Hi,
In 2023 Dr. Ben Goertzel praised back to
normal, today in 2024 everybody has mysterious
eyeinfections and a new wave is reported:
Flirt-Varianten: Sommer-Coronawelle nimmt Fahrt auf
https://www.mdr.de/wissen/medizin-gesundheit/corona-fallzahlen-sommerwelle-100.html
Bye
Mild Shock schrieb:
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.
--- SoupGate-Win32 v1.05
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