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

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

On 5/8/2024 4:20 PM, Ross Finlayson wrote:

On 05/08/2024 11:40 AM, Jim Burns wrote:

>

My guess is that 'A' is the ASCIIfication of '∀'
Thus
for-any ∀?
for-each ∀+
for-every ∀*
for-all ∀$
>
Please use each of ∀? ∀+ ∀* ∀$ in a sentence.

>
If you don't want to use ∀? ∀+ ∀* ∀$ in a sentence,
that's certainly your choice to make.
>
It's not a choice which encourages
efforts to understand you.
>

https://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te

>
François Viète, Seigneur de la Bigotière
(Latin: Franciscus Vieta; 1540 – 23 February 1603)
>
| In his dedication of the Isagoge to
| Catherine de Parthenay, Viète wrote:
|
| "These things which are new are wont in the beginning
| to be set forth rudely and formlessly and must then
| be polished and perfected in succeeding centuries.
| Behold, the art which I present is new,
| but in truth so old,
| so spoiled and defiled by the barbarians,
| that I considered it necessary,
| in order to introduce an entirely new form into it,
| to think out and publish a new vocabulary,
| having gotten rid of all its pseudo-technical terms..."
>
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.
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".
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.