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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 2) 
Thanks for the reply, Forbes.
ForbesYou 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.
I understand what you mean. I understand that I should be only interested in those who actually fly. Still, I do not see what it necessarily means there must be at least one person who flies who does not have a pilot's license. Is this how I should interpret this whole statement? Or did the phrase "restricted to" imply that there is at least one person who flies who does not have a pilot's license.

If only 1 people who actually flies, does this necessarily means that he does not have a pilot's license?
ForbesThe only way to be healthy is to give up smoking.
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.
Now you are bringing rules into it! There is no mention of rules. People being admitted to Hong Kong University are not restricted to local students is simply a statement about who is admitted.

If the statement All students admitted to Hong Kong University are local students is true then the statement People being admitted to Hong Kong University are not restricted to local students cannot 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 students then 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 University is a group of people and so is local students. The statement People being admitted to Hong Kong University are not restricted to local students tells us how those two groups relate to each other. If we replace People being admitted to Hong Kong University with X and local students with Y we get X are not restricted to Y. If you accept that are not restricted to is equivalent to do not include only, then we get X do not include only Y which means X include Y plus at least one other person who is not a Y. If we put the words back into that we get People being admitted to Hong Kong University include local students plus at least one other person who is not a local student.
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Yes, Forbes, true, but again, in reality probably nine times out of ten the person writing the statement will actually mean something they didn't actually say, that being the statement that Clive said. It isn't a good way to begin a logic problem, is it now?
Thanks for the replies.

I believe I have complicated the matter by talking about rules.
ForbesIf the statement All students admitted to Hong Kong University are local students is true then the statement People being admitted to Hong Kong University are not restricted to local students cannot be true.

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"?
Thanks for the replies.

I think I have complicated the matter by talking about rules.
ForbesIf it is the case that there is a rule that says: people who can be admitted to HKU are not restricted to local students then 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.
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"?
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The basic meaning of "restrict" is "to keep within limits". Membership is restricted to graduates means only graduates can be part of the membership or the membership includes only graduates. If the statement is negated Membership is not restricted to graduates it 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 graduates means.

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.
The basic meaning of "restrict" is "to keep within limits". Membership is restricted to graduates means only graduates can be part of the membership or the membership includes only graduates. If the statement is negated Membership is not restricted to graduates it 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 graduates means.

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.
Jon SaltYes, Forbes, true, but again, in reality probably nine times out of ten the person writing the statement will actually mean something they didn't actually say, that being the statement that Clive said.
Precisely! That is why there are classes in Elements of Logic and Clear Thinking.
Jon Salt It isn't a good way to begin a logic problem, is it now?
"Logic problems" that fill magazines you can buy at the newsagent all have their propositions set out in a neat form. The course seems to have got to the stage where they are converting the sort of statements that people tend to make into categorical propositions. As this thread demonstrates, that process can lead to results that are counterintuitive. There will come a moment when Winsonli will see, but until then s/he will continue to think that it is I and the lecturer who cannot think straight. Emotion: big smile
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Thanks for the explanation. I think I understand it now.

I 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 Emotion: smile
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