Talk:Possible world

CSTAR
My edit consisted primarily of breaking up a very long paragraph and deleting what seemd like extraneous examples. CSTAR 00:33, 29 Dec 2004 (UTC)

?
Why aren't false propostions listed as one of the possible states, early in the articile, under possibility and contigency? Am I missing something?

Fixed now. See my edit summary.--Noetica 22:23, 8 January 2006 (UTC)

Comparison of possible worlds and many worlds
These differences I don't think are accurate. Causal relation? No, at least not in any cklassical sense. They are entangled yes. I wil try to correct this. CSTAR 15:01, 24 Jan 2005 (UTC)


 * Well, in the Everett & Wheeler version of the many-worlds interpretation, both components of the wave function continue to exist after measurement because the world splits into many worlds &mdash; which means that each of those resulting worlds is causally (or quasi-causally?) as well as temporally related to the parent world. Possible worlds, on the other hand, are defined by Lewis as being spatiotemporally and causally isolated, and while this has been challenged as a defining characteristic, I don't think that anyone (realist or ersatzist) has denied that it holds true of them. You also removed the point about potential and actual infinity; why?  Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; ) 15:46, 24 Jan 2005 (UTC)


 * Possible worlds, on the other hand, are defined by Lewis as being spatiotemporally and causally isolated: Is this really true for time modality? (e.g. If I exercise for a few a few days, then  I may lose weight)  The possible worlds semantics in this case, are branching worlds (which of course are not entangled).


 * Well no &mdash; few possible-worlds theorists accept branching worlds (though possible-situation theorists like Edgington &amp; Humberstone argue for them), and certainly not Lewis. Your exercise example would normally be expressed in terms of PWs as: "There's at least one possible world at which I exercise for a few days and then lose weight."  There's no temporal relation between the actual world and the possible world in question (though, of course, the possible world is itself temporal). Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; )
 * Your PW expression isn't accurate. For instance, if I work at it tomorrow, I may find a proof of Goldbach's conjecture, but that doesn't mean that there's necessarily at least possible world in which I will find a proof of Goldbach's conjecture -- it may be undecidable, in which case there is no such proof to find. 68.6.40.203 12:27, 17 August 2005 (UTC)


 * about potential and actual infinity: Well because I don't think the statement there was true. In the technically most refined form of the many-world interpretation, the many worlds state space is a continuous superposition of Hilbert spaces. In this case case, it seems misleading to say this is only a "potentially" infinite number of many worlds. The infinity of the worlds is as actual as the many worlds themselves.  CSTAR 17:48, 24 Jan 2005 (UTC)


 * OK, I'd been thinking in terms of the Everett/Wheeler account that I referred to above &mdash; on that account the worlds come into being when the act of measurement leads to the splitting into multiple worlds. My expertise is on the philosophical side rather than the physics side.  Could you recommend a (reasonably introductory) account of the view you describe?  I could find no mention in the books I happened to have on my shelves. Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; ) 18:30, 24 Jan 2005 (UTC)


 * There is the WP reference. Note that I made most of the edits to it, so if you want a more neutral account maybe look at Michael Price's FAQ which is listed as a reference. BTW I am not myself a many-worlder, although I think the account I gave in that article is fair, technically very accurate and pretty much complete.  The usual accounts of many worlds do only have finitely many splittings at discrete time instants.  However, the reason for this is technical. One can easily have


 * Infinitely many splittings at each measurement (this actually is accounted for in the WP article)
 * Continuously occurring splittings. For instance, one could argue, that conscious observation which occurs continuously is a form of measurement. (Now I am completely agnostic on this and I am not sure it even means anything, but I just propose it as a possible example). This is only hinted at in the WP article.


 * I'm certainly happy that you are making modifications to the article. I'm a little out of my depth here.  Although I am more of mathematical physicist,  I jumped in because (a) I am fairly at ease with issues of logics and formal semantics and (b) what was in the article before was some pretty wild stuff.  Please edit the introductory section as well. The article needs input from a technical philosopher.CSTAR 19:19, 24 Jan 2005 (UTC)

Thanks for your responses. I'll have to go away and think about this. I'd certainly like to expand this article, so watch this space! Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; ) 19:45, 24 Jan 2005 (UTC)

I'll weigh in. Modal realism and the philosophy of David Lewis is not my strong point, to be honest I don't have a lot of sympathy for either, but I think: I suggest that we define possible worlds semantics to subsume possible situations semantics, and point out that some people may use a narrower reading of possible worlds. Charles Stewart 13:44, 25 Jan 2005 (UTC)
 * Mel is quite right to say that David Lewis conceives of possibility as being isolated: everythig I have read about Lewis has him conceiving of them as alternate realities;
 * This is not true of all possible worlds theorists: I have heard a philosopher defend the existence of non-actual possible worls on the grounds that the world as it was in 1950 is a possible world that has ceased to be actual: there were several philosophers there and noone found this claim strange; I also have the idea that I heard Stalnaker talk of the possible worlds semantics of time. Michael Dummett, though no possible worlds theorist, talks about S4 and M as being rivals to S5 for the mantle of the alethic modality: clearly a conception of necessity that insists there is no branching structure is insisting that S5 is the right alethic modality, which looks controversial to me;
 * CSTAR's example of continuous Kripke structures is to the point, though one intuitionists have models of the continuum that are based only on potential infinities (by means of choice sequences, which have a very natural modal reading);

Postscript Mel wrote on CSTAR's talk page:
 * The comment that you left on my own talk page, though, propmpts another worry &mdash; are we using &quot;potential infinity&quot; differently? I meant by it that at no point in time is there an actual infinity of worlds, though there's no built-in end to the sequence (leaving Armageddon out of it).  If that usage is the problem, can you suggest a way of expressing my point that would be unambiguous? Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; ) 18:41, 24 Jan 2005 (UTC)

If you say that the fine structure of past time is a mapping from a real valued time variable onto "the world at that past point", then one is positing an uncountable infinity of past worlds in the last second. Yes, the model is naive, but it's also how the simplest continuous models will work. Charles Stewart 13:56, 25 Jan 2005 (UTC)


 * Thanks Chalst. I'm glad to see the page is getting some attention. I was a little daunted at first, but thought the confusion that exists between many worlds and possible worlds was worth the risk of being in over my head. Note one other remark: my comparison of interpretation of quantum mechanics and interpretation of modal logic.  Now this comparison is strained and also risks confusion. Many worlds conceivably could be thought of as a semantics for wave-function collapse, but I'm skeptical whether this view will stand critical analysis, and is not just a play on words. I went ahead and did it anyway almost as a high-brow joke.  But if there is a philosopher out there who wants to tackle that part, please do so.CSTAR 14:47, 25 Jan 2005 (UTC)

Not sure who wrote this: "For another example, the claim that you can't eat just one more potato chip would be formulated in terms of possible worlds by saying: there is no possible world in which you eat just one more potato chip." That's not quite right. For there to be no possible world in which etc, it would have to be necessarily false that you could eat etc., which of course it wouldn't be. SlimVirgin 09:23, Feb 1, 2005 (UTC)
 * It wouldn't be because the statement is false -- you can eat just one more potato chip. We don't know whether, if the statement were true, it would necessarily be true. 68.6.40.203 12:27, 17 August 2005 (UTC)
 * Understanding that there are other worlds isnt hard for me, i guess i dont understand if i should make up things or if i am somehow supposed to know information. It is driving me insane actually, not getting this. I am just frustrated and feeling left out. Any advice ? 174.251.135.26 (talk) 15:20, 30 July 2023 (UTC)
 * But the original quotation confuses ability with possibility (and possibly ignores the difference between physical and logical necessity). Mel Etitis ( &Mu;&epsilon;&lambda; &Epsilon;&tau;&eta;&tau;&eta;&sigmaf; ) 09:41, 1 Feb 2005 (UTC)

And is this right? Paragraph three:
 * "The concept of a "possible world" employed here is that of a complete specification of a way the world could be (or could have been). So, for example, if I could choose to blow off work to go to the movies today, and I could choose not to blow off work to go to the movies today, then that distinguishes two sets of possible worlds: those worlds in which I did go to the movies, and those in which I did not."

I've rewritten paragraph two. Para three needs it too, I would say. SlimVirgin 09:47, Feb 1, 2005 (UTC)
 * I've deleted paragraph three in the meantime, as it's confusing what's really possible with what is logically possible, which is what possible-worlds logic deals with. There may be some way it can be rewritten. Hope that's okay. SlimVirgin 09:56, Feb 1, 2005 (UTC)

I really don't think the two have much to do with each other, I would seriously consider deleting this section, even if there were some kind of link between the two concepts this section would probably just confuse readers. Don't the "many worlds" of quantam physics share the same history?- Timothy J Scriven

I'm going to comment on a six year old thread to say Mr Scriven was correct, it's a totally different ballgame and textbook WP:SYN. Apparently, it's been deleted.—Machine Elf 1735 (talk) 02:37, 28 November 2010 (UTC)

New intro section
It seems to me that the phrasing of the current intro section has needlessly entered a dangerous combat zone:


 * the proposition that I am writing this for the Wikipedia can be expressed as: "There is a possible world in which I am writing this for the Wikipedia," which means that the proposition is contingent; that is, it could be otherwise.

This is confusing, because there is also the litle fact about what is actually true. You did write that for wikipedia in the world that is actually true right? Could we please avoid that whole discussion (of actualism etc ) by using some other example at least in the intro?


 * On the other hand, the proposition "Two plus two equals four" is necessarily true — that is, it is true by definition.

Whoa! You are entering an extremly active war zone: The nature of mathematical truth, truth by definition. Yikes, I want get outta this one before I get hit by an RPG.

Wasn't this disproved by Godel?


 * This can be expressed as: "There is no possible world in which two plus two does not equal four."

Well, I don't know. If ZF is inconsistent is not the opposite also true? Is there a possible world in which ZF is inconsistent? I mean, I don't claim I have anything intelligent to say about these questions, but unless you are prepared to stave off philosophical RPG's I "wouldn't go there". In conclusion, I suggest you replace that example. Although the Potato Chip example wasn't mine, maybe it wasn't so bad after all.


 * Could somebody please remove the potential infinities from the many worlds example? The statement is simply not true. I tried doing so and it was put back in.CSTAR 17:35, 1 Feb 2005 (UTC)

Hi CSTAR, the intro confused real possibility with logical possibility. Possible worlds logic (modal logic) deals with logical possibilities. Two plus two equals four is a necessary truth, which means it is true in all possible worlds. On the other hand, the proposition "There is an online encyclopedia" is true only in some. There is a debate about the nature of logical possibility. Some would agree that there is a possible world in which I am a fried egg. Others would say that is not correct, because it misses the point about my identity, so the issues are not clear cut regarding how far from the actual world our possible worlds may stray (how far from real possibility logical possibility may stray), but the potato chip example was simply a question of physical ability in this world -- I don't recall it exactly but it was connected to a person's actual ability to eat a certain amount, and that has nothing to do with possible worlds.

Regarding your inconsistency query: A contradiction is false in all possible worlds. "The cat is on the mat and the cat is not on the mat" is necessarily false. Is that what you meant? SlimVirgin 18:35, Feb 1, 2005 (UTC)


 * Not quite. We don't know if ZF is inconsistent (as I'm sure you know better than I do we have relative proofs etc). However, the following statement is perfectly sensible (I am arguing only that it is sensible, meaning that if I said it in a conversation, I bet you would probably know what I meant, not that it uses the notion of possible world correctly)


 * (A) In a possible world that ZF is false, set theorists would have a hard time finding jobs.


 * Now does (A) fit into a possible worlds semantics? As I mentioned we don't know for sure that it is a contradiction, and in fact at one point in his carreer Edward Nelson regarded himself as "working like a termite" to bring down the edifice of set-theoretic math (I think he gave up). Possibly (A) does not fit into the possible worlds semantics (and I admit I don't know enough about possible worlds) but this is something that thoroughly confuses the issue in the introductory sentence.


 * Incidentally, the metric on the set of possible worlds should be more clearly defined. If we think of a possible world as specified  by a set of atomic propositions, then is the distance the Hamming distance between the infinite bitstring of truth values of these atomic propositions? CSTAR 19:18, 1 Feb 2005 (UTC)


 * Is this the sentence you meant: "There is an actual infinity of possible worlds but only a potential infinity of quantum-theoretical worlds."?


 * I'm also unclear what the difference would be between an actual infinity and a potential one; and how would anyone know that the actual infinity really was actual; and can we have actual infinities of possible worlds? Hmmm . . . Having said that, I know almost nothing about quantum physics, so perhaps it does make sense. SlimVirgin 18:44, Feb 1, 2005 (UTC)


 * Yes that is the sentence; as a I said in an earlier exchange (with someone else) the infinity of the possible worlds is as actual as the actual worlds themselves. CSTAR 19:18, 1 Feb 2005 (UTC)


 * This is mathematics so I'm happy to say I don't know how to address it. Sorry. Did you ask the person who put it back in? SlimVirgin 19:46, Feb 1, 2005 (UTC)

Some suggestions
This article seems to be in a bit of a confused state, and I think that's because it's diving into difficult issues without getting its bearings. My suggestion for how to resolve this is to write a more introductory article on the exdpanded topic of Alethic modalities and possible world semantics, which begins from scratch with the general idea of alethic modalities, Lewis's systems S1-S5 and system M, which will crystalise where the controversies are. Then: I've thought a bit about the dispute between CSTAR and Mel, and I think I know what's going on. Mel has a very tight conception of what the alethic modalities are, which I think means he thinks S5 is the right axiomatisation of possibility: given this then the two disputed points that Mel reinstated from the possible worlds/ many worlds comparison are seen to be valid. I've deleted them again, because I think as it stands Mel is using a conception of modality that is itself disputed, so his points are POV. For the sake of completenes they were:
 * We have a better introductory article for modal logic than modal logic;
 * When we talk about the metaphysical subtleties in possible world semantics, we are armed with the right vocabulary to characterise them.
 * quantum-theoretical worlds are temporally (and perhaps causally) related, while possible worlds are not;
 * there is an actual infinity of possible worlds but only a potential infinity of quantum-theoretical worlds Charles Stewart 20:32, 1 Feb 2005 (UTC)

I can see how you're using the term potential infinity, but how are you using actual infinity to refer to possible worlds? SlimVirgin 22:24, Feb 1, 2005 (UTC)


 * I'm not sure if this question is directed to me: my point was that it makes no sense to refer to a potential infinity in referring to the set of universes whose pure quantum states are superposed to obtain a description mathematically equivalent the mixed quantum state describing the statistical behavior of the universe and instrumentally described by the various quantum algorithms. CSTAR 22:43, 1 Feb 2005 (UTC)


 * If it wasn't clear, the last two bullet points in my post above came from Mel. An issue may confuse: you may have an actual infinity of things that don't exist, or a potential infinity that exceeds any finite bound of things that do.  So the non-actuality of only-possible worls is not a proble with the number of them being an actual infinity.  The S5 interpretation of possibility says that all possibilties are equally accessible from each other, which suggests you think of the collection of possible worlds as an actual infinity; this being philosophy, of course one can resist the suggestion.  Above, in the exchange with Mel, I pointed out an argument for considering the infinitude in many worlds interpetation as also being an actual infinity.  Charles Stewart 13:52, 2 Feb 2005 (UTC)

Comments on remarks above, and on my recent editing
Notes on things above


 * Yes, for Lewis worlds are indeed utterly without temporal, spatial, and causal relations between them. If any two objects have such relations between them, that means they are "worldmates". He allows for other notional ways of individuating worlds, but firmly prefers this one (usually and most explicitly presented in terms of spatiotemporal relations). He is as definite about temporal relations as he is about the others. Some of the discussion above is mixed up because of a confusion between absolute and relative conceptions of time (as we might put it). A theorist might say that there is a possible world at which history stopped in 1950, for example: but this does not require any commitment to some absolute, transworld 1950.


 * I think that the whole business of potential and actual infinities is obscure, and best not mentioned in the article. It is not particularly germane, anyway.


 * SlimVirgin wrote: "the intro confused real possibility with logical possibility. Possible worlds logic (modal logic) deals with logical possibilities." But the differences between this "real" possibility and "logical" possibility are the subject of a great deal of dispute. For Lewis (no great friend of "graded" possibilities), the extension of the two in the space of possible worlds is the same. (Lewis was always unhappy with the characterisation of his theory as modal realism, by the way. But of course it stuck!) It seems that David Chalmers, among others, believes in a crucial difference between real and logical possibilities; and the difference seems to correspond to some well-entrenched but scarcely ever well-examined intuition.

My editing

I have strong views in this domain, but I have suppressed these in the interest of NPOV. I have copy-edited the entire article, fixing (as I boldly say!) some small matters of punctuation, grammar, and style (in the interests of clarity and consistency). I have removed a couple of inaccurate uses of "physical", in the presentation of Lewis's theory. I have split things at the beginning, to provide a section on the relations between talk of possible worlds and talk of necessity and contingency. I have fixed an example at the very start that had gone badly awry. I have provided a useful external link to Alex Pruss's superb doctoral thesis; it has a wealth of philosophical, mathematical, and physics detail, and I strongly recommend that people have a look at it. (I disagree with a good deal of it myself, but for now I prefer to continue setting aside my own opinions.) I have continually borne in mind the need for precision and clarity, and I hope that this attitude will cause my edits to be received as not too intrusive! I would welcome comments. --Noetica 10:29, 26 Feb 2005 (UTC)

Radgeek's editing

Radgeek, some of your alterations are just fine, I think. But unfortunately the quite rational classification you present does not correspond perfectly with standard usage. It's good enough, I say, except for your actual proposition. This is not an accepted way of referring to true propositions, as a Google search will demonstrate. Consider this excerpt that I found, of a rare occurrence of actual proposition in philosophical discourse, where actual and true are not equivalent:

The definition of truth-object brings to light a feature of propositional senses which, to my knowledge, has not previously been explicitly identified, namely that in order for an actual proposition to be true, its sense -- the state of affairs in which it is true -- must entail a state of affairs in which the proposition is inscribed as a propositional sign. [from www.cs.yorku.ca/~peter/MH/truth.html]

I note that your link from actual proposition led to modal logic, where there is quite properly no use of the phrase! I have substituted a link to truth.

I have lightly edited the section again, retaining what I consider to be the worthy structure that you have imposed. See my edit summary; but note that I have also sought to put the "the" back in "consider the actual world to be one of the many possible worlds". We could discuss this, if you think we need to. Did you have a reason for removing it?

I think the section is quite satisfactory as it now stands. --Noetica 21:39, 26 Feb 2005 (UTC)

Proximity
I am still unhappy with the lack of explanation of what it means for a possible world W1 to be near possible world W2 in respect of R as in the paragraph:


 *  A possible world W1 is said to be near to another possible world W2 in respect of R to the degree that the same things happen in W1 and W2 in respect of R; the more different what happens in two possible worlds in a certain respect, the "further" they are from one another in that respect.) To use the example of a counterfactual given earlier, "If George W. Bush hadn't become president of the U.S. in 2000, Al Gore would have," this sentence would be taken to express a claim that could be reformulated as follows: "In all nearest worlds to our actual world (nearest in relevant respects) where George W. Bush didn't become president of the U.S. in 2000, Al Gore became president of the U.S. then instead." And on this interpretation of the sentence, if there is some nearest world to the actual world (nearest in relevant respects) where George W. didn't win but Gore didn't either, then the claim expressed by this counterfactual would be false.

Is a possible world W determined by an assignment of truth-values to a maximal set P of atomic propositions which completely describes a possible world (e.g.once atomic proposition in P would be George W. Bush tried to eat a pretzel at 7:03 PM EST Friday February 25, 2005 in the oval office)

Is nearness of W1 and W2 a measure of how many atomic propositions in P are assigned different truth values in W1 and W2? What is the role of R ? Is R to be interpreted as a subset of P?

This may be an excessively formalistic view of the concept, but how else are we going to produce an acceptable understanding of the above?CSTAR 22:09, 26 Feb 2005 (UTC)

CSTAR, I agree that there are some difficulties with the paragraph you quote, and I commented in my edit summary that the section still needs some work. I meant that very paragraph. The expression is somewhat opaque, apart from anything else. As I said to you on your own talk page, the specific matters here are not my area. It is generally said that nearness of possible worlds is a vague matter, and the matters of context that would settle nearness are hard to get specific about. This will make the more formally and mathematically inclined uneasy; I for one sympathise, but can do little to help. I think the practical solution in the paragraph you quote is to retract some of the detail, or to add a note about nearness being irremediably vague. --Noetica 22:59, 26 Feb 2005 (UTC)

Section on the nature of possible worlds?
I'm thinking of adding a new section to the article that discusses the nature of possible worlds (i.e. what a possible world is), and sketch the popular theories, like modal realism, actualism etc, and link to the actual pages for more information. What does everyone think of this? Athanatis 00:42, 8 November 2006 (UTC)


 * Nature of possible worlds is a bit broad. Surely much that could be called that is already covered here. Do you mean ontological status, or what? (There is, of course, the article Modal realism, which is not very well developed, to link to, as you suggest. I've been meaning to work on it myself, but haven't found the time. I did remove some poorly written and heavily POV material, earlier.) More information please! – Noetica 00:50, 8 November 2006 (UTC)

Bias?
I know that this being the english language wikipedia, it does have a bias and has extensive content dealing with topics concerning the anglosphere but I am sure that you will agree with me that other examples could be written, examples that don't primarily deal with U.S former presidents. This is a philosophical topic, therefore for the sake of clarity and (as far as possible) universal comprehension of this article to everyone that speaks english (not just americans or brits), can somebody write a non-america focused example of true and false propositions? I was thinking in making the edit straight away but I somehow sense I would have faced widespread opposition. Thanks in advance Rodrigo Cornejo 20:00, 19 December 2006 (UTC)

"Necessary" as a sufficient condition for being "possible"?
In the "Formal semantics of modal logics" section I disagree with the following sentence:

(Note that by these definitions all necessary statements are also counted among the possible statements, and of course among the true statements.)

To quote Graham Priest (An Introduction to Non-Classical Logic, p. 22): "Note that if w accesses no worlds, everything of the form ◊A is false at w - if w accesses no worlds, it accesses no worlds at which A is true. And if w accesses no worlds, everything of the form □A is true at w - if w accesses no worlds, then (vacuously) at all worlds that w accesses A is true" (◊ meaning possible and □ meaning necessary) and in a footnote following this text: "Recall that 'all Xs are Ys' is logically equivalent to 'there are no Xs that are not Ys '.

Therefore, a necessary statement is not necessarily (!) also a possible statement nor even a true statement. --Rasmuskold 02:13, 11 January 2007 (UTC)


 * Fair enough, Rasmuskold. But note that you (and Priest) are talking about the very peculiar case in which w is not accessible even to itself. So ◊A is false at w even if A is true at w. The serious question we must ask ourselves is this: Should we bother with this oddity, in an elementary article? Surely it would be sufficient that there be a link to modal logic (which I am now adding, by the way), and there is already a link from that article to accessibility relation. If there are further amendments to make, let them be made at this last-mentioned article. – Noetica 02:49, 11 January 2007 (UTC)


 * Perhaps I should have elaborated a bit. Of course it depends on which modal logic you apply. My main concerns are that: 1) It was not mentioned, that accessibility plays an important role here and 2) the sentence is placed under "Formal semantics of modal logic", which IMO should be a section (also) covering exactly this kind of "oddities". Rasmuskold 14:06, 11 January 2007 (UTC)


 * Yes, it does depend on which logic you are concerned with. A great deal in this article is rough and intuitive. I don't see that as a bad thing, provided that a caution is issued early on, and that readers are directed to more rigorous treatments in other articles. It is sufficient here that the general idea of possible worlds be conveyed, I think. If we try for the strictest propriety everywhere else and here, Wikipedia would become forbidding and unusable. I'll add such a caution now. – Noetica 22:32, 11 January 2007 (UTC)


 * I think the caution does the job. And I very much agree, that as much information as possible does more harm than good - any elaboration of a matter should be carried out in the appropriate article and not also everywhere the topic is mentioned. Rasmuskold 22:55, 11 January 2007 (UTC)

I've removed the sentence. The sentence in question is false in many systems. For an example, take a frame where there is only one world and where that world cannot see any worlds. At this world, under Kripke semantics, all propositions are necessary and no propositions are possible. Systems like these (i.e., those that are neither reflexive nor serial) are not especially unusual.--Heyitspeter (talk) 02:26, 21 May 2010 (UTC)

Modal Realism
Reading over this article, I feel it is somewhat uneven. It talks about possible worlds in terms of Lewis's modal realism, almost as if this is the only conception of possible worlds. More attention needs, to be given to those theories that make use of possible worlds, but consider them in terms of sets of consistent propositions. Maybe some explanation of the problems with possible world theories would be nice too. 212.120.237.72 23:35, 11 April 2007 (UTC)


 * Fine, anonymous editor. Why not add some more, then? I have corrected something in the article about this. See this change, and take note of my edit summary:
 * "Clarification concerning possible-world theorists (all of whom believe that there ARE possible worlds and that the actual world is one of them) and possible-world theorists who are ALSO modal realists"
 * If you disagree with me, please discuss the matter here before making a further alteration. And please note: it is normal practice (and useful and considerate) to provide such edit summaries.
 * –&thinsp; Noetica ♬♩&thinsp;Talk 00:03, 12 April 2007 (UTC)

It is debatable how to describe the ontological status that ersatzists give to possible worlds, but it is quite clear that modal fictionalists do not believe in the existence of possible worlds, but do make use of the concept. 87.127.73.65 02:43, 24 May 2007 (UTC)


 * Well, Anonymeditor, surely it depends first on which fictionalists we mean. And those that make use of possible-world talk do in a way allow that there "are" possible worlds, yes? As (maximal?) fictional objects of some sort? There are still questions of ontological status to address for all non-Lewisians, perhaps. Indeed, at least as far as Lewis is (tenselessly) concerned, the ultimate differences between ersatzists themselves and fictionalists may not be so great. It's a bit hard to capture all that in an edit summary, I think you will concede! Have you a problem with the text of the article itself, now? Can I help?
 * –&thinsp; Noetica ♬♩&thinsp;Talk 06:54, 24 May 2007 (UTC)

Melissa and Toby are taller than each other, isn't that possible with relativity?
If they move at significant fractions of the speed of light in opposite directions with their bodies aligned with the direction of motion (head or feet first), wouldn't they be each be taller than the other in each one's perspective? --TiagoTiago (talk) 00:19, 25 October 2011 (UTC)

Dead link and a question
The external link to Alexander Pruss's thesis is dead. (But is this really the best external resource we can find?)

Also, how relevant is Ladyman and Ross' critique (it's a book not just a paper, isn't it?)? They seem to attack analytical metaphysics quite generally, so their rejection of possible worlds is probably just an instance of a general reflection, not a specific criticism. Even if it is: Though their book has gotten some attention due to its provocative claims, it isn't that well-received, and their approach has received harsh criticism itself (see for instance Cian Dorr's review). (For the record, I do think that possible worlds---and modal logic quite generally---deserve much more suspicion than they have received in the past decades. But I'm sure their are more prominent critics than Ladyman and Ross. Quine for instance.).TheseusX (talk) 14:02, 28 July 2014 (UTC)

Possible Worlds Theory in Literary Studies
I'm not sure this requires an extra section; many of the concerns brought up here have been touched upon much more profoundly in the philosophical literature. If this section is kept, though, it needs to be beefed up with at least a dozen (or more) of the recent works on literature (fiction) and possible worlds. Also, some of the descriptions are perhaps too vague to be well-understood / of use. 2602:302:D150:1930:C072:91F2:A4BC:8C22 (talk) 23:43, 20 December 2015 (UTC)

2 + 2 = 4 ?
From the section 'Possibility, necessity, and contingency':

Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried").

There certainly seem to be a number of solutions to 2 + 2, even in this (highly unlikely) world. See, for example Does 2+2=4 in all possible universes?. I am no mathematician, logician or philosopher, but I suspect that some of the answers there are valid, including
 * "The statement 2+2=4 is a valid deduction from the Peano axioms which are the prototypical definition of the Natural number system. But 2+2=4 is not true in all number systems, e.g., Arithmetic over the integers modulo 3, in which "4" is not even defined. In such a mathematical universe 2+2=4 is not true or even meaningful."

Anyway, in base 3, 2 + 2 = 11 and in base 2 it is impossible. Even my nan says so. MinorProphet (talk) 22:10, 30 March 2018 (UTC)