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
- 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.
- Two or more meanings are resolved into one. Empson characterizes this as using two different metaphors at once.
- Two ideas that are connected through context can be given in one word simultaneously.
- Two or more meanings that do not agree but combine to make clear a complicated state of mind in the author.
- 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.
- 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.
- 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.
'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
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).
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.