From: iad@cogsci.ed.ac.uk (Ivan A Derzhanski)
Newsgroups: alt.usage.english
Subject: Re: quite unique
Date: 23 Nov 92 11:36:44 GMT
Organization: Centre for Cognitive Science, Edinburgh, UK

In article <1992Nov21.053013.16266@Princeton.EDU> roger@astro.princeton.edu (Roger Lustig) writes:
>In article <11636@scott.ed.ac.uk> iad@cogsci.ed.ac.uk (Ivan A Derzhanski) writes:
>>In article <1992Nov18.192304.15503@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>>>Come to think of it, consider the following two uniquenesses:
>
>>>a)	2 is the unique integer that is an even prime number.
>
>>>b)	1/3 is the unique real number x satisfying the equation 3x = 1.  
>
>>>Since there are infinitely more real numbers than integers, 
>>>perhaps it *does* make sense to say that 1/3 is "more unique" 
>>>than the number 2, in the above contexts.
>
>>Not really.  We agree that "unique" means `only one [of a kind]', but
>>why should something be called more or less unique just because it was
>>selected from a larger or smaller set?
>
>Because we don't generally speak of things as being unique if they 
>come from a small set, and because we usually *do* use unique to
>indicate the ultimate in rarity.  "Unique" is usually used -- though
>not in mathematics, I'll grant you -- in ways closely related to        
>scales of rarity.

I'll grant you that "unique" is usually used to indicate the ultimate
in rarity, but examples (a) and (b) above have to do with mathematics,
where it is not used in that way.  The specific overrides the usual.

Besides, from an intuitive point of view (one on which the intuitive
meaning of a word can be based) the set of integer numbers is not a
small set just because calculus says that there are sets of greater
cardinality.  My training in mathematics tells me that there are more
real numbers than there are integers, but my language intuition refuses
to reflect this knowledge.

>>a) 2 is the only integer that is an even prime number.
>>b) 1/3 is the only real number x satisfying the equation 3x = 1.
>
>>Is 1/3 onlier than 2, or what?  :-) (If "more unique" makes sense,
>>then so does "onlier", since the two mean the same thing.)
>
>They don't mean the same thing.

They do here.

>Or rather, "unique" may be used in the sense of "only" that you're
>using, but most uses of "unique" aren't like that.

Most uses aren't, because most of us don't talk about mathematics most
of the time.  When we do, we switch to the lingo where "the unique"
means "the only".

>"Unique" is generally used for emphasis, to draw
>attention to some other quality--as in these two sentences, which
>have explanatory clauses to say *how* it's unique.  We don't say
>"my unique son" anymore (though one did say that in the 17th C).

I am now going to make a crazy suggestion.  I think that the meaning
of "unique" depends on the definiteness of the phrase.  That is, "the
unique" and "a unique" mean vastly different things.

c) 2 is the unique integer that is an even prime number.
d) 2 is a unique integer number: it is both even and prime.

This is closer to the intuitive sense, and therefore I feel exactly as
comfortable with it as with

e) $\pi$ is a unique real number: <insert favourite property of $\pi$ here>

despite the different cardinality of the sets from a strict math point
of view.  Yet since it is "a", not "the", you can't substitute "only".

Still, "a unique" here means `one of a kind', not just `one of few',
but that's because the set of integers is well-defined and observable;
"a unique opportunity" may mean that you don't know of many others, or
something like that.

Further exploring the intuitive sense of "a unique" within the context
of mathematics, note the following:

d) 2 is a unique integer number: it is both even and prime.
f) 2 is a unique integer number: it satisfies the equation $3x=6$.

Which sounds more convincing?  I'd say (d).  The source sets are the
same, but the property is a more interesting one.

-- 
 `Haud yer wheesht!  Come oot o the man an gie him peace.' (The Glasgow Gospel)
Ivan A Derzhanski   (iad@cogsci.ed.ac.uk;  iad@chaos.cs.brandeis.edu)
* Centre for Cognitive Science,  2 Buccleuch Place,  Edinburgh EH8 9LW,  UK
* Cowan House, Pollock Halls, 18 Holyrood Park Road, Edinburgh EH16 5BD, UK