# Your Interpretation On This Statement.

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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
Hi,

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,

I think the lecturer is right; "are restricted to" means "include only" and so "are not restricted to" must mean "do not include only".

People 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.
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I think you are right Forbes, but as Clive said, the sentence is poor English. It very much reminds one of the example that Clive gave, and you would guess that the writer meant to say that, and it would mean something very slighty different. Since the writer has not obeyed the normal conventions of standard English, and we are left to guess at his meaning somewhat, it renders the discussion a bit pointless.
Thank you for the replies. It is nice to have some different views, so we can have some discussion.

I 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)
I think we need to forget about whether or not the sentence is good English. Winsonli was attending a lesson in Logic and Critical Thinking - that includes trying to work out what poorly phrased sentences mean.

"Restrict" means to impose limits. The choice at lunch was restricted to spaghetti and salad means 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 students lies 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 license

We 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 license

We 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 mammals

Some mammals are dogs

No fish is a mammal

Or to reduce it

All x are y

Some x are y

No x is a y

However, 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 students

Can be reduced to:

Some x are y

In logic speak some x are y means y is predicated of some x or to put it another way there is at least one y which is not an x.
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Forbes
Those permitted to fly our aeroplanes are restricted to those with a pilot's license

We 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 license

We know we can have a go if we do not have a license.
As you said in the example, we know we can have a go if we do not have a license, but does this necessarily means that at least one of us without the license flied an aeroplane?

If 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.
Forbes
Those permitted to fly our aeroplanes are restricted to those with a pilot's license

We 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 license

We know we can have a go if we do not have a license.

As you said in the example, we know we can have a go if we do not have a license, but does this necessarily means that at least one of us without the license flied an aeroplane?

If 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.

You are going beyond the premise and confusing those permitted to fly with those who actually flie. You are only interested in those who actually fly if the premise is:

Those who fly our aeroplanes are not restricted to those with a pilot's license.

In that case we can see that there must be at least one person who flies who does not have a pilot's license.

The purpose of studying logic as an aid to clear thinking is so that you concentrate on the words in front of you and do not draw a conclusion that is in fact true from premises that do not support the conclusion or a conclusion that is false from premises that are true. Logic is only concerned with the validity of arguments. The first step is to make sure that you understand what a premise is saying. I came across this very good example:

The only way to be healthy is to give up smoking.

People make statements like that all the time and we often don't notice. We know what it means, but it is not what it says. There are some words missing. It ought to be:

If you smoke, the only way to be healthy is to give up smoking.

Otherwise the literal meaning is:

The only way to be healthy is to start smoking and then give it up.

I spelt "licence" wrong - I did that on purpose.
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