Of course in most contexts we use a to refer to a generic, non-specific example of some class (or the first mention of a specific member of that class), and the to refer to a specific previously-mentioned member of that class. This is not the case here.
In this usage, both a and the can be used to describe an exemplary peasant, taking some random peasant in ...
We can use the indefinite article (a peasant) if we are discussing an unknown peasant, or the definite article if we are discussing the generic peasant (considered as a type of person). Either is appropriate in the context you quoted.
In both cases, you’re using ’peasant’ as a generic, but the generic forms are different in their meaning.
A generic formed with the definite article in English is generally categorical. In other words, it talks about the noun as a category of person/place/thing/idea, describing all items referenced by that noun as one group. This is essentially the same as ...
No, you cannot say "none of people", because when you say "none of X", you are referring to none of some specific collection of people (like "the people I know"). Therefore you have to say "the people".
Just to add a reference that proves @stangdon's answer right:
We use none with of before the, demonstratives (this, that), possessives (my, your) or pronouns:
None of his old friends knew what had happened to him. (Cambridge)
So you definitely need the in your case because none of will always be followed by a particular group of persons or things.
In the rivers would imply in all the rivers of Australia. This cannot be possibly true, though, ok, maybe some Guiness Book fisherman may have done it. It is more accurate to say in rivers:
in (some) rivers all over Australia.
This post from ELU, Definite article before “Houses”, deals with a similar issue.
Both constructs are acceptable. However, there can be a difference in interpretation.
'A peasant' uses peasant as a generic category: that class of people known as peasants. 'The peasant' may also use peasant in this generic, categorical sense. However, 'the peasant' might also refer to a particular, singular person: 'The Peasant, name unknown, social caste -...
The question states, "it is clear that we are talking about particular rivers in Australia."
This is not correct. This appears to be a misreading of the sentence, which analyses it like this, "my father has fished in the rivers that are all over Australia."
The sentence should rather be understood like this, "My father has fished in ...
Here's some guidance from Jakub Marian providing a nice rule for using the word "future" as an adjective or a noun:
When ["future" is] used as an adjective, it doesn’t take any article itself; it is preceded by the article of the noun it modifies ....
When “future” means “the time or the events that will come after the present”,...
The word "of" serves a lot of purposes in English, so you must consider it in context. The following are both correct:
I would like a liter of water.
The density of water is 997 kg/m³.
The difference is that a liter indicates one random part of all the water in the universe, while the density indicates a unique property of water.
We can imagine ...
You're right about the definition of "the".
The structure is: ["the" + noun1 + "of" + noun2].
In this structure, "of [noun2]" defines which [noun1] we're talking about, so in your example sentence, "the" points forward to the long prepositional phrase "of a ... grown-ups", which defines the specific ...
"The" is used when the reader knows exactly what it's talked about. So it's shared information between both the writer and the reader. However, in this sentence, "a" is used in "a small house" and in "a village" because it could be any house in any village located in the Netherlands, the reader doesn't acknowledge this....
You would use a if you are referring to one of many possibilities, for example:
The phone switches to a network with a stronger connection than the current one.
This sentence suggests that there might be multiple connections that are stronger than the current network, and the phone could switch to any of those networks.
We use the when there is only one ...
Both your examples, with and without the articles, are grammatically correct.
We use the definite article when referring to something specific that the audience is already aware of. It can also be used to refer to something previously mentioned.
'The information' refers to specific information. You don't have to use the article here, but you might want to ...
I do not see anything ungrammatical about
we have reached a main result of ...
Indeed in some contexts use of "the" instead might be incorrect.
Computer grammar checkers are not yet good enough to be relied on for decisions, in my view. The most they are good for is to highlight text for human examination and decision.