Society without an article is the abstract concept of society:
Society as a whole needs to take responsibility for these problems
Society with an article refers to a particular organization
I keep my money in a building society
I am a member of the amateur dramatic society
Something is generally countable except for
- abstract concepts like peace and fairness
- activities like swimming
- substances that are infinitely divisible (water, sugar, leather, soap cheese, etc)
Note that you can still use a plural for something that is uncountable, to
indicate there are multiple types of it:
I tried several cheeses at the food fair (meaning several types of cheese)
Going back to your examples,
Society doesn't pay enough to old people.
This is society as an abstract concept.
The society doesn't pay enough to old people.
This would be a particular organization, for example a charity that helps old people.
Societies don't pay enough to old people
This could be either referring to several different organizations (for example charities) or different kinds of abstract society, for example in different countries.
I think that the first example has the intended meaning and the other two, while grammatically correct, probably do not have the intended meaning.
When you want to make a general statement about something, and the noun is countable, you don't use the article:
Horses have hooves.
The above means "All horses".
If you use the article, you're not referring to all horses, but to specific horses:
The horses have been training in a simulated high altitude environment with low oxygen, to improve their lung capacity for the big race.
If you say:
The horses have hooves.
someone might reply, "Of course they do! All horses have hooves".
Best Answer
Surgery is both a mass noun and a count noun. Note the Cambridge dictionary uses U for uncountable noun (mass noun) and C for count noun.
In brief, it is a mass noun when referring to
It is a count noun, when it refers to
See operation. And while operation is used in both American English (AmE) and British English (BrE), It seems that this particular count-noun use of 'surgery' to mean 'an operation' is used mainly in AmE.
The following questions regard 'surgery' as a mass (uncountable) noun:
or
or
The following questions refer to 'surgery' as a count noun. It is asking about countable instances of surgery or surgeries as operations. Again the dictionaries I have checked indicate this is mainly an AmE usage. To me, it is also important to notice that these questions use the word 'surgery' as a plural count noun:
and
The American (?) usage as both mass and count noun allows both the following sentences, which convey the same information:
As a mass noun
As a count noun
Note that even though 'surgery' can be used as a singular count noun, we would not normally use 'a surgery' in the last sentence. And, in general, although Americans do say 'a surgery', it sounds weird to me. Therefore, I think the answer to to your question
may depend on which speaker of American English that you ask. I personally would probably not say it. I might say 'a surgical procedure' or, of course, 'an operation'.
Whereas, I don't think any American in their right mind would ask:
Although, usage may vary, not only among speakers, but regarding which part of the body is being operated on. I can see someone saying 'I have a knee surgery tomorrow', but not 'I have a brain surgery tomorrow'. Maybe because we have two knees but only one brain? I dunno.
You can do an Internet search for 'had a surgery' and 'had surgery' to get a good idea of this difference in usage (mass versus count).
Note that 'surgery' also has some other, related meanings, which vary in usage between American English and British English. For instance, in BrE, 'a surgery' is where you go to see a doctor; in AmE we say 'office' for this. You can read about this and a couple other definitions in most dictionaries, including this one.