Re: Replacement of Cardinality (quantifier disambiguation)

On 08/05/2024 06:01 AM, Jim Burns wrote:

On 8/4/2024 9:41 PM, Ross Finlayson wrote:

On 08/04/2024 05:49 PM, Ross Finlayson wrote:

On 08/04/2024 05:24 PM, Moebius wrote:

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[...]

[...]

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This is for something like
Zeno and the limit and the infinite limit,
there being a difference, and that
Zeno particularly says that
"if you don't get all the way across,
then close enough is also
close enough to half, to a quarter,
and on down the inverse powers of two,
to none".

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Or Zeno says the opposite of that.
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No distance can be completed without
half the distance having been completed,
and thus,
in order to complete the distance,
these tasks,
among which no task begins them,
must have been completed.
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No distance can be begun to be completed.
Ignore your lying eyes:
motion is impossible.
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Better:
A half, a quarter, an eighth, kai ta hetera
is not close enough.
We do not get across any finite distance.
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I.e. Zeno explains that
the analytical bridge
has an inductive impasse and
must be surpassed as an infinite super-task.

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Another possibility is that
motion is possible, but
the description of motion as
(not.a.supertask but) an unbeginnable set
is not a correct description.
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It is a notable property of a finite ordered set
that its greatest lower bound is in the set.
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However,
that is not a property shared by all sets.
In particular, as Zeno of Elea points out,
the greatest lower bound of distances covered
is zero, which isn't a distance covered.
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Perhaps our eyes are not lying, but
the set of distances covered isn't finite.
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[...] inductive impasse [...] infinite super-task.

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Induction is a finite task
which reasons about infinitely.many.
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A finite.length claim can be true of
infinitely.many by
being stated about an indefinite one, and
being true without exception.
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In order to prevent exceptions,
we engage in hypocrisyᴿꟳ ==
not.making claims for what claims are not.for.
>
Perhaps, without hypocrisyᴿꟳ, motion is impossible.
I haven't really considered the hypothetical.
If you haven't noticed, I really like hypocrisyᴿꟳ.
You will get my hypocrisyᴿꟳ
when you pry it from my cold, dead hands.
>
>

Well, you seem about half-way there, ....
For the past several several months, I've been recording
a pod-cast about each week of about an hour, under the
subject "Moment and Motion", where the previous topic of
about 50 hours was "Descriptive Differential Dynamics".
In "Moment and Motion", I go about describing the theory
of motion and of moments as is usually rather well-known
as what is classical mechanics, and explain for example
how it is undefined how things meet and part, at all,
in the usual laws of mechanics.
What I've arrived at is a sort of deconstructive account
about particularly the "infinitely-many higher orders
of acceleration" that are formally non-zero somewhere
between before and after any application of otherwise force.
Along the way, Zeno is a constant companion, and indeed,
a recent notion of "Zeno's swath" joins Zeno's other
theories, of what must be comprehended to make reasonable,
sound models of motion, and dynamics in motion or change,
mostly as with regards to the model of a wave as a model
of change in open systems, in physics.
Of course, this is a mathematical physics, thusly the point
mostly is to equip mathematics with sound, reasonable models
of dynamics in motion thusly to automatically equip the
physics, also.
So, you can browse to this "Philosophical Foreground" play-list
under my pod-casts channel https://www.youtube.com/@rossfinlayson ,
where is entertained a theory where zero meters per second:
is infinity seconds per meter.
tempus fugit