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Most adjectives can be seen to add requirements. In other words, the set of all things with the adjective is smaller. For example,

  • Red ball is more specific than ball
  • Continuous function is more specific than function
  • Beautiful woman is more specific than woman

However, certain adjectives can be seen to actually remove requirements

  • Partial function is LESS SPECIFIC than function
  • A semiring is LESS SPECIFIC than a ring
  • (Nonstandard terminology) A generic market (the housing market, the stock market) is less specific than a market (a tuple of a time, a place, and a unique good)

What is the name of the former type of adjective? What is the name of the latter type of adjective?

  • In fact, any qualifier is restrictive, whether it semantically functions to limit requirements or not. All qualifiers add restrictions to a noun. – Robusto Jun 12 '18 at 13:44
  • You seem to be denying your own point. "Partial function" is not less but clearly more specific than function, so long as you look at the word without prejudice. I'd never met your "semiring" but Google thinks that follows the same route, and your "markets" clearly get us back on the straight and narrow. In the sense of your explanation, every adjective necessarily "adds requirements vs. removes requirements". In that sense, that's what adjectives are for. – Robbie Goodwin Jun 12 '18 at 22:24
  • @RobbieGoodwin 'In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.' (en.wikipedia.org/wiki/Semiring) It is removing requirements. If you read the definitions of each of these objects, you will see that this is indeed the case. Put another way, every ring is a semiring, but not the other way around. – extremeaxe5 Jun 14 '18 at 10:27
  • @RobbieGoodwin I do not understand. How is partial function 'clearly' more specific than function? If you have studied mathematics, you will know that partial function is less restrictive than function. Ask any mathematician. – extremeaxe5 Jun 14 '18 at 10:30
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I think the following, Warren's analysis, quoted in Kullenberg: Functions of attributive adjectives in English, explains well that there is usually a restriction involved:

Over the last four or so decades, there have been sporadic attempts at accounting for functions of attributive adjectives (Eg Teyssier 1968, Bache 1978, Warren 1984a, 1984b, Halliday 1994). One of the most thorough and exhaustive studies presented so far is probably Warren’s Classifying Adjectives (1984a), in which it is suggested that premodifying adjectives may identify, classify or describe.

Classifiers and identifiers are claimed to differ from descriptors in that they somehow restrict the range of the head noun; the former restrict semantic range, pointing to a subcategory, and the latter restrict reference, indicating a certain referent or group of referents within the class denoted by the noun.

An example of a typical classifier is polar in

I saw some polar bears at the zoo,

where polar indicates a subcategory within the class of bears.

An example of a typical identifier is red in

Give me the red book,

where red ’picks out’ the intended referent from the class of books (or rather, from a contextually determined set of books).

Descriptors, on the other hand, are seen as optional elements adding extra, nonrestrictive information. An example of a typical descriptor is cuddly in

I saw some cuddly teddies,

where the adjective simply adds descriptive information about the teddies in question.

Of course, a given adjective may perform different roles in different contexts.

.................

But the terms you then go on to ask about are essentially new terms, compounds. Unlike 'Danish butter', 'peanut butter' is not a subclass of 'butter', but a related product. A new two-orthographic-word lexeme.

A partial function has different definitional requirements from a function (though hypernymy will be involved). And Wikipedia for instance states that 'In abstract algebra, a semiring is an algebraic structure similar to a ring'. As for 'market', it's a famously polysemic word, so trying to compare 'the market at Bury' with 'the stock market' is nonsensical.

  • So you are saying that the words 'partial' and the prefix 'semi' in this case are essentially creating new concepts? – extremeaxe5 Jun 12 '18 at 8:24
  • Taking the Wikipedia statement 'a semiring is an algebraic structure similar to a ring' as being true, whether or not a new concept is involved is essentially playing semantics. But one must concede that a semiring is not a ring. When it comes to polysemy-with-hypernymy (definitions of 'animal' exist that contradict, some rejecting reptiles as members and some including them), definition of terms is required, and consistency (so no changing which sense of a word is being used in running text). Sadly, even within maths, the terminology surrounding 'function' isn't universally accepted. – Edwin Ashworth Jun 15 '18 at 18:06
  • wow. Umm... could you provide some evidence of that last claim? – extremeaxe5 Jun 15 '18 at 22:03
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    'Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a subset of the fields R or C) and the term mapping for more general functions.' {Wikipedia} But 'In mathematics, a partial function from X to Y (written as f: X ↛ Y or f: X ⇸ Y) is a function f: X ′ → Y, for some subset X ′ of X.' (again Wikipedia) is clear enough: the partial function is a function, but with a different domain from that of the associated total function (in fact, a subset). If the original starting ... – Edwin Ashworth Jun 16 '18 at 11:27
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    set is considered, some elements will not have images, so the whole relation is not a function. The term 'partial function' is a convenience to flag that if the imageless elements are discarded, a function ensues. – Edwin Ashworth Jun 16 '18 at 11:28
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Your terminology is not quite precise. The phrase partial function is more specific than function alone; it constrains the possible number of functions to those that are partial.

In the same way red ball only refers to balls that are red, selecting a subset of all balls.

I cannot think of any adjectives that actually broaden the scope of a noun. The bare noun is always less specific/more general than one that is modified by an adjective.

UPDATE: There seems to be a terminological mismatch between maths and linguistics. You state a partial function is less specific than a function; while this might be true for a mathematical definition of specific, it does not apply to a linguistic one. You are talking about a different meaning of specific in that case.

Linguistically speaking it is still more specific: a partial function is a special kind of function, which does not require that it has a complete mapping from every value to another value. So even though it is broader/looser in its applicability, it is still a restriction on functions in general. One clue is that on Wikipedia it says "a partial function ... is a function ... for ..." -- it does not say "a function is a partial function for which the full domain is known".

  • Mathematically speaking, the term partial preceding the word function does in fact broaden the scope of the class of objects it is referring to. Wikipedia gives a good explanation; essentially, a function is the special case of a partial function where the domain of definition is equivalent to the domain. – extremeaxe5 Jun 12 '18 at 8:23
  • I should add that there is good reason for this; functions are much more often used in mathematics than partial functions, and are thus deserving of the shorter identifier. – extremeaxe5 Jun 12 '18 at 8:25
  • @extremeaxe5 I'm afraid I disagree. "Function" refers to all functions. "Partial function " only refers to partial functions. As all partial functions are also functions, but not all functions are partial functions, adding the adjective restricts the sets of potential referents for the term. – Oliver Mason Jun 12 '18 at 8:28
  • Umm... no. Ask any mathematician. "Function" is more restrictive than "partial function." Mathematicians didn't choose these terms for linguistic reasons. You can't just "disagree" with this fact. – extremeaxe5 Jun 12 '18 at 9:21
  • @extremeaxe5 But this is about language, not maths... – Oliver Mason Jun 12 '18 at 9:22

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