Re: French Philosophy in 2024 (Was: Minimal Logics in the 2020's: A Meteoric Rise)

Hi,
Actually thridness is not only the art of making
three-fold divisions. Usually one aims a finding
a 3 that is the relation between 1 and 2, so that
we have this relation satisfied:
    3(1, 2)
Of course we can have the stance, and say that |-
does that already. Only |- is highly ambigious,
if you see Γ |- α you don't know what was the last
inference rule applied. But for proof extraction
you want exactly know that.
Bye
P.S.: And Peirce isn't wrong when he says thirdness
is enough, just take set theory, which can do all
of mathematics? Its based on  this thirdness only:
    x ∈ y
The set membership. But set membership is as ugly as |-,
it also doesn't say why an element belongs to a set.
LoL
Mild Shock schrieb:

Hi,
 Now I had an extremly resilient correspondent, who
wants to do proof extraction, but at the same
time refuses to learn the Curry-Howard isomorphism.
 But its so easy, was just watching:
 Hyperon Session with Dr. Ben Goertzel
https://www.youtube.com/watch?v=5Uy3j4WCiXQ
 At t=1853 he mentions C. S. Peirce thirdness, which
you can use to explain the Curry-Howard isomorphism:
  1 *\        Γ = Context
   | \
   |  * 3    t = λ-Expression
   | /
2 */        α = Type
  The above is a trikonic visualization of the judgement
Γ |- t : α, applying the art of making three-fold divisions.
 But I guess C. S. Peirce is not read in France, since
it requires English. Or maybe there is a french translation?
 Bye
 Mild Shock schrieb:

Could be a wake-up call this many participants
already in the commitee, that the whole logic
world was asleep for many years:
>
Non-Classical Logics. Theory and Applications XI,
5-8 September 2024, Lodz (Poland)
https://easychair.org/cfp/NCL24
>
Why is Minimal Logic at the core of many things?
Because it is the logic of Curry-Howard isomoprhism
for symple types:
>
----------------
Γ ∪ { A } ⊢ A
>
Γ ∪ { A } ⊢ B
----------------
Γ ⊢ A → B
>
Γ ⊢ A → B           Δ ⊢ A
----------------------------
Γ ∪ Δ ⊢ B
>
And funny things can happen, especially when people
hallucinate duality or think symmetry is given, for
example in newer inventions such as λμ-calculus,
>
but then omg ~~p => p is nevertheless not provable,
because they forgot an inference rule. LoL
>
Recommended reading so far:
>
Propositional Logics Related to Heyting’s and Johansson’s
February 2008 - Krister Segerberg
https://www.researchgate.net/publication/228036664
>
The Logic of Church and Curry
Jonathan P. Seldin - 2009
https://www.sciencedirect.com/handbook/handbook-of-the-history-of-logic/vol/5/suppl/C >
>
Meanwhile I am going back to my tinkering with my
Prolog system, which even provides a more primitive
logic than minimal logic, pure Prolog is minimal
>
logic without embedded implication.