Thinking about it, part of the reason why not is because of a programming-related mindset. I'm inclined to use the word unique in this way to refer to a property of a thing. But "smallest" isn't a property of a thing, because it can be lost without changing the thing itself.
For example, this line of reasoning fails...
* It is known that thing A is unique because P(A) is true. * We add a new thing B to the environment such that P(B). * Now neither A nor B is unique in satisfying P(X), because P(A) and P(B) hold.
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Date: 2008-05-29 11:46 am (UTC)Thinking about it, part of the reason why not is because of a programming-related mindset. I'm inclined to use the word unique in this way to refer to a property of a thing. But "smallest" isn't a property of a thing, because it can be lost without changing the thing itself.
For example, this line of reasoning fails...
* It is known that thing A is unique because P(A) is true.
* We add a new thing B to the environment such that P(B).
* Now neither A nor B is unique in satisfying P(X), because P(A) and P(B) hold.
(Edited to fix typo 'is' -> 'in'.)