Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/5/2024 2:30 PM, Ross Finlayson wrote:

On 05/05/2024 10:59 AM, Jim Burns wrote:

The meaning of (1.) depends upon
'n' NOT being
the true name of any number which CAN be counted.to,
the way that "Rumpelstiltskin" is the true name of
a certain straw.into.gold.spinner.
>
An analogy better than "name" is "pronoun"
'n' is more like a pronoun than a name.
"It is a natural number", etc.
>
Variable.names are a big improvement over pronouns
because, in every natural language I'm aware of,
there are no more than a handful of pronouns,
used with many handfuls of referents, and
their distinct referents are kept distinct
by context, AKA, figuring.it.out.
Even if the figuring.out doesn't fail, a lot of work.
>
The expression
| x < y and y < z implies x < z
|
is a big improvement in clarity over
a paragraph of muddle with three pronouns.
x y z act like pronouns, though.

How about disambiguating quantifiers so that
something like the universal quantifier
gets disambiguated to reflect
a for-any/for-each/for-every/for-all
when it's so that
things like the Sorites/Heap or transfer principle
apply.
>
Similarly
the existential quantifier is often to be disambiguated
"exists", "exists-unique", "exists-plural",
these kinds of things.
>
English as a language has a rich variety of copulas.

I think that your wished.for supplements of
standard.issue quantifiers
can be defined given
standard.issue quantifiers.
For my wish,
I would like everyone to be clear on what
standard.issue quantifiers and variables
mean.
I think that,
way off in that glorious future,
both you and I will be able to be
satisfactorily understood.
And what more could there be
to wish for?