ambiguity, scope

[Jaskin]

Hi,

Some cat is feared by every mouse.

Is that sentence in anyway to anyone here ambiguous ?

Cheers

 

[emsr2d2]

It's ambiguous and unnatural. What do you mean by "Some cat"? Do you mean "Some cats" (ie "not all cats")? Do you mean "Some cat or other" (ie an unspecified individual cat).

If you mean "All mice are scared of cats" then just say that. I see no reason to make it more complicated.

 

[Roman55]

Is that sentence in anyway to anyone here ambiguous?

I am not a teacher.

Any way should be two words.

 

[Raymott]

Some cat is feared by every mouse.

Yes, it's a simple example from logic. The two possible meanings are:
1. There exists a cat which is feared by every mouse.
2. For every mouse, there is some cat that the mouse fears. (There is no mouse which does not fear at least one cat).

 

[Jaskin]

Hi,
I'm aware where the example is coming from and that it is unnatural; somehow I still fail to notice the second interpretation that Raymott listed.
If we use a bit more natural sounding sentence 'every mouse is afraid of some cat' is the ambiguity still preserved ?

Cheers

 

[Roman55]

I am not a teacher.

The two sentences have the same meaning. Some cat is feared by every mouse = Every mouse is afraid of some cat.

It's some cat that poses the problem. It either means an unspecified, unnamed yet particular cat, or any one of the set of unspecified unknown cats (but not the same one in each instance).

 

[Jaskin]

Hi,

The thing I'm trying to wrap my head around is that Polish, my native language, is nearly totally free word order language whereas in English the word order is more restricted hence I was just wandering whether the order of the sentence, in case of the two sentences, will have an influence on its meaning.

It's like with the temporal relation that is expressed by the conjunction 'and' in natural languages where the order indicates what happen first; even though in formal logic the propositions are equivalent. With the classic example being 'she got pregnant and got married' vs 'she got married and got pregnant.'
But by what you saying is that there is no difference in possible interpretation, by putting the equality sign between the two sentences.

Yet my seems to not very well developed language intuition is telling me that the two sentences would have different 'gut','first' interpretation.
Some cat is feared by every mouse. <=> There exists a cat which is feared by every mouse.
Every mouse is afraid of some cat. <=> For every mouse, there is some cat that the mouse fears.

Is the ambiguity very apparent for native speakers ?


Cheers,

 

[SoothingDave]

No, the word order doesn't change the meaning. The ambiguity is whether the "some cat" that every mouse is afraid of is the same cat for all of them.

1. There exists one cat, a particular cat, that every mouse in existence fears. A million mice all fear the same one cat.

2. There is a cat that every mouse fears, but not the same cat for every mouse. A million mice fear a million different cats, or a thousand different cats. But each fears at least one.

 

[Rover_KE]

What prompted your question, Jaskin?

Where did you encounter the very odd sentence 'Some cat is feared by every mouse'.

 

[Jaskin]

Hi,

I'm preparing myself for a few hard reads in philosophy of language, philosophical logic and mathematical logic. I printed a Wiki book 'Logic and metalogic' to have a general overview, and while reading it I followed a link to, in my opinion rather badly written, entry in Wikipedia on the problem of multiple generality. That's where the sentence with 'some cat [..]' comes from.

Cheers,

 

[emsr2d2]

It would have been helpful if you had put a link to that Wikipedia entry in your first post.

 

[Raymott]

The sentence is ambiguous. It's supposed to be.
It comes from First Order logic, which uses an existential quantifier (some), and a universal quantifier (all). In formal logic, there is an order in which the terms have to be set out to give a non-ambiguous meaning. This sentence is an example of one that might be given to a student as an exercise in disambiguation.
If you are going to learn formal logic - which is a fine thing to do - yes, you will have to recognise an ambiguous sentence in English if you are to disambiguate it with symbols, or natural language.

Actually, I will show the symbols. The above means "(If the proposition P(x) does not apply to All x) then this implies that (there exists an x for which the proposition P(x) does not apply).
http://en.wikipedia.org/wiki/First-order_logic
I was hoping the cat example would be on that page, but it's not.

 

[MikeNewYork]

My main problem with the sentence is that it is impossible. Trying to explain it with logic seems to be, in itself, illogical. There is no cat on the planet that has been in contact with every mouse. So every mouse cannot fear a particular cat. For the second, I am quite certain that there are some mice on the planet that have not encountered any cat. It would only take one such mouse to make the second interpretation false.

 

[Raymott]

English, as I guess most languages, does not have a problem with this.
It is very simple logically to consider the possible meanings of the sentence "All mice are afraid on some cat", even though it's impossible to interview every mouse to ascertain the truth of the assertion. As far as language is concerned, the impossibility of a proposition contained in a sentence is almost irrelevant.
"All mice are afraid of some cat" means "There is no mouse which is not afraid of some cat" in English - despite the impossiblity of ascertaining the truth of it. The truth of a sentence has no necessary bearing on its meaning.

 

[Jaskin]

Hi,
I didn't put the link in my first post as I didn't intent to discuss it in terms of predicate logic. I got some training in mathematics so I'm familiar with quantifiers but I learnt it previously to English language. I've just recently started getting back to the problems of logic and philosophy of language but in English only.

So I'm more interested with ambiguity or disambiguation in natural language, that's English. Some examples are quite simple to grasp; but not the one with 'some cat'.
In every day life the ambiguity is ruled out by context alone or situation of an utterance.
Let's take: (I'll replace the 'some' to perhaps more natural sounding 'there is ')
There is chocolate for all of you.
There is chocolate for each of you.
There is chocolate for every one of you.
I think the first is the most ambiguous in the same way or in the same sense as the unfortunate example with cat. The last one I find to be the least ambiguous.
How to disambiguate such statement in natural language ? Is there any good literature on that ?

Cheers


PS. I think there was and still is a point in discussing sentences such as the famous 'colourless green ideas sleep furiously' or 'apples grows on noses'. Even though the sentences are completely nonsensical. I think it is their nonsensical nature that helps us to focus on its structure without being to distracted with its actual meaning.

Whether something stands contrary to the factual information of the world we might have (what I understand Mike is talking about), may be in some discussions irrelevant. Interestingly it's exactly where and where we start talking about the impossible or non-existing entities where most models of language collapse and where in logic the paradoxes start surfacing.

 

[Jaskin]

Hi,

My main problem with the sentence is that it is impossible. Trying to explain it with logic seems to be, in itself, illogical. There is no cat on the planet that has been in contact with every mouse. So every mouse cannot fear a particular cat. For the second, I am quite certain that there are some mice on the planet that have not encountered any cat. It would only take one such mouse to make the second interpretation false.

It's quite easy to make the sentence sensible, meaningful or possible just by restricting what we talking about; let say some cat,a cat or cats and all or every mice in a specific barn. Let's even make that sentence more natural; I'm not sure if I manage but I'll do my best. Note that it's still a contractual sentence; I don't rally have a barn.

In my barn, every mouse is afraid of some cat.
In my barn, some cat is feared by every mouse.
In my barn, all mice are afraid of some cat.

Are those sentences still equally ambiguous ?
@moderators : Please do not close my thread ... if you think due to the subject and nature of the discussion it might need moving to general language discussion that's fine but please don't close it.

 

[MikeNewYork]

Good. By restricting the universe to a barn, you have made the sentences possible. Using practical knowledge, one can assume that there is more than one cat in your barn and more than one mouse in your barn. This is supported by your articles/determiners. If there were only one cat, one would say "the" cat. Your use of "all" and "every" means that there is more than one mouse.

1. Every single mouse is afraid of one or more cats.
2. Every mouse is afraid of one particular cat or one of a number of cats.
3. Same as number 2.

At least that is my analysis. If you change the universe to include outside cats, it is not so clear. If you change "some cat" to "some cats", the meaning changes.

 

[Raymott]

There is chocolate for all of you.
There is chocolate for each of you.
There is chocolate for every one of you.
I think the first is the most ambiguous in the same way or in the same sense as the unfortunate example with cat. The last one I find to be the least ambiguous.
How to disambiguate such statement in natural language ? Is there any good literature on that ?

They all mean practically the same thing to me. I don't see how "There is chocolate for all of you" is ambiguous like the 'cat' sentences.
To me, it only means one thing. "None of you need/will go without chocolate." What do you see as an alternative meaning?

 

[Jaskin]

Hi,

They all mean practically the same thing to me. I don't see how "There is chocolate for all of you" is ambiguous like the 'cat' sentences.
To me, it only means one thing. "None of you need/will go without chocolate." What do you see as an alternative meaning?

But is the meaning you see matter of formal logic interpretation or pragmatic implicature? The pragmatic implicature wasn't so obvious with 'some cat' example.
It's in the same sense as cat example because there is the 'some chocolate', 'all of you' and functional connective in between.

There is some chocolate (one bar) or so you must decide who will get it.

@ Mike
Using practical knowledge, one can assume that's would be pragmatics. I'm more concerned with situation where there is no practical knowledge to relay on, and I don't want to make assumptions either. I'm interested in the intersection in between the pragmatics and pure logic consideration.

This is supported by your articles/determiners. that's where my problem might steam from in the first place. Polish doesn't have articles.

Cheers

 

[Raymott]

But is the meaning you see matter of formal logic interpretation or pragmatic implicature?
Er ... the meaning I saw in that sentence was purely from experience of the language. I guess that's pragmatic implicature.

The pragmatic implicature wasn't so obvious with 'some cat' example.
Maybe. I'd put it that there were two possible pragmatic meanings in the 'cat' example.

It's in the same sense as cat example because there is the 'some chocolate', 'all of you' and functional connective in between.
There is some chocolate (one bar) or so you must decide who will get it.

No, I don't think you can infer that. "There is chocolate for all of you" has the pragmatic meaning that there's enough to go around. It can't mean "There is some chocolate for all of you to fight over."
Since language isn't always logical, there's a limit to how strictly you can apply formal logic to any sentence. That's a question for a logic forum. But I can't imagine how I'd format the chocolate sentence into two credible logical formulae that were different, whereas in the 'some cat' example, it's simple.