Vagueness
Encyclopedia
The term vagueness denotes a property of concept
s (especially predicates). A concept is vague:
In everyday speech, vagueness is an inevitable, often even desired effect of language usage. However, in most specialized texts (e.g., legal documents), vagueness is distracting and should be avoided whenever possible.
s.
Vagueness is also a problem which arises in law, and in some cases judges have to arbitrate regarding whether a borderline case does, or does not, satisfy a given vague concept. Examples include disability (how much loss of vision is required before one is legally blind?), human life (at what point from conception to birth is one a legal human being, protected for instance by laws against murder?), adulthood (most familiarly reflected in legal ages for driving, drinking, voting, consensual sex, etc.), race (how to classify someone of mixed racial heritage), etc. Even such apparently unambiguous concepts such as gender can be subject to vagueness problems, not just from transsexuals' gender transitions but also from certain genetic conditions which can give an individual both male and female biological traits (see intersexual).
Many scientific concepts are of necessity vague, for instance species
in biology cannot be precisely defined, owing to unclear cases such as ring species
. Nonetheless, the concept of species can be clearly applied in the vast majority of cases. As this example illustrates, to say that a definition is "vague" is not necessarily a criticism. Consider those animals in Alaska that are the result of breeding Huskies
and wolves: are they dog
s? It is not clear: they are borderline cases of dogs. This means one's ordinary concept of doghood is not clear enough to let us rule conclusively in this case.
is bald", to "perfect truth", for, say, "Patrick Stewart
is bald". In ordinary logics, there are only two truth-values: "true" and "false". The fuzzy perspective differs by introducing an infinite number of truth-values along a spectrum between perfect truth and perfect falsity. Perfect truth may be represented by "1", and perfect falsity by "0". Borderline cases are thought of as having a "truth-value" anywhere between 0 and 1 (for example, 0.6). Advocates of the fuzzy logic approach have included K. F. Machina (1976) and Dorothy Edgington
(1993).
and Rosanna Keefe. Fine argues that borderline applications of vague predicates are neither true nor false, but rather are instances of "truth value gaps". He defends an interesting and sophisticated system of vague semantics, based on the notion that a vague predicate might be "made precise" in many alternative ways. This system has the consequence that borderline cases of vague terms yield statements that are neither true, nor false.
Given a supervaluationist semantics, one can define the predicate 'supertrue' as meaning "true on all precisifications". This predicate will not change the semantics of atomic statements (e.g. 'Frank is bald', where Frank is a borderline case of baldness), but does have consequences for logically complex statements. In particular, the tautologies
of sentential logic, such as 'Frank is bald or Frank is not bald)', will turn out to be supertrue, since on any precisification of baldness, either 'Frank is bald' or 'Frank is not bald' will be true. Since the presence of borderline cases seems to threaten principles like this one (excluded middle), the fact that supervaluationism can "rescue" them is seen as a virtue.
(1994), R. A. Sorensen (1988) and (2001), and Nicholas Rescher
(2009). They maintain that vague predicates do, in fact, draw sharp boundaries, but that one just does not know where these boundaries lie. One's confusion about whether some vague word does or does not apply in a borderline case is explained as being due to one's ignorance. For example, on the epistemic view, there is a fact of the matter, for every person, about whether that person is old, or not old. It is just that one may sometimes be ignorant of this fact.
(from his famous 1980 paper, "The Problem of the Many") : it's not clear where the boundary of a cloud lies; for any given bit of water vapor, one can ask whether it's part of the cloud or not, and for many such bits, one won't know how to answer. So perhaps one's term 'cloud' denotes a vague object precisely. This strategy has been poorly received, in part due to Gareth Evans's
short paper "Can There Be Vague Objects?" (1978). Evans's argument appears to show that there can be no vague identities (e.g. "Princeton = Princeton Borough"), but as Lewis (1988) makes clear, Evans takes for granted that there are in fact vague identities, and that any proof to the contrary cannot be right. Since the proof Evans produces relies on the assumption that terms precisely denote vague objects, the implication is that the assumption is false, and so the vague-objects view is wrong.
Still by, for instance, proposing alternative deduction rules involving Leibniz law or other rules for validity some philosophers are willing to defend vagueness as some kind of metaphysical phenomenon. One has, for example, Peter van Inwagen
(1990), Trenton Merricks and Terence Parsons (2000).
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
s (especially predicates). A concept is vague:
- if the concept's extensionExtension (semantics)In any of several studies that treat the use of signs - for example, in linguistics, logic, mathematics, semantics, and semiotics - the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of...
is unclear; - if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this predicate (so-called "border-line cases");
- if the Sorites paradoxSorites paradoxThe sorites paradox is a paradox that arises from vague predicates. The paradox of the heap is an example of this paradox which arises when one considers a heap of sand, from which grains are individually removed...
applies to the concept or predicate.
In everyday speech, vagueness is an inevitable, often even desired effect of language usage. However, in most specialized texts (e.g., legal documents), vagueness is distracting and should be avoided whenever possible.
Importance
Vagueness is philosophically important. Suppose one wants to come up with a definition of "right" in the moral sense. One wants a definition to cover actions that are clearly right and exclude actions that are clearly wrong, but what does one do with the borderline cases? Surely, there are such cases. Some philosophers say that one should try to come up with a definition that is itself unclear on just those cases. Others say that one has an interest in making his or her definitions more precise than ordinary language, or his or her ordinary concepts, themselves allow; they recommend one advances precising definitionPrecising definition
A precising definition is a definition that extends the lexical definition of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition....
s.
Vagueness is also a problem which arises in law, and in some cases judges have to arbitrate regarding whether a borderline case does, or does not, satisfy a given vague concept. Examples include disability (how much loss of vision is required before one is legally blind?), human life (at what point from conception to birth is one a legal human being, protected for instance by laws against murder?), adulthood (most familiarly reflected in legal ages for driving, drinking, voting, consensual sex, etc.), race (how to classify someone of mixed racial heritage), etc. Even such apparently unambiguous concepts such as gender can be subject to vagueness problems, not just from transsexuals' gender transitions but also from certain genetic conditions which can give an individual both male and female biological traits (see intersexual).
Many scientific concepts are of necessity vague, for instance species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
in biology cannot be precisely defined, owing to unclear cases such as ring species
Ring species
In biology, a ring species is a connected series of neighboring populations, each of which can interbreed with closely sited related populations, but for which there exist at least two "end" populations in the series, which are too distantly related to interbreed, though there is a potential gene...
. Nonetheless, the concept of species can be clearly applied in the vast majority of cases. As this example illustrates, to say that a definition is "vague" is not necessarily a criticism. Consider those animals in Alaska that are the result of breeding Huskies
Sled dog
Sled dogs, known also as sleigh man dogs, sledge dogs, or sleddogs, are highly trained types of dogs that are used to pull a dog sled, a wheel-less vehicle on runners also called a sled or sleigh, over snow or ice, by means of harnesses and lines.Sled dogs have become a popular winter recreation...
and wolves: are they dog
Dog
The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...
s? It is not clear: they are borderline cases of dogs. This means one's ordinary concept of doghood is not clear enough to let us rule conclusively in this case.
Approaches
The philosophical question of what the best theoretical treatment of vagueness is - which is closely related to the problem of the paradox of the heap - has been the subject of much philosophical debate.Fuzzy logic
One theoretical approach is that of fuzzy logic, developed by American mathematician Lotfi Zadeh. Fuzzy logic proposes a gradual transition between "perfect falsity", for example, the statement "Bill ClintonBill Clinton
William Jefferson "Bill" Clinton is an American politician who served as the 42nd President of the United States from 1993 to 2001. Inaugurated at age 46, he was the third-youngest president. He took office at the end of the Cold War, and was the first president of the baby boomer generation...
is bald", to "perfect truth", for, say, "Patrick Stewart
Patrick Stewart
Sir Patrick Hewes Stewart, OBE is an English film, television and stage actor, who has had a distinguished career in theatre and television for around half a century...
is bald". In ordinary logics, there are only two truth-values: "true" and "false". The fuzzy perspective differs by introducing an infinite number of truth-values along a spectrum between perfect truth and perfect falsity. Perfect truth may be represented by "1", and perfect falsity by "0". Borderline cases are thought of as having a "truth-value" anywhere between 0 and 1 (for example, 0.6). Advocates of the fuzzy logic approach have included K. F. Machina (1976) and Dorothy Edgington
Dorothy Edgington
Dorothy Edgington is a philosopher active in metaphysics and philosophical logic. She was Waynflete Professor of Metaphysical Philosophy at the University of Oxford from 2003 to 2006. Before moving to Oxford Edgington taught for many years at Birkbeck College, London and now teaches there again...
(1993).
Supervaluationism
Another theoretical approach is known as "supervaluationism". This approach has been defended by Kit FineKit Fine
Kit Fine is Silver Professor of Philosophy and Mathematics at New York University. He previously taught for several years at UCLA...
and Rosanna Keefe. Fine argues that borderline applications of vague predicates are neither true nor false, but rather are instances of "truth value gaps". He defends an interesting and sophisticated system of vague semantics, based on the notion that a vague predicate might be "made precise" in many alternative ways. This system has the consequence that borderline cases of vague terms yield statements that are neither true, nor false.
Given a supervaluationist semantics, one can define the predicate 'supertrue' as meaning "true on all precisifications". This predicate will not change the semantics of atomic statements (e.g. 'Frank is bald', where Frank is a borderline case of baldness), but does have consequences for logically complex statements. In particular, the tautologies
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
of sentential logic, such as 'Frank is bald or Frank is not bald)', will turn out to be supertrue, since on any precisification of baldness, either 'Frank is bald' or 'Frank is not bald' will be true. Since the presence of borderline cases seems to threaten principles like this one (excluded middle), the fact that supervaluationism can "rescue" them is seen as a virtue.
The epistemic view
A third approach, known as the "epistemic view", has recently been defended by Timothy WilliamsonTimothy Williamson
Timothy Williamson is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics....
(1994), R. A. Sorensen (1988) and (2001), and Nicholas Rescher
Nicholas Rescher
Nicholas Rescher is an American philosopher at the University of Pittsburgh. In a productive research career extending over six decades, Rescher has established himself as a systematic philosopher of the old style and author of a system of pragmatic idealism which weaves together threads of...
(2009). They maintain that vague predicates do, in fact, draw sharp boundaries, but that one just does not know where these boundaries lie. One's confusion about whether some vague word does or does not apply in a borderline case is explained as being due to one's ignorance. For example, on the epistemic view, there is a fact of the matter, for every person, about whether that person is old, or not old. It is just that one may sometimes be ignorant of this fact.
Vagueness as a property of objects
One possibility is that one's words and concepts are perfectly precise, but that objects themselves are vague. Consider Peter Unger's example of a cloudCloud
A cloud is a visible mass of liquid droplets or frozen crystals made of water and/or various chemicals suspended in the atmosphere above the surface of a planetary body. They are also known as aerosols. Clouds in Earth's atmosphere are studied in the cloud physics branch of meteorology...
(from his famous 1980 paper, "The Problem of the Many") : it's not clear where the boundary of a cloud lies; for any given bit of water vapor, one can ask whether it's part of the cloud or not, and for many such bits, one won't know how to answer. So perhaps one's term 'cloud' denotes a vague object precisely. This strategy has been poorly received, in part due to Gareth Evans's
Gareth Evans (philosopher)
Gareth Evans was a British philosopher.-Life:Gareth Evans studied Philosophy, Politics and Economics at University College, Oxford . His philosophy tutor was Peter Strawson...
short paper "Can There Be Vague Objects?" (1978). Evans's argument appears to show that there can be no vague identities (e.g. "Princeton = Princeton Borough"), but as Lewis (1988) makes clear, Evans takes for granted that there are in fact vague identities, and that any proof to the contrary cannot be right. Since the proof Evans produces relies on the assumption that terms precisely denote vague objects, the implication is that the assumption is false, and so the vague-objects view is wrong.
Still by, for instance, proposing alternative deduction rules involving Leibniz law or other rules for validity some philosophers are willing to defend vagueness as some kind of metaphysical phenomenon. One has, for example, Peter van Inwagen
Peter van Inwagen
Peter van Inwagen is an American analytic philosopher and the John Cardinal O'Hara Professor of Philosophy at the University of Notre Dame. He previously taught at Syracuse University and earned his PhD from the University of Rochester under the direction of Richard Taylor and Keith Lehrer...
(1990), Trenton Merricks and Terence Parsons (2000).
Legal principle
In the common law system, vagueness is a possible legal defence against by-laws and other regulations. The legal principle is that delegated power cannot be used more broadly than the delegator intended. Therefore, a regulation may not be so vague as to regulate areas beyond what the law allows. Any such regulation would be "void for vagueness" and unenforceable. This principle is sometimes used to strike down municipal by-laws that forbid "explicit" or "objectionable" contents from being sold in a certain city; courts often find such expressions to be too vague, giving municipal inspectors discretion beyond what the law allows. In the US this is known as the vagueness doctrine and in Europe as the principle of legal certainty.See also
- Essentially contested conceptEssentially contested conceptIn a paper delivered to the Aristotelian Society on 12 March 1956, Walter Bryce Gallie introduced the term essentially contested concept to facilitate an understanding of the different applications or interpretations of the sorts of abstract, qualitative, and evaluative notions — such as...
- Unconstitutional vaguenessUnconstitutional vaguenessUnconstitutional vagueness is a concept that is used to strike down certain laws and judicial actions in United States federal courts. It is derived from the due process doctrine found in the Fifth and Fourteenth Amendments to the United States Constitution...
- ObfuscationObfuscationObfuscation is the hiding of intended meaning in communication, making communication confusing, wilfully ambiguous, and harder to interpret.- Background :Obfuscation may be used for many purposes...
- RelevanceRelevance-Introduction:The concept of relevance is studied in many different fields, including cognitive sciences, logic and library and information science. Most fundamentally, however, it is studied in epistemology...
- UnderstandingUnderstandingUnderstanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object....
External links
- Stanford Encyclopedia of Philosophy entry
- A defence of the fuzzy view of vagueness
- Extensive bibliography maintained by David Angler