Discussion:
The mathematical nature of truth
(too old to reply)
peteolcott
2017-05-08 18:30:57 UTC
Permalink
Raw Message
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence

// Defining Tarski’s (1933) Formal correctness of True: ∀x True(x) ↔ φ(x)
True(x) = "∀L ∈ Formal Systems ∀x ∈ Finite Strings, ∃Γ ⊂ L (Γ ⊢ x)"

The truth or falsity of every (declarative sentence / logical proposition) is determined entirely on the basis of the existence of a set of finite string rewrite rules (meaning postulate axioms) that derive this (declarative sentence / logical proposition) through syntactic logical consequence.

If there are no meaning postulate axioms deriving the expression or its negation then the expression is not a (declarative sentence / logical proposition).

Copyright 2017 by Pete Olcott
DKleinecke
2017-05-08 22:37:43 UTC
Permalink
Raw Message
Post by peteolcott
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
// Defining Tarski’s (1933) Formal correctness of True: ∀x True(x) ↔ φ(x)
True(x) = "∀L ∈ Formal Systems ∀x ∈ Finite Strings, ∃Γ ⊂ L (Γ ⊢ x)"
The truth or falsity of every (declarative sentence / logical proposition) is determined entirely on the basis of the existence of a set of finite string rewrite rules (meaning postulate axioms) that derive this (declarative sentence / logical proposition) through syntactic logical consequence.
If there are no meaning postulate axioms deriving the expression or its negation then the expression is not a (declarative sentence / logical proposition).
This has nothing to do with natural (or even artificial
language.
Athel Cornish-Bowden
2017-05-10 15:43:45 UTC
Permalink
Raw Message
Post by peteolcott
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
// Defining Tarski’s (1933) Formal correctness of True: ∀x True(x) ↔ φ(x)
True(x) = "∀L ∈ Formal Systems ∀x ∈ Finite Strings, ∃Γ ⊂ L (Γ ⊢ x)"
The truth or falsity of every (declarative sentence / logical
proposition) is determined entirely on the basis of the existence of a
set of finite string rewrite rules (meaning postulate axioms) that
derive this (declarative sentence / logical proposition) through
syntactic logical consequence.
If there are no meaning postulate axioms deriving the expression or its
negation then the expression is not a (declarative sentence / logical
proposition).
Copyright 2017 by Pete Olcott
Who is likely to be tempted to copy it?
--
athel
peteolcott
2017-05-10 15:59:31 UTC
Permalink
Raw Message
Post by Athel Cornish-Bowden
Post by peteolcott
https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence
// Defining Tarski’s (1933) Formal correctness of True: ∀x True(x) ↔ φ(x)
True(x) = "∀L ∈ Formal Systems ∀x ∈ Finite Strings, ∃Γ ⊂ L (Γ ⊢ x)"
The truth or falsity of every (declarative sentence / logical proposition) is determined entirely on the basis of the existence of a set of finite string rewrite rules (meaning postulate axioms) that derive this (declarative sentence / logical proposition) through syntactic logical consequence.
If there are no meaning postulate axioms deriving the expression or its negation then the expression is not a (declarative sentence / logical proposition).
Copyright 2017 by Pete Olcott
Who is likely to be tempted to copy it?
Anyone that fully understands that it correctly refutes Tarski's TUT and Gödel's GIT.
Loading...