"a special case of" or "the special case of"

[zorank]

Which version is correct?

 

[emsr2d2]

Which version is correct?

Context is vital in language questions. Please post a whole sentence involving each version, as you did with the lawnmower question, and then we will be able to give our opinions.

Also, follow the advice given in your other question, about using COCA.

 

[zorank]

Ok, this means it can be both.

The real example is from mathematics. I will try to construct an equivalent non mathematical example and post it. More later...

 

[zorank]

"Being mad is a special case of being angry in general."

"Being manodepressive is a special case of schizophrenia." (Have no clue if this is actually true).

Would this make sense?

 

[5jj]

"Being mad is a special case of being angry in general."

"Being manodepressive is a special case of schizophrenia." (Have no clue if this is actually true).

Would this make sense?

In the first, 'the' is not appropriate; there may well be other cases of 'being angry'.
The second is a pointless example. We can give you a sensible answer only if we are dealing with an authentic utterance.

 

[zorank]

Okay, I start to see, I think:

X is a special case of Y.

This implies that Y has many realizations and X is one of them.

If there are many cases of something, i..e Y, then one should use "a", but if there is only one modification (or case) then one should use "the".

Is this correct?

For example, this should be correct I presume

"The circle is the special case of the elipse."

the = to emphasize class; hope this usage of "the" is correct.

Since there is more or less only one way of making an elipse into a circle. Right?

 

[5jj]

X is a special case of Y.

This implies that Y has many realizations and X is one of them.

Not necessarily.

If there are many cases of something, i..e Y, then one should use "a", but if there is only one modification (or case) then one should use "the".

Is this correct?

Not necessarily. We could speak of 'a unique case' (45 examples in COCA). Look at the 35 examples of 'the unique case' in COCA and see how they are used.

For example, this should be correct I presume

"The circle is the special case of the elipse."

the = to emphasize class; hope this usage of "the" is correct.

Since there is more or less only one way of making an elipse into a circle. Right?

No. There are perhaps many special cases - this is merely one of them.

 

[zorank]

In the first, 'the' is not appropriate; there may well be other cases of 'being angry'...

Now I am confused. Why did you say the above then? To say it in another way: If there are other special cases of something then do not not use "the". Isn't that the message?

I will check COCA.

 

[zorank]

okay, I think I can define the problem better.

Assume that we have an object call it X, and I will label it with integer numbers.

X(1), X(2), X(3), ...

Assume that X(1) and X(2) are identical with Y

X(1) = Y
X(2) = Y

Can I say that Y is the special case of X?

 

[5jj]

Now I am confused. Why did you say the above then? To say it in another way: If there are other special cases of something then do not not use "the". Isn't that the message?

I used those words of one example. You have rephrased my words as a generalisation. That doesn't get us anywhere.

As has been suggested a couple of times before, you are better off with the corpora.

In many of your threads you have been asking about cases where there are no clearly established conventions - if there were, it would be easy to direct you to Swan, Leech, Quirk, or a dozen other books. This is why trying to generalise from individual examples is unwise.

You also sometimes make the (what appears to me to be) mistake of trying to solve these issues by logic. The 'rules' of language do are not always logical in a scientific sense., although the prescriptive garmmarians of the past tried to make them so. Most of the rules are simply conventions accepted by the majority of speakers. For example, the pattern I live/you live/he live is perfectly acceptable in the spoken language of people in some parts of England, as is I lives/you lives/he lives in other parts. The pattern I live/you live/he lives is no better or more logical - it is simply the one that the majority of speakers of all major varieties accept as 'correct'.

Look in the corpora to see how people use the forms you are interested in. If there are several examples, then the form is presumably acceptable. If there are no examples of a form, this does not prove that it is unacceptable, but it does suggest that it is rare.

 

[birdeen's call]

okay, I think I can define the problem better.

Assume that we have an object call it X, and I will label it with integer numbers.

X(1), X(2), X(3), ...

Assume that X(1) and X(2) are identical with Y

X(1) = Y
X(2) = Y

Can I say that Y is the special case of X?

Surely, you mean X is a class of objects? What you wrote doesn't make sense if X is just one object.

If you have two classes of objects X and Y, and X is a subclass of Y, then it often makes sense to say that being an X-object is a special case of being an Y-object. Say, X is the class (set in this case) of natural numbers and Y is the class (again set in this case) of integer numbers. It makes sense to say

Being a natural number is a special case of being an integer number.

Or, shortly,

Natural numbers are a special case of integer numbers.

We don't say it this way usually though. We just say that natural numbers are a subset of integer numbers.

You are dealing with probability distibutions. It also makes sense to say that

The exponential distribution is a special case of the gamma distribution.

I don't think it will hurt if you post your original sentence. We may or may not have the answer but there's always a chance.

 

[zorank]

This was wonderful! Now I can formulate it even better. Please bear with me...

Let X be a class of objects with elements {X1, X2, X3, X4}

and Let Y be a class of objects {Y1,Y2,Y3} and Y is a subset of X such that

Y1=X1, Y2=X2, Y3=X3

Also, let Z be a class with just one element Z = {Z1} where

Z1=X4

Which statements are correct (and why, if not too hard to explain):

(1) "Y is a special case of X."
(2) "Y is the special case of X."
(3) "Z is a special case of X."
(4) "Z is the special case of X."

This should cover all combinations I think.

p.s. The original sentence is

"Thus the PARNES method is the special case of the XARNES method with X=P."

Meaning that XARNES is a class of methods {MARNES, PARNES, TARNES, QARNES, ...}

and PARNES is one element in the class. I presume that it would be wrong to say "a" but I am not sure.

 

[birdeen's call]

This was wonderful! Now I can formulate it even better. Please bear with me...

Let X be a class of objects with elements {X1, X2, X3, X4}

and Let Y be a class of objects {Y1,Y2,Y3} and Y is a subset of X such that

Y1=X1, Y2=X2, Y3=X3

Also, let Z be a class with just one element Z = {Z1} where

Z1=X4

Which statements are correct (and why, if not too hard to explain):

(1) "Y is a special case of X."
(2) "Y is the special case of X."
(3) "Z is a special case of X."
(4) "Z is the special case of X."

Without any further context, (1) and (3) are the ones. You'd want to use "the" if you were talking about a special case that had been previously specified. It doesn't matter that Z has just one element. What could matter is how many possible special cases there are.

"Thus the PARNES method is the special case of the XARNES method with X=P."

Meaning that XARNES is a class of methods {MARNES, PARNES, TARNES, QARNES, ...}

and PARNES is one element in the class. I presume that it would be wrong to say "a" but I am not sure.

It wouldn't be wrong. "The" is justified here because "with X=P" specifies. As in

It's the girl with a big hat.

said while pointing at a girl wearing a big hat. But in your sentence, "a" is OK too, perhaps a comma between "method" and "with" would be good in this case, but I don't think it's necessary.