Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/13/2024 05:43 PM, Jim Burns wrote:

On 11/13/2024 7:05 PM, FromTheRafters wrote:

Jim Burns formulated on Wednesday :

On 11/13/2024 4:29 PM, WM wrote:

On 13.11.2024 20:38, Jim Burns wrote:

>

----

 Bob.

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KING BOB!
https://www.youtube.com/watch?v=TjAg-8qqR3g
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If,
  in a set A which
  can match one of its proper subsets B,

>
That is nonsense too.

>
[repaired]
>
A finite sequence of claims in which
each claim is true.or.not.first.false
is
a finite sequence of claims in which
each claim is true.
>
Some claims are true and we know it
because
they claim that
when we say this, we mean that,
and we, conscious of our own minds, know that
when we say this, we mean that.
>
Some claims are not.first.false and we know it
because
we can see that
no assignment of truth.values exists
in which they are first.false.
q is not first.false in ⟨ p p⇒q q ⟩.
>
Some finite sequences of claims are
each true.or.not.first.false
and we know it.
>
When we know that,
we know each claim is true.
>
We know each claim is true, even if
it is a claim physically impossible to check,
like it would be physically impossible
to check each one of infinitely.many.
>
We know because
it's not checking the individuals
by which we know.
It's a certain sequence of claims existing
by which we know.
>

In my source window:

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[...]

That is nonsense too.

>
A finite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀
in which
each claim is true.or.not.first.false
is
a finite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀
in which
each claim is true.

[...]
>

================================================
I follow some of this mostly from context. :)

>
Sorry about that.
The other fonts weren't strictly necessary,
I just had a brainstorm over
how to (maybe) explain logical validity better,
and I couldn't resist.
>
>

Some usual laws, or criteria, rather, of convergence,
fail, for example Stirling's formula.
When are they ever wrong? Are there simply more
than a usual naive law of large numbers what's
merely the law of small numbers?
Then, asymptotic freedom, or the Arago spot, make
examples of what do not arrive from inductive inference.
So, these super-classical concerns are a thing.
There's one rhyme,
"I like traffic lights,
I like traffic lights,
I like traffic lights, ...."
Also usually called slippery slope,
shifting sands, or ad absurdam.
Usually of course arrived at ultimately.untrue
from more objective concerns.
Take a look to Chrysippus, he establishes great
grounds for modal (mood-al) logic and relevance logic about
hundreds of years before Plotinus arrived at
the "material inductive implication" the "quasi-modal",
and provides reasoning for more thorough accounts
when people might not have time to read and follow
both Aristotle's Prior, and Posterior sur-rounds
of inference.
Or, "not.first.false" must yet also be "not.ultimately.untrue",
when _all_ the cases are run out.
(Or, maybe it's the other way, ....)
As long as you might agree that _all_ your stipulations be
read off in any order, that might help, it's a usual
criterion of constructivism.
For structuralists and not merely the shallow feels.