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Are illogical worlds possible?

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Are illogical worlds possible?

nawitus
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Posted 05/07/08 - 05:00 AM: Subject: Are illogical worlds possible?	#1
Most physicist are starting to believe that there exists a massive number of different worlds with different physics than us, which would explain the fine-tuning argument for one, and explain why our world happens to have these laws and not others. Many philosophical arguments also use so called "possible worlds" that could exist, even though they don't have to actually exist, like so called p-zombie worlds which is identical to our world but no person is conscious. My question is that since people assume that different kinds of worlds that are logically possible can exist, can also illogical worlds exist? Maybe this question is impossible to answer using our logical systems and our rationality. If both logical and illogical worlds can exist, I wonder what else is possible.
"In a place like this, words fail. In the end, there can only be a dread silence, a silence which is a heartfelt cry to God -- Why, Lord, did you remain silent? How could you tolerate all this?" - Pope Benedict

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1 of 1 people found this post helpful Posted 05/08/08 - 06:11 PM:	#2
If we were to say that an illogical world could possibly exist, our statement would be literally meaningless because the only statements that we can make that are intelligible to us are logical statements. To say that an illogical world could possibly exist is to say words for which we can form no intelligible concept, and are therefore, merely words empty of meaning for us. Of course none of this has stopped theologians. Cheers. jd
OTOH I might be exhaustively wrong about everything I've ever thought--with the possible exception of this sentence.

muxol
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Posted 05/09/08 - 03:00 PM:	#3
This belongs probably in Metaphysics. In any case, some people analyze "impossible world" relative to worlds. For instance, a world w' is possible relative to a world w iff w' is a metaphysical "alternative" of w, so an impossible world, relative to a world w, is one that is not an alternative of w. (Here people may ask how to analyze "x is a metaphysical alternative of y".) Or you might think an impossible world is a "non-normal" one, in the formal sense. Then necessitation (if p is valid (w.r.t. a structure) then []p) fails there, and so in a sense it is "illogical" from the modal logical point of view. If you are asking whether there are possible worlds such that a contradiction holds there, then I think you have taken the notion of "possible" (and "world") too far, to the point of incoherence.

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Posted 05/10/08 - 02:36 AM:	#4
In relevant logics, you can have 'worlds' or 'states' at which both P and ~ P obtain. These are the non-normal worlds, but they are different than the standard non-normal worlds in modal logic mentioned by Muxol because those make every statement possible and no statement necessary, but they still make contradictions false. Relevant logic interprets negation differently. If ~P is true at a world w, then P is false at its star world w*, though not necessarily at w itself. Another possibility is one of the many valued logics. I would be interested in a many valued logic integrated into modal logic, but I'm not aware of such a thing.

muxol
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Posted 05/10/08 - 02:46 AM:	#5
We may call negation anything we like, but whatever it is, it is not analyzed in terms of the star operator for relevant semantics.

DoctorInWaiting
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Posted 05/11/08 - 06:16 AM:	#6
Noam Chomsky back in the day was the leader of this ideology. He devised that there are words that can sound logical despite they are nonsense.

WW_III_ANGRY
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Posted 05/11/08 - 07:42 AM:	#7
DoctorInWaiting wrote: Noam Chomsky back in the day was the leader of this ideology. He devised that there are words that can sound logical despite they are nonsense. Meh, millions if not more have devised this already and devise it without ever hearing it from Noam.

7
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Posted 05/11/08 - 12:44 PM:	#8
muxol wrote: We may call negation anything we like, but whatever it is, it is not analyzed in terms of the star operator for relevant semantics. I was only trying to illustrate the point that there are illogical (from a classical perspective) logics. If you believe that contradictions can be true, a many valued logic is your most likely choice. Whether or not contradictions can be true is a metaphysical issue, not a logical one.

muxol
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Posted 05/11/08 - 01:57 PM:	#9
7 wrote: I was only trying to illustrate the point that there are illogical (from a classical perspective) logics. If you believe that contradictions can be true, a many valued logic is your most likely choice. Whether or not contradictions can be true is a metaphysical issue, not a logical one. An "illogical logic"...hmmm. Common relevant logics lack a negation operator, which is why there are consistent sets (relative to a relevant logic) for sentences of the form A & ~A -> B. Of course, '~' does not denote negation in the corresponding relevant semantics. It is a substantial claim that all truth is metaphysically grounded, and most people believe it is (probably) false. Why should the truth of A -> A depend on anything metaphysical?

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Posted 05/11/08 - 02:47 PM:	#10
An "illogical logic"...hmmm. Illogical relative to classical logic, not illogical relative to itself, of course. Common relevant logics lack a negation operator, which is why there are consistent sets (relative to a relevant logic) for sentences of the form A & ~A -> B. Of course, '~' does not denote negation in the corresponding relevant semantics. Hmm, if w* = w, then relevant negation and classical negation are the same. P & ~P is always false at normal worlds. ~(P & ~P) is a theorem of R. I tried to prove this fast, but it requires the R rules, not just the B ones, so it is not that easy to prove. It is a substantial claim that all truth is metaphysically grounded, and most people believe it is (probably) false. Why should the truth of A -> A depend on anything metaphysical? I don't see any alternatives. It is not logically grounded. There are logics in which it is not valid, so in those logics there are counterexamples to it. You can say that these logics are irrelevant, that our world does not follow their rules, but this is metaphysics, not logic.

muxol
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Posted 05/11/08 - 04:18 PM:	#11
7 wrote: Hmm, if w* = w, then relevant negation and classical negation are the same. P & ~P is always false at normal worlds. ~(P & ~P) is a theorem of R. I tried to prove this fast, but it requires the R rules, not just the B ones, so it is not that easy to prove. Yes, and if you restrict the class of models to those all of whose worlds w are such that w* = w, then you don't have a relevant logic (in the sense that such a class of models fails to characterize a relevant logic). I don't see any alternatives. It is not logically grounded. There are logics in which it is not valid, so in those logics there are counterexamples to it. You can say that these logics are irrelevant, that our world does not follow their rules, but this is metaphysics, not logic. That depends on what do you mean by 'logic' here.

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Posted 05/11/08 - 04:41 PM:	#12
muxol wrote: Yes, and if you restrict the class of models to those all of whose worlds w are such that w* = w, then you don't have a relevant logic (in the sense that such a class of models fails to characterize a relevant logic). True, but even if you don't, you have classical negation at all of the worlds over which validity guarantees truth preservation. The only worlds at which it fails are the ones used to avoid the conditional paradoxes. Anyway, I don't hold that classical negation is the same as relevant negation in all cases, so I think we can let this rest. That depends on what do you mean by 'logic' here. I am not sure what you mean. Please elaborate.

muxol
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Posted 05/13/08 - 11:15 AM:	#13
Well I mean you say that there are "logics" which do not validate p -> p (or probably that for any formula whatever, there is a "logic" that invalidates it), but some people might refuse to call those "logics" 'logics'. Suppose you have a "logic" where transitivity of deducibility fails (e.g. one of Neil Tennant's relevant systems). One might have thought that transitivity is a necessary property of deducibility!

MoeBlee
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Posted 05/13/08 - 02:41 PM:	#14
nawitus wrote: My question is that since people assume that different kinds of worlds that are logically possible can exist, can also illogical worlds exist? What is an "illogical world"?

Boethiusman
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Posted 05/14/08 - 06:07 AM:	#15
What is an "illogical world"? I will attempt to answer MoeBlee here because it is clearly a question that must be answered before the actual question at hand. However, I have written with people unfamiliar with logic and math in mind. In the classical sense a illogic world would be one in which things exist and do not exist simultaneously (the same things). In this sense I would say illogical worlds do not exist. And I would be right! for everything in illogical worlds do not exist, according to the logic of illogic. But ... at the same time I would be wrong since those very things that don't exist also exist. However, classicism is on the way out it seems for abstract logic, but this doesn't get rid of the question "can classically illogic worlds exist". In new logic "a logic" is simply a system rigid rules, and so one interpretation of an illogical world would be "a world that doesn't follow the system of rules that it follows (indeed, that it follows rigorously ... without exception)". In both cases I do not think such worlds can exist, but I don't see how they can be "proven" to not exist for all the reasons already mentioned. However, there is another interpretation of illogic which is usually called "informal" - not a rigid set of rules. For instance, the mind seems to be an informal system. If the mind is informal then informal worlds can exist (indeed, we're living in one). Ironically, "informality" cannot be "formally proved", neither disproved, since by definition a formal system cannot "capture" an informal system to prove things about it's totality. A thing that is "suspicioned" to be informal can always be "suspicioned" to be formal, just much more complex than any formal system currently known. Neither proposition is provable as far as I know. However, formality of the mind would negate free will. Deciding one cannot make decisions I would argue is pointless to assume ... but it is another topic. The informal worlds hypothesis is interesting but I'm not sure it is the purpose of this thread (informal does not necessarily implicate contradictions or exceptions to the classical logical rules). Edited by Boethiusman on 05/14/08 - 06:18 AM

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Posted 05/16/08 - 01:21 AM:	#16
nawitus wrote: My question is that since people assume that different kinds of worlds that are logically possible can exist, can also illogical worlds exist? Maybe this question is impossible to answer using our logical systems and our rationality. If both logical and illogical worlds can exist, I wonder what else is possible. No, no, no. You just shifted your question erroneously. This is like a violation of the distributive and associative properties of multiplication. Your first statement is a proper reflection of a philosophical idea, such as that of Putnam's. You say: "[philosophers] assume that different kinds of worlds that are logically possible can exist...." Good. But then you followed it with: "Can illogical worlds [also] exist?" Er, false move. We ascribe logic or illogic to our ideas or thoughts or concepts. "Logically possible" means "It is logical for us to think [or assume] that..." So we say: If there is nothing illogical about thinking that p-zombie, twin-world, or BIV world can exist, then it is possible that p-zombie, twin-world, or BIV exist. We do not say an "illogic" world can exist. No such thing. To understand this better, read Putnam's Brains in a vat.
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