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Hello, this would be my first post.

I am studying in Hong Kong. In our Elements of Logic and Critical Thinking class, we are having different interpretations on an English statement. I would be grateful if you would share your ideas.

We were given the following statement:

1. People being admitted to Hong Kong University are not restricted to local students.

We were asked to convert this statement into a categorical proposition, which is a standard form of a proposition in logic. The lecturer's answer was:

2. Some people being admitted to Hong Kong University are non-local students.

The reason we think his answer was wrong is that, the second statement means that there is at least one non-local student. However, the first statement only said that the admitted students are not restricted to local ones, there do not have to be at least one non-local one.

Let me illustrate this with an example. Say HKU admitted 10 students this year, all 10 of them are local students. The fact that the admitted students "are not restricted to local students" still holds true. However, the second statement implies that there is at least one student who is not local, and thus the contradiction as all admitted students are local.

Our lecturer thinks otherwise, he believes that the first statement should be interpreted as "there is at least one non local student".

We are not trying to challenge the lecturer. After a discussion with him, we were not able to come up with a conclusion. As English is not our first language in Hong Kong, we cannot be certain on our views. He advised us to consult English teachers. It would be the best if you would advise whether:

a) Understanding the first statement as "the admitted students are not restricted to non-local students, and there do not necessarily have to be at least one non-local student, as all of them could be local ones" be correct.

and b) Understanding the first statement as "there must be at least one admitted student who is a non-local" be wrong.

Your help is much appreciated. Thank you Emotion: smile
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Comments  (Page 4) 
The snow is restricted to the high peaks by the laws of the local climate. This does not indicate snow is present.
AnonymousThe snow is restricted to the high peaks by the laws of the local climate. This does not indicate snow is present.

No, indeed.

But the statement snow is restricted to the high peaks can be reduced to only the high peaks have snow on them.
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AnonymousThe snow is restricted to the high peaks by the laws of the local climate. This does not indicate snow is present.
"The" is a definite article and I think it gives the impression that you are referring to something that was mentioned previously and therefore very likely exists. If you want to talk about the weather in the region, this may be better:

Snow is restricted to the high peaks by the laws of the local climate.

> This does not indicate snow is present at this moment.

Compare with this:

The snow that was falling in the past few days is restricted to the high peaks.

> This indicates snow is present.

The second sentence is closer in structure to the statement we were discussing. You have to look at the whole sentence. "restricted" does not indicate if snow is present, but the first part of the sentence does.

By saying that the subject does not necessarily exist because of the word "restricted", you are taking the word "restricted" out of context from a sentence that was already taken out of context.
AnonymousPerhaps hypothetical isn't quite the correct term, but it is used in rules rather than talking about concrete situations. Can you give me an example where that isn't the case?
I did a Google search and found some sentences with a similar use of the word "restricted". I would leave it to the native speakers to comment on whether they are good English. I quote them here just for illustration.

From a UK discussion forum:
Also the Geneva convention signatories were not restricted to Europeans.

==> This means some non-Europeans have signed the Geneva convention.

From "THE DEPARTMENT OF ENERGY'S ADMINISTRATIVE INQUIRY":
These names are not restricted to Chinese surnames.

==> This means some names are non-Chinese.

From the book "Towards a Transcultural Future. Literature and Society in a ‘Post’-Colonial World." by Geoffrey V. Davis
Besides, his memories are not restricted to Chinese food.

==> This means his memories include something other than Chinese food.

The Google hits are not restricted to Chinese sources.

==> This means some hits are from non-Chinese sources.
It is an interesting question. Wherever it might be talking about rules, as in the example with Chinese names, it becomes a little bit unclear what is meant. So you could argue that this concrete usage sometimes leads to ambiguity and is not good English due to that. You can find Google hits for almost anything, of course, though I would accept that it probably is reasonably common to "misuse" the word. In the example given by the OP, however, this ambiguity is certainly present, so in such a situation it is certainly a misuse of the word.
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AnonymousIt is an interesting question. Wherever it might be talking about rules, as in the example with Chinese names, it becomes a little bit unclear what is meant. So you could argue that this concrete usage sometimes leads to ambiguity and is not good English due to that. You can find Google hits for almost anything, of course, though I would accept that it probably is reasonably common to "misuse" the word. In the example given by the OP, however, this ambiguity is certainly present, so in such a situation it is certainly a misuse of the word.
None of the examples I quoted above is talking about rules. Perhaps you misunderstood that because I quoted them out of context. The whole paragraph is quote below:
http://fas.org/irp/ops/ci/bellows_chap7.html
The first reference to Wen Ho Lee's name in OEI's "Kindred Spirit" paperwork is on June 6, 1995, just days after Trulock received the memorandum from [deleted] that set KSAG into motion. Lee's name appears on a handwritten note537 which appears to have been made in connection with a meeting that day between Trulock [deleted] (DOE 1865, 2038, 1850-1852) A number of other names are listed on the note. These names are not restricted to Chinese surnames. (DOE 1854)
It was talking about a handwritten note with a list of names.

For the example of Google hits, it was
http://chi.proz.com/kudoz/1322185
Google abounds with "independent legal person qualification". However, this is the first time I've ever heard of such a phrase in English. Can it be translated simply as "It shall be a legal person".
The Google hits are not restricted to Chinese sources... so it seems there's some degree of currency (12500 hits by "independent legal person")

It was talking about a particular set of search results by searching the keyphrase "independent legal person qualification". It was not talking about what could be returned by Google.

I am not saying the quoted examples above are good English, but just that their meanings are pretty obvious.

As I have repeated several times before, the statement "People being admitted to Hong Kong University are not restricted to local students." is not written in good English, I even said that if we assume the word "restricted" is used correctly, the only conclusion is that "People being admitted to Hong Kong University" are a pool of resources. Haven't you read that?

Certainly, I wouldn't use the word "restricted" in this situation. The whole argument can be avoided if "are not restricted to" is replaced by "do not only include".
I said "wherever it might be talking about rules". I didn't say they were. However if the sentence seems to allow that possibility, then rules are what people will assume it refers to.

That is the very reason that the initial sentence represents poor English. Why do you think the original sentence is poor English?
Forbes,

I have followed your argument all the way through. I completely agree with and understand everything you've said, and I greatly admire your patience in your continued attempts to put your point across.

Nevertheless, I hit a snag on this part:

if we have the propositions:
Some teachers are jazz lovers

and

John is a teacher

The conclusion:

John is a jazz lover

is said to be false.
When I took logic, we said that it was impossible, from the argument, to determine the truth or falsity of the conclusion. It would be a matter of empirical observation to determine the truth of that conclusion. The reason is that the argument is invalid. Only valid arguments with true premisses can generate true conclusions. The conclusion statement in an invalid argument may be coincidentally true, but it can't be true by reason of the invalid argument that purports to prove it. Likewise, the conclusion may be coincidentally false, but it can't be false simply because it is the conclusion of an invalid argument.

Did I miss something in my logic class?

CJ

But "false" here just has the special meaning "cannot be derived from the propositions".
Aha! Upon rereading your post I saw this statement. However, I can't agree that sometimes 'false' has a special meaning. I think the better way to say it is that the argument is invalid and therefore the truth of the conclusion cannot be guaranteed by the argument. The truth of that conclusion must be sought in empirical observation or derived from a different, valid argument, if possible.
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CalifJim
But "false" here just has the special meaning "cannot be derived from the propositions".
Aha! Upon rereading your post I saw this statement. However, I can't agree that sometimes 'false' has a special meaning. I think the better way to say it is that the argument is invalid and therefore the truth of the conclusion cannot be guaranteed by the argument. The truth of that conclusion must be sought in empirical observation or derived from a different, valid argument, if possible.
On reflection I ought perhaps not to have said that as false does not really have a special meaning, it is rather that the word applies to the conclusion and not the statement.

Let's take the following argument:

Some politicians are Republicans

George W. Bush is a politician

Conclusion

George W. Bush is a Republican

The statement George W. Bush is a Republican is true (a correct statement of fact), but the conclusion is false (not derived from the propositions).

Let's take another argument:

All buildings in Egypt are made of bread

The pyramid of Cheops is a building in Egypt

Conclusion

The pyramid of Cheops is made of bread

In this case the statement The pramid of Cheops is made of bread is false (an incorrect statement of fact), but the conclusion is true (derived from the premises).

I have been trying to emphasise that logic is concerned solely with the validity of arguments. A logical argument is one in which if the premises are true (i.e correct statements of fact), then the conclusion must be true (i.e. a correct statement of fact). However, an argument in which both the premises and the conclusion happen to be true (i.e. correct statements of fact) is not necessarily a logical argument.
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