621. B. Ph TEXT V – 2 Ambiguity

V – 2    Ambiguity

 

Seven Types of Ambiguity

Seven Types of Ambiguity was first published in 1930 by William Empson. It was one of the most influential critical works of the 20th century and was a key foundation work in the formation of the New Criticism school.

The book is organized around seven types of ambiguity that Empson finds in the poetry he criticises. The first printing in America was by New Directions in 1947.

Seven Types of Ambiguity ushered in New Criticism in the United States. An ambiguity is represented as a puzzle. We have ambiguity when "alternative views might be taken without sheer misreading."

Seven types

1. The first type of ambiguity is the metaphor, that is, when two things are said to be alike which have different properties. This concept is similar to that of metaphysical conceit.
2. Two or more meanings are resolved into one. Empson characterizes this as using two different metaphors at once.
3. Two ideas that are connected through context can be given in one word simultaneously.
4. Two or more meanings that do not agree but combine to make clear a complicated state of mind in the author.
5. When the author discovers his idea in the act of writing. Empson describes a simile that lies halfway between two statements made by the author.
6. When a statement says nothing and the readers are forced to invent a statement of their own, most likely in conflict with that of the author.
7. Two words that within context are opposites that expose a fundamental division in the author's mind.

 

Sir John Tenniel's illustration of the Caterpillar for Lewis Carroll's Alice's Adventures in Wonderland is noted for its ambiguous central figure, whose head can be viewed as being a human male's face with a pointed nose and pointy chin or being the head end of an actual caterpillar, with the first two right "true" legs visible.^[1]

Ambiguity is an attribute of any concept, idea, statement or claim whose meaning, intention or interpretation cannot be definitively resolved according to a rule or process consisting of a finite number of steps.

The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately apparent), whereas with information that is vague, it is difficult to form any interpretation at the desired level of specificity.

Context may play a role in resolving ambiguity. For example, the same piece of information may be ambiguous in one context and unambiguous in another.

 

Linguistic forms

Structural analysis of an ambiguous Spanish sentence:
'Pepe vio a Pablo enfurecido
Interpretation 1: When Pepe was angry, then he saw Pablo
Interpretation 2: Pepe saw that Pablo was angry.
Here, the syntactic tree in figure represents interpretation 2.

The lexical ambiguity of a word or phrase pertains to its having more than one meaning in the language to which the word belongs. "Meaning" here refers to whatever should be captured by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "financial institution" and "edge of a river". Another example is as in "apothecary".

One could say "I bought herbs from the apothecary". This could mean one actually spoke to the apothecary (pharmacist) or went to the apothecary (pharmacy).

The context in which an ambiguous word is used often makes it evident which of the meanings is intended. If, for instance, someone says "I buried $100 in the bank", most people would not think someone used a shovel to dig in the mud. However, some linguistic contexts do not provide sufficient information to disambiguate a used word. For example,

Lexical ambiguity can be addressed by algorithmic methods that automatically associate the appropriate meaning with a word in context, a task referred to as word sense disambiguation.

Intentional application

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 which hinder economic growth", an example of a glittering generality. Some will think he opposes taxes in general, because they hinder economic growth.

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.

 

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, any aspect of music.

 

Visual art

The Necker cube, an ambiguous image

In visual art, certain images are visually ambiguous, such as the Necker cube, which can be interpreted in two ways. Perceptions of such objects remain stable for a time, then may flip, a phenomenon called multistable perception. The opposite of such ambiguous images are impossible objects.

Pictures or photographs may also be ambiguous at the semantic level: the visual image is unambiguous, but the meaning and narrative may be ambiguous: is a certain facial expression one of excitement or fear, for instance?

 

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, focusing chiefly on syntactic ambiguity as well. The languages can be both spoken and written. These languages are intended to provide a greater technical precision over big natural languages, although historically, such attempts at language improvement have been criticized. Languages composed from many diverse sources contain much ambiguity and inconsistency. The many exceptions to syntax and semantic rules are time-consuming and difficult to learn.

 

Mathematical notation

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.

 

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 requires 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 Talk:Elliptic integral#List of notations; dealing with complex values, this may cause problems.
• Exponential integral,
• Hermite polynomial,

 

Expressions

Ambiguous expressions 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.  Then, if one sees, there is no way to distinguish whether it means multiplied by, or function evaluated at argument equal to

Notations in quantum optics and quantum mechanics

It is common to define the coherent states in quantum optics with …and states with fixed number of photons with…. Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and ….photon state if the Latin characters dominate. The ambiguity becomes even worse, if ….is used for the states with certain value of the coordinate, and ….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. Expression may mean a state with single photon, or the coherent state with mean amplitude equal to 1, or state with momentum equal to unity, and so on. The reader is supposed to guess from the context.

 

Ambiguous terms in physics and mathematics

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).

The term intensity is ambiguous when applied to light. The term can refer to any of irradiance, luminous intensity, radiant intensity, or radiance, depending on the background of the person using the term.

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.

Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal.