Why is it OK to claim that a language "has no grammatical cases"?

Question

My question is a direct consequence of this question and its answers and comments.

What completely baffles me (as a non-linguist) is the claim (decision? definition?) that there can be a language on Earth (at least, the most used languages and language groups) that has no grammatical cases (at least according to my understanding of cases).

I will not talk about my personal feelings and personal conclusions - I am not an expert. But the definition of "grammatical case" taken from Wikipedia clearly states:

A grammatical case is a category of nouns and noun modifiers (determiners, adjectives, participles, and numerals) which corresponds to one or more potential grammatical functions for a nominal group in a wording.

Also, the definition of the tag "case" here on Linguistics is:

Inflectional forms that indicate the grammatical functions of nouns, pronouns and their modifiers (such as adjectives).

and also:

Case is a system of marking dependent nouns for the type of relationship they bear to their heads. Traditionally the term refers to inflectional marking, and, typically, case marks the relationship of a noun to a verb at the clause level or of a noun to a preposition, posposition or another noun at the phrase level.

So as long as a language actually sends information about "things", as long as the words are useful for transmitting a message, grammatical cases have to exist - as a minimum, in an undefined way. Before the "invention" of grammar, the cases still existed, but nobody called them so.

In my mind, any language needs at least 3 cases (or their equivalents): nominative, accusative and genitive. Dative and vocative come very close too.

So, why is it OK to claim (or: why was it defined) that a language "has no grammatical cases"? Because as long as the language can transmit information, the words of the language serve a purpose and thus have a function. And with function comes the grammatical case, unavoidably.

I can understand that the French language (or whoever) might not want to recognize the existence of its grammatical cases, or that there are some word hacks to avoid admitting the existence of cases, but the idea remains: if the words have a function inside the sentences, they have grammatical cases.

Note: it is not the main scope of this question to compare the case systems of any languages. The comparison is acceptable of course for supporting the main question.

Answer 1

ONE: As Yellow Sky and Keelen explained in their comments, case is an explicit way of marking a noun for its grammatical function and the term "case" does not signify the function itself.

a) One can mark case with an affix (usually a suffix), for example, as we see in Latin.

(https://classics.osu.edu/Undergraduate-Studies/Latin-Program/Grammar/Cases/latin-case#:~:text=There%20are%206%20distinct%20cases%20in%20Latin%3A%20Nominative%2C,clicking%20the%20case%20names%20in%20the%20prior%20sentence.)

b) However, one could also mark case chiefly through the choice of the articles that a noun may take, as we see in German.

https://www.thoughtco.com/the-four-german-noun-cases-4064290

c) Marking pronouns for case may involve using different word-stems depending on case. We see this in English.

Nominative (subject, subject complement, citation form) first person singular is "I."

Accusative or dative (direct or indirect object) first person singular is "me."

d) There may be other ways of marking nouns & pronouns (and adnominal words like adjectives and determiners for case-agreement) for case that we might hear about in any comments about this answer.

TWO: In many languages, the function of a noun isn't marked in the noun phrase itself but is instead marked by word-order.

Let's leave aside English's possessive case, which behaves more like a clitic than a case, as we see in group possessives. (e.g. "Don and Linda's cat.")

When it comes to which noun is a subject, subject complement, citation form, or object, English relies on word order, NOT cases. The nouns must occur in certain positions in a sentence in order to have a certain grammatical function, but they are not modified to mark case. English has no nominative versus accusative-dative cases for nouns.

THREE: The reason it is OK to say that French doesn't have a case system is that French doesn't have a case system. It doesn't mark nouns for grammatical function but uses word order instead.

FOUR: There are other ways to mark who does what to whom in a sentence, but let's stop here.