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

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

Comments (Page 2)

If only 1 people who actually flies, does this necessarily means that he does not have a pilot's license? If I were given this statement, I would conclude that I am not a healthy person, as I didn't give up smoking. I did not give up smoking as I did not even smoke in the first place.

As you said, we know what it means, but we do not know what it says. I believe we should interpret it as what it says, instead of what we know it means. We should not try to understand it in the way the speaker intended it to mean, it is the speaker's responsibility to ensure the statement tells what he wants to tell.

Please point out the flaw in this reasoning:

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

Firstly, there is a rule stating that "people who can be admitted to HKU are not restricted to local students".

Secondly, even if the admitted students are all local students, the rule still stands.

Thirdly, 10 students were admitted in accordance to the rule. Only 10 students were admitted.

Therefore, all admitted students could be local ones, and there do not necessarily have to be one non-local student.

WinsonliPeople being admitted to Hong Kong University are not restricted to local studentsis simply a statement about who is admitted.If the statement

All students admitted to Hong Kong University are local studentsis true then the statementPeople being admitted to Hong Kong University are not restricted to local studentscannot be true.If it is the case that there is a rule that says:

people who can be admitted to HKU are not restricted to local studentsthen whoever is admitted does not change the rule and the rule will not tell us who is at HKU - only a statement about who is at HKU tells us who is at HKU.People being admitted to Hong Kong Universityis a group of people and so islocal students.The statementPeople being admitted to Hong Kong University are not restricted to local studentstells us how those two groups relate to each other. If we replacePeople being admitted to Hong Kong Universitywith X andlocal studentswith Y we getX are not restricted to Y. If you accept thatare not restricted tois equivalent todo not include only,then we getX do not include only Ywhich meansX include Y plus at least one other person who is not a Y.If we put the words back into that we getPeople being admitted to Hong Kong Universityincludelocal students plus at least one other person who is not a local student.ForbesJon SaltI believe I have complicated the matter by talking about rules. I'm afraid I have to disagree. I believe the latter statement cannot be true only if the former statement is "All students admitted to Hong Kong University are restricted to local students".

I do not think "not restricted to" is equivalent to "do not include only". What do you think about understanding "not restricted to" as "not necessarily is"?

anonymousI think I have complicated the matter by talking about rules. I'm afraid I have to disagree. I believe the latter statement cannot be true only if the former statement is "All students admitted to HKU are restricted to local students".

I do not think "not restricted to" is equivalent to "do not include only". "Restricted" talks about where things cannot be, while "include only" is certain that at least one thing is in the group. What you you think about explaining "not restricted to" as "not necessarily is"?

WinsonliMembership is restricted to graduatesmeans only graduates can be part of the membership or the membership includes only graduates. If the statement is negatedMembership is not restricted to graduatesit must mean something different i.e. not only graduates can be part of the membership or the membership does not include only graduates. I think that part of the problem lies in that "restricted" has a something of a negative feel about it and it is therefore puzzling to work out exactly what "not restricted" means - I am sure that is why your lecturer chose the sentence.An analysis of "is not necessarily" will lead to the same result; think what

Members are not necessarily graduatesmeans.People being admitted to Hong Kong University are not restricted to local students.

and

Some people being admitted to Hong Kong University are non-local students.both convey the same information.

anonymousMembership is restricted to graduatesmeans only graduates can be part of the membership or the membership includes only graduates. If the statement is negatedMembership is not restricted to graduatesit must mean something different i.e. not only graduates can be part of the membership or the membership does not include only graduates. I think that part of the problem lies in that "restricted" has a something of a negative feel about it and it is therefore puzzling to work out exactly what "not restricted" means - I am sure that is why your lecturer chose the sentence.An analysis of "is not necessarily" will lead to the same result; think what

Members are not necessarily graduatesmeans.People being admitted to Hong Kong University are not restricted to local students.

and

Some people being admitted to Hong Kong University are non-local students.both convey the same information.

Forbessee, but until then s/he will continue to think that it is I and the lecturer who cannot think straight.ForbesI understood "not restricted to" as "no restriction", which is wrong. I realized that when you mentioned the term "negated".

People being admitted by HKU are not restricted to local students.

"People being admitted to HKU are restricted to local students" means "non-local students were not be admitted", and negating it becomes "non-local students were being admitted".

So at least one non-local student was admitted.

It is possible that all admitted students are non-local.

It is not possible that all admitted students are local.

If only one student was admitted, he is non-local.

If only ten students were admitted, nine students being local implies that the other one must be non-local.

What I understood incorrectly by "not restricted to" was "admitted students may or may not be local", and if we negate that it becomes "admitted students may not or may be local", which is not the meaning of the original statement.

I still have some questions though. When we negate "only", it becomes "not only", and that means "some of the other kind are", is that right?

Thank you all for the explainations, especially Forbes

Winsonli