I don't know if you covered this objection but his plan ultimately fails in essance he is hoisted by his own petard. promise one can only be destroyed if promise 2 and vice versa. HOWEVER if ether promise is destroyed the instant that sentence that destroys it is finished the promise is already gone and therefore CANNOT be destroyed at the EXACT second you would do a check to see if the condition is true to destroy the other. it is therefore humanly impossible by standard game logic to make fools plan work if timing is indeed a factor
On Tue, Aug 6, 2013 at 1:02 AM, Tanner Swett <[email protected]> wrote: > On Aug 4, 2013, at 7:07 PM, Jonathan Rouillard wrote: > > > > ============================== CFJ 3381 ============================== > > > > I am a player. > > > > ======================================================================== > > > > Caller: omd > > Arguments: > > Recently, Fool purported to deregister all first-class players other than > emself, by means of a logical deduction from a certain set of Promises. > This CFJ asks whether Fool's attempt succeeded. > > At first glance, it seems like the unavoidable conclusion is that Fool's > attempt did indeed succeed. Fool submitted two promises, titled > "Paraconsistency is overrated, part 1" and "Paraconsistency is overrated, > part 2" (which we will abbreviate as P1 and P2), with (essentially) the > following conditions for destruction by author: > > P1: P2 CAN be destroyed with notice. > P2: If P1 CAN be destroyed with notice, then Fool CAN deregister all other > first-class players. > > Rule 2337 "Promises" (along with the other clause in the rules stating > that if one rule says an action CAN be taken under certain circumstances, > then the action CANNOT be taken outside those circumstances) states (again, > essentially) that a promise can be destroyed with notice if and only if its > destruction condition is satisfied. So we apparently have the following two > axioms: > > (D-P1) P1 can be destroyed if and only if P2 can be destroyed. > (D-P2) P2 can be destroyed if and only if (if P1 can be destroyed, then > Fool can deregister all other first-class players). > > Under classical logic, it can be proven from these axioms that Fool can > deregister all other first-class players. The proof is as follows: > > Suppose that P2 cannot be destroyed. Then, by D-P1, P1 cannot be > destroyed, either. This means that the statement "if P1 can be destroyed, > then Fool can deregister all other first-class players" is vacuously true. > But this means that the left-hand side of the biconditional of D-P2 is > false, whereas the right-hand side is true; this is a contradiction. So we > can conclude that P2 can be destroyed. > > Since P2 can be destroyed, by D-P1, P1 can be destroyed, too. Thus, by > D-P2, Fool can deregister all other first-class players. > > It has been suggested that intuitionistic logic ought to be used to > interpret the rules, instead of classical logic. Unless I have made a > mistake in querying lambdabot, intuitionistic logic does not allow us to > conclude that Fool can deregister all other first-class players: > > <tswett> @djinn (p2 -> p1) -> (Not p2 -> Not p1) -> ((p1 -> fool) -> p2) > -> (Not (p1 -> fool) -> Not p2) -> fool > <lambdabot> -- f cannot be realized. > > However, intuitionistic logic does allow us to conclude that it is not > IMPOSSIBLE for Fool to deregister all other first-class players. This > conclusion seems no better than the conclusion that it is POSSIBLE for em > to do so. > > Agoran tradition seems to be to use a sort of vague paraconsistent rule of > thumb when dealing with paradoxes, namely, something like this: "when some > part of a rule contradicts itself, declare the truth value of the > contradictory statements to be 'paradoxical', and do not let this > declaration lead to any unreasonable consequences". But this is irrelevant > here, because there is no contradiction; Agora has no tradition (and > probably shouldn't have a tradition) of using any form of paraconsistent or > otherwise non-classical logic in the absence of contradictions. > > So, to recap, given the statements in the rules, it seems to be an > unavoidable logical conclusion that Fool's attempts to deregister all other > first-class players succeeded. However, I think there is a reasonable > nomic-philosophical (nomicological?) viewpoint according to which Fool's > attempts to deregister failed. > > Agora is a game that is played according to its rules. But what does it > mean to play according to a set of rules? One interpretation, perhaps the > traditional interpretation of Agora, is that the rules should be treated as > axioms in a logical system, and then the state of the game is whatever can > be concluded from these axioms. But the axiom interpretation is not without > its problems; indeed, one significant failing of this interpretation seems > to be the fact that it can produce paradoxes. > > I would like to suggest an alternative interpretation of the rules: > namely, that the rules are a complete and comprehensive set of mechanisms > for interacting with the game. Thus, even if it is possible to prove, using > classical logic, that some action CAN be taken, this proof is irrelevant to > the possibility of the action; the action can still only be taken if there > is in fact a mechanism for taking that action. > > Let us take another look at Rule 2337 "Promises" using the mechanism > interpretation. The relevant paragraph says: > > 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. > > Under the mechanism interpretation, this paragraph provides a conditional > mechanism for destroying a promise, and no other mechanisms. Even though > the paragraph logically entails that Fool CAN deregister all other > first-class players, e in fact CANNOT do so, because there is no mechanism > for doing so. > > So is the mechanism interpretation acceptable? I dunno. I feel like there > are a few things going against it. > > One objection to the mechanism interpretation is that you just aren't > actually playing the game if you're using the mechanism interpretation; > you're only actually playing the game if you're treating the rules as > axioms. Though a similar argument would claim that you're only actually > playing the game if you're treating the rules as axioms *under classical > logic*, in which case Agora became unplayable as soon as its first paradox > was introduced, or perhaps even as soon as two rules contradicted each > other. > > Another objection is that some clauses consist of definitions, and it > doesn't make sense to interpret a definition as a mechanism. But this could > perfectly well be fixed just by saying that some clauses are mechanisms, > and some clauses are definitions instead. > > Another objection is that a statement of the form "if X then Y" can't > really be interpreted as a mechanism, since the "if" and "then" form a > logical connective that's meaningless as a mechanism. I don't think this > objection is right at all, because you could perfectly well interpret that > as a mechanism for doing Y that can only be used under circumstance X. > > I definitely feel like there are more possible objections I've missed, but > I can't actually think of any. > > Consideration of the best interests of the game seems to prefer the > mechanism interpretation over the axiom interpretation: after all, under > the axiom interpretation, everyone but Fool has been deregistered, whereas > under the mechanism interpretation, we're all still players. > > TRUE appears to be appropriate. > > —Machiavelli
