Can you clarify "Is vanishing of cases reflects a general trend (anything)…"? It might be possible to guess what that meant but any Answer would depend on that guesswork… Can you Post two or more paraphrases for "Is vanishing of cases reflects a general trend across the languages"?

"Modern Slav languages...less developed than in the Proto-Indo-European." really this is only true of South Slavic and Czech/Slovak; East Slavic and Polish still have complex case systems similar to PIE.

@MarkBeadles thank you for this precision. If I am not mistaken, Polish has 7 cases and Russian 6, vs. the 8 of PIE?

English and Romance languages are not case languages. German, Greek, Russian Latin, for example, have cases. So, your question is a little odd.

@Lambie they all originate from the Proto-Indo-European (PIE), which had cases, but some of these languages lost them. The romance languages originate from PIE via Latin, which still had cases, whereas English is a Germanic language which also lost the cases (which survived in German.)

@RogerVadim If the question is whether there is unidirectional evolution from synthetic languages towards more analytic ones, why not edit it to say that - or at least, something like that? I stand to be corrected, and how could "Vanishing of cases: general trend or specific to indo-European family?" be correct in any language, including the English we're using here? If you meant "Is the vanishing of cases a general trend in all languages, or specific to the indo-European family?" why would you not have put it that way?

I know where they originate. And we all originated from the apes. But I won't ask if hirsutism means women are more ape-like. :)

" Can we claim that a language is more mature, if it lost the inflections?" Depends on what you mean by 'mature'. If you are just referring to age, well, all PIE languages are equally 'old'

@RobbieGoodwin I am not sure about what you are getting at: it seems that you are suggesting that not having a complete sentence in the title is a poor English style... that might be the case - I take your word for it. However, there is the body of the question explaining it. Merely losing cases does not make language analytical - but if you think you can provide an answer about the (absence of) unidirectional evolution towards analytic languages, please feel free to post it.

@Lambie we all descend from LUCA, and there is no way of saying that apes are more evolved than trees or vice versa. However, we do know that both are more evolved than bacteria.

@MarkBeadles maturity and age usually mean different things - e.g., a person can be very old and still very immature. If one takes the example of biological evolution (see also the comment above): humans and bacteria originated from the same ancestor, but it is fair to say that one is more evolved and the other is more primitive. Note that we cannot say that humans and bacteria are equally 'old', and I think we cannot say it about PIE languages either, for the same reason. There is also Convergent evolution

@RogerVadim generally ime biologists object to phrases like "more evolved" ("more primitive" is less clearcut, but I'd usually expect to hear other phrases like "more archaic" instead). If anything bacteria are more evolved than we are as their genetic makeup changes much faster due to their much more rapid reproduction. It's only from a human-centric pov that they appear to be unevolved

in the other direction, French is almost analysable as having four cases for nouns - a plain nominative-accusative, a genitive with prefix de, a partitive with prefix du/de la/de l'/des (which merges with the genitive in the definite), and a dative with prefix a. The few preposed adjectives are a stumbling block but if you take a more polysynthetic analysis (as is sometimes done with the verbs) even this isn't insurmountable. A similar analysis of Spanish has no partitive, but does have a distinct accusative for personal nouns (identical to the dative), but adjectives are more problematic

@Tristan Bacteria have lower complexity, and they are also at a lower stage of evolution than, e.g., eukaryotes or multicellular organisms, because they lack many features that the latter acquired in the process of evolution. However, one could say that biological evolution is largely idiosyncratic - it took a random path, and higher organisms are not necessarily better adapted to environment than bacteria. This is contrary to the statements made by Draconis in the comments to their answer - that language evolution has explored all the morphological possibilities.

@Tristan I appreciate your comment about French.

@RogerVadim again, terms like "lower stage of evolution" and "higher organisms" are generally not used by biologists today in my experience. They only seem so from our human perspective that places us at the pinnacle of evolution (if we were somehow sentient bacteria we'd probably view mammals as a weird overly-complex dead-end of evolution). In certain contexts bacteria are indeed lower complexity though

For a historical case (!) of a new case being added to a language, consider Estonian. Like Finnish, Estonian has postpositions used mostly with the genitive of nouns; one of them is Fi. kanssa / Est. kaasa(s) ‘together with’. In Finnish, you’d thus have isä ‘father’ > isän kanssa ‘with (the) father’. Kanssa has a short form colloquially, kaa, which eventually became fused with the noun in Estonian and created the comitative case -ga, so you now have isa ‘father’ > isaga ‘with (the) father’.

@Tristan You are the one who is loading these terms with anthropocentric meaning. I have clearly stated that I am talking about complexity, which is quantifiable and can be regarded as higher/lower. We also know the chronological order of evolution, which means that stage is a meaningful term. I don't count myself as an authority on what exact terms biologists use - I was not trained in this domain... but I do have academic/professional experience in evolutionary biology.

@RogerVadim Your point about complexity is valid, however linguistic complexity is found in many places. A language with low complexity in noun cases might have considerable complexity in verbal conjugation (e.g. Western Romance), in noun gender (e.g. Swahili), in verb phrase construction (e.g. English), etc. Languages with an isolating tendency like English or Mandarin may nevertheless be complex in terms of syntax.

French is not a case language. No matter how you twist your analysis to fit it. The question is not relevant to languages that don't have cases: nominative, accusative, dative, ablative and so forth.

@MarkBeadles it has been lost somewhere in the comments, but the question actually emerged as my pushback against a post in another forum, cited above, where case languages were called primitive. I am all for the equality of languages, and it well might be the case that the complexity of a language does not diminish/increase when it loses case. But this does not exclude a possible trend towards isolating languages. From Draconis' answer I gather that there's simply not enough evidence to attest such trend or its absence - we only know that sometimes cases can be are acquired.

@Lambie the question is about language evolution, and English and French were given as examples of languages that lost their cases - precisely because they do not have them. Further, one could be more precise and distinguish cases as relations between words and inflections as changes of words that some languages use to express cases - in this sense French does have cases, but they are expressed by prepositions rather than inflections.

@Lambie this is provably false. Analysing French as polysynthetic with incorporated adjectives it can be analysed as having case prefixes (fused to a certain extent with marking of definiteness) for a nominative-accusative, partitive, genitive, and dative case. Analysing French as polysynthetic is definitely not usual, and at this stage still probably not the most helpful analysis, but it has been suggested in the literature so is not just something I've pulled out of thin air (Spanish is though, and as I said, the arguments are much weaker there anyway)

@RogerVadim interesting to note that whilst overall complexity seems to be broadly consistent across languages and across language history there is some evidence that it might not be completely static and that environment (including the sociolinguistic circumstances) may play some role in it cf the collection of essays Language Complexity as an Evolving Variable by the OUP global.oup.com/academic/product/…

@Tristan thanks for the reference!

@RogerVadim I'd suggest a companion or follow-on question to consider then: Is there a trend toward simplification of verbal morphology in PIE languages? Armenian and Spanish are a couple examples of high complexity in TAM. I'd think any trend toward isolating would need to include simplification of verb forms.

@MarkBeadles in particular whilst Romance has lost much of Latin's complexity (distinct passives, infinitives, and some tenses) the core (not Romanian or Sardinian) also innovated a new future & conditional by agglutinating habeo onto the infinitive