(Still confused.) Then it is possible to say, in principle, “for every combination of n out of the whole set of n, property(x) hold)” and mean ordered combinations? Is there any other meaning for “every 30 out of 30″?
(yes, it is probably because of my language background. I don’t even use the Russian analogues all that often!)
It is possible to say that, but the work is being done by “combination.” You can also say “for every permutation of n” and that means something different.
Typically when you say “for every x out of 30, property(x) holds” it means something like:
“every poster on lesswrong is a human being” (or more formally, “for every poster on lesswrong, that poster is a human being.” (Note, this statement is meaningful but probably evaluates to false.)
Quantification is always over a set. If you are talking about permutations, you are first making a set of all permutations of 30 things (of which there are 30 factorial), and then saying “for every permutation in this set of permutations some property holds”).
edit: realized your native language might be Ukrainian: I think a similar issue exists in Ukrainian quantifier adjectives.
And then, Ukrainian too has всяк/усякий (всякий) that is different from кожен (каждый)… If I were to translate усякий into English distinctly from both “every” and “any”, I would probably have to say “of all kinds”, but how do you say that about one thing?! anyway, this is silly.
(а мой “исходный” язык - русский + татарский + украинский. Даже не помню, что там в татарском делается.)
(Still confused.) Then it is possible to say, in principle, “for every combination of n out of the whole set of n, property(x) hold)” and mean ordered combinations? Is there any other meaning for “every 30 out of 30″?
(yes, it is probably because of my language background. I don’t even use the Russian analogues all that often!)
It is possible to say that, but the work is being done by “combination.” You can also say “for every permutation of n” and that means something different.
Typically when you say “for every x out of 30, property(x) holds” it means something like:
“every poster on lesswrong is a human being” (or more formally, “for every poster on lesswrong, that poster is a human being.” (Note, this statement is meaningful but probably evaluates to false.)
Quantification is always over a set. If you are talking about permutations, you are first making a set of all permutations of 30 things (of which there are 30 factorial), and then saying “for every permutation in this set of permutations some property holds”).
edit: realized your native language might be Ukrainian: I think a similar issue exists in Ukrainian quantifier adjectives.
And then, Ukrainian too has всяк/усякий (всякий) that is different from кожен (каждый)… If I were to translate усякий into English distinctly from both “every” and “any”, I would probably have to say “of all kinds”, but how do you say that about one thing?! anyway, this is silly.
(а мой “исходный” язык - русский + татарский + украинский. Даже не помню, что там в татарском делается.)
Крымская tатарка?
Я одессит, родился в Крыму.
Русская киевлянка, первые 4 класса училась в Казани. Татарский, говорят, сильно отличается от крымско-татарского.
It is very annoying that
любой is translated both as “any” and “every.”
какой-либо is closer to formal logical “there exists” or “any.”
It is also very annoying that I know damn right what I mean by любой, and so does любой with whom I speak.
Sometimes, it seems to me that English is just too precise. Or maybe it’s just me.
In Ukrainian, we have жодний, which means “none of the above” or smth like it… now that’s a word worth having!