Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[CuddleBeam]

I just realized that if Principle of Explosion could be used at some
moment, Agora would become senseless chaotic soup, even if I attempted to
use my Explosion powers to remove the contradiction and re-stabilize Agora.

Yeah, it can be provable that I can do anything, but:

It can also be provable that I can do nothing.

It would just be Special Pleading to choose the stuff that is more
convenient to me. Everything would be indeterminate and nothing could be
known forever, even if the rule of Ossification even exists now, in the
past, in the future, at some time that was before itself, up, down, right,
potato, bananas...

So the Explosion thing actually wouldn't work to my advantage (unless I'm
some kind of arsonist of abstract spaces) even if at some moment I could do
it.

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Ørjan Johansen]

On Sat, 27 May 2017, Martin Rönsch wrote:

This is because the principle of explosion is a characteristic specific to 
classic first order predicate logic and it's extensions.


Actually you just need propositional logic, and intuitionistic is enough.

not A =def= A -> False
False -> B

are essentially axioms/definitions of the latter.

Greetings,
Ørjan.

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Martin Rönsch]

Am 27.05.2017 um 13:51 schrieb Alex Smith:

On Sat, 2017-05-27 at 11:10 +0200, Martin Rönsch wrote:

If that's not valid (which I don't think it is, but I'm new, so I know
nothing) then you'd have to somehow reconstruct Agora's logical calculus
from all the rules, CFJs etc. in order to see whether Explosion is
necessary to make it work.
This seems like an almost impossible task to me. Has anyone ever tried
to something like this in a thesis?

This thesis of mine was about a scam attempt using Curry's Paradox:


In particular, it talks about how there's no way to use Curry's Paradox
to create a gamestate change under Agoran law (rather, it ends up being
treated like an Epimenedes paradox, which is just a straightforward
DISMISS if done in a CFJ statement due to the
undecidability/circularity).



Thanks for sharing. I don't think I would have found that by searching 
on my own.
This is some well thought out stuff. Only after reading your thesis, 
your conclusion that the rules of Agoran don't really behave like a 
closed system of logical expressions seems obvious to me.


Veggiekeks

Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[CuddleBeam]

I personally picture Agora's (or any nomic's) "information-processing" to
be a sort of a sea of "axioms" which vary over time and whether you have
these axioms or those not depends on "where" you are, for example, who
judges your CFJs or who approaches to vote on other certain
"truth"-obtaining items ("truth" being simply a "tag" from a Platonic point
of view, we're never going to be truely Platonically Ideal because we're
suckass humans).

Since I imagine it to be "axiomatic" like that, I thought "well, there is
some combination of "axioms" which lets me pull the Principle of Explosion.
So I thought:

Am I at the right time and place for that to be be "true" in the nomic and
pull the trick?

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Nic Evans]

On 05/27/2017 09:10 AM, Nic Evans wrote:
There was a short-lived nomic that was loosely based of Agora's rules, 
including the power system, called nommit.


I should point out that if you search for 'nommit' you'll find a 
subreddit. That's where the game I'm thinking of was played, but 
nommit's gone through a few nomics since then I believe.

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Publius Scribonius Scholasticus]

It might be interesting to start a Nomic in which rules are expressed through a 
formal logic and that is grounded in a solid logical foundation.

Publius Scribonius Scholasticus
p.scribonius.scholasti...@gmail.com



> On May 27, 2017, at 10:10 AM, Nic Evans  wrote:
> 
> On 05/27/2017 04:10 AM, Martin Rönsch wrote:
>> I don't think the rules specify what kind of logic the game uses, so in 
>> order to get to Explosion you'd have to argue that Agora's logic is first 
>> order predicate logic by default.
>> 
>> If that's not valid (which I don't think it is, but I'm new, so I know 
>> nothing) then you'd have to somehow reconstruct Agora's logical calculus 
>> from all the rules, CFJs etc. in order to see whether Explosion is necessary 
>> to make it work.
>> This seems like an almost impossible task to me. Has anyone ever tried to 
>> something like this in a thesis?
>> 
>> Veggiekeks
> 
> There was a short-lived nomic that was loosely based of Agora's rules, 
> including the power system, called nommit. In that one we considered the 
> nomic to be based in a fuzzy logic. I don't think it came up at the time, but 
> I also think that you'd have to include modals.
> 
> In such a scheme, you could assign each statement the power of the document 
> that makes or secures it, modifying it (perhaps with > or < or other symbols) 
> to signify a statement that explicitly mentions an exception or priority.
> 
> The findings of CFJs and the statements made in them don't have any power 
> over rules, so they'd all have a power between 0 and 0.1. Additionally, the 
> statements in the reasoning of a CFJ should probably be considered 
> Possiblies. If we found two Possiblies that seemed entirely contradictory, 
> we'd just do a CFJ to determine which is correct. Formally that'd look 
> something like:
> 
> From CFJ X, 0.01◇(A)
> From CFJ Y, 0.01◇(-A)
> 
> CFJ Z:
> 
> Given CFJ X and Y, and [other reasoning employed by judge], I find that 
> >0.01◇(A).
> 
> Even this is over-simplified because, as veggiekeks alluded to, Agora isn't 
> really based on a logic. We'd have to build a logical notation out of Agora, 
> and such a thing would change frequently with the rules.
> 

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Nic Evans]

On 05/27/2017 04:10 AM, Martin Rönsch wrote:
I don't think the rules specify what kind of logic the game uses, so 
in order to get to Explosion you'd have to argue that Agora's logic is 
first order predicate logic by default.


If that's not valid (which I don't think it is, but I'm new, so I know 
nothing) then you'd have to somehow reconstruct Agora's logical 
calculus from all the rules, CFJs etc. in order to see whether 
Explosion is necessary to make it work.
This seems like an almost impossible task to me. Has anyone ever tried 
to something like this in a thesis?


Veggiekeks


There was a short-lived nomic that was loosely based of Agora's rules, 
including the power system, called nommit. In that one we considered the 
nomic to be based in a fuzzy logic. I don't think it came up at the 
time, but I also think that you'd have to include modals.


In such a scheme, you could assign each statement the power of the 
document that makes or secures it, modifying it (perhaps with > or < or 
other symbols) to signify a statement that explicitly mentions an 
exception or priority.


The findings of CFJs and the statements made in them don't have any 
power over rules, so they'd all have a power between 0 and 0.1. 
Additionally, the statements in the reasoning of a CFJ should probably 
be considered Possiblies. If we found two Possiblies that seemed 
entirely contradictory, we'd just do a CFJ to determine which is 
correct. Formally that'd look something like:


From CFJ X, 0.01◇(A)
From CFJ Y, 0.01◇(-A)

CFJ Z:

Given CFJ X and Y, and [other reasoning employed by judge], I find that 
>0.01◇(A).


Even this is over-simplified because, as veggiekeks alluded to, Agora 
isn't really based on a logic. We'd have to build a logical notation out 
of Agora, and such a thing would change frequently with the rules.

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Alex Smith]

On Sat, 2017-05-27 at 11:10 +0200, Martin Rönsch wrote:
> If that's not valid (which I don't think it is, but I'm new, so I know 
> nothing) then you'd have to somehow reconstruct Agora's logical calculus 
> from all the rules, CFJs etc. in order to see whether Explosion is 
> necessary to make it work.
> This seems like an almost impossible task to me. Has anyone ever tried 
> to something like this in a thesis?

This thesis of mine was about a scam attempt using Curry's Paradox:


In particular, it talks about how there's no way to use Curry's Paradox
to create a gamestate change under Agoran law (rather, it ends up being
treated like an Epimenedes paradox, which is just a straightforward
DISMISS if done in a CFJ statement due to the
undecidability/circularity).

-- 
ais523

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Martin Rönsch]

Am 27.05.2017 um 06:36 schrieb Nic Evans:

On 05/26/2017 10:24 PM, Ørjan Johansen wrote:

On Sat, 27 May 2017, CuddleBeam wrote:


So, "absurdity" is not meant in a formal way (non sequitur) but rather
how the consequences of the application of laws of logic feels like?


No, it _is_ formal, but from logic. "Reductio ad absurdum" (reduction 
to the absurd) is the Latin term for proof by contradiction.


Greetings,
Ørjan.


It's also worth noting that no proof via CFJs overrides rules. Given 
that many important actions are Secured (which explicitly restricts 
the mechanisms that can trigger them), these proofs couldn't grant you 
the power to perform them even if we accepted the proof.




I think even without all the reasons already mentioned, why the 
principle of explosion is not a thing with CFJs, it still wouldn't be a 
thing.


This is because the principle of explosion is a characteristic specific 
to classic first order predicate logic and it's extensions.


I don't think the rules specify what kind of logic the game uses, so in 
order to get to Explosion you'd have to argue that Agora's logic is 
first order predicate logic by default.


If that's not valid (which I don't think it is, but I'm new, so I know 
nothing) then you'd have to somehow reconstruct Agora's logical calculus 
from all the rules, CFJs etc. in order to see whether Explosion is 
necessary to make it work.
This seems like an almost impossible task to me. Has anyone ever tried 
to something like this in a thesis?


Veggiekeks

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Nic Evans]

On 05/26/2017 10:24 PM, Ørjan Johansen wrote:

On Sat, 27 May 2017, CuddleBeam wrote:


So, "absurdity" is not meant in a formal way (non sequitur) but rather
how the consequences of the application of laws of logic feels like?


No, it _is_ formal, but from logic. "Reductio ad absurdum" (reduction 
to the absurd) is the Latin term for proof by contradiction.


Greetings,
Ørjan.


It's also worth noting that no proof via CFJs overrides rules. Given 
that many important actions are Secured (which explicitly restricts the 
mechanisms that can trigger them), these proofs couldn't grant you the 
power to perform them even if we accepted the proof.

Re: Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Kerim Aydin]

On Sat, 27 May 2017, Quazie wrote:
> You used to be able to win by paradox - I think that got boring after a 
> while which is why it's gone - but two CFJs of the type you're talking 
> still wouldn't have met the bar for a win back then methinks.

We strictly barred CFJ-logic from paradox wins because they were trivial.
We started with this (R2110):

   If the legality of an action cannot be determined with finality,
   or if by a Judge's best reasoning, not appealed within a week of
   eir Judgement, an action appears equally legal and illegal, then
   the Speaker shall award the Patent Title of Champion to the
   first Player to publicly note that condition.  The Herald shall
   record that this Title was achieved "by paradox" in eir report.

This tied it to actions, trying to keep it from straight undecidable
CFJ statements.  It did lead to a CFJ-self-paradox win or two, so we
blocked a bunch of those trivial conditions by the end:

   A tortoise is an inquiry case on the possibility or legality of
   a rule-defined action (actual or hypothetical, but not arising
   from that case itself, and not occurring after the initiation of
   that case) for which the question of veracity is UNDECIDABLE.

   Upon a win announcement that a tortoise has continuously been a
   tortoise for no greater than four and no less than two weeks,
   the initiator satisfies the Winning Condition of Paradox.

Probably a bit of ennui in getting rid of it; whenever a true gamestate
paradox comes up, I think you'll want it back, so you might want to bring 
it ahead of time...

Re: Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Quazie]

You used to be able to win by paradox - I think that got boring after a
while which is why it's gone - but two CFJs of the type you're talking
still wouldn't have met the bar for a win back then methinks.
On Fri, May 26, 2017 at 20:48 Kerim Aydin  wrote:

>
>
> On Sat, 27 May 2017, CuddleBeam wrote:
> > OK so let me confirm to see if I get it and sorry for my insistence:
> >
> > So if I had:
> >
> > CFJ 1: A is True.
> > CFJ 2: A is False.
> >
> > I can reductio ad absurdum (although a really short one) CFJ 1 by just
> presenting CFJ 2, and CFJ 2 by presenting CFJ 1.
> >
> > With that, I would be barred from deducing anything from those ad
> absurdum (i.e. attempt to summon Principle of Explosion?)
>
> It would be just as if two people disagreed with each other, each
> asserting their opinion.  Then you moot one of them, and if it's
> upheld it's the guiding one, otherwise the other one is.
>
> Or, you could simply call CFJ 3.  We would go by the most recent one.
>
>
>

Re: Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Kerim Aydin]

On Sat, 27 May 2017, CuddleBeam wrote:
> OK so let me confirm to see if I get it and sorry for my insistence:
> 
> So if I had:
> 
> CFJ 1: A is True.
> CFJ 2: A is False.
> 
> I can reductio ad absurdum (although a really short one) CFJ 1 by just 
> presenting CFJ 2, and CFJ 2 by presenting CFJ 1.
> 
> With that, I would be barred from deducing anything from those ad absurdum 
> (i.e. attempt to summon Principle of Explosion?)

It would be just as if two people disagreed with each other, each
asserting their opinion.  Then you moot one of them, and if it's
upheld it's the guiding one, otherwise the other one is.

Or, you could simply call CFJ 3.  We would go by the most recent one.

Re: Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[CuddleBeam]

OK so let me confirm to see if I get it and sorry for my insistence:

So if I had:

CFJ 1: A is True.
CFJ 2: A is False.

I can reductio ad absurdum (although a really short one) CFJ 1 by just
presenting CFJ 2, and CFJ 2 by presenting CFJ 1.

With that, I would be barred from deducing anything from those ad absurdum
(i.e. attempt to summon Principle of Explosion?)

Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Kerim Aydin]

On Sat, 27 May 2017, CuddleBeam wrote: 
> >Moreover, the Principle of Explosion is the quintessence of what Rule 217's 
> >second paragraph is meant to forbid.
> 
> This, yes?
> 
>   Definitions and prescriptions in the rules are only to be
>   applied using direct, forward reasoning; in particular, an
>   absurdity that can be concluded from the assumption that a
>   statement about rule-defined concepts is false does not
>   constitute proof that it is true.  Definitions in lower-powered
>   Rules do not overrule common-sense interpretations or common
>   definitions of terms in higher-powered rules.
> 
> So, "absurdity" is not meant in a formal way (non sequitur) but rather how 
> the consequences of the application of laws of logic feels like?
> 
> I do honestly believe I need a better definition of the nature of CFJs too 
> though.

My personal thoughts, not everyone may agree:

CFJs are like house rules.  When the rules of a board game are unclear, there's
some general discussion about what's plausible, and eventually there's a 
decision
"well, let's interpret it this way."  It's good to be consistent (follow the
house rule once you've made it) because that's only fair in a game - so that's 
precedent.  But sometimes later on a contradiction comes up ("well if we made 
decision A, now later on it means we can't do B, so A must have been wrong").
Then you can decide to play like !A instead.  You might sometimes take back a
few moves as a result, back to a reasonable limit (for us, that's back to 
ratification).

If a situation comes up only once in a while, you might eventually forget the
old house rule, and the next time it comes up you make a different house rule.
That's fine.  Precedent fades.  And if the rules themselves are changing, 
sometimes you say - oh hey, that old house rule doesn't make sense, there's
an actual rule now.

In the middle of all this, if someone said "oh hey:  new house rule - there are
no house rules!" everyone would say, well that's silly, and dismiss the idea.

Also:  these are not too hard to spot in the CFJ archives, there's several.
I think it would be a REALLY INTERESTING THESIS for someone to do a
comparative study of some of the attempts over time.

Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Ørjan Johansen]

On Sat, 27 May 2017, CuddleBeam wrote:


So, "absurdity" is not meant in a formal way (non sequitur) but rather
how the consequences of the application of laws of logic feels like?


No, it _is_ formal, but from logic. "Reductio ad absurdum" (reduction to 
the absurd) is the Latin term for proof by contradiction.


Greetings,
Ørjan.

Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[CuddleBeam]

>Moreover, the Principle of Explosion is the quintessence of what Rule 217's 
>second paragraph is meant to forbid.

This, yes?

  Definitions and prescriptions in the rules are only to be
  applied using direct, forward reasoning; in particular, an
  absurdity that can be concluded from the assumption that a
  statement about rule-defined concepts is false does not
  constitute proof that it is true.  Definitions in lower-powered
  Rules do not overrule common-sense interpretations or common
  definitions of terms in higher-powered rules.

So, "absurdity" is not meant in a formal way (non sequitur) but rather
how the consequences of the application of laws of logic feels like?

I do honestly believe I need a better definition of the nature of CFJs
too though. I think Principle of Explosion would be extremely hard to
pull upon anything that has explicit hierarchy like the Ruleset, but
CFJs have no such explicit hierarchy, so I assume they're all at the
same level, so if there's contradiction, Principle of Explosion could
be summoned.

Unless CFJs themselves aren't to be considered really pure "Platonic"
items. Just official "Educated Guesses" on what is.

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Ørjan Johansen]

On Fri, 26 May 2017, Josh T wrote:


I also don't think the Principle of Explosion applies because DISMISS is an
option.


Moreover, the Principle of Explosion is the quintessence of what Rule 
217's second paragraph is meant to forbid.


Greetings,
Ørjan.

Re: Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[CuddleBeam]

I feel a lot less Platonist about Agora's formal space right now.

>I also don't think the Principle of Explosion applies because DISMISS is
an option.

Once two contradictory CFJs are found, why go back to DISMISS it?

Either:
1) The Principle of Explosion actually works and its an attempt to patch
it. In which case, it works anyway and you got god powers. How would trying
to go back and change it help?
2) The Principle of Explosion actually doesn't work. In which case, there
wouldn't be anything that actually merits a DISMISS in the first place, so
DISMISSING would be inappropriate, because there would be no actual target.

(Or do you mean DISMISSING a very obvious attempt to bait two contradictory
CFJs? Yeah, those cases would be easy to detect, I admit, but I don't see
how they could be DISMISSED. I meant more like contradictory CFJs created
by oversight which people don't notice and have gotten the TRUE/FALSE
stamps already a while ago)

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Josh T]

I also don't think the Principle of Explosion applies because DISMISS is an
option.

天火狐

On 26 May 2017 at 22:32, Nicholas Evans  wrote:

> More like guidelines, and generally newer overrides older.
>
> On May 26, 2017 9:30 PM, "CuddleBeam"  wrote:
>
>> Would this be a valid way to scam?
>>
>> Or are CFJs more like guidelines?
>>
>

Re: DIS: Find two contradictory CFJs -> Principle of explosion -> Do anything

[Nicholas Evans]

More like guidelines, and generally newer overrides older.

On May 26, 2017 9:30 PM, "CuddleBeam"  wrote:

> Would this be a valid way to scam?
>
> Or are CFJs more like guidelines?
>