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Encyclopedia > Vagueness

Ambiguity is one way in which the meanings of words and phrases can be unclear, but there is another way, which is different from ambiguity: vagueness. One example of a vague concept is the concept of a heap. Two or three grains of sand is not a heap, but a thousand is. How many grains of sand does it take to make a heap? There is no clear line. (See the paradox of the heap.) Look up ambiguity in Wiktionary, the free dictionary. ... The paradox of the heap (or the Sorites Paradox, sõros being Greek for heap and sõrites the adjective) is a paradox that arises when people apply formal logic to informal concepts which are vague. ...

Vagueness is a linguistic and philosophical term. To say that a concept is vague is to say that there may be cases in which there is no clear fact of the matter whether the concept applies or not.



Consider those animals in Alaska that are the result of breeding Huskies and wolves: are they dogs? It is not clear: they are borderline cases of dogs. This means our ordinary concept of doghood is not clear enough to let us rule conclusively in this case. Official language(s) English Capital Juneau Largest city Anchorage Area  Ranked 1st  - Total 663,267 sq mi (1,717,855 km²)  - Width 808 miles (1,300 km)  - Length 1,479 miles (2,380 km)  - % water 13. ... Sled dogs, known also as sleigh dogs, sledge dogs or sleddogs are a group of dogs that are used to pull a wheel-less vehicle on runners (a sled or sleigh) over snow or ice, by means of harnesses and lines. ... Wolf Wolf Man Mount Wolf Wolf Prizes Wolf Spider Wolf 424 Wolf 359 Wolf Point Wolf-herring Frank Wolf Friedrich Wolf Friedrich August Wolf Hugo Wolf Johannes Wolf Julius Wolf Max Franz Joseph Cornelius Wolf Maximilian Wolf Rudolf Wolf Thomas Wolf As Name Wolf Breidenbach Wolf Hirshorn Other The call... Trinomial name Canis lupus familiaris The dog (Canis lupus familiaris) is a domestic subspecies of the wolf, a mammal of the Canidae family of the order Carnivora. ...

Vagueness is important philosophically. Suppose we want to come up with a definition of "right" in the moral sense. We want a definition to cover actions that are clearly right and exclude actions that are clearly wrong, but what do we do with the borderline cases? Surely there are such cases. Some philosophers say we should try to come up with a definition that is itself unclear on just those cases. Others say that we have an interest in making our definitions more precise than ordinary language, or our ordinary concepts, themselves allow; they recommend we advance precising definitions. A precising definition is a definition that extends the dictionary definition (lexical definition) of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition. ...

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). A transsexual (sometimes transexual) person establishes a permanent identity with the opposite gender to their assigned (usually at birth) sex. ... An intersexual or intersex person (or animal of any unisexual species) is one who is born with genitalia and/or secondary sexual characteristics of indeterminate sex, or which combine features of both sexes. ...

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. In biology, a species is one of the basic units of biodiversity. ... In this diagram, interbreeding populations are represented by coloured blocks. ...


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. The paradox of the heap (or the Sorites Paradox, sõros being Greek for heap and sõrites the adjective) is a paradox that arises when people apply formal logic to informal concepts which are vague. ...

Fuzzy logic

One theoretical approach is that of fuzzy logic, developed by American mathematician (of Azerbaijan origin) Lotfi Zadeh. Fuzzy logic proposes a gradual transition between "perfect falsity", for example, the statement "Bill Clinton 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 (1997). Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ... Lotfi A. Zadeh (2004) Lotfi Asker Zadeh (in Persian:لطفی علی‌عسکرزاده), (born February 4, 1921) is a mathematician and computer scientist, and a professor of computer science at the University of California at Berkeley. ... William Jefferson Bill Clinton (born William Jefferson Blythe III[1] on August 19, 1946) was the 42nd President of the United States, serving from 1993 to 2001. ... Patrick Stewart OBE (born July 13, 1940) is an Emmy and Golden Globe nominated English film, television and stage actor. ... Dorothy Edgington is a philosopher active in metaphysics and philosophical logic. ...


Another theoretical approach is known as "supervaluationism". This approach has been defended by Kit Fine 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. Kit Fine (born March 26, 1946) is Silver Professor of Philosophy at New York University. ...

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.

The epistemic view

A third approach, known as the "epistemic view", has recently been defended by Timothy Williamson (1994) and R. A. Sorensen (1988). They maintain that vague predicates do, in fact, draw sharp boundaries, but that we just do not know where these boundaries lie. Our confusion about whether some vague word does or does not apply in a borderline case is explained as being due to our 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 we may sometimes be ignorant of this fact. The epistemic view, though initially counter-intuitive, has been defended with some interesting and forceful philosophical arguments. Timothy Williamson Timothy Williamson, FBA, FRSE, (born Uppsala, Sweden, 6 August 1955) is a distinguished British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. ...

Vagueness as a property of objects

One possibility is that our words and concepts are perfectly precise, but that objects themselves are vague. Consider David Lewis' example of a cloud: it's not clear where the boundary of a cloud lies; for any given bit of water vapor, we can ask whether it's part of the cloud or not, and for many such bits, we won't know how to answer. So perhaps our 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. David Kellogg Lewis (September 28, 1941 – October 14, 2001) is considered to have been one of the leading analytic philosophers of the latter half of the 20th century. ... Cumulus mediocris clouds, as seen from a plane window. ... Gareth Evans (12 May 1946 – 10 August 1980) was a British philosopher at Oxford University during the 1970s. ...

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. See Vagueness doctrine. Void for vagueness is a legal concept in American constitutional law, whereby a civil statute or, more commonly, a criminal statute is adjudged unconstitutional when it is so vague that persons of common intelligence must necessarily guess at its meaning and differ as to its application, as the United States...

See also

In a paper delivered to the Aristotelian Society on 12 March 1956,[1] Walter Bryce Gallie (1912-1998) 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[2] -- such as art and social justice...


  • Edgington, D. 1997. "Vagueness by degrees", in Keefe & Smith eds. (1999), pp. 294-316.
  • Keefe, R. & Smith, P., eds. 1997. Vagueness: A Reader. Cambridge, Massachusetts: MIT Press
    The editors' long introduction gives a clear and very useful overview of theories of vagueness, and they collect many classic papers on the subject.
  • Keefe, R. 2000. Vagueness. Cambridge: Cambridge University Press
  • Machina, K.F. 1976. "Truth, belief and vagueness", in Journal of Philosophical Logic Vol. 5. pp. 47-78
  • Sorensen, R.A. Blindspots. Oxford: Clarendon Press
  • Williamson, T. 1994. Vagueness London: Routledge. The history of the problem of vagueness is traced, from the first Sorites Paradox to contemporary attempts to deal with higher-order vagueness such as many-valued logic, supervaluationism, and fuzzy logic. Technicalities are kept to a minimum to favour a clear account, extremely useful to both students and researchers.
Informal fallacies
v  d  e
Special pleading | Red herring | Gambler's fallacy and its inverse
Fallacy of distribution (Composition | Division) | Begging the question | Many questions
Correlative-based fallacies:
False dilemma (Perfect solution) | Denying the correlative | Suppressed correlative
Deductive fallacies:
Accident | Converse accident
Inductive fallacies:
Hasty generalization | Overwhelming exception | Biased sample
False analogy | Misleading vividness | Conjunction fallacy
False precision | Slippery slope
Amphibology | Continuum fallacy | False attribution (Contextomy | Quoting out of context)
Equivocation (Loki's Wager | No true Scotsman)
Questionable cause:
Correlation does not imply causation | Post hoc | Regression fallacy
Texas sharpshooter | Circular cause and consequence | Wrong direction | Single cause
Other types of fallacy

Timothy Williamson Timothy Williamson, FBA, FRSE, (born Uppsala, Sweden, 6 August 1955) is a distinguished British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. ... The Sorites paradox (σωρός (sōros) being Greek for heap and σωρίτης (sōritēs) the adjective) is a paradox that arises from vague predicates. ... Multi-valued logics are logical calculi in which there are more than two possible truth values. ... In logic, supervaluationism is a semantics for dealing with irreferential singular terms and vagueness. ... Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ... In Philosophical logic, an informal fallacy is a pattern of reasoning which is false due to the falsity of one or more of its premises. ... Special pleading is a form of spurious argumentation where a position in a dispute introduces favorable details or excludes unfavorable details by alleging a need to apply additional considerations without proper criticism of these considerations themselves. ... Ignoratio elenchi (also known as irrelevant conclusion) is the logical fallacy of presenting an argument that may in itself be valid, but which proves or supports a different proposition than the one it is purporting to prove or support. ... The gamblers fallacy is a logical fallacy which encompasses any of the following misconceptions: A random event is more likely to occur because it has not happened for a period of time; A random event is less likely to occur because it has not happened for a period of... The inverse gamblers fallacy is a tempting mistake in judgments of probability, comparable to the gamblers fallacy whence its name derives. ... A fallacy of distribution is a logical fallacy occurring when an argument assumes there is no difference between a term in the distributive (referring to every member of a class) and collective (referring to the class itself as a whole) sense. ... A fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some (or even every) part of the whole. ... A fallacy of division occurs when someone reasons logically that something that is true of a thing must also be true of its constituents. ... This article or section does not adequately cite its references or sources. ... This article or section does not adequately cite its references or sources. ... In logic, correlative-based fallacies, also known as fallacies of distraction, are logical fallacies based on correlative conjunctions. ... This article does not cite its references or sources. ... The perfect solution fallacy is a logical fallacy that occurs when an argument assumes that a perfect solution exists and/or that a solution should be rejected because some part of the problem would still exist after it was implemented. ... The logical fallacy of denying the correlative is the opposite of the false dilemma, where an attempt is made at introducing alternatives where there are none. ... The logical fallacy of suppressed correlative is a type of argument which tries to redefine a correlative (two mutually exclusive options) so that one alternative encompasses the other, i. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... The logical fallacy of accident, also called destroying the exception or a dicto simpliciter ad dictum secundum quid, is a deductive fallacy occurring in statistical syllogisms (an argument based on a generalization) when an exception to the generalization is ignored. ... The logical fallacy of converse accident (also called reverse accident, destroying the exception or a dicto secundum quid ad dictum simpliciter) is a deductive fallacy that can occur in a statistical syllogism when an exception to a generalization is wrongly called for. ... A faulty generalization, also known as an inductive fallacy, is any of several errors of inductive inference: Hasty generalization is the fallacy of examining just one or very few examples or studying a single case, and generalizing that to be representative of the whole class of objects or phenomena. ... Hasty generalization, also known as fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, leaping to a conclusion, hasty induction, law of small numbers, unrepresentative sample or secundum quid, is the logical fallacy of reaching an inductive generalization based on too little evidence. ... A biased sample is one that is falsely taken to be typical of a population from which it is drawn. ... False analogy is a logical fallacy applying to inductive arguments. ... The logical fallacy of misleading vividness involves describing some occurrence in vivid detail, even if it is an exceptional occurrence, to convince someone that it is a problem. ... The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. ... This article or section does not cite its references or sources. ... In debate or rhetoric, the slippery slope is an argument for the likelihood of one event given another. ... Look up ambiguity in Wiktionary, the free dictionary. ... Amphibology or amphiboly (from the Greek amphibolia) is, in logic, a verbal fallacy arising from ambiguity in the grammatical structure of a sentence. ... Continuum fallacy, also called fallacy of the beard is a logical fallacy which abuses the paradox of the heap. ... The fallacy of a false attribution occurs when an advocate appeals to an irrelevant, unqualified, unidentified, biased or fabricated source in support of an argument. ... // Contextomy Contextomy refers to the selective excerpting of words from their original linguistic context in a way that distorts the source’s intended meaning, a practice commonly (and erroneously) referred to as the fallacy of quoting out of context. ... It has been suggested that Contextomy be merged into this article or section. ... Equivocation is a logical fallacy. ... Lokis Wager is a form of logical fallacy. ... It has been suggested that this article or section be merged with Special Pleading . ... Fallacies of questionable cause, also known as causal fallacies, non causa pro causa (non-cause for cause in Latin) or false cause, are informal fallacies where a cause is incorrectly identified. ... Correlation does not imply causation is a phrase used in statistics to indicate that correlation between two variables does not imply there is a cause-and-effect relationship between the two. ... The West Wing, see Post Hoc, Ergo Propter Hoc (The West Wing). ... The regression (or regressive) fallacy is a logical fallacy. ... The Texas sharpshooter fallacy is a logical fallacy where a cluster of statistically non-significant data is taken from its context, and therefore thought to have a common cause. ... Circular cause and consequence is a logical fallacy where the consequence of the phenomenon is claimed to be its root cause. ... Wrong direction is a logical fallacy of causation where cause and effect are reversed. ... The fallacy of the single cause, also known as joint effect or causal oversimplification, is a logical fallacy of causation that occurs when it is assumed that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient...

External links

  • Stanford Encyclopedia of Philosophy entry
  • A defence of the fuzzy view of vagueness

  Results from FactBites:
Vagueness (3412 words)
A proposition is vague when there are possible states of things concerning which it is intrinsically uncertain whether, had they been contemplated by the speaker, he would have regarded them as excluded or allowed by the proposition.
Vagueness is standardly defined as the possession of borderline cases.
Thus the logic of vagueness is a logic for equivocators.
  More results at FactBites »



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