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In "Mathematical Methods in Linguistics" by Partee, Meulen and Wall (1990), it is stated on page 385 that the determiner any has been a notorious problem for semantic analysis, since it is sometimes equivalent to every, but sometimes it is not equivalent to it, while in other contexts it is simply unacceptable.

I wonder if there is any improvement been made on this since then.

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I'm not aware of an improvement. Sometimes "any" is used in generalizations, like the universal quantifier of predicate logic, and sometimes it is used as a negative polarity word, as in "I want some caviar" versus "I don't want any caviar". Compare "I don't like any caviar", which makes a generalization.

I think it was Robin Lakoff who observed that "Do you want any caviar?" expects a negative answer, as compared with "Do you want some caviar?".

There is a suspicion that these two uses are somehow related. But how? What do generalization and negation have in common?

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  • That's clearly not a (at least not a well founded) answer, and with just a little effort, it would fit into a comment. But I can't fault you for a bad answer, if the question is not precise. It's not clear that there's a generally accepted problem formulation, so who's supposed to have made progress, any of the authors in context? KThat is, you seem to agree that it's a problem, but who will pick-up the slack and substantiate that claim? – vectory Apr 11 '19 at 15:27
  • Sure the negation plays a role, good thinking. – vectory Apr 11 '19 at 15:30
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    Any is the prototype negative polarity item. It has a different use of "free-choice any", which is a possible polarity item (i.e, it requires a diamond, possible modal like can or may the same way negative polarity any requires a negative). Famous article by Zeno Vendler on the topic of the English words corresponding to logical quantifiers "Each and Every, Any and All"; after 50 years it's still behind a paywall. – jlawler Apr 11 '19 at 16:47
  • @Greg Lee, I just checked that Robin Lakoff was born in 1942. So her observation of "Do you want any caviar" expecting a negative answer could happen no earlier than 1960s. But I think the fact "some" is (generally) used in positive sense while "any" is used in negative and question has been known for a long time. I knew this in early 1980s when I first learned English. So are you serious about it? – hermes Oct 13 '19 at 16:58
  • @MathWizard, I don't understand what you are asking me. Am I serious about what? – Greg Lee Oct 13 '19 at 18:19
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they are partly complementary (as every can not determine uncountable nouns) e.g. ...any harm will be eliminated..., but not every harm

also in some contexts the use of any implies choice, e.g. We need to take every one of those things seriously... versus We need to take any of those things seriously... (though in this case every one is a specific phrase)

and sometimes any only implies a possibility, e.g. the only viable option for tobacco companies is to fight every damage claim versus the only viable option for tobacco companies is to fight any damage claim

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It is basically an adverb of an. Compare German eins "one", ein- "a, an*, quantifier einige "some, a couple, at least one", adverbial "Ich mache einiges". The negation of einige is not in use, doesn't exist, and would be ambiguous (nothing? many?).

Yet, not any means "nothing". Someone might figure the opposite of nothing were "everything", which is not necessarily the case, hence the confusion. Logically, the opposite is any, "there exists at least one" (this is very basic in logic). The negation of that is "not any" = "nothing".

I think that explains the semantic difference, but its hard to say when it appeared. I believe that would give a better answer than a strictly synchronic grammar.

Getting all the different variants together, "anyone can", "any one man can", "has anyone seen", ... would be a start. Comparing German to just these, we have "ein jederman", alternatively "jederman", "jeder" in the sense "everybody"; And "irgend-jemand", "irgendwer" in the sense "someone". For "je", which has a complicated history (confer Grimm), I find tempting to see it in the "y" in "anyone" (anyman??), but that's just an unsubstantiated hunch. Further we have "want any?", which would be "willst du welche", to which one can answer "ja, einige", though it would be rather "ja, ein paar" (a couple). Incidentally, "je" also translates to "ever" ("wenn ich je ..." - if I ever) in some context, and akin to "yet" eventually ("hast du je, jemals..." - have you ever, have you yet?) ...

The really funny one is the case where any is seemingly replacing a ~ an. Do you have any idea? At all? Germans would just say "hast du eine Idee?" Since we had this deranged thread today about the correct lambda expression for "Alice and Bob eat two cookies", that is necessarily ambiguous ... while I have no idea about that it appears intuitive to understand "have any idea" adverbail, not counting the objects, but the verb. This finds a parallel in "hast du mal einen Stift". "mal" is also hard to explain, even for native speakers, e.g. in du kannst schon mal auspacken. Since "schon" translates most often to "yet" ("hast du schon" - do you have yet?), and "schon mal" is a colocation, it may be reasonable to compare "mal" to "je", "jemals", "yet", "ever", circling back to the above argument.

There's a dense cluster of multiple parallel developments. More examples would be required, preferably archaic ones. Preferably about "any" itself.

Finally, "einige" is not to be confused with "einig" (united, in agreement) or even "geeinigt", "vereint" (united), though "uni" might be interesting to compare. Since the -ig appeared hard for me to explain for a second, I came to remember "einje", which is common in northern dialects, at least Berlin and surroundings. That would be much closer to "any", phonetically. That might be just a common development. Or it might imply that "einige" was a backformation from "einje", which would be a composition of "ein" and "je". Just which "je", of which there were many, I don't know. We also say "einwas" (an what; sounds like an ones without nasalisation), so make of that what you will.

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