Ambiguity Totally Explained

Everything about Ambiguity totally explained

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 wouldn't 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're 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” isn't 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 shouldn't 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's 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.
   Linguistic ambiguity can be a problem in law (see Ambiguity (law)), because the interpretation of written documents and oral agreements is often of paramount importance.

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. 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,(External Link

) metonymy encompasses any potentially-ambiguous word substitution that's 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.

Psychology and Management

In sociology and social psychology, the term "ambiguity" is used to indicate situations that involve uncertainty. An increasing amount of research is concentrating on how people react and respond to ambiguous 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 organized 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 David 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.”

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 names of functions

The ambiguity in the style of writing a function shouldn't be confused with a multivalued function, which can (and should) be defined in a deterministic and unambiguous way. Several special functions still don't 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's 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's 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, doesn't 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's 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's also ambiguous notation. If it's written $~T_x$ ) depend on the character used to denote its argument. If the Greek letter is used, it's 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 $~ au~$ , 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're ambiguous and should be avoided in serious deduction.


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