I have been thinking about all of this for some time now and I believe I have come to understand it a little bit better -- although still not fully. Here is what I think. It's going to be long so I will understand if nobody reads it, but I do hope somebody does.
The main question is
Why can't we say, "Either man is rich"?
We can say
1) Both men are rich.
or
2) Every one of the two men is rich.
(the last being awful, but meaningful and grammatical) but
3) Either man is rich.
doesn't sound right However, we can say either of the following.
4) Either man can help you.
5) Both men can help you.
and perhaps
6) Every one of the two men can help you.
The problem of these three sentences is particularly difficult for me because they don't want to fit my newly created theory (newly for me obviously -- if it's anywhere near the truth, someone has certainly thought of this before). I will leave them for now. I'd like to take a look at some other sentences first.
"Either", "both" and "every one of the two" clearly refer to two objects. It seems natural to me to try to find their "more plural" counterparts and try to find an explanation that would encompass those too. I think those counterparts are, respectively, "any", "all" and "every". I think
either =
any of the two
both =
all of the two
and, well,
every one of the two =
every one of the two
since there is no specifically dual version of "every". This doesn't seem to be a problem though because "both" serves this purpose well. It does differ from "every" in that it is plural as a pronoun and takes plural nouns as a modifier -- unlike "every". It doesn't seem to affect the meaning very much though. It looks as if
Both man are rich. =
Every one of the two men is rich.
I think this leaves us with the necessity of comparing these two groups of words
either,
any
and
both, every.
Let's focus on "any" and "every" first. The following sentences are correct.
7) I do not see any cat.
8) I do not see every cat.
These sentences clearly mean two different things. Suppose we have an enumeration of
all cats in the world. Let's denote the number of all cats by
n (which must be, of course, the number of the last cat in our enumeration.)
Then, I think, 7) means exactly the same as
(It is not true that I see cat number 1
) and (it is not true that I see cat number 2
) and ...
and (it is not true that I see cat number n
).
and 8) means exactly the same as
It is not true that [(I see cat number 1
) and (I see cat number 2
) and ...
and (I see cat number
n)
].
Whoever remembers De Morgan's laws will recognize these two as different. The first tells us that there is no cat that I see. The second tells us that there is at least one cat that I don't see. Anyway, what seems important to me is that the two differ
only in the placement of "it is not true that".
Let's call
atomic the statements
I see cat number 1.
I see cat number 2.
...
I see cat number n.
Let's call "it is not true that" an
operator. Then 7) applies the operator "it is not true that" to
every atomic statement and then "ands" them all together, 8) first "ands" the atomic statements together and then applies the operator "it is not true that" to the resulting big "anded" statement.
Let's take next two sentences..
9) Any boy in this room may be your brother.
10) Every boy in this room may be your brother.
The second sentence seems ambiguous to me, but it apparently doesn't seem such to
Robert Stoothoff. I will use what I understand to be his understanding (note that I can see only the first page of what I have linked to though), at least for now.
Again, let's imagine the boys are enumerated and there are
n of them. Then, I think, 9) means exactly the same as
(It may be that boy number 1 is your brother
) and (it may be that boy number 2 is your brother
) and ...
and (it may be that boy number
n is your brother
).
and 10) becomes
It may be that [(boy number 1 is your brother
) and (boy number 2 is your brother
) and ...
and (boy number
n is your brother)
].
If we call "it may be that" an operator and if we call atomic the statements
Boy number 1 is your brother.
By number 2 is your brother.
...
Boy number n is your brother.
then we can see that the structures are analogous to the stractures that we produced for 7) and 8).
If we accept all that has been said so far, we can make a hypothesis that when there is in a sentence something that works like "it is not true that" or "it may be that" (we may agree to call this something an operator) then what happens when "any" is present is
1. we generate a number of statements that we call atomic;
2. we apply the operator to every atomic statement;
3. we "and" the resulting statements together.
What happens when "every" is present is
1. we generate a number of statements that we call atomic;
2. we "and" the atomic statements together;
3. we apply the operator to the resulting statement.
The first step in both doesn't seem real to me. It's an auxiliary step which is there merely to make the analysis easier. The other steps seem to be actually occuring in our sentences. I think it makes sense to say that
- step 2 of the first list and step 3 of the second are simply "what the operator does";
- step 2 of the second list and step 3 of the first are simply "what 'any' and 'every' do".
The simple conclusion would be that "any" works after operators and "every" works before them.
Now, of the two following sentences, only the first sounds right.
Everyone is in the living room.
Anyone is in the living room.
The only thought these two could express is
(The person number 1 is in the living room
) and (The person number 2 is in the living room
) and ...
and (The person number
n is in the living room)
There is nothing here that looks like an operator so we cannot make the distinction we made before. But "any"
needs an operator to work before it. Therefore,. "any
" cannot be used here.
I think it's clear what I want to do next. "Either" is a dual version of "any" and "both" is a dual version of "every" (although it's different in the grammatical number), so the same hold s for them. We can't say
Either man is rich.
because there is no operator in this sentence and "either", like "any" needs an operator.
I'm very tired now, so I won't get back to 4), 5) and 6). I will appreciate and try to understand any comments on what I've written and on what I haven't. I'm not satisfied with the above. It's too long, inelegant (although much more elegant than my previous thoughts) and doesn't answer all the questions I can ask about this (and probably others, which I can't ask).
.
Furthermore, I just plagiarised fivejedjon's reply to a similar post. ;-)
