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

On 5/9/2024 3:56 PM, Ross Finlayson wrote:

On 05/08/2024 02:14 PM, Jim Burns wrote:

Consider
| ∀x:B(x) ⇒ B(t)
| ∀x:(B⇒C(x)) ⇒ (B⇒∀x:C(x))
| B(x)  ⊢  ∀x:B(x)
| ∃x:B(x) ⇔ ¬∀x:¬B(x)
>
Is it possible that
several centuries of polishing and perfecting
have given us, in 2024, something which
François Viète had only set out in search of?
>
I am not a giant.
However, I can stand on giants' shoulders.
Since I can, why shouldn't I?

>
Sort of, I suppose.

| I beseech you, in the bowels of Christ,
| think it possible that
| I cannot read your mind.
|
<pseudo.Cromwell>

Like Russell stood on Frege and Peirce,
and von Neumann and Zermelo stood on Mirimanoff,
and Cantor stood on duBois-Reymond, well,
Newton of course is very well-known for
his quote "I stood on people left and right".

| If I have seen further
| it is by standing on ye sholders of Giants.
|
<Newton>

Here it's still "Amicus Plato"

| Amicus Plato — amicus Aristoteles — magis amica veritas
<Newton>
==
| Plato is my friend -- Aristotle is my friend --
| but my best friend is truth.
|
<Newton>

Here it's still "Amicus Plato"
and it's very old-fashioned,
yet every few hundred years at least
it comes back around,
unsurprisingly much the same.
>
So, ye adherents of Russell's retro-thesis and
semi-Aristotleans of
the "I say" logical positivist variety,
too often thinking that
circa-20'th-century-classical quasi-modal logic
is either classical or full for DeMorgan:
can you get down?
>
Not.first.false?  Largest.number.ever.

Compare
finite sequences of only not.first.false claims
to
logarithmic slide rules.
When used correctly,
they both give what they're advertised to give.
Doubts that they give that,
to the extent that there are doubts that they give that,
originate from it being less.than.immediately.obvious
that they give what they're advertised to give.
But they do give that,
and it can be shown that they give that,
even if it is challenge and more.than.a.challenge
to _immediately_ show that they give that.