Proper nouns are always definite (i.e. are names of people or names of places).
They are also always capitalized.
Does that mean that the capital letter is considered a marker for definiteness?
Do we use capital letters because they are proper nouns or because they are definite?
John went to Italy yesterday. So did Sam
In English, the capitalisation of proper nouns is not attributed to the definiteness of the noun. That is why the definite nouns capitalisation, definiteness and noun in the previous sentence aren’t capitalised.
Similarly, while one can imagine an English in which capitalisation signals definiteness, the standard variant capitalises proper nouns even when they aren’t definite, as this sentence illustrates.
So no, capitalisation cannot be considered a “marker for definiteness“.
Does that mean that the capital letter is considered a marker for definiteness?
No. Often they are but you are trying to create a “rule” and there are no “rules” in English – only guidance. Some guidance may look like a rule, but it is not. The following is guidance:
Capital letters are used for
Proper nouns Beijing; Taj Mahal; John; Monopoly (the game).
The purpose of expressing respect “I spoke with Her Majesty”; “I spoke to God, and He spoke to me.”
For nouns and important words in media titles: Love’s Labour Lost; “The Man with the Golden Gun” “A Tale of Two Cities”; “Lost Boy found in Forest!”
For titles of rank: “The man in charge is General Smith.” (but “Many of the generals were asleep.”)
For titles when used for direct address: “I don’t know the answer, ask Dad.” (but “I’ll tell my dad what you have done!”)
At the start of sentences and lines of poetry.
In philosophy to distinguish between an item and the essence of that item: See Wikipedia Capitonym https://en.wikipedia.org/wiki/Capitonym
Some other cases
