# re: Your Interpretation On This Statement.page 3

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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
But Forbes, the word "restricted" is basically only used for hypothetical situations. So one half of the sentence is real, and the other unreal. Therefore the sentence means nothing much at all.
Why do you think 'restricted' is only for hypothetical situations? This isn't the case.
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Perhaps 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?
Hi Winsonli,

As Clive has already mentioned, the statement was not written in good English. Since it was taken out of context, we can only guess what it means by making different assumptions. Some may interpret this statement as talking about the admission policy, however, it could also be interpreted as a statement of fact. A statement about a group of people who are "being admitted to Hong Kong University".

If it is talking about an admission policy and there is not a single non-local student, this policy is certainly not an effective one, although you can argue from pure logic that the policy does not imply there must be at least one non-local student. In fact, you can even argue that the statement does not imply there is any student in the university at all. In predicate logic, a universal quantifier does not assert the existence of a subject.

However, because the sentence starts with "People being admitted .... are ....", I would interpret that as saying "Some people are being admitted to Hong Kong University" and the rest of the sentence as describing this group of people. "Some people are being admitted" obviously means there are at least two people being admitted. In predicate logic, this statement has existential import, and asserts the existence of the subject.

I absolutely agree with what Forbes said and I think your lecturer is right.

P.S. I am also from Hong Kong but not a native speaker.
Just want to elaborate a little more.

If you want to talk about the admission policy, you should use
People who can be admitted to Hong Kong University ....
If you want to talk about what actually happened in the past, you should use
People admitted to Hong Kong University ....
"People being admitted to Hong Kong University are ...." means that HKU is still taking in new students. The statement would simply be false if no non-local students are being admitted.
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I think that Petr has hit the nail on the head. We are talking about classes. "People who are admitted" and "people who can be admitted" are two different classes of people.

I also think that part of the problem is that beginners in logic have a problem with the words "some" and "false".

All teachers are jazz lovers tells us that the class of teachers is contained wholly within the class of jazz lovers. Show me a teacher and he will be a jazz lover.

No teachers are jazz lovers tells us that the class of teachers is not to be found in the class of jazz lovers. Show me a jazz lover and he will not be a teacher.

Some teachers are jazz lovers tells us that the classes of teachers and jazz lovers overlap, but not to what extent. All we know is that at least one teacher is a jazz lover and that at least on jazz lover is a teacher.

In diagrammatic form, where T = teachers and J = jazz lovers:

[url=http://xs.to ][/url]

The top diagram represents All teachers are jazz lovers. We can see the circle of teachers is wholly within the circle of jazz lovers.

The middle diagram represents No teachers are jazz lovers. We can see that you have to be in one circle or the other.

The lower digram represents Some teachers are jazz lovers. We can see that the two circles overlap. However, if all we are told is that X is a teacher, all we know is that he comes in the teachers' circle; we do not know if he comes in the shaded part.

So, 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.

This puzzles some people because (whilst they will concede that John is a jazz lover cannot be asserted from the propositions) they will argue (looking at the lower diagram) that John may come in the shaded area and that to say "John is a jazz lover is false" cannot be right as there is a possibilty that John may come in the shaded area and be a jazz lover; it seems as if saying that the conclusion is false is the same as saying that John cannot be a jazz lover. But "false" here just has the special meaning "cannot be derived from the propositions".
A quick note on the side issue of the use of 'restricted'.

It doesn't only apply to rules. Example

During the summer months, snow is restricted to mountain peaks over 3000m, so you won't have any problem driving through the pass.
Nona The BritA quick note on the side issue of the use of 'restricted'.

It doesn't only apply to rules. Example

During the summer months, snow is restricted to mountain peaks over 3000m, so you won't have any problem driving through the pass.
Similar, we can say a disease, a condition, an effect, etc. is not restricted to certain people or location. However, I think this is not what he is asking.

Winsonli, as it was pointed out from the very beginning, the sentence was not written in good English. I think you are not going to learn anything by drilling on the implication of the use of "restricted" in this sentence. If you must, I can only say "People being admitted to Hong Kong University" are a pool of resources that are restricted (only accessible) to local students!
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I find it irritating that the forum just accepts anonymous postings without asking me to log in. This is re-posted after logging in.
Nona The BritA quick note on the side issue of the use of 'restricted'.

It doesn't only apply to rules. Example

During the summer months, snow is restricted to mountain peaks over 3000m, so you won't have any problem driving through the pass.
Similar, we can say
A disease, a condition, an effect, etc. is not restricted to certain people or locations.
A resource is restricted to some people.

However, I think this is not what he is asking.

Winsonli, as it was pointed out from the very beginning, the sentence was not written in good English. I think you are not going to learn anything by drilling on the implication of the use of "restricted" in this sentence. If you must, I can only say "People being admitted to Hong Kong University" are a pool of resources that are restricted (only accessible) to local students!