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The name Elizabeth Alexandra Mary, the unique title The Queen of England, and the definite description the elder daughter of Cecilia Bowes Lyon all refer to the same unique entity. We might think of them as species of one kind of thing, as they have at least one feature in common: they refer (designate a single entity).

They are all nominals. However, nominals includes words that don't (at least not obviously) designate a single entity. For example, the word running in the sentence running is good for you. Is there a hypernym (general term) that designates all, and only, linguistic entities that refer?

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    The core of the phrase "the elder daughter of Cecilia Bowes Lyon" which doesn't have to designate a single entity. You make it specific by adding modifiers to make it definite. It's the same for all nominals. Other than the word "definite" itself, I don't know how there could be a meaningful hypernym for that! – curiousdannii Jun 9 '17 at 0:11
  • Oops, The core of the phrase "the elder daughter of Cecilia Bowes Lyon" is "daughter" which doesn't have to designate a single entity. – curiousdannii Jun 9 '17 at 1:33
  • @curiousdannii daughter itself indeed doesn't designate a single entity - what makes the expression denote an inidividual is the combination with the definite article "the", which can be viewed as a function that operates on singleton sets to return the only individual that the set contains, thereby transforming the predicate into a singular term. (This obiviously works only if the set contains exactly one element: Applying the definite article is otherwise semantically infelicitous.) – lemontree Jun 9 '17 at 12:42
  • So while the "core phrase" is a predicate denoting sets of individuals, the entire expression is indeed a definite description denoting a single individual, under the assumption that the application of the definite article returns that individual that is the element of the set of individuals denoted by the complex predicate "elder daughter of C.B.L.", which needs to contain at least one and no more than one element in order for applying "the" to make sense. This account of the definite article works parallely for simple common nouns that denote singleton sets (like "the chancellor"). – lemontree Jun 9 '17 at 12:43
  • @lemontree The only way this question can make sense to me is if it's asking for a term for context-less definiteness. I know people have discussed that, but I don't know what terms are used. – curiousdannii Jun 9 '17 at 12:59
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What you are looking for is probably the singular term, i.e. a term that inherently refers to an object, see here. On the other hand, following Frege, we have predicates (or functions) denoting concepts, and propositions that refer to truth-values (which are thought as two really existing object: the Truth and the False).

Note that Frege's intention was to describe the formal language of science, where all terms are, effectively, singular and where there are no humans involved, just numbers. This is why he was able to use the German word Eigenname ‘proper name’ as a synonym for what we call singular term nowadays.

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    +1 (Though I think "singuar" is usually omitted.) Note the nice parallelism between terms in formal and in natural language: A term is an expression that denotes an individual object. Terms can be individual constants (which behave like proper names), variables (which behave like pronouns) or terms yielded by functional application (which behave like definite descriptions/unique titles). In mathematics, the individual objects are numbers, while in natural language the individual objects are humans and all kinds of concrete objects. The correlations are similar with predicates and propositions. – lemontree Jun 9 '17 at 12:28

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