3 ms·
> if the axioms at the start are all true. Axioms are true by definition; that's what "axiom" means. (They might also be false, but (if and) only if your syste
by a1369209993 5y ago
> if the axioms at the start are all true.
Axioms are true by definition; that's what "axiom" means. (They might also be false, but (if and) only if your system is inconsistent.)
> Case (1) that machine doesn't really halt
This is not a state of affairs: all you know at any given time is that the machine hasn't halted yet (after some specific finite number of steps), or that it has aquired some termination-precluding invariant like a infinite loop (which you can detect only strictly less than all of).
- rssoconnor 5y agoAxioms are most certainly not true by definition. Regardless, the particular technical definition of truth I'm using is Tarski's definition of truth[1]. We don't have to agree whether Tarski's definition is "correct", and I'm happy to qualify my use of the word "truth" here, but I'm referring to a specific technical definition here. [1] https://en.wikipedia.org/wiki/Semantic_theory_of_truth#Tarski's_theory_of_truth https://en.wikipedia.org/wiki/Semantic_theory_of_truth#Tarsk...