"on a farm" vs "on the farm"

Question

What had thrown me into perplexity were collocations of a subject in the plural and the indefinite article with the word "farm" in the phrase "on a farm" (and others of the kind).

My specific question would be about the articles in the patterns of this sort: "Some, different ("what" in interrogations) animals live on a/the farm" and "Farmers grow wheat (or whatever) on a/the farm". And, particularly, when these sentences are being said just to inform the interlocutor about something that he is not fully in the know of, if at all.
A situation may be something like this: "I'd like to know something about animals? - Well, some animals live on a/the farm and some live in a/the forest". Or: "What do farmers usually do and where? - Farmers grow wheat on a/the farm".

Having looked it up on Ngram I found that in 1950 the phrase "animals live on the farm" could be come across more than 10 times often than "animals live on a farm" (with a zero result for "on a farm" in 1951). Then around 2007 the indefinite article version got ahead by a threefold margin. And in 2019 the "animals live on the farm" took the lead by almost the same threefold margin.

It is noteworthy that both "a" and "the" readings are to be encountered in contexts that seem almost, not to say absolutely, akin to one another (book titles: "Chickens on the Farm", "Chickens on a Farm, "Pigs on the Farm", "Pigs on a Farm" and so on).

I can easily take in: "Where do you live? - I live on a farm" or "What is the life on a farm like?". Because it is clear that here it goes about one farm, any farm of many etc.

But I can't tell the reason why it is: "Different animals live on a farm" or "Farmers grow wheat on a farm". However neither animals nor farmers can live or grow something on one farm or on any (every) farm, to what the article "a" decisively alludes. Thus it could be turning up the faulty assumption if using the indefinite article in such sentences. Because "farm" here obviously infers its generic implication, i.e. that "farm" is a certain facility whereat agricultural or cattle breeding activities are carried on. And the subjects in the plural also convey the idea of them [subjects] bringing in the generic sense.
To my mind here is a good example of the generic implication of "farm": "... and forget the unpleasant by wrapping themselves in a woolly humanitarianism; in this way the public conscience has been dulled and is unmindful of the conditions under which animals live on the farm, are transported to the market...".

Thus, my inquiry has led me up to the following questions:

• could the sentences in question be also said with the definite article: "Some/different etc. (or "what" in interrogations) animals live on the farm" or "Farmers grow wheat (or whatever) on the farm"?
• (it is the most important part of my question) why is the indefinite article used with subjects in the plural in such patterns as: "Some/different etc. (or "what" in interrogations) animals live on a farm" or "Farmers grow wheat (or whatever) on a farm"?

Answer 1

In most settings, the normal rules about the indefinite article "a" vs the definite article "the" apply - if you're making a general observation about any particular farm or speaking about one farm your audience is not familiar with, you should say "a farm", but if you're talking about a specific farm you have previously identified or is known to the audience then say "the farm".

Examples:

• My family own a farm (your audience was not previously aware and doesn't know any specifics about the farm yet)
• I work on the farm owned by my family (you have specified which farm you work on)
• It is tough running a farm (general statement, could apply to any farm)

However, "on the farm" can also be an idiomatic way of referring to farms in general, and that seems to be the case with your example. "What kind of animals live on the farm?" could be a general question about the typical animals on any farm.

This isn't unusual - we do the same with other animal habitats, too; for example, you can say "fish inhabit the ocean", or "giraffes live on the savanna", even though there are many oceans and savannas.

Answer 2

Both "Cows live on a farm" and "Cows live on the farm" are correct and natural to describe the general habitat of cows.

There are a few words for places in English which can be preceded by "the" and not indicate a specific location, but the concept of the place in general, particularly in terms of its function or as a habitat. These include:

function

• the post office
• the bank
• the store
• the gas station

habitat

• the zoo
• the desert
• the ocean
• the forest
• the farm

Note: Not all habitats or places with functions can use "the" this way:

Catfish live in the lake.
George spent all day at the restaurant.

Here, "the lake" and "the restaurant" necessarily refer to a specific lake and restaurant. The first sentence means there are catfish in the specific lake, and makes no mention of the natural habitat of the catfish species. The second sentence means George spent the day at a specific restaurant, and indicates nothing about why he was there or what he did.

There is no rule that governs which words can use "the" like this. The learner has to learn which are which.

Answer 3

You can have any combination of a and the in terms of grammar.

The animal lives on a farm. [specific animal, already discussed]
An animal lives on a farm or zoo. [generality]
An animal lived on the farm. [= There was an animal on that previously discussed farm]
The animal lives on the farm. [two specifics, already discussed].

More academic and formal:
The lion is a noble beast. [use of the for a category of something followed by a generality] Another example: The cathedral has a complicated structure.

Why? Because in English, what you can't have is this:
Animal live on farm.

Countable nouns require determiners of some kind or an s (except for headlines and some legal texts). You can have: animals live on farms.

Lastly, in terms of generalities, this often happens, you go from a to the, like this:

• I got a job in a restaurant. The restaurant is light, airy and beautifully decorated. And the job is great!

Answer 4

For some application, but not all applications, I recommend modeling English sentences using first order logic and set theory, but without any discussion of cardinality or bijections.

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In particular, English-style syntax for first order logic focuses on the following two phrases:

1. "for any"

2. "there exists"

Imagine that you are in an receptionist's room or lobby and there is exactly one desk and on the desk is exactly one custom-decorated soup can containing more than a half dozen ballpoint pens.

The following two phrases differ in meaning:

• *There exists a dry pen p inside of the empty soup can.

• for any pen, p, inside of the empty soup can, pen p is dry.

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Set Theory allows us to talk about categories.

Informally, consider the set -- or category -- of all clothing items intended by a fashion designer to be worn on your feet.

Socks and Shoes belong in the set of clothing items intended to be worn on human feet.

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Specifics Regarding the Word THE

	English Syntax	Syntax English & Logic	Logical Syntax
Semantic Example One	"We learned how to sew amaranth on a farm.	"There exists a farm f such that we learned how to sew amaranth on f." Perhaps, more than one farm exists in the world. We drew lots, and chose one out of the many farms to visit and learn about sewing amaranth.	"∃ f ∈ FARMS such that we learned how to sew amaranth on farm f."
Semantic Example Two	"We learned how to sew amaranth on the farm."	There exists a unique farm f such that we learned how to sew amaranth on farm f. There is one and only one farm in the current scope; not two farms, and not three farms, and not four farms.	"∃ f ∈ FARMS such that we learned how to sew amaranth on farm f." and ∀ g ∈ FARMS and ∀ h ∈ FARMS we have that g is h and h is g

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In English, the word "THE" is used to refer to an element of a set such that there is exactly one element of that set.

For example, if I told a volunteer at a food bank to give a loaf of bread "to the woman" standing outside, and there was a line of more than a dozen women standing outside, then the volunteer at the food bank would be likely to take exception with me.

The word THE connotes existence and uniqueness.

The world THE is almost a quantifier for the number one.

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Note that there is an old saying.... "e pluribus unum"

Note, that it is the choice of the author to decide whether something is one or many.

Consider the house-cats people keep as pets.

We can consider the set of all house-cats on earth to be a single object.

A set is one object, not many objects.

Thus, we can write, "the cat is a small furry animal having two ears and whiskers"

When people write about "the cat", then there is only one cat in our model or our linguistic framework.

When an author writes about "a cat", then that particular author has chosen to select one element of a set and disregard the other elements.

For example, an author might write, "a cat was stalking a grasshopper while the farmer tried to explain to us that a planting stick required fewer labor hours to produce than a steel garden trowel."

When we speak of "a cat", then the farmer owns more than one cat, perhaps with different color fur coats, and our attention is directed to a specific feline while disregarding the other felines.

When we speak of "the cat", then perhaps the farmer owns only one cat. It is not the case that the farmer has two or more cats.

In most English writing, there exists a unique cat in the current context.

We use the word the to show that the cat referred to in the current sentence is the same as the cat referred to in the previous sentence.

The word "a" choses a new element from a set of elements each time the word "a" is used.

The word "the" indicates that the current element of interest is the same as the element taken in a previous sentence.

The word "the" is analogous to an anonymous function in computer programming.

Instead of an anonymous function, we have an anonymous variable.

Sentence Order	Labeled Variable	Anonymous Variable
1	"Let x be a decimal number"	"We take a decimal number"
[2 ... 3]	[...]	[...]
4	Therefore, x is an element of the quotients	Therefore, the decimal number [we took earlier] is an element of the quotients.

Sometimes, an element of a set is chosen, but the element is not named.

A cat is chosen from the set of farmer's cats, but the cat is not given a name such as "Tom", or "Stripes", or "Socks", or "Pooh Bear", or any other name.

Sometimes, cat is without label, anonymous, and the cat is devoid of any name.

Then, the cat is said to be "the cat".

The scope of "the cat" bridges across multiple sentences.

Use of the word "*the" shows that are not discussing a new and different cat in each sentence.

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An instance of the cat class is inserted into the current workspace.

After the initial instantiation, the phrase "the cat" is valid if and only if the workspace contains exactly one instance of the cat class.

The phrase, "the cat", could be replaced with a specific name for the cat, if you chose to name it "x" or somthing like that.

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In English writing before the year 1900, the phrase "the cat" refers to the cat class, instead of cat instances.

When you hold time constant, then an instance of the cat class has specific coordinates in three-dimensional space (x-y-z-coordinates).

For example, an instance of the cat class might be asleep in your specific bedroom.

However, the cat class has no specific coordinates in space.

The cat class is a generality and the cat instance is more specific.