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From Feferman to Peyton Jones, no luck with ∃

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Hi,

Now this is an interesting find. It seems
not only the Verse Calculus by Peyton Jones
hit a wall with existential quantifier ∃.

Especially the type free case. Its like in
Rossy Boys Russell thing, people are not
anymore trained to think about "individuals",

the are more bothered by "bags", because this
is what the Antinomies of the formal revolution
tought us. But the formal revolution has also

some nice easter eggs, like Fefermans OST
("Operational Set Theory"), an early form of
Predicte Abstraction. With each formula A is

associated a term t_A such that:

     ∀x[A(x) <=> t_A(x) = tt]

https://math.stanford.edu/~feferman/papers/OperationalST-I.pdf

The nice thing about the t_A, its a term,
possibly a open or closed term, depending
on whether there are parameters, and thats

what I am now doing for Arrow Functions, when
the Prolog systems compiles 0rReference(P1,..,Pk),
its basically a term, an individual, that

later gets called by call/n, which makes the
translation for individual to proposition.

Bye

P.S.: But somehow Feferman shyed away from
definition the unbounded existential quantifier
as a projection, there is a easy geometric

intution, and every SQL database can do it.
Instead he falls back to some Hilber Epsilon
analogue such as:

Given A(x) = ∃yB(x, y) and t_B for B(x, y);
then we can take t_A = λx.t_Bx(C(λyt_Bxy)),
using the general choice operator C.

https://math.stanford.edu/~feferman/papers/OperationalST-I.pdf

Funny!

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From Feferman to Peyton Jones, no luck with ∃ Mild Shock <janburse@fastmail.fm> - 2025-11-08 20:31 +0100

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