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Anonymous Posted 15 years ago
Science & IT
Quantifier changes when statement is posed as a question rather than statement?
I noticed this slight discrepency when I was doing homework for my discrete math class when we were studying predicate logic. Is it me or does the quantifier sometimes change when posing a statement as a question? For example, let's say we have the predicate function:
P(x) = x is in this room and can speak Japanese
then the question "Is there a person in this room that can speak Japanese?" is basically asking ExP(x) or "is there at least one person x, where x is in this room and can speak Japanese?" (Sorry, I couldn't find the backwards E character for the existential operatior.)
However, when posing the question as it's corresponding statement, "There is a person in this room that can speak Japanese," it hints that the quantifier is different. When a phrase like this is said, does that mean that there is one and only one person in the room that can speak Japanese? That is the sense that I am getting. Basically, does the phrase equate to E!x(P(x))?
Is it just me or does it seem strange that we use different quantifiers when we pose a statement into a question. The question asks if there is at least one person, while the statement makes it seem like there is one and only one person. I find this nuance in the English language to be quite perplexing.
P(x) = x is in this room and can speak Japanese
then the question "Is there a person in this room that can speak Japanese?" is basically asking ExP(x) or "is there at least one person x, where x is in this room and can speak Japanese?" (Sorry, I couldn't find the backwards E character for the existential operatior.)
However, when posing the question as it's corresponding statement, "There is a person in this room that can speak Japanese," it hints that the quantifier is different. When a phrase like this is said, does that mean that there is one and only one person in the room that can speak Japanese? That is the sense that I am getting. Basically, does the phrase equate to E!x(P(x))?
Is it just me or does it seem strange that we use different quantifiers when we pose a statement into a question. The question asks if there is at least one person, while the statement makes it seem like there is one and only one person. I find this nuance in the English language to be quite perplexing.
Top answer
Hi I'm not quite sure, but I think this is partly to do with designation. " then you mean the one unique thing that you are pointing out ("I know one person in this room who can speak Japanese and there he is"). x) but in fact you are not ruling out the possibility that there are others (Ex) If I go into a room and say..
- Hi I'm not quite sure, but I think this is partly to do with designation.
- " then you mean the one unique thing that you are pointing out ("I know one person in this room who can speak Japanese and there he is").
- x) but in fact you are not ruling out the possibility that there are others (Ex) If I go into a room and say..
- - There's a cat in this room!
- x)Cx.
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2 Answers
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Hi
I'm not quite sure, but I think this is partly to do with designation. If you point to one thing or person and say "There is a..." then you mean the one unique thing that you are pointing out ("I know one person in this room who can speak Japanese and there he is"). So it can sound as if you mean (E!x) but in fact you are not ruling out the possibility that there are others (Ex)
I'm not quite sure, but I think this is partly to do with designation. If you point to one thing or person and say "There is a..." then you mean the one unique thing that you are pointing out ("I know one person in this room who can speak Japanese and there he is"). So it can sound as if you mean (E!x) but in fact you are not ruling out the possibility that there are others (Ex)
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Thanks for your insight! (This is the original poster by the way.) The reason why I asked is because I had a few problems I had to translate from English to predicate logic notation that started with something like "There is a.." and ambiguity threw me off. But I get what you mean now in the sense that (in some cases) "There is a..." could mean that (E!x)P(x) may be true but it doesn't rule
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