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

Welcome to the Forum.

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. I agree with your interpretation.

I think the confusion may partly arise from the fact that the first statement is not written in good English. It's not people who are restricted, it's admission that is restricted. I'd write it as Admittance to Hong Kong University is not restricted to local students. When you consider this form of the statement, it's clearer that the statement is just about the policy. There may be no non-local students, and perhaps even no local students. Maybe the University has no students at all. The statement gives us no information about the actual students.

Best wishes,Clive,

ClivePeople being admitted to Hong Kong University are not restricted to local students.Is therefore the same as:

People being admitted to Hong Kong University do not include only local students.Since "include only local students" means "all those included are local students", "do not include only local students" must mean "not all those included are local students".

People being admitted to Hong Kong University do not include only local students.Is therefore the same as:

Not all of the people admitted to Hong Kong University are local students.i.e. at least one of them is a person who is not a local student.

ForbesJon SaltI agree that this sentence is written in poor English.

However, I disagree with Forbes. I believe "are restricted to" should not be understood as "include only". I've looked up the dictionary and "restricted" is explained as "limited".

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

Would become:

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

The statement does not imply that there must be at least one admitted student who is a non-local.

I would love to hear more opinions. Thanks you

(post edited for logical mistakes)

Winsonli"Restrict" means to impose limits.

The choice at lunch was restricted to spaghetti and saladmeans that only spaghetti and salad were available. Suppose that the choice was always between spaghetti and salad, but one day there was suddenly a wide choice of dishes; you may write home and say:For a change, the choice at lunch today was not restricted to spaghetti and salad. The meaning is surely clear: the choices included spaghetti, salad and something else.The problem in grasping the meaning of

People being admitted to Hong Kong University are not restricted to local studentslies I think in the use of a negative with "restricted". If you take out the "not" you have a sentence that clearly means that only local students are admitted. If you put the "not" back in you must change the meaning.The structure may appear clearer in the following:

Those permitted to fly our aeroplanes are restricted to those with a pilot's licenseWe know it is no use asking to fly if we do not have a license.

Those permitted to fly our aeroplanes are not restricted to those with a pilot's licenseWe know we can have a go if we do not have a license.

When introduced to logic, statements are usually presented in forms such as:

All dogs are mammalsSome mammals are dogsNo fish is a mammalOr to reduce it

All x are ySome x are yNo x is a yHowever, in "real life" assertions people make do not always appear in such convenient packages and you have to reduce them to a form that you can "play with." As I hope I have shown:

People being admitted to Hong Kong University are not restricted to local studentsCan be reduced to:

Some x are yIn logic speak

some x are ymeansy is predicated of some xor to put it another waythere is at least one y which is not an x.ForbesIf a license is not needed to fly an aeroplane, and we gather all people who flied and is flying an aeroplane. Say there are 1000 of them. If 999 of them have a license, does it conclude that one does not have a license? I think not.

If my reasoning and examples are flawed, please point them out. Thank you.

WinsonliForbesForbes