[Sending to agora-official because this is a very long message, which
IIRC is long enough to be blocked by agora-business at least when Taral
ran it; I have a higher posting limit to agora-official because I used
to be Notary. It's of a comparable length to my other theses; slightly
shorter, but not by much.]
I judge CFJ 3381 TRUE.
The rest of this message, below this paragraph, is a thesis. I submit it
with intent to qualify for a degree. It is /also/ my judge's arguments
and evidence.
JUDGE'S ARGUMENTS AND EVIDENCE ON CFJ 3381
or, what logic do the rules follow anyway?
So, Fool's scam (in which e claims to have deregistered everyone else,
obtaining a dictatorship via being the only person capable of voting) is
really dominating the discussion recently (and for good reason; the lack
of certainty about what happened makes it hard to do anything else), and
this is the first CFJ that really depends on the success or failure of
the scam (the only reasons why omd would possibly not be a player are if
Fool's scam fully succeeded, or in the very unlikely event that Wooble's
theory that the entire playerlist was emptied years ago and Fool was
never a player is correct, and we've taken corrective action for
Wooble's version of events recently, just in case; I'm not going to
consider that theory here because it would detract from the main
arguments). As such, I'd like to preserve a description of the events
behind the scam, and the arguments being presented, for historical
impact; it's possible to read some of it from the list archives, but
that's always a frustrating form from which to look over the historical
events of the past. This means, necessarily, that my arguments and
evidence are going to be mixed together and not neatly separated; this
is a minor breach of a recommendation in rule 2205/4 (which recommends I
separately label the arguments and the evidence), but I consider the aim
of producing a usable historical record more important than that
recommendation, and as it's only a recommendation I can ignore it if I
have a good reason.
First, though, I'd like to talk about the role of a judge in such
matters. There are four ways that I could judge this CFJ, and remain
within the requirement of my Rules duties as a judge:
1. I could just rule TRUE on the basis that if omd is not a player, then
neither am I, and thus if tthe judgement is validly made, it cannot
possibly be incorrect. This complies with the letter of all the relevant
rules, but would fail to solve any of the underlying problems, and as
such would be unsatisfactory. Agora looks to judges to resolve
controversies; and even if it turns out that I'm not a player and can't
give the judgement, the important part of the judgement – the reasoning
– will still be available and settle matters.
2. I could check to see if the scam had succeeded at least as far as the
purported deregistration, ignoring everything that happened after that.
(For instance, as will be seen later, it's possible to make a reasonable
argument that the scam currently prevents reregistration, but did not
allow the purported deregistration to occur.) This would solve the
individual question asked in the status of the CFJ – whether omd is a
player – but still leave a lot of ambiguity (for instance, as to whether
teucer, who registered recently, is a player). This is what I'm going to
focus on first, and is also what will guide the actual final verdict
(because the statement of the CFJ, "I am a player" by omd, is inquiring
into whether the scam deregistered omd in particular, not whether it at
least partially worked in general, not whether it could have worked if
corrected).
3. I could look over the specific details of how the scam happened,
aiming to poke holes in them; it wouldn't be the first time that a scam
had failed due to minor errors by its perpetrator, or even minor errors
by someone unrelated (the Threat Trombones scam back in 1998 failed
because the Promotor made a typo, for instance). This does not solve the
underlying problems, in that varying the details could cause different
outcomes. However, it does serve a very useful purpose for Agora as a
whole; a gamestate change as major as deregistering most of the players
and gaining a dictatorship causes a /huge/ amount of uncertainty as to
what the true gamestate is, and discovering that this particular
instance of it failed would clean up the uncertainty (if not, perhaps,
potentially invite more damage due to players attempting to repeat the
scam; this would likely be considered very bad form, but a dictatorship
might be a large enough prize that players would try it anyway). I'll
consider this after considering the question of whether omd is a player,
because it's important to know which gamestate we're in.
4. I could rule about the underlying logical principles behind the scam.
This judgement is less important in the sense of determining what the
true gamestate is (something that I've repeatedly admitted is my highest
priority right now, especially because the rules that would normally fix
an uncertain gamestate for us are broken for reasons unrelated to the
scam), but many players are interested in knowing what the answer is.
I'll cover this later, after I cover whether Fool's attempt at the scam
worked or not.
I'm going to ignore option 1 as it's a total cop-out, and consider 2, 3,
and 4 in turn.
So first, a summary of what happened.
First, there were a few relevant proposals in the distribution of
proposals numbered 7530-7547 (whose voting period ended around the same
time the scam happened, and which thus had to be created first, over a
week before the scam itself); the most relevant ones are:
7535 by omd, which (if passed) would repeal rule 101 (a rule both most
aspirational, and which also contains many anti-scam restrictions, some
of which are definitely relevant here);
7537 by Fool, which uncontroversially gives em a dictatorship if it
passes (the proposal has AI 3 and the rule it creates Power 3,
sufficiently high for em to use eir dictatorship rule to perform any
action);
7541 by Fool, which fixed a bug in the definition of Parties (which
might incidentally have been used as a method to counterscam, although
it's unlikely such a counterscam could have succeeded).
The timing of proposal 7535 appears to have been entirely coincidental,
although fortunate for Fool's purposes. Interestingly, proposal 7537
contained the following footnote, which is a little chilling in
retrospect:
[ Same as failed prop 7494, but removed the controversial clause "Fool
SHALL respect the long tradition of players relinquishing the
dictatorship after a time and not actually abusing it." I expect this
will pass now. ]
The main part of the scam came in a few messages after that. First, Fool
created two Promises, quoted in full here because they're so key to the
case:
######################################################################
Title: Paraconsistency is overrated, part 1
Text: I transfer 1 Yak to the casher
Cashing condition: Casher is a first-class player.
Destruction by author condition:
The promise titled "Paraconsistency is overrated, part 2" CAN be
destroyed by its author with notice.
######################################################################
Title: Paraconsistency is overrated, part 2
Text: I transfer 1 Yak to the casher
Cashing condition: Casher is a first-class player.
Destruction by author condition:
IF the promise titled "Paraconsistency is overrated, part 1" CAN be
destroyed by its author with notice, THEN:
- the author of this promise CAN de-register all first-class
players other than himself by announcement; AND
- persons other than the author of this promise CAN NOT register.
######################################################################
In the same message, e took two further steps: giving notice that e
intended to destroy the promises (which, if the destruction by author
conditions are met, allows a promise to be destroyed between 4 and 14
days after the intent is given), and attempting to deregister every
first-class player other than emself. (Second-class players are rare in
Agora at the moment, and it's likely none of them can take any actions;
the Best Party is the only second-class player that claimed to be able
to take actions, but I think Agora as a whole did not believe that
claim. At any rate, it hasn't tried.) Note that under Agoran law, it's
possible to submit intent to perform an action, even if you don't
actually plan to perform it in the future; there's no current rule
against lying, and the intent is successful even if it's not the truth
when performed.
In eir next message, e purported to resolve the proposals, claiming that
eir own voting limit was 4 and everyone else's was 0, meaning that each
proposal passed or failed according to eir own vote. E voted FOR each of
the above proposals (7535, 7537, 7541).
And later that day, e sent one further message, purporting to use the
dictatorship rule created via proposal 7537 to allow nonplayers to
create proposals, prevent all other players registering, and destroy all
Parties with no members (which would only affect the Best Party in any
gamestate that I've heard mentioned as potentially correct).
So, about this specific scam attempt. Before coming to the main point
(the interaction of the promises themselves), I'm going to talk about
the proposals Fool attempted to force through. Fool made the following
argument on the discussion forum: "See the recent TIME OUT scam...
making someone not an eligible voter does set their voting limit to 0."
However, e seems to have missed the way that voting limits work in
Agora. An excerpt from Rule 683/17 gives us the basic definition:
{{{
Among the otherwise-valid votes on an Agoran decision, only the
first N submitted by each entity are valid, where N is the
entity's voting limit on that decision. The voting limit of an
entity that is not an eligible voter on an Agoran decision is
zero. The voting limit of an eligible voter on an Agoran
decision is two, except where rules say otherwise.
}}}
So as Fool points out, ineligible voters have a voting limit of 0, and
eligible voters have a voting limit that defaults to 2, but can be
modified. However, what about the purportedly deregistered players? We
have rule 1950/28 for that:
{{{
The eligible voters on a decision with an adoption index are
those entities that were active first-class players at the start
of its voting period. Setting or changing an entity's voting
limit on such a decision is secured with a power threshold of 2.
}}}
In other words, even if you deregister everyone, they're still eligible
voters on proposals that were pending at the time (because decisions to
adopt proposals have an adoption index). So their voting limit isn't
forced to 0 after all. (The recent TIME OUT scam, which made players
inactive, likewise doesn't actually work on vote resolution, for this
reason; however, it would have worked on proposal /distribution/, back
before the loophole was patched.)
If it isn't forced to 0, what is it? The decision in question were all
Ordinary, which gives us this definition, from rule 2389/8 (which was
the rule in force at the time of the scam; it's since been amended):
{{{
Ordinary is a Voting Chamber.
VVLOP is a player switch, tracked by the Assessor, whose value
is a non-negative integer; the default value for a player's
VVLOP is eir DVLOP. The voting limit of an entity on an
Ordinary Decision is eir VVLOP.
}}}
So, for players, we have a defined voting limit in rule 2389; they have
a VVLOP, and that's their voting limit. For nonplayers, rule 2389 has
trouble defining a voting limit; as a player switch, VVLOP isn't a
meaningful concept for nonplayers. There are only two reasonable ways to
interpret rules 683/17 and 2389/8 in this circumstance: that because an
eligible nonplayer doesn't have a VVLOP, they don't have a voting limit,
and thus have infinitely many votes; or because they don't have a VVLOP,
rule 2389 fails to set a voting limit, so it defaults to the definition
of 2 in rule 683. The second interpretation seems a lot more reasonable,
because we have a high-powered rule (683, at 3) strongly implying that
voting limits have to exist and are numbers, and because both game
custom and past judgements imply that values tend to be at their
defaults if there's no other reasonable value they could have (e.g. CFJ
3254, where a ruble was transferred back and forth infinitely many times
and ended up in the Lost & Found Department, even though nobody had
tried to transfer it there). As such, there is no gamestate in which
Fool's attempts to force proposals through passed, because rule 208/10
requires a tally of ballots:
{{{
[...] To be valid,
this announcement must satisfy the following conditions:
[...]
(c) It specifies the outcome, as described elsewhere, and, if
there was more than one valid option, provides a tally of
the voters' valid ballots on the various options.
}}}
and there is no reasoning via which the tally in Fool's purported
resolution is correct.
Probably the most noticeable effect of this is that none of Fool's
attempted actions matter, apart from the initial message; without a
dictatorship, e can't use it to do anything. Additionally, rule 101/14's
protection against unannounced Rule Changes is therefore very much in
force:
{{{
iv. Every person has the right to not be considered bound by
an agreement, or an amendment to an agreement, or a Rule
Change, which e has not had the reasonable opportunity to
review. For the purpose of protecting this right, a rule
change which would otherwise take effect without its
substance being subject to general player review through a
reasonably public process is wholly prevented from taking
effect.
}}}
With the uncertainty about the ruleset cleared up, I turn to the subject
of the uncertainty about the player list, and this impacts at the heart
of Fool's scam. The argument is a logical one; people have suggested
various different logics for evaluating things, but I'll restrict myself
to good old-fashioned classical logic (in which a contradiction implies
anything) to see whether the scam works even with the most favourable
interpretation. Here's Fool's argument as to why it works:
{{{
The sentences in question are not directly self-referential or even
mutually-referential. This is more of a Curry-flavoured confused
deputy,
with rule 2337 as the deputy. It says that the author can destroy a
promise with notice IFF the sentence in its "destruction by author
condition" slot is true. So:
- Sentence A: I can do Y.
- Sentence B: IF (I can do X), THEN (Z is true).
- Rule 2337 says that (I can do X) IFF (sentence A is true)
- Rule 2337 says that (I can do Y) IFF (sentence B is true)
As a result, R2337 says that (I can do X) IFF (IF (I can do X) THEN (Z
is true)). So, R2337 says that Z is true. And Z in this case is that I
can de-register everyone else, and that nobody else can register. This
is consistent and within the power of R2337: R869 secures
de-registration, and it has Power 2. And it does not secure the
prevention of people from registering. R2337 has Power 3.
}}}
The relevant parts of rules are this excerpt from 2337/7:
{{{
If a promise has one or more conditions under which the author
of the promise can destroy it, and they are all satisfied, then
the author CAN destroy that promise with notice.
}}}
and this excerpt from rule 2125/7:
{{{
c) The rules explicitly state that it CAN be performed while
certain conditions are satisfied. Such an action CANNOT be
performed except as allowed by the rules. In particular, if
the action in question is publishing a type of document, then
a public message is not that type of document (even if it is
labeled as such) except as allowed by the rules.
}}}
(Both rules have a power of 3, giving them effectively total power over
any part of the gamestate except when there's an outright contradiction
between one rule and another.)
However, there's been something of a deceit here. Fool has hidden
various complex statements inside eir variables X, Y, and Z. First, I
want to focus on the phrase "CAN destroy that promise with notice",
because performing an action with notice is something well defined in
the rules (here, 1728/32):
{{{
A rule which purports to allow a person (the performer) to
perform an action by a set of one or more of the following
methods (N is 1 unless otherwise specified):
[...]
4) With Notice.
thereby allows em to perform the action by announcement if all
of the following are true:
a) A person (the initiator) announced intent to perform the
action, unambiguously and clearly specifying the action and
method(s) (including the value of N for each method), at
most fourteen days earlier, and (if the action depends on
objections or notice) at least X days earlier, where X is a
number which depends on the Speed at the time of intention
as follows: Slow: 5, Normal: 4, Fast: 2.
}}}
This is a "dependent action"; you can destroy something by announcement,
if a) a rule purports to allow you to destroy it with notice; b) you
gave intent at least 4 (and at most 14) days earlier.
So how, from a strictly logical point of view, do we parse the statement
"the promise X CAN be destroyed by its author with notice"? The
definition in rule 1728 only technically applies to rules, but if we
make the reasonable expansion that it applies to promise conditions,
too, we get "the promise X can be destroyed by its author with
announcement, if e announced intent between 4 and 14 days earlier" (the
Speed is Normal at the moment). This backwards definition of dependent
actions takes a little getting used to, but not only does it follow from
the letter of the rules, it is also game custom ("I intend to do X with
Notice" ... wait 4 days ... "with Notice, I do X"). The only other
expanded definition that seems plausible is the one that Fool presumably
intended, "If promise X's author announces intent to destroy it with
Notice, e will be able to destroy it between 4 and 14 days later". The
second interpretation is only amenable to a subjunctive definition of
"if"; the first interpretation could use either a subjunctive or
indicative (i.e. strictly logical) definition of "if", which gives us
three potential interpretations for the chaos hiding inside Fool's
"Sentence A" (the destruction condition of eir first promise):
1. (first interpretation, logical) At least one of the following
statements is true: a) the author of the promise titled "Paraconsistency
is overrated, part 2" did not give intent to do so between 4 and 14 days
earlier; b) e can destroy that promise by announcement;
2. (second interpretation, subjunctive) If the author of the promise
titled "Paraconsistency is overrated, part 2" gives intent to do so now,
e will be able to destroy it by announcement between 4 and 14 days in
the future;
3. (first interpretation, subjunctive) If the author of the promise
titled "Paraconsistency is overrated, part 2" had given intent to do so
between 4 and 14 days earlier, then e would be able to destroy it by
announcement right now.
With the strictly logical point of view in 1., it is clear that at the
time Fool attempted to use the scam to deregister players, it simply
wasn't true that the intent had been given, and thus sentence A is
simply uncontroversially true (and sentence B uncontroversially false).
As such, the scam fails with this interpretation.
With the hypothetical in 2., we get time travel problems. In general, a
statement about things that will happen in the future is something that
can't meaningfully be considered to be necessarily true or false at any
point in time in Agora, because of the risk that the rules are amended
out from underneath it, and in particular, conditionals that talk about
future events are considered to be too ambiguous to be satisfied. (See,
for instance, CFJ 2926.) In this particular case, the risk of rules
being amended out from underneath the loop is very high; often it's
possible to at least make an argument about there being insufficient
time to pass a proposal or ratify a document, but in the case of a
dictatorship scam, whose entire purpose is to allow persons to perform
arbitrary actions, there's definitely a possibility that whether the
future conditional is true or false will affect actions in the future,
i.e. a time paradox. It would be uncontroversial that even an author
destruction condition as simple as "The day after the promise is
destroyed, its author posts 'CREAMPUFF' to a public forum" is not
satisfiable; the condition's truth or falsity cannot be determined at
the time at which it would have to be true. Besides, the promises might
be destroyed by other means in the meantime (if you don't have a
dictatorship, then you can't deregister other players, meaning that
attempts to cash the promises in question will succeed and destroy
them).
This brings us to expansion 3. The precedents are quite poor on whether
this sort of subjunctive conditional that talks about past conditions
that don't actually exist can work, but given that subjunctives are the
subject of CFJs all the time, it seems reasonable that the general
principle is valid. However, it has another issue: the intent to destroy
the promise would have to be before the promise's actual creation, in
order for the condition loop to exist in time for Fool's attempt to
deregister everyone to work. The relevant precedent is CFJ 2927, but
it's a poor precedent (not only are the arguments perfunctory and hard
to make sense of, they also don't match the judgement). It does seem
clear, though, that the promise would have to be clearly identified in
order to make an intent to destroy it (and even that might not be
enough); identifying a nonexistent promise merely via its title is
impossible (at least in part because someone could create another
promise with the same title), and if the promise were identified via its
text and conditions then it seems likely that players would attempt a
counterscam (e.g. restarting the Gerontocracy so as to be able to object
to the destruction). Besides, this sort of subjunctive, which doesn't
specify full details of the past action, doesn't evaluate as true merely
for there being some way to make the intent that would cause the
destruction to work; it only evaluates to true if all methods of making
the intent would cause the destruction to work, and that's clearly
false. So with this point of view, sentence A is definitely false, and
sentence B true, again without worrying about Z.
In other words, during the 4 days after Fool created eir promises, they
didn't cause any sort of logical loop or the like. Because eir mass
deregistration is pragmatic, rather than platonic (e has to specifically
announce that e deregisters players), and e didn't make such an
announcement after the 4 days had passed, it failed, and we're all still
players. (One of the things I did to prevent em fixing the scam in
response to this judgement was to cash eir promises, destroying them and
thus preventing them from being destroyed by their author in the future;
Fool will need a new intent in order to restart the scam, likely giving
us 4 days and some new leeway to counterscam.)
Now, this solves the issue of whether or not omd is a player (e is; at
the time Fool attempted to deregister em, e definitely couldn't),
allowing me to judge this CFJ TRUE, but it doesn't resolve the question
of whether the scam nonetheless worked (just with a 4 day delay while
the intents worked themselves out). With expansion 1. or 3. above, we
don't have any temporal problems due to the use of "CAN ... with
notice", because the notice was actually given (Fool believed this to be
irrelevant, but e's wrong). However, there are other potential holes
here. Let's quote Fool's argument again, as a reminder:
{{{
- Sentence A: I can do Y.
- Sentence B: IF (I can do X), THEN (Z is true).
- Rule 2337 says that (I can do X) IFF (sentence A is true)
- Rule 2337 says that (I can do Y) IFF (sentence B is true)
As a result, R2337 says that (I can do X) IFF (IF (I can do X) THEN (Z
is true)). So, R2337 says that Z is true.
}}}
I've been focusing on X and Y, but this time I want to focus on
something that Fool was taking for granted; the security restrictions on
the various actions involved. Here's the security restriction in 869/33
(which secures things at power 2 by default):
{{{
Changes to citizenship are secured.
}}}
and from 2337/7, the (power-3) rule being scammed:
{{{
Creating and cashing promises is secured with power threshold 3;
any other modifications to promise holdings are secured with
power threshold 2.
]}}
Now, let me expand this logical argument, in the same style as Fool's,
but adding rule 869, and making the security restrictions explicit:
{{{
- Sentence A: I can do Y.
- Sentence B: IF (I can do X), THEN (Z is true).
- Rule 2337 says that (I can do X) IFF (sentence A is true) OR
there is a power 2+ rule that allows destruction of promises
- Rule 2337 says that (I can do Y) IFF (sentence B is true) OR
there is a power 2+ rule that allows X OR that allows Y
- Rule 869 says that Z is false OR there is a power 2+ rule
that implies that Z true
}}}
Now, Fool is arguing that the rule 2337 loop is sufficiently powerful to
imply a mechanism for deregistering players into rule 2337. This takes a
bit of a split personality viewpoint on the rules; first the argument is
that "rule 2337 says that promises can't be destroyed except as written
in the rules, and there are no other rules that allow destruction of
promises in another entity's possession, thus the biconditional is a
true biconditional not a one-way conditional" (i.e. assuming outright
that any rules that don't specify a mechanism for destroying promises
can't destroy promises), and then later, "because the biconditionals
imply that rule 2337 allows deregistration of players, it gets around
the security in rule 869, being of a high enough power to imply a new
mechanism into the rules" (assuming that even if a rule doesn't specify
a mechanism for deregistering players, it can deregister players).
However, this argument is just as easily reversed. Rule 869 says (via
securing citizenship at 2, and the fact that there are no other rules
that allow a player to deregister another by announcement except as the
result of dependent actions that aren't satisfied) that players can't
(with the current set of intents, at least) deregister other players by
announcement. As such, if we follow the logic of the promise loop, we
find that there must be a mechanism to destroy promises other than the
one in rule 2337; any other situation would lead to a contradiction.
Fortuitously, rule 869, with its power of 2, happens to be sufficiently
powerful to get around the security restriction on promises.
So, following Fool's argument, we find that rule 2337 has a secret,
unwritten ability to block registrations and allow Fool to deregister
other players. But, there's another possibility using the same sort of
reasoning: instead of rule 2337 being able to deregister players and
block registrations, it's possible for rule 869 to allow Fool to destroy
eir own promises.
If we assume that these are the only possibilities, we quickly find that
the second possibility, which implies a mechanism to destroy promises
into rule 869, is less absurd, because it doesn't cause a contradiction
between rules. Adding a new mechanism to deregister players is "fine" in
that it creates no contradictions with any rule. However, blocking the
registration of players would cause an outright contradiction between
2337 and 869, because there's also the following paragraph of rule
869/33:
{{{
A first-class person CAN (unless explicitly forbidden or
prevented by the rules) register by publishing a message that
indicates reasonably clearly and reasonably unambiguously that e
intends to become a player at that time.
}}}
Sure, there's an "unless" clause that would mean no contradiction if
rule 2337 outright stated "Players other than Fool CAN NOT register".
But there's an "explicitly" in there, and I don't think anyone can
seriously argue that rule 2337 /explicitly/ prevents any players from
registering.
At this point, it's clearly been established that Fool's promises don't
do anything useful, interacting outside themselves; if they do anything
at all, it's to allow Fool to destroy them when e otherwise would be
unable to do so. However, this doesn't solve the problem of whether this
sort of scam could work in general, if the other problems could be
avoided (e.g. if promises were destructible by announcement rather than
with notice so that there were no time travel issues, and if Fool were
attempting to imply a mechanism to interfere with gamestate secured by a
rule with power below 2, so that the interpretation of the other rules
allowing destruction of Promises logically failed).
(As an aside, it's also worth talking about the counterscam attempts
along similar lines to Fool's, which used different statements, in order
to clarify the gamestate. Teucer's counterscam attempted to allow em to
repeal rules as its Z, which rams into both rule 101's prevention of
unannounced Rule Changes and rule 105's mindbogglingly high level of
security on rule changes, and also has the notice problem because I
cashed the promises before the notice period could run out; mine, which
prevents the creation Promises and allows me to change their conditions,
has the notice problem only partially, because I actually got the 4 days
of notice, but otherwise has the same problems as Fool's, because rule
2337 would self-contradict if it's forcing Z to possible and not X or Y
to true. As such, I conclude that none of the counterscam attempts did
anything either in terms of counterscamming, although Teucer's was
mostly a paradox attempt and I'm not opining on whether there's an
actual paradox there or not.)
Still, we have a bit of a problem in general here. Following the
reasoning so far, we can conclude that the scam implies that either it's
possible for Fool to destroy the "part 1" promise even if its author
destruction condition is true, or that it's possible for Fool to destroy
the "part 2" promise even if its author destruction condition is true,
or both. Rules normally logically collapse to something along the lines
of "X is possible AND Y is possible", but a rule that logically expands
to the form "X is possible OR Y is possible" is not the sort of thing
that players enact intentionally, because it leaves it very unclear as
to whether either of the actions is possible. In general, this seems to
indicate a problem with interpreting rules as logical expressions; the
nature of a rule isn't that of a logical expression, because there are
logical expressions that simply don't translate to rule form.
Even if you believe that Fool's scam worked entirely and my above
analysis on rule 869 is incorrect, it's still possible to draw
absurdities in general from this sort of scam, as we could substitute
any statement we wanted for Z, under Fool's reasoning. Time travel
paradoxes? Sure! What about a payload of the form "Either Fool can
deregister arbitrary players by announcement, or Fool can transfer Yaks
from arbitrary players to emself by announcement, but not both"? What's
a player trying to determine whether an action succeeded meant to make
of that (especially if e tries to take both actions)? There's clearly
something wrong with the kind of logical argument that lets you conclude
that one of a set of actions is possible, but without any knowledge as
to which.
The fundamental misunderstanding here, then, is to do with what it means
for a rule to prevent or permit something. If a rule permits a specific
action X via a specific mechanism Y, is that equivalent to saying that
the statement "A player CAN perform action X via mechanism Y" is true?
I'd argue that the answer here is "no". Consider the following
hypothetical rules:
{{{
Hypothetical Rule 1 (power 2)
A player CAN create a Hypothetical Example Asset by announcement.
A player CAN destroy a Hypothetical Example Asset by announcement.
Hypothetical Rule 2 (power 3)
Hypothetical Example Assets CANNOT be destroyed.
}}}
>From a strictly logical point of view, the first hypothetical rule can
be read as (X AND Y), where X is the ability to create our hypothetical
assets, and Y is the ability to destroy them. The second hypothetical
rule can likewise be read as (NOT Y). Clearly, there's a contradiction
here; and clearly, we'd resolve it as (X AND NOT Y) because higher-power
rules take precedence. From our strictly logical point of view, though,
we can't do that; if Y is false, then (X AND Y) is also false regardless
of the value of X, so there's no particular reason to conclude X to be
true. However, I think everyone would conclude players to be able to
create the hypothetical assets in this situation. This is a big clue
that Agora isn't interpreting the rules as logical statements.
So how are the rules being interpreted, then, if not from a logical
viewpoint? I'd argue that they're defining elements of gamestate, or
permitting/preventing/mandating/prohibiting actions, under certain
conditions. This gives us a clear way to resolve precedence problems
like the above; the two hypothetical rules conflict because one tries to
permit asset destruction and the other tries to prevent it, but there's
no conflict as to whether the asset creation is allowed. Likewise, the
plain language of rule 2337 permits destruction of promises under
certain circumstances, and the scam promises are simply just a circular
definition, just as much as "Author destruction condition: The author of
this promise CANNOT destroy it by announcement" would be a circular
definition. In a way, saying "action X is possible" as a promise
condition is just a form of shorthand, for a logical expression combined
out of all the conditions on rules that would permit or prevent action
X, and the problem with promise loops like these is that the condition
cannot be expanded, because it leads to an infinite regress. (Agora
always has had a custom that shorthand that would expand to an infinite
statement is not allowed.)
Even with a more logical view of conditions, the interpretation of rule
2337 as being "first, evaluate this condition; then, based on its truth
value, determine whether the destruction is allowed or not" completely
sidesteps the scam. You just end up with a straightforward UNDECIDABLE
evaluating the actual condition (which leads to a FALSE when determining
whether the destruction can be performed). The operation of the
condition itself has to be separated from that of the rule, just like
the multiple clauses of a rule have to be separated from each other; the
two cannot be merged into one statement, because then it'd be impossible
to resolve precedence wars between rules in any sort of sensible way.
(And besides, what is a power-0 condition doing trying to affect the
operation of a power-3 rule, anyway? It should go make its own mind up
whether it's true, false, or undecidable. What it can't do is imply text
into the rule to make itself more decidable.)
In the case of Fool's scam, we can create a version of eir argument more
accurate to the way the rules work like this:
{{{
- Sentence A: Y is permitted by some rule.
- Sentence B: IF (X is permitted by some rule), THEN
(Z1 is permitted by some rule and Z2 is prevented by some rule).
- Rule 2337 permits X when sentence A is true (and thus not
undecidable)
- Rule 2337 permits Y when sentence B is true (and thus not
undecidable)
- No other rule permits X or Y.
}}}
If we attempt to evaluate the truth value of sentence A, for instance,
we determine that it's undecidable; Z1 is not permitted and Z2 is not
prevented, so it collapses into an Epimenides paradox. Z1 and Z2 have no
reason to suddenly become permitted and prevented respectively in order
to resolve the paradox, because there's no Magical Paradox Prevention
Fairy trying to imply clauses into the rules in order to avoid
paradoxes. No rule permits Z1 (and at least one rule, 869, prevents it),
so it's disallowed, in just the same way as no rule permitting X means
that X is disallowed.
Or to put the fundamental flaw in this scam into sharp relief: the scam
only appears to work in paraconsistent logic because Fool carefully
(perhaps unintentionally) hid the parts of the reasoning that would fall
down under it. (In particular, reading about paraconsistent logic, the
mistake appears to have been interpreting "If a promise has one or more
conditions [...] then the author CAN [...]" as a logical if/then; in
paraconsistent logic, this phrasing doesn't translate to "Either the
conditions are false, or the rule permits...", but rather to "Either the
conditions are false, or the conditions are undecidable, or the rule
permits...") We can't decide that Z must be true because it'd cause A
and B to become undecidable otherwise; instead, we note that Z is false,
and A and B are undecidable as a result. Fool ignores this line of
argument entirely by assuming that there's a phantom IFF there right at
the start of eir argument!
In general, though, even ignoring paraconsistency, there is clearly
something wrong with a purely logical style of reasoning that merges all
the rules and conditions together first and then looks for paradoxes
later. You can't meaningfully evaluate precedence under such
circumstances; if multiple rules are involved in your paradox, you can
end up with actions being permitted when there's no obvious rule to
permit them; you can end up with rules that permit one action or
another, but you don't know which. The fact that you can produce Curry's
Paradox using this style of reasoning is relatively unimportant, given
that you can create much more absurd situations. Far better, then, to
look at what the rules imply first, and evaluate your conditions later.
Even if they're undecidable by then.
(As a side note, I was planning to hold off judging this until the 4-day
intent period had passed on my own counterscam promises; the idea would
be that with the reasoning that lead to Fool's promises working, mine
would too, and I could thus use them to combat the scam with no risk of
interference. Given that I'm pretty certain that the counterscam fails
for the same reason the original scam did, though, I see no reason to
wait.)
Summary of conclusions that apply regardless of the logical principles
behind Agora, for people trying to reconstruct the gamestate and who
don't want to read that wall of text:
- Fool's scam failed to deregister anyone
- Fool's scam failed to prevent anyone registering
- Fool's dictatorship rule never passed, and wouldn't have passed even
if the scam had succeeded in deregistering eveyone
- My counterscam failed (except inasmuch as I cashed Fool's promises);
- Teucer's counterscam failed to allow em to repeal rules
(no opinion on whether it's a paradox)
- and the statement of the CFJ is TRUE.
--
ais523
Judge, CFJ 3381
