On 5/6/2020 10:44 AM, Tanner Swett via agora-discussion wrote:
> You seem to be saying that it's possible for a value to be unambiguous
> despite being indeterminate. That sounds impossible to me; that obviously
> contradicts the meaning of the word "unambiguous".
Ambiguous and indeterminate are not synonyms, due to R2518. Using the
explicit definition of R2518, it is possible for something to be
unambiguously indeterminate, that's the basis for mathematical paradox.
The Halting Problem, Incompleteness Theorem, Barbershop Paradox, etc. are
"proven" to be undecidable and the proof is considered unambiguous.
> You seem to be saying that if a rule says "a player gets a coin" without
> specifying who, then even though the rule does not specify who gets the
> coin, and even though it is not clear who gets the coin, the rule is
> nevertheless NOT "silent or unclear" as to who gets the coin. Am I
> understanding you right?
The Rules are clear that then coin is possessed by one of {set of
players}. Players in that set can take actions (e.g. transferring coins to
Agora) to drop out of that set. When there's only one member of the set
left, logical reasoning could determine that e holds the coin. The rules
are clear that, before that happens, the information is provably and
clearly R2518 indeterminate and subject to the paradoxical judgement.
> For what it's worth, I steadfastly refuse to consider Agora to be
> insusceptible to classical reasoning.
If the rules actually stated "use classical reasoning" or were silent on
the matter, we might decide to use "legal" reasoning ("a disputed coin
exists in the judge's hand, the judge has to give it to someone, so a
decision must be made based on fairness or something"). But the rules are
currently very explicit that when you hit something logically unproveable,
you judge "paradoxical".
