For other uses, see Ambiguity (disambiguation).
"Ambiguous" redirects here. For the film, see Ambiguous (film).
Ambiguity is a type of uncertainty of meaning in which several interpretations are plausible. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved according to a rule or process with a finite number of steps. (The ambi- part of the term reflects an idea of "two", as in "two meanings".)
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 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.
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". 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 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.
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 "weasel words" and obfuscation are necessary to gain support from multiple constituents 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").
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. For the notion of, and theoretic results about, syntactic ambiguity in artificial, formal languages (such as computer programming languages), see Ambiguous grammar.
Spoken language can contain many more types of ambiguities which 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.
Semantic ambiguity happens when a sentence contains an ambiguous word or phrase—a word or phrase that has more than one meaning. In "We saw her duck" (example due to Richard Nordquist), the word "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").
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, because the interpretation of written documents and oral agreements is often of paramount importance.
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. Others may think he opposes only those taxes that he believes 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 philosophers and they [men] have thought, most of them have tried to mask it...And the ethics which they have proposed to their disciples have 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 have 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.
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 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.
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 which fascinates humans.[dubious – discuss] The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts which he found ambiguous, or to reveal meaning often overlooked or forgotten in common phrases. (The title of one of his most famous books, Orthodoxy, itself employing such a paradox.)
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.
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."
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?
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 for this, 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.
In computer science, the SI prefixeskilo-, mega- and giga- were historically used in certain contexts to mean either the first three powers of 1024 (1024, 10242 and 10243) contrary to the metric system in which these units unambiguously mean one thousand, one million, and one billion. This usage is particularly prevalent with electronic memory devices (e.g. DRAM) addressed directly by a binary machine register where a decimal interpretation makes no practical sense.
Subsequently, the Ki, Mi, and Gi prefixes were introduced so that binary prefixes could be written explicitly, also rendering k, M, and G unambiguous in texts conforming to the new standard — this led to a new ambiguity in engineering documents lacking outward trace of the binary prefixes (necessarily indicating the new style) as to whether the usage of k, M, and G remains ambiguous (old style) or not (new style). Note also that 1 M (where M is ambiguously 1,000,000 or 1,048,576) is less uncertain than the engineering value 1.0e6 (defined to designate the interval 950,000 to 1,050,000), and that as non-volatile storage devices began to commonly exceed 1 GB in capacity (where the ambiguity begins to routinely impact the second significant digit), GB and TB almost always mean 109 and 1012bytes.
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 or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:
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 (C++ and Fortran) require the character * as symbol of multiplication. The Wolfram Language used in 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, 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. Sometimes, one uses italics letters to denote elementary functions. In the scientific journal style, the expression means product of variables , , and , although in a slideshow, it may mean .
A comma in subscripts and superscripts sometimes is omitted; it is also ambiguous notation. If it is written , the reader should guess from the context, does it mean a single-index object, evaluated while the subscript is equal to product of variables , and , or it is indication to a trivalent tensor. The writing of instead of 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.
Subscripts are also used to denote the argument to a function, as in .
Examples of potentially confusing ambiguous mathematical expressions
, which could be understood to mean either or . In addition, may mean , as means (see tetration).
, which by convention means , though it might be thought to mean , since means .
, which arguably should mean but would commonly be understood to mean .
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 easily 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
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."
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.
The Berry paradox arises as a result of systematic ambiguity in the meaning of terms such as "definable" or "nameable". Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal.
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 X is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system—such as , which has no solution.
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.
|Look up ambiguity in Wiktionary, the free dictionary.|
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.
- ^"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.
- ^ abCritical Thinking, 10th ed., Ch 3, Moore, Brooke N. and Parker, Richard. McGraw-Hill, 2012
- ^ abAbramovits, M.; Stegun, I. Handbook on mathematical functions. p. 228.
- ^Wittgenstein, Ludwig (1999). Tractatus Logico-Philosophicus. Dover Publications Inc. p. 39. ISBN 0-486-40445-5.
- ^Russell/Whitehead, Principia Mathematica
- ^Goldstein, Laurence (1996). "Reflexivity, Contradiction, Paradox and M. C. Escher". Leonardo. The MIT Press. 29 (4): 299–308. doi:10.2307/1576313. JSTOR 1576313
Ambiguity, polysemy and vagueness are terms used in cognitive semantics referring to different instances of plurality of meaning. According to Deane (1988) these three phenomena “form a gradient between total semantic identity” (vagueness) “and total semantic distinctness” (p. 327) (ambiguity). Therefore, polysemy is a case somewhere in between these two extremes. The borders between the categories of ambiguity, polysemy and vagueness are fuzzy. Thus, there are lexical examples that can be assigned to more than one category.
Ambiguity is a term used to characterise phenomena that have more than only one meaning. These meanings are distinct from each other and have no close schema in common. That is why a single expression may lead to multiple interpretations. In natural language many words, strings of words and sentences are ambiguous, simply because of the fact that numerous words cover several distinct meanings, or specific structural elements give rise to different readings. That means that “an expression or utterance is ambiguous if it can be interpreted in more than one way” (Löbner 2002: p. 39). However, disregarding puns (see 1.5), in every linguistic situation only one meaning of an ambiguous expression can be used. There are several forms of ambiguity to be distinguished – according to their trigger:
Lexical ambiguity is concerned with multiple interpretations of lexemes. A word is ambiguous if it involves two lexical items that have identical forms, but have distinct, i.e. unrelated meanings. There are numerous examples of lexical ambiguity. A clear-cut one is the lexeme ball. This word may either denote the round object which is used for several sports, like football, volleyball or basketball, or it can be used to refer to a large formal dancing party. Both forms are identically written and pronounced but just accidentally share the same form: ball in the sense of the round object originates in the Old Norse word ‘ballr’, whereas ball as the formal event comes from Greek ‘ballizar’ (meaning ‘to dance’) and was first attested in the English language in the 1630s being introduced through Old French. (Online Etymological Dictionary) Another example by Chierchia & McConnell-Ginet (1993) is the following sentence: You should have seen the bull we got from the Pope. The sentence is ambiguous, because the word bull may stand for several distinct things – either a male animal of different kinds, a swearword or an official order or statement from the Pope. As ambiguity is context dependent lexical disambiguation (knowing which word meaning has been used) is quite easy in most cases when considering previous expectations and context (p. 32).
The most classical example of lexical ambiguity is bank, which may either denote an organisation providing financial services, or the side of a river – just to mention two of the lexeme’s possible meanings.
Further examples of lexical ambiguity are:
bright - a bright (intelligent) person vs. bright (sunny) weather
file - arranged collection of papers vs. metal tool
Structural ambiguity is a result of two or more different syntactic structures that can be attributed to one string of words. That means that a sentence is structurally ambiguous not because it contains a single lexeme that has several distinct meanings, but because the syntactic structure of the sentence causes multiple interpretations.
(1) Young boys and girls love the adventure playground.
This sentence is syntactically ambiguous, because the reference of young is unclear. There are two possible interpretations of the subject. It may either be that [young boys] and girls love the adventure playground, or young [boys and girls] love [it]. The structural analysis shows that the sentence may be interpreted in a way that young only refers to the boys, or it may be understood as characterising the boys as well as the girls.
(2) Flying planes can be dangerous.
This often quoted example of structural (also called syntactic) ambiguity comes from Noam Chomsky. Sentences that contain lexemes that change their word form or even word class depending on the sentence’s interpretation are part of this category. Flying planes in this example sentence may be understood as “to fly planes” as well as “planes, which fly”. Therefore, the lexeme flying can be interpreted as the gerund form of a verb in a verb phrase, or as an attribute of a noun phrase.
There are several linguists, who have come up with similar examples like the last one. Lyons (1975) (cf. pp. 212f.) as well as Langacker (1993) (cf. p. 432), for example, determine those instances as grammatically ambiguous. The terms structural, syntactic and grammatical ambiguity are basically interchangeable.
Lyons’ examples for grammatical ambiguity are the following:
(3) They can fish.
The ambiguous interpretation is a result of “the double classification” of fish (either intransitive verb or noun) as well as of can (either auxilliary or transitive verb).
(4) beautiful girl’s dress
This is an example similar to the first one of structural ambiguity. It is a question of reference and therefore, may either be understood as [beautiful girl’s] dress or beautiful [girl’s dress]. Is the adjective beautiful attributed to the girl or to the dress? That question makes the reading of the sentence ambiguous.
However, Lyons points out that these cases of free interpretation are hardly leading to misinterpreations in natural language use. It usually gets quite obvious which meaning is aimed at through the rest of the sentence and the context.
The category of transformational ambiguity is mentioned by Lyons (1975), who characterises its prototypes as “ambiguous constructions which depend upon the ‘deeper connexions’” (p. 249). Furthermore, he points out that these constructions are mostly only ambiguous out of context. One of his examples is the phrase the love of God. Isolated from any textual relations it is unclear whether God is the subject or the object in this noun phrase. Additionally, Lyons quotes Chomsky’s already mentioned example of flying planes, which he – in contrast to other linguists – counts as belonging to transformational ambiguity. Basically, neither categorisation is wrong as many linguists do not distinguish transformational from grammatical ambiguity. Thus, transformational ambiguity is a subcategory of grammatical ambiguity.
Another Chomskian example mentioned by Lyons is: the shooting of the hunters. This is the same case as the God-example: it is unclear whether the hunters are subject or object in this phrase.
A further type of ambiguity called scope ambiguity is discussed by Chierchia and McConnell-Ginet(1993), among others. It is a subcategory of structural ambiguity. However, scope ambiguity can be distinguished from structural ambiguity through its “single surface syntactic structure” (p. 33). Chierchia and McConnell-Ginet’s example for this subcategory is: Someone loves everyone. This sentence can either mean ‘Everyone is loved by (at least) one person.’ or ‘There is a person and this person loves everyone.’ Note that in the former case someone may denote several different individuals, whereas it is only one single individual in the latter case.
A pun is a special form of ambiguity (mostly lexical) that is consciously used to create statements with ambiguous – distinct – meanings. That means that a pun is a play with words involving and creating double contexts (cf. Tuggy 1993: pp. 168, 178). Puns in spoken discourse make use of homophones, and puns in written discourse utilize homographs. Punning is a useful tool for jokes, creating at least two meanings – mostly a literal as well as a figurative one. Here is one example: After he ate the duck, the alligator got a little down in the mouth.
Tuggy (1993) offers a classical definition of vagueness. He characterises it as a linguistic phenomenon, where “two or more meanings associated with a given phonological form are […] united as non-distinguished subcases of a single, more general meaning” (p. 167). That means that vagueness involves “a lexeme with a single but nonspecific meaning” (ibid., p. 168).
Typical examples of vagueness are kinship terms, e.g. child, as well as lexemes with flexible boundaries, e.g. gradable adjectives like tall (cf. Löbner 2002: p. 45). An utterance like “It’s my child’s birthday tomorrow.” is vague, because the lexeme child is vague. There are two possible instantinations, namely [a female human under 18] and [a male human under 18]. When receiving such an uttereance it is much more likely that the common schema [a human under 18] is activated instead of its instantiations.
The lexeme tall in the statement “He is a tall man.” is vague as well. Tall belongs to the group of gradable adjectives. Therefore, the boundaries of the category tall are flexible depending on the context it is used in. From the perspective of a little child, a 5-foot-tall man will be considered tall. But the same man will not be considered with the same quality – tall – from the perspective of a 6-foot-tall woman. Thus, categorisations of this kind are always matter of norms (cf. Löbner 2002: p. 195).
On a scale of meaning variance ambiguity and vagueness are the two extremes, whereas polysemy is in between the other two. It shares features with both and is a common phenomenon in everyday language use. Polysemy involves lexemes that are clearly united (share a common schema) as well as clearly seperable at the same time. Polysemous words are the result of lexemes gaining new usages over time which share the same phonological form and appear to have separate meanings to non-etymologists. Foot is one example of polysemy. There are distinct usages of the word – either as a body part or as a scale unit (1 foot = 30.48 centimetres). Even though it appears that these are two very different meanings, both forms go back to the Old English word fot. Other examples of polysemy are earth (the planet vs. ground/ soil) and brother (kinship term vs. term of address for a male person living in a cloister).
Polysemy is sometimes mixed up with homonymy. However, as e.g. Langacker (1991) points out, there is a clear-cut distinction between these two (p. 268). Polysemous lexems always share the same etymological background and/or are conceived of as being semantically related by speakers, whereas homonymous words just happen to end up with the same phonological form. Therefore, homonymy may be seen as a subcategory of lexical ambiguity. Some linguists, like Löbner (cf. 2002: p. 39), claim the same for polysemy.
Metaphorical uses of words are instances of polysemy as well. The foot of a mountain, for example, makes use of the polysemous lexeme foot and denotes the bottom part of the mountain, just as a person’s foot refers to the bottom part of the human body.
Online Etymological Dictionary, 23. January 2010.
Chierchia, Gennaro & McConnell-Ginet, Sally. 1993. Meaning and Grammar: An introduction to Semantics. Cambridge, Messachusetts [a.o.]: MIT Press.
Deane, Paul.1988. Polysemy and Cognition. Lingua 75.
Langacker, Ronald W. 1991. Concept, Image, and Symbol: The Cognitive Basis of Grammar. Berlin [a.o.]: Mouton de Gruyter.
Langacker, Ronald W. 1991. Foundations of Cognitive Grammar. Volume II. Descriptive Application. Stanford, California: Stanford University Press.
Lyons, John. 1975. Introduction to Theoretical Linguistics. Cambridge [a.o.]: Cambridge University Press.
Löbner, Sebastian. 2002. Understanding Semantics. London [a.o.]: Arnold [a.o.].
Tuggy, David. 1993. “Ambiguity, polysemy, and vagueness.” Cognitive Linguistics 4-3.
Spencer, Andrew. 1991. Morphological Theory: An Introduction to Word Structure in Generative Grammar. Oxford: Blackwell.
Langacker, Ronald W. 1987. Foundations of Cognitive Grammar. Volume I. Theoretical Prerequisites. Stanford, California: Stanford University Press.