Re: how

On 6/8/2024 8:40 PM, FromTheRafters wrote:

Jim Burns laid this down on his screen :

On 6/8/2024 8:42 AM, WM wrote:

But they will never be defined

>
Irrelevant.
Numbers between 0 and Avogadroᴬᵛᵒᵍᵃᵈʳᵒ
will never be all defined.
Numbers between 0 and Avogadroᴬᵛᵒᵍᵃᵈʳᵒ
are all definable.
>
An apple can be
  edible and not eaten.
A tree falling in the forest can be
  audible and not heard.
A natural number can be
  definable and not defined.

>
But can you have
a non-empty set of undefined natural numbers? Distinguishable but not distinguished?
Discernible yet not discerned? One should be able to discern
each and every element
at least enough to decide on membership.
Ghost naturals might exist somewhere,
but are not a subset of the naturals.
WM seems to just 'not get' real numbers.

There is a mix here of statements
about actions by agents and
about descriptions without agents.
I think that
the usual practice is to re.state without agents,
so we've learned to automatically ignore the mix.
Mückenheim does not ignore the mix.
He uses the difference between our reading and his
to sow confusion about what is meant.

One should be able to discern
each and every element
at least enough to decide on membership.

Yes, but
what does that mean?
Is that a constraint on elements or
a constraint on the agent "one"?
"One" can't perform a supertask.
That is the crack through which
WM's rhetoric enters.
If we take "one should be able to discern" as
a constraint on elements
(whatever "one" does or does not do),
in line with taking "one should be able to see" as
a constraint on how some physical object
interacts with electromagnetic radiation,
then there is no crack.
No supertask is needed for
each nonzero natural number to have
a definable predecessor.
There is no "one" in that description.