous or Inconsistent/Incomplete Statements

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