Definite or indefinite article for non-singletons?

[MRAB]

On 2019-07-29 03:59, Cameron Simpson wrote:
> On 29Jul2019 10:15, Chris Angelico <rosuav at gmail.com> wrote:
>>On Mon, Jul 29, 2019 at 10:06 AM Richard Damon <Richard at damon-family.org> wrote:
>>> When talking of empty strings, we need to look a bit at context.  "The
>>> empty string" implies that there is only one of them, and if we are
>>> talking about values, then there is only one empty string values, so
>>> "The empty string value" would be correct (and the term value might be
>>> implied by context). If we are talking about object, like with the
>>> python word "is", then the empty string is not promised to be a
>>> singleton, so grammatically, it should be "A empty string object", and
>>> again the term object might be implied by the context.
>>
>>So I guess the original question can be reworded as:
>>
>>When you're describing indistinguishable objects, are you really
>>talking about objects, or are you talking about values?
>>
>>With numbers, it's pretty obvious that you talk about values. You can
>>logically say "if the spamminess is zero, blah blah blah" even though
>>you'd actually say "if spam == 0:" in the code. With strings, is it
>>therefore logical to say "is the empty string" even though you'd
>>actually be comparing to see if it "==" another empty string?
> 
> I wouldn't be saying "the empty string". I'd being describing the
> string: "if the string is empty", "if s is an empty string", etc. So
> values again.
> 
> I think the wish to use the phrasing "the empty string" either comes
> from an implied metaphorthat assumes deduped immutable objects or from a
> mathematical background where eg in set theory one talks about "the
> empty set". Someone else posted a better description of the methematical
> context, where "the empty set" is effectively naming a category of sets
> (those of size 0) and considering that a single thing in that context.
> 
> I'm for running with "values" in the example you started with. I think
> the "the empty string" is mathematical context specific terminology
> leaking into the wrong domain.
> 
There's also the use of the definite article when referring to the 
members of a class as whole, e.g. "the elephant is a large mammal".