On 12/05/2024 10:14 AM, Jim Burns wrote:
On 12/4/2024 5:44 PM, Ross Finlayson wrote:
On 12/04/2024 02:12 PM, Jim Burns wrote:
On 12/4/2024 4:39 PM, Ross Finlayson wrote:
On 12/04/2024 11:37 AM, Jim Burns wrote:
On 12/3/2024 8:09 PM, Ross Finlayson wrote:
>
Yet, I think that I've always been
both forthcoming and forthright
in providing answers, and context,
in this loooong conversation [...]
>
Please continue being forthcoming and forthright
by confirming or correcting my impression that
"yin-yang ad infinitum"
refers to how, up to ω, claim [1] is true,
about immediate [predecessors],
but, from ω onward, it's negation is true.
>
Thank you in advance for confirming or correcting
my impression of what you mean
(something you have not yet done),
in furtherance of your
forthcoming and forthright posting history.
>
The thing is,
'not.first.false' is not used to describe ordinals,
in the way that 'yin.yang.ad.infinitum'
is used to describe ordinals.
>
'Not.first.false' is used to describe
_claims about ordinals_ of which we are
here only concerned with finitely.many claims.
There is no 'ad infinitum' for 'not.first.false'.
>
It is in part the absence of 'ad infinitum'
which justifies claims such as [1] and [2]
>
A linearly.ordered _finite_ set must be well.ordered.
If all claims are true.or.not.first.false,
there is no first false claim.
Because well.ordered,
if there is no first false,
then there is no false,
and all those not.first.false claims are justified.
>
The natural numbers are not finitely.many.
But that isn't a problem for this argument,
because it isn't the finiteness of the _numbers_
which it depends upon,
but the finiteness of the claim.sequence.
>
About your posited point of detail, or question,
about this yin-yang infinitum,
which is non-inductive, and
a neat also graphical example of the non-inductive,
a counter-example to the naively inductive,
as with regards to whether it's not so
at some finite or not ultimately untrue,
I'd aver that it introduces a notion of "arrival"
at "the trans-finite case",
>
Anyways your point stands that
"not.first.false" is not necessarily
"not.ultimately.untrue",
and so does _not_ decide the outcome.
>
Thank you for what seems to be
a response to my request.
>
You seem to have clarified that
your use of
'not.ultimately.untrue' and 'yin-yang ad infinitum'
is utterly divorced from
my use of
'not.first.false'.
>
⎛ When, inevitably, you and I will have moved on
⎜ to other discussions,
⎜ I (JB) would like to be able to think back on
⎜ at least leaving you (RF) with
⎜ _an awareness of what I am saying_
⎜ even if nothing else was accomplished.
⎜
⎜ Currently, it seems as though
⎜ I have not cleared that low, low bar.
⎜ You seem to be responding to some _other_ 'JB'
⎜
⎜ Upon once more reading what I've said and
⎜ what you've said, I feel
⎜ what.I'm.going.to.call 'intellectual.dizziness':
⎜ something approximating what I felt
⎜ just a couple days ago, when I re.watched
⎜ the Minions movie (2015)
⎜ https://www.imdb.com/title/tt2293640/
⎜ A perpetual dance.and.wave _just beyond_
⎜ the edge of comprehensibility,
⎜
⎜ It is what it is.
⎜
⎝ But, enough about me.
>
A couple thousand years ago,
the Pythagoreans developed a good argument
that √2 is irrational.
>
⎛ The arithmetical case was made that,
⎜ for each rational expression of √2
⎜ that expression is not.first.√2
⎜
⎜ But that can only be true if
⎜ there _aren't any_ rational expressions of √2
⎜
⎜ So, there aren't any,
⎝ and √2 is irrational.
>
Mathematicians,
ever loath to let a good argument go to waste,
took that and applied it (joyously, I imagine)
in a host of other domains.
>
Applied, for example, in the domain of claims.
>
In the domain of claims,
there are claims.
There are claims about rational.numbers,
irrational.numbers, sets, functions, classes, et al.
>
An argument over the domain of claims
makes claims about claims,
claims about claims about rational numbers, et al.
>
We narrow our focus to
claims meeting certain conditions,
that they are in a finite sequence of claims,
each claim of which is true.or.not.first.false.
>
What is NOT a condition on the claims is that
the claims are about only finitely.many, or
are independently verifiable, or,
in some way, leave the infinite unconsidered.
>
We narrow our focus, and then,
for those claims,
we know that none of them are false.
>
We know it by an argument echoing
a thousands.years.old argument.
⎛ There is no first (rational√2, false.claim),
⎝ thus, there is no (rational√2, false.claim).
>
>
No, I say "not.ultimately.untrue" is
_more_ than "not.first.false".
The account where you have drawn thinkers
into your shell and closed the door, is
not an accurate account of thorough reasoning.
Now, it may be a delightful and non-controversial
space, the balk's clam's inductive world, yet,
somehow, what's arrived at, for example as
the clam extrudes in its sandy bed to filter
micronutrients the juice, above it the surf
crests, breaks, and recedes, each anonce never
again, that when the clam-digger arrives to
harvest the meat of the balk's clam after the
tide, that the clam that doesn't open,
or the clam that doesn't close, is discarded.
Usually not because it will ever clam again,
rather because it usually won't.
So, the, ..., "claim clam", lives in a world
where there are other claims that direct whether
it's complete or merely partial, and the finite:
is merely partial.
The clam that always clams and clams again
may make a delightful soup, yet only by
opening it shell and tasting the entire ocean.
The, "intellectual dizziness" you mention,
seems to be that you interpret any falsehood,
ex falso, as quodlibet, and taboo, instead of
nihulum, and a demand to repair, that then
"divide by zero" requires re-establishing
more thoroughly a fuller, wider dialectic.
There's a model of reals that is rationals,
including infinite and non-standard rationals, though.
Here there are at least three models of continuous
domains and formally for set theory's and ZF set theory's
usual account of after descriptive set theory and model
and description of continuum analysis, ..., that
the facts about the un-countable are, "merely finite".
So, what is "yin-yang ad-infinitum"?
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)