3 ms·
Although [Gödel 1931] failed to proved inferential undecidability of Russell's Principia Mathematica, there is a fairly simple undecidable proposition namely,
by ProfHewitt 6y ago
Although [Gödel 1931] failed to proved inferential
undecidability of Russell's Principia Mathematica, there is a
fairly simple undecidable proposition namely, the proposition
*Undecidable*≡Halt<ExpressionFromString<Natural>>[RunOne.[]]
where RunOne.[]≡Eval.[SelectOne.[0]] such that
SelectOne.[i:Natural]≡ExpressionFromString<Natural>.[i] *finishesFirst* SelectOne.[i+1]
Eval.[anExpression] evaluates anExpression and where the expression
(expression1 *finishesFirst* expression2)
returns the value of whichever of the expressions expression1
and expression2 evaluation finishes first.
The procedure SelectOne selects one of the expressions
created from strings.
For details see: https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021
- ProfHewitt 6y agoThere is a small typo in the above: Undecidable ≡ Halt<ExpressionFromString<Natural>>[⦅RunOne.[]⦆] is inferentially undecidable in the theory Actors, that is, ⊬Undecidable and ⊬¬Undecidable where RunOne.[]≡Eval.[SelectOne.[0]] and ⦅RunOne.[]⦆ is the expression for the procedure application RunOne.[]