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While I know how to use the words that I use, I do not know if there is a term to describe words that are uncountable nouns, but at the same time are countable in other circumstances. "Cheese" is one example perhaps. I find researching this does not clarify anything - words seem to be countable and uncountable at the same time (depending on context) - is there a term for this or do we just have to accept the context rather than having an overriding term?

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    No, there isn't any such term. Virtually all mass nouns can be used as if they were count nouns under certain circumstances, and vice versa. It's the circumstances that determine, not the nature of the noun itself. There are many subcategories of mass and count, each with their own peculiarities, and no reason for a special term that simply describes the normal situation.
    – John Lawler
    Commented May 24, 2013 at 17:38
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    I have come across such a usage - I think one dictionary (it might be Cobuild) uses 'mass noun' for that subset of non-count nouns that countify for different varieties (cheese, wine, rice, coffee...). (I'm not sure I'm allowed to use 'countify' ergatively. But I just have.)
    – Edwin Ashworth
    Commented May 24, 2013 at 21:19
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    @OC2PS When you're talking about types of cheese, according to the Longman dictionary. I suppose it works like the plural of fish (it only has one if you're 'counting' species of fish). But I do wonder if cheese could also be used as countable when you're talking about a whole unit, similar to 'an egg' vs 'some (scrambled) egg'.
    – SC for reinstatement of Monica
    Commented Jun 8, 2013 at 14:03
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    @SaraCosta You can count types of cheese (four cheese pizza), you can even add a unit and say four blocks of cheese. But cheese itself is not countable.
    – OC2PS
    Commented Jun 8, 2013 at 17:40
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    The phenomenon @JohnLawler points to is sometimes referred to as the "Universal Grinder" (notionally count nouns acting as mass nouns) or the "Universal Packager" (notionally mass nouns acting as count nouns).
    – user31341
    Commented Jun 9, 2013 at 1:17

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The Wikipedia entry for mass nouns notes:

In linguistics, a mass noun, uncountable noun, or non-count noun is a noun with the syntactic property that any quantity of it is treated as an undifferentiated unit, rather than as something with discrete subsets. Non-count nouns are distinguished from count nouns.

Given that different languages have different grammatical features, the actual test for which nouns are mass nouns may vary between languages. In English, mass nouns are characterized by the fact that they cannot be directly modified by a numeral without specifying a unit of measurement, and that they cannot combine with an indefinite article (a or an). Thus, the mass noun "water" is quantified as "20 litres of water" while the count noun "chair" is quantified as "20 chairs". However, both mass and count nouns can be quantified in relative terms without unit specification (e.g., "so much water," "so many chairs").

Some mass nouns can be used in English in the plural to mean "more than one instance (or example) of a certain sort of entity"—for example, "Many cleaning agents today are technically not soaps, but detergents." In such cases they no longer play the role of mass nouns, but (syntactically) they are treated as count nouns.

It also observes:

Some nouns have both a mass sense and a count sense (for example, paper).

Cheese appears to be another of these nouns with both a mass sense and a count sense. The Oxford Dictionaries website includes the following as a definition of cheese:

[COUNT NOUN] A complete cake of cheese with its rind.

It offers the following example sentence:

"the cheeses are trimmed and wrapped in sterilized muslin."

This is sufficient to reassure me that I could legitimately say, "Nine of the cheeses are finished and we have three more to go." The word cheese can, then function as both a mass noun and a count noun, meaning slightly different things in the two uses.

It also seems clear that most mass nouns can make an appearance as a count noun. The Wikipedia article cited above notes:

Some mass nouns can be used in English in the plural to mean "more than one instance (or example) of a certain sort of entity"—for example, "Many cleaning agents today are technically not soaps, but detergents." In such cases they no longer play the role of mass nouns, but (syntactically) they are treated as count nouns.

I've tried but haven't been able to find an example of a noun that cannot become a count noun in this way.

The lab tested 7 gasolines. 12 different coffees are on offer.

I admit that I would like the sentence above better if it said "7 brands of gasoline" or "7 samples of gasoline", but nothing about it seems to me wrong or even particularly surprising. Even abstract nouns seem to be amenable to this transformation:

FDR's Four Freedoms

10 Hopes I Have For Past Loves (Title of Huffington Post Article)

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  • The trouble with the definitions given is that we have to refer to a noun which exhibits both behaviours as both a count noun and a non-count noun. It's far better to refer to the noun as a noun, and label individual usages as count or non-count.
    – Edwin Ashworth
    Commented Jul 23, 2019 at 18:52
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Cheese is not countable in any situation.

You can count types of cheese (four cheese pizza), you can even add a unit and say four blocks of cheese. But cheese itself is not countable.

Remember:

In English, uncountable nouns are characterized by the fact that they cannot be directly modified by a numeral without specifying a unit of measurement, and that they cannot combine with an indefinite article (a or an).

Uncountable nouns CAN be modified by numbers if units of measurement are included.

Also, uncountable nouns can be used in English in the plural to mean "more than one instance (or example) of a certain sort of entity" (refer to my four cheese pizza example)...

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    Cheese can be a countable noun, e.g. There is a good selection of local cheeses in the local cheese shop. - see Longman.
    – TrevorD
    Commented Jun 8, 2013 at 23:28
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    -1 As @JohnLawler said in a previous comment Virtually all mass nouns can be used as if they were count nouns under certain circumstances. Your definition appears to be quoting from somewhere: would you please provide the source?
    – TrevorD
    Commented Jun 8, 2013 at 23:32
  • @TrevorD Your example is the same as mine - local cheeses is analogous to four cheese.
    – OC2PS
    Commented Jun 9, 2013 at 0:54
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    No it's not. You wouldn't say four-chesses pizza. You're using cheese in the singular and as an adjective: I'm using it as a plural noun. (You haven't answered my question about the source of your definition.)
    – TrevorD
    Commented Jun 9, 2013 at 11:44
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    @OC2PS, there are certainly "blocks of cheese" but there are also individual, distinct, countable cheeses. Check out this definition from the Oxford Dictionaries website: [COUNT NOUN] A complete cake of cheese with its rind. The following example sentence is also included: ‘the cheeses are trimmed and wrapped in sterilized muslin’. (The notation "COUNT NOUN" is part of the dictionary definition; I didn't add it.)
    – user193445
    Commented Sep 21, 2016 at 20:27

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