Ambiguity
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Ambiguity is the type of
The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity.
Linguistic forms
Lexical ambiguity is contrasted with
Ambiguity in human language is argued to reflect principles of efficient communication.[2][3] Languages that communicate efficiently will avoid sending information that is redundant with information provided in the context. This can be shown mathematically to result in a system that is ambiguous when context is neglected. In this way, ambiguity is viewed as a generally useful feature of a linguistic system.
Linguistic ambiguity can be a problem in law, because the interpretation of written documents and oral agreements is often of paramount importance.
Lexical ambiguity
The lexical ambiguity of a word or phrase applies to it having more than one meaning in the language to which the word belongs.[4] "Meaning" here refers to whatever should be represented by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "financial institution" and "edge of a river". Or consider "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 clearer which of the meanings is intended. If, for instance, someone says "I put $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 make a used word clearer.
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.
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 "
More problematic are words whose multiple meanings 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), "
Semantic and syntactic ambiguity
Semantic ambiguity occurs when a word, phrase or sentence, taken out of context, has more than one interpretation. In "We saw her duck" (example due to Richard Nordquist), the words "her duck" can refer either
- to the person's bird (the noun "duck", modified by the possessive pronoun "her"), or
- to a motion she made (the verb "duck", the subject of which is the objective pronoun "her", object of the verb "saw").[5]
Syntactic ambiguity arises when a sentence can have two (or more) different meanings because of the structure of the sentence—its syntax. This is often due to a modifying expression, such as a prepositional phrase, the application of which is unclear. "He ate the cookies on the couch", for example, could mean that he ate those cookies that 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. "To get in, you will need an entrance fee of $10 or your voucher and your drivers' license." This could mean that you need EITHER ten dollars OR BOTH your voucher and your license. Or it could mean that you need your license AND you need EITHER ten dollars OR a voucher. Only rewriting the sentence, or placing appropriate punctuation can resolve a syntactic ambiguity.[5] For the notion of, and theoretic results about, syntactic ambiguity in artificial,
Usually, semantic and syntactic ambiguity go hand in hand. The sentence "We saw her duck" is also syntactically ambiguous. Conversely, a sentence like "He ate the cookies on the couch" is also semantically ambiguous. Rarely, but occasionally, the different parsings of a syntactically ambiguous phrase result in the same meaning. For example, the command "Cook, cook!" can be parsed as "Cook (noun used as vocative), cook (imperative verb form)!", but also as "Cook (imperative verb form), cook (noun used as vocative)!". It is more common that a syntactically unambiguous phrase has a semantic ambiguity; for example, the lexical ambiguity in "Your boss is a funny man" is purely semantic, leading to the response "Funny ha-ha or funny peculiar?"
Spoken language can contain many more types of ambiguities that are called phonological 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 according to the context. A mishearing of such, based on incorrectly resolved ambiguity, is called a mondegreen.
Philosophy
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 they oppose taxes in general because they hinder economic growth. Others may think they oppose only those taxes that they believe will hinder economic growth. In writing, the sentence can be rewritten to reduce possible misinterpretation, either by adding a comma after "taxes" (to convey the first sense) or by changing "which" to "that" (to convey the second sense) or by rewriting it in other ways. The devious politician hopes that each constituent will interpret the 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 continental philosophy (particularly phenomenology and existentialism), there is much greater tolerance of ambiguity, as it is generally seen as an integral part of the human condition. Martin Heidegger argued that the relation between the subject and object is ambiguous, as is the relation of mind and body, and part and whole. In Heidegger's phenomenology, Dasein is always in a meaningful world, but there is always an underlying background for every instance of signification. Thus, although some things may be certain, they have little to do with Dasein's sense of care and existential anxiety, e.g., in the face of death. In calling his work Being and Nothingness an "essay in phenomenological ontology" Jean-Paul Sartre follows Heidegger in defining the human essence as ambiguous, or relating fundamentally to such ambiguity. Simone de Beauvoir tries to base an ethics on Heidegger's and Sartre's writings (The Ethics of Ambiguity), where she highlights the need to grapple with ambiguity: "as long as there have been philosophers and they have thought, most of them have tried to mask it ... And the ethics which they have proposed to their disciples has always pursued the same goal. It has been a matter of eliminating the ambiguity by making oneself pure inwardness or pure externality, by escaping from the sensible world or being engulfed by it, by yielding to eternity or enclosing oneself in the pure moment." Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science. She states: "Since we do not succeed in fleeing it, let us, therefore, try to look the truth in the face. Let us try to assume our fundamental ambiguity. It is in the knowledge of the genuine conditions of our life that we must draw our strength to live and our reason for acting". Other continental philosophers suggest that concepts such as life, nature, and sex are ambiguous. Corey Anton has argued that we cannot be certain what is separate from or unified with something else: language, he asserts, divides what is not, in fact, separate. Following Ernest Becker, he argues that the desire to 'authoritatively disambiguate' the world and existence has led to numerous ideologies and historical events such as genocide. On this basis, he argues that ethics must focus on 'dialectically integrating opposites' and balancing tension, rather than seeking a priori validation or certainty. Like the existentialists and phenomenologists, he sees the ambiguity of life as the basis of creativity.
Literature and rhetoric
In literature and rhetoric, 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. How he got in my pajamas, I'll never know". 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 the 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.
Mathematical notation
Names of functions
The ambiguity in the style of writing a
- Sinc function
- Mathematica, one should replace the second argument to its square; dealing with complex values, this may cause problems.
- Exponential integral[6]
- Hermite polynomial[6]: 775
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, for example, . Then, if one sees , there is no way to distinguish whether it means multiplied by , or function evaluated at argument equal to . 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 (
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, is interpreted as ; 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. In the scientific journal style, one uses roman letters to denote elementary functions, whereas variables are written using italics. For example, in mathematical journals the expression does not denote the
Commas in multi-component subscripts and superscripts are sometimes omitted; this is also potentially ambiguous notation. For example, in the notation , the reader can only infer from the context whether it means a single-index object, taken with the subscript equal to product of variables , and , or it is an indication to a trivalent tensor.
Examples of potentially confusing ambiguous mathematical expressions
An expression such as can be understood to mean either or . Often the author's intention can be understood from the context, in cases where only one of the two makes sense, but an ambiguity like this should be avoided, for example by writing or .
The expression means in several texts, though it might be thought to mean , since commonly means . Conversely, might seem to mean , as this
The expression can be interpreted as meaning ; however, it is more commonly understood to mean .
Notations in quantum optics and quantum mechanics
It is common to define the
Ambiguous terms in physics and mathematics
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. Many terms are ambiguous. Each use of an ambiguous term should be preceded by the definition, suitable for a specific case. Just like Ludwig Wittgenstein states in Tractatus Logico-Philosophicus: "... Only in the context of a proposition has a name meaning."[7]
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
The
Mathematical interpretation of ambiguity
In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, leaves open what the value of is—while its opposite[
Logical ambiguity and self-contradiction is analogous to visual ambiguity and impossible objects, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher.[9]
Constructed language
Some
Biology
In structural biology, ambiguity has been recognized as a problem for studying protein conformations.[10] The analysis of a protein three-dimensional structure consists in dividing the macromolecule into subunits called domains. The difficulty of this task arises from the fact that different definitions of what a domain is can be used (e.g. folding autonomy, function, thermodynamic stability, or domain motions), which sometimes results in a single protein having different—yet equally valid—domain assignments.
Christianity and Judaism
Christianity and Judaism employ the concept of paradox synonymously with "ambiguity". Many Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery that fascinates humans.[dubious ] The apocryphal Book of Judith is noted for the "ingenious ambiguity"[11] expressed by its heroine; for example, she says to the villain of the story, Holofernes, "my lord will not fail to achieve his purposes", without specifying whether my lord refers to the villain or to God.[12][13]
The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts that he found ambiguous or to reveal meaning often overlooked or forgotten in common phrases: the title of one of his most famous books, Orthodoxy (1908), itself employed such a paradox.[14]
Music
In
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.[15]
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?
Social psychology and the bystander effect
In social psychology, ambiguity is a factor used in determining peoples' responses to various situations. High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for help) elicit more consistent intervention and assistance. With regard to the bystander effect, studies have shown that emergencies deemed ambiguous trigger the appearance of the classic bystander effect (wherein more witnesses decrease the likelihood of any of them helping) far more than non-ambiguous emergencies.[16]
Computer science
In
Subsequently, the Ki, Mi, and Gi prefixes were introduced so that
See also
- Abbreviation
- Ambiguity (law)
- Ambiguity tolerance
- Amphibology
- Buzzword
- Decision problem
- Discrete mathematics
- Double entendre
- Equivocation
- Essentially contested concept
- Fallacy
- Formal fallacy
- Golden hammer
- Informal fallacy
- Pleonasm
- Self reference
- Semantics
- Uncertainty
- Volatility, uncertainty, complexity and ambiguity
- Word-sense disambiguation
References
- ^ "And do you see its long nose and chin? At least, they look exactly like a nose and chin, that is don't they? But they really are two of its legs. You know a Caterpillar has got quantities of legs: you can see more of them, further down." Carroll, Lewis. The Nursery "Alice". Dover Publications (1966), p 27.
- S2CID 13726095.
- ^ Finn, Emily (19 January 2012). "The advantage of ambiguity". MIT Press.
- ISBN 978-0-08-051013-2.
- ^ a b Critical Thinking, 10th ed., Ch 3, Moore, Brooke N. and Parker, Richard. McGraw-Hill, 2012
- ^ a b Abramovits, M.; Stegun, I. Handbook on mathematical functions. p. 228.
- ISBN 978-0-486-40445-5.
- ^ Russell/Whitehead, Principia Mathematica
- S2CID 191403643.
- ^ PMID 28097215.
- ^ Jerusalem Bible (1966), footnote a at Judith 11:5
- ^ Judith 11:6
- ISBN 978-1-4934-1307-2.
- ^ Chesterton, G. K., Orthodoxy, especially p. 32
- ^
ISBN 978-1554071722.
- .
External links
- Media related to Ambiguity at Wikimedia Commons
- Zalta, Edward N. (ed.). "Ambiguity". Stanford Encyclopedia of Philosophy.
- Ambiguity at the Indiana Philosophy Ontology Project
- Ambiguity at PhilPapers
- Collection of Ambiguous or Inconsistent/Incomplete Statements
- Leaving out ambiguities when writing