Vagueness

Key takeaways

Vagueness belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Vagueness to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Vagueness from memory before moving on to harder problems.

Reference excerpt

In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is not vague since every number is definitively either prime or not. Vagueness is commonly diagnosed by a predicate's ability to give rise to the Sorites paradox. Vagueness is separate from ambiguity, in which an expression has multiple denotations. For instance the word "bank" is ambiguous since it can refer either to a river bank or to a financial institution, but there are no borderline cases between both interpretations. Vagueness is a major topic of research in philosophical logic, where it serves as a potential challenge to classical logic. Work in formal semantics has sought to provide a compositional semantics for vague expressions in natural language. Work in philosophy of language has addressed implications of vagueness for the theory of meaning, while metaphysicians have considered whether reality itself is vague.

Importance The concept of vagueness has philosophical importance. 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 definitions.

In law 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 biological sex can be subject to vagueness problems, not just from transsexuals' gender transitions but also from certain genetic conditions which can give an individual mixed male and female biological traits (see intersex).

In science 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 dogs? 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, a.k.a. sorites paradox—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 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 (1993).

Supervaluationism

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. 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.

Subvaluationism

Subvaluationism is the logical dual of supervaluationism, and has been defended by Dominic Hyde (2008) and Pablo Cobreros (2011). Whereas the supervaluationist characterises truth as 'supertruth', the subvaluationist characterises truth as 'subtruth', or "true on at least some precisifications". Subvaluationism proposes that borderline applications of vague terms are both true and false. It thus has "truth-value gluts". According to this theory, a vague statement is true if it is true on at least one precisification and false if it is false under at least one precisification. If a vague statement comes out true under one precisification and false under another, it is both true and false. Subvaluationism ultimately amounts to the claim that vagueness is a truly contradictory phenomenon. Of a borderline case of "bald man" it would be both true and false to say that he is bald, and both true and false to say that he is not bald.

Epistemicist view

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Vagueness

Start with the simplest possible case. Write down what Vagueness claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vagueness before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vagueness ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vagueness

In research: Vagueness appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Vagueness in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Vagueness is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ambiguity, Concepts in logic, Concepts in the philosophy of language, so understanding it makes those chapters shorter.
In everyday life: Look for Vagueness outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Vagueness in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vagueness means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Vagueness out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vagueness in simple terms?

In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height.

Why does Vagueness matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vagueness?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vagueness.