I have recently noticed a curious phenomenon with the word "any", in that it sometimes does not behave like the universal quantifier "every". Consider this pair of sentences: "John can outrun every man on the sports team" and "John can outrun any man on the sports team". In this particular case, the word "any" functions as a universal quantifier, and so the sentences mean the same thing. However, now consider this pair of sentences: "John cannot outrun every man on the sports team" and "John cannot outrun any man on the sports team". Those two sentences do not mean the same thing. So, my real question is, are there papers that do a logical analysis of the word "any"? I would be very interested in such texts.
If you are asking a question about how 'every' and 'any' work in the English language, and the differences between them, then this article has some useful information.
They tend to differ when negated, or when used in a conditional, or when embedded in another expression, or when used in a question. E.g. contrast:
I do not own any book written by Schopenhauer.
I do not own every book written by Schopenhauer.
If any person here is from New Zealand, that would be surprising.
If every person here is from New Zealand, that would be surprising.
This piano is too heavy for any man here to lift.
This piano is too heavy for every man here to lift.
Is any book in this library by a Greek author?
Is every book in this library by a Greek author?
Another difference is that 'any' can be used with mass nouns, but 'every' cannot. "Is there any water?" makes sense, but "Is there every water?" does not.
For added confusion, 'each' is different again, and is not always identical with 'every'.
If you asking about how these terms differ when rendering them into formal logic, then there are some subtleties to observe. 'Any' usually suggests an arbitrary item, and can be ambiguous. 'Every' indicates an entire class of things. 'Each' may differ from 'every'. For example, there is a difference between asserting that F(n) holds for each natural number n, and asserting that (∀x)F(x) holds, which would naturally be read as that F(x) holds for every x. The difference is to be found in the ω-rule.