Talk:Possible world

message: 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)
thread_title: CSTAR

message: 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)
thread_title:  ? 

message: 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:
*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. 
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:
*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)
replies: text:  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)

text: 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)
thread_title: Some suggestions

message: 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)
thread_title:  Comments on remarks above, and on my recent editing 

message: 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)
thread_title:  Proximity 

message: 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)
replies: text: 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)
thread_title:  Section on the nature of possible worlds? 

message: 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)
thread_title:  Bias? 

message: 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)
replies: text: 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)
replies: text: 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)

text: 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)
replies: text: 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)
thread_title:  "Necessary" as a sufficient condition for being "possible"? 

message: 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)
thread_title:  Melissa and Toby are taller than each other, isn't that possible with relativity? 

message: 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)
thread_title:  Dead link and a question 

message: 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)
thread_title:  Possible Worlds Theory in Literary Studies 

message: 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)
thread_title:  2 + 2 = 4 ?