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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)
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)
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 (Μελ Ετητης) 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)
Postscript Mel wrote on CSTAR's talk page:
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)
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)
And is this right? Paragraph three:
I've rewritten paragraph two. Para three needs it too, I would say. SlimVirgin 09:47, 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)
It seems to me that the phrasing of the current intro section has needlessly entered a dangerous combat zone:
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?
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?
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.
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)
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:
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)
Notes on things above
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)
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:
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)
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)
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)
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)
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)
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)
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
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)
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)
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)
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)
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
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)
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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)
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)
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 (Μελ Ετητης) 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)
Postscript Mel wrote on CSTAR's talk page:
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)
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)
And is this right? Paragraph three:
I've rewritten paragraph two. Para three needs it too, I would say. SlimVirgin 09:47, 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)
It seems to me that the phrasing of the current intro section has needlessly entered a dangerous combat zone:
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?
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?
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.
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)
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:
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)
Notes on things above
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)
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:
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)
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)
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)
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)
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)
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)
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
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)
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)
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)
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)
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
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)