Peter Olcott or Pete Olcott returned, and already starts multiplying his
threads, instead of developing an idea in a single thread, so I revive
this thread here, as he goes on reducing natural logic to mathematical
logic, and driving life out of language.
Peter Olcott is again multiplying his threads, decided to take over also
sci.lang in the name of his phantasm of the absolute and complete and total
truth, never saying anything understandable let alone useful about language,
providing ever more final and finaller and more ultamterer versions of his
alleged proofs that Goedel and Turing were wrong, not understanding their
work, claiming that the truth has always been his first priority, yet
dismissing some of the finest pieces of truth humankind achieved, the proven
theorems of Goedel and Turing, by mere word magic and lines that look as if
they were logical formulae but are not, which is why he never can finish
his papers, only shove around the bug.
You're not the person most suited to write this,
but I agree that Peter Olcott's outpours of delirium do not belong here.
What is Linguistics about if it is not about the notion of Truth within language? That none of you guys have enough math background to understand that I just refuted Tarski Undefinability is no indication what-so-ever that my posts pertaining to the same do not belong in sci.lang.
My Halting Problem proofs don't belong in a sci.lang forum and I only cross post some of them because there is a guy here that is also in the comp.theory forum.
To update the details of this post:
Semantic subatomic compositionality is the constituent parts of a semantic atom. A semantic atom is one whole relation/predicate from predicate logic.
Semantic atoms are connected to their constituent parts as the directed paths from nodes in a directed acyclic graph. Each node and each directed path of this Relation is a unit of subatomic semantic compositionality.
By forming these relations this way one can see for the first time how the constituent parts of a relation relate to each other in two dimensional space.
Higher Order Logic expressions are translated into directed acyclic graphs in strict left-to-right becomes top to bottom order. Identifiers are not duplicated.
The first reference to an identifier in a HOL expression is the only instance that is copied to the directed acyclic graph. All other references to this identifier have directed paths formed to this single reference.
By doing this we can see exactly how and why the Liar Paradox is semantically ungrounded as Kripke pointed out in his famous paper: [Outline of a Theory of Truth] Saul Kripke (1975)
This is the key aspect of Minimal Type Theory that allows pathological self-reference(Olcott 2004) to be detected and rejected as semantically incorrect.
Prior to minimal type theory there were many expressions of language that were thought to be paradoxical rather than simply incorrect.
"This sentence is not true"
LP ≡ ~True(LP) // HOL with self-reference semantics
"This sentence is not provable"
G ≡ ~∃Γ Provable(Γ, G) // HOL with self-reference semantics
Tarski's undefinability theorem Wikipedia
"The undefinability theorem shows that this encoding cannot be done
for semantic concepts such as truth. It shows that no sufficiently
rich interpreted language can represent its own semantics."
The following link shows exactly how to define a Truth predicate in each formal or natural language, thus directly refuting Tarski by doing what he concluded was impossible.
When we plug the Liar Paradox or the simplified Incompleteness Theorem into the above Truth formula we see that the David Hilbert style formalist syntactic logical inference chain (formal proof) never reaches either True or False.
Unlike historical misconceptions the 1931 GIT is not True and improvable, it is simply incorrect because it is neither True nor False.
Copyright 2016, 2017, 2018 Pete Olcott
*∀L ∈ Formal_Systems
True(L, X) ↔ ∃Γ ⊆ Axioms(L) Provable(Γ, X) *