should truth entail possible truth The 2019 Stack Overflow Developer Survey Results Are In ...

Variable with quotation marks "$()"

Is every episode of "Where are my Pants?" identical?

For what reasons would an animal species NOT cross a *horizontal* land bridge?

How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time

Why doesn't shell automatically fix "useless use of cat"?

One-dimensional Japanese puzzle

60's-70's movie: home appliances revolting against the owners

Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?

Would an alien lifeform be able to achieve space travel if lacking in vision?

Define a list range inside a list

How many cones with angle theta can I pack into the unit sphere?

How to handle characters who are more educated than the author?

Does Parliament need to approve the new Brexit delay to 31 October 2019?

Do warforged have souls?

How to make Illustrator type tool selection automatically adapt with text length

Nested ellipses in tikzpicture: Chomsky hierarchy

Identify 80s or 90s comics with ripped creatures (not dwarves)

How do spell lists change if the party levels up without taking a long rest?

Why not take a picture of a closer black hole?

Does Parliament hold absolute power in the UK?

Single author papers against my advisor's will?

Match Roman Numerals

Can a flute soloist sit?

Why doesn't a hydraulic lever violate conservation of energy?



should truth entail possible truth



The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Which kinds of Philosophy.SE questions should be taken from (or tolerated in)…What happens if we accept inconsistency?What determines accessibility of possible worlds?How is Kripke-style modal logic distinct from classical propositional logic with additional axioms?Modal Realism: Possible Worlds spatio-temporally isolated?Why might truth imply necessity?Is there modal logic without possible worlds?Necessity and possibility (again)Is it possible to not know that one knows p?Truth that requires two possible worlds not causally linkedIs it possible to have truth if objective randomness exists?Modal validity & vagueness












3















It is a well-accepted axiom of modal logic truth implies possible truth.



Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?










share|improve this question



























    3















    It is a well-accepted axiom of modal logic truth implies possible truth.



    Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?










    share|improve this question

























      3












      3








      3








      It is a well-accepted axiom of modal logic truth implies possible truth.



      Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?










      share|improve this question














      It is a well-accepted axiom of modal logic truth implies possible truth.



      Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?







      epistemology truth modal-logic






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 4 hours ago









      puzzledpuzzled

      242




      242






















          2 Answers
          2






          active

          oldest

          votes


















          2














          If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose we reject truth implies possibility (that is, we reject that for every formula P, if P then possibly P). Then for some formula A, we have A and not-possibly A. Not-possibly A is equivalent to necessarily-not-A. So we have A and necessarily-not-A, meaning the necessity of not-A doesn't imply the actual truth of not-A.



          However formally within modal logic itself, you can mess around with axioms and frame conditions in whatever way you want. Rejecting "if P then possibly P" amounts to rejecting reflexivity as a frame condition. See https://en.m.wikipedia.org/wiki/Accessibility_relation for more about frame conditions and their corresponding axioms. (EDIT: Frame conditions tell us what worlds we "see" when evaluating possibly P and necessarily P at a world w. If at least one world that w "sees" satisfies P, then w satisfies possibly P. If every world w "sees" satisfies P, then w satisfies necessarily P. Reflexivity tells us that w always "sees" itself when evaluating statements of possibility and necessity. It may be that P is true in the actual world, but if we reject reflexivity then we're not looking at the actual world to determine the truth of possibly P! And maybe every other world we "see" indeed fails to satisfy P.)



          (Noah Schweber's comments below should be heeded as well. The box and diamond operators can be interpreted in different ways for different modalities!)






          share|improve this answer





















          • 1





            +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

            – Noah Schweber
            1 hour ago








          • 1





            This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

            – Noah Schweber
            1 hour ago



















          0














          Obviously truth implies possibility. So let me make a case for truth not implying possibility.



          Let's start with an "applied logic" example. Suppose I'm trying to reason about the world using imperfect information (i.e. my senses and informal induction). At any given moment, I'll have some idea of what the world is, but that idea will probably be contradictory in subtle ways. For example, I may "accept" - for some meaning of the word - two physical theories which each work extremely well in their appropriate contexts but which as currently posed contradict each other (think about general relativity versus quantum mechanics). I believe each of a set of statements the conjunction of which is not possible. This is a situation in which I might want a formal system in which <> is interpreted as "is possible" but I don't have the rule "from p, infer <>p." And this issue also arises, with somewhat more urgency, in the context of artificial intelligence and more generally any situation where a machine is "making decisions" based on data about the world around it, and we're modeling that process (either in implementing it or in analyzing it after-the-fact) with a logical system.



          Of course, what's true and what's currently believed are different (duh!), and so this isn't really an example of the phenomenon you're interested in. But implicitly invoked in our bringing this up is the principle that there are no true contradictions, and this is not universally held; the rejection of this principle is called dialetheism.




          • And on the formal logic side, you may be interested in paraconsistent logic and relevant/relevance logic; note that this is very different from intuitionistic logic, which rejects the law of the excluded middle but nonetheless does not permit contradictons.


          Now we get into a very interesting mess: how should a dialetheist think of possibility? I don't know of anyone who's argued - within the dialetheist context - that possibility entails consistency, and hence that there are true impossible facts as well as true contradictions, but I can sort of see how an argument for this might go. Since I think producing "original research" here isn't really appropriate (you asked "is there any argument" not "can there be any argument," after all) I won't go into this, but I do think it's worth mentioning in this context: that dialetheism puts us in a situation where the question becomes at the very least not trivially trivial.






          share|improve this answer
























          • Incidentally, this answer of mine may be of tangential interest.

            – Noah Schweber
            1 hour ago












          Your Answer








          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "265"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f61776%2fshould-truth-entail-possible-truth%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2














          If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose we reject truth implies possibility (that is, we reject that for every formula P, if P then possibly P). Then for some formula A, we have A and not-possibly A. Not-possibly A is equivalent to necessarily-not-A. So we have A and necessarily-not-A, meaning the necessity of not-A doesn't imply the actual truth of not-A.



          However formally within modal logic itself, you can mess around with axioms and frame conditions in whatever way you want. Rejecting "if P then possibly P" amounts to rejecting reflexivity as a frame condition. See https://en.m.wikipedia.org/wiki/Accessibility_relation for more about frame conditions and their corresponding axioms. (EDIT: Frame conditions tell us what worlds we "see" when evaluating possibly P and necessarily P at a world w. If at least one world that w "sees" satisfies P, then w satisfies possibly P. If every world w "sees" satisfies P, then w satisfies necessarily P. Reflexivity tells us that w always "sees" itself when evaluating statements of possibility and necessity. It may be that P is true in the actual world, but if we reject reflexivity then we're not looking at the actual world to determine the truth of possibly P! And maybe every other world we "see" indeed fails to satisfy P.)



          (Noah Schweber's comments below should be heeded as well. The box and diamond operators can be interpreted in different ways for different modalities!)






          share|improve this answer





















          • 1





            +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

            – Noah Schweber
            1 hour ago








          • 1





            This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

            – Noah Schweber
            1 hour ago
















          2














          If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose we reject truth implies possibility (that is, we reject that for every formula P, if P then possibly P). Then for some formula A, we have A and not-possibly A. Not-possibly A is equivalent to necessarily-not-A. So we have A and necessarily-not-A, meaning the necessity of not-A doesn't imply the actual truth of not-A.



          However formally within modal logic itself, you can mess around with axioms and frame conditions in whatever way you want. Rejecting "if P then possibly P" amounts to rejecting reflexivity as a frame condition. See https://en.m.wikipedia.org/wiki/Accessibility_relation for more about frame conditions and their corresponding axioms. (EDIT: Frame conditions tell us what worlds we "see" when evaluating possibly P and necessarily P at a world w. If at least one world that w "sees" satisfies P, then w satisfies possibly P. If every world w "sees" satisfies P, then w satisfies necessarily P. Reflexivity tells us that w always "sees" itself when evaluating statements of possibility and necessity. It may be that P is true in the actual world, but if we reject reflexivity then we're not looking at the actual world to determine the truth of possibly P! And maybe every other world we "see" indeed fails to satisfy P.)



          (Noah Schweber's comments below should be heeded as well. The box and diamond operators can be interpreted in different ways for different modalities!)






          share|improve this answer





















          • 1





            +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

            – Noah Schweber
            1 hour ago








          • 1





            This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

            – Noah Schweber
            1 hour ago














          2












          2








          2







          If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose we reject truth implies possibility (that is, we reject that for every formula P, if P then possibly P). Then for some formula A, we have A and not-possibly A. Not-possibly A is equivalent to necessarily-not-A. So we have A and necessarily-not-A, meaning the necessity of not-A doesn't imply the actual truth of not-A.



          However formally within modal logic itself, you can mess around with axioms and frame conditions in whatever way you want. Rejecting "if P then possibly P" amounts to rejecting reflexivity as a frame condition. See https://en.m.wikipedia.org/wiki/Accessibility_relation for more about frame conditions and their corresponding axioms. (EDIT: Frame conditions tell us what worlds we "see" when evaluating possibly P and necessarily P at a world w. If at least one world that w "sees" satisfies P, then w satisfies possibly P. If every world w "sees" satisfies P, then w satisfies necessarily P. Reflexivity tells us that w always "sees" itself when evaluating statements of possibility and necessity. It may be that P is true in the actual world, but if we reject reflexivity then we're not looking at the actual world to determine the truth of possibly P! And maybe every other world we "see" indeed fails to satisfy P.)



          (Noah Schweber's comments below should be heeded as well. The box and diamond operators can be interpreted in different ways for different modalities!)






          share|improve this answer















          If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose we reject truth implies possibility (that is, we reject that for every formula P, if P then possibly P). Then for some formula A, we have A and not-possibly A. Not-possibly A is equivalent to necessarily-not-A. So we have A and necessarily-not-A, meaning the necessity of not-A doesn't imply the actual truth of not-A.



          However formally within modal logic itself, you can mess around with axioms and frame conditions in whatever way you want. Rejecting "if P then possibly P" amounts to rejecting reflexivity as a frame condition. See https://en.m.wikipedia.org/wiki/Accessibility_relation for more about frame conditions and their corresponding axioms. (EDIT: Frame conditions tell us what worlds we "see" when evaluating possibly P and necessarily P at a world w. If at least one world that w "sees" satisfies P, then w satisfies possibly P. If every world w "sees" satisfies P, then w satisfies necessarily P. Reflexivity tells us that w always "sees" itself when evaluating statements of possibility and necessity. It may be that P is true in the actual world, but if we reject reflexivity then we're not looking at the actual world to determine the truth of possibly P! And maybe every other world we "see" indeed fails to satisfy P.)



          (Noah Schweber's comments below should be heeded as well. The box and diamond operators can be interpreted in different ways for different modalities!)







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 1 hour ago

























          answered 2 hours ago









          AdamAdam

          682110




          682110








          • 1





            +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

            – Noah Schweber
            1 hour ago








          • 1





            This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

            – Noah Schweber
            1 hour ago














          • 1





            +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

            – Noah Schweber
            1 hour ago








          • 1





            This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

            – Noah Schweber
            1 hour ago








          1




          1





          +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

          – Noah Schweber
          1 hour ago







          +1. For the OP, keep in mind that "should 'p is true' imply 'p is possible'?" is a very different question from "should 'p is true' imply '<>(p)'?" There are many ways to interpret the modality <> (and its dual, []) - 'is possible' is one, but others include 'is possibly true in the future' (and the present isn't the future!), 'is permitted' (and life isn't fair!), and 'is consistent' (and Godel's theorem makes this surprisingly subtle!). (contd)

          – Noah Schweber
          1 hour ago






          1




          1





          This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

          – Noah Schweber
          1 hour ago





          This answer's second paragraph reflects this: modal logic isn't just about the modalities 'is possible'/'is necessary' (and for that matter, frames aren't the only way to provide semantics for modal logic, and often aren't even appropriate for a given task!). This is all an aside, since your question really does focus on possibility specifically, but it's a point worth mentioning given the "modal-logic" tag.

          – Noah Schweber
          1 hour ago











          0














          Obviously truth implies possibility. So let me make a case for truth not implying possibility.



          Let's start with an "applied logic" example. Suppose I'm trying to reason about the world using imperfect information (i.e. my senses and informal induction). At any given moment, I'll have some idea of what the world is, but that idea will probably be contradictory in subtle ways. For example, I may "accept" - for some meaning of the word - two physical theories which each work extremely well in their appropriate contexts but which as currently posed contradict each other (think about general relativity versus quantum mechanics). I believe each of a set of statements the conjunction of which is not possible. This is a situation in which I might want a formal system in which <> is interpreted as "is possible" but I don't have the rule "from p, infer <>p." And this issue also arises, with somewhat more urgency, in the context of artificial intelligence and more generally any situation where a machine is "making decisions" based on data about the world around it, and we're modeling that process (either in implementing it or in analyzing it after-the-fact) with a logical system.



          Of course, what's true and what's currently believed are different (duh!), and so this isn't really an example of the phenomenon you're interested in. But implicitly invoked in our bringing this up is the principle that there are no true contradictions, and this is not universally held; the rejection of this principle is called dialetheism.




          • And on the formal logic side, you may be interested in paraconsistent logic and relevant/relevance logic; note that this is very different from intuitionistic logic, which rejects the law of the excluded middle but nonetheless does not permit contradictons.


          Now we get into a very interesting mess: how should a dialetheist think of possibility? I don't know of anyone who's argued - within the dialetheist context - that possibility entails consistency, and hence that there are true impossible facts as well as true contradictions, but I can sort of see how an argument for this might go. Since I think producing "original research" here isn't really appropriate (you asked "is there any argument" not "can there be any argument," after all) I won't go into this, but I do think it's worth mentioning in this context: that dialetheism puts us in a situation where the question becomes at the very least not trivially trivial.






          share|improve this answer
























          • Incidentally, this answer of mine may be of tangential interest.

            – Noah Schweber
            1 hour ago
















          0














          Obviously truth implies possibility. So let me make a case for truth not implying possibility.



          Let's start with an "applied logic" example. Suppose I'm trying to reason about the world using imperfect information (i.e. my senses and informal induction). At any given moment, I'll have some idea of what the world is, but that idea will probably be contradictory in subtle ways. For example, I may "accept" - for some meaning of the word - two physical theories which each work extremely well in their appropriate contexts but which as currently posed contradict each other (think about general relativity versus quantum mechanics). I believe each of a set of statements the conjunction of which is not possible. This is a situation in which I might want a formal system in which <> is interpreted as "is possible" but I don't have the rule "from p, infer <>p." And this issue also arises, with somewhat more urgency, in the context of artificial intelligence and more generally any situation where a machine is "making decisions" based on data about the world around it, and we're modeling that process (either in implementing it or in analyzing it after-the-fact) with a logical system.



          Of course, what's true and what's currently believed are different (duh!), and so this isn't really an example of the phenomenon you're interested in. But implicitly invoked in our bringing this up is the principle that there are no true contradictions, and this is not universally held; the rejection of this principle is called dialetheism.




          • And on the formal logic side, you may be interested in paraconsistent logic and relevant/relevance logic; note that this is very different from intuitionistic logic, which rejects the law of the excluded middle but nonetheless does not permit contradictons.


          Now we get into a very interesting mess: how should a dialetheist think of possibility? I don't know of anyone who's argued - within the dialetheist context - that possibility entails consistency, and hence that there are true impossible facts as well as true contradictions, but I can sort of see how an argument for this might go. Since I think producing "original research" here isn't really appropriate (you asked "is there any argument" not "can there be any argument," after all) I won't go into this, but I do think it's worth mentioning in this context: that dialetheism puts us in a situation where the question becomes at the very least not trivially trivial.






          share|improve this answer
























          • Incidentally, this answer of mine may be of tangential interest.

            – Noah Schweber
            1 hour ago














          0












          0








          0







          Obviously truth implies possibility. So let me make a case for truth not implying possibility.



          Let's start with an "applied logic" example. Suppose I'm trying to reason about the world using imperfect information (i.e. my senses and informal induction). At any given moment, I'll have some idea of what the world is, but that idea will probably be contradictory in subtle ways. For example, I may "accept" - for some meaning of the word - two physical theories which each work extremely well in their appropriate contexts but which as currently posed contradict each other (think about general relativity versus quantum mechanics). I believe each of a set of statements the conjunction of which is not possible. This is a situation in which I might want a formal system in which <> is interpreted as "is possible" but I don't have the rule "from p, infer <>p." And this issue also arises, with somewhat more urgency, in the context of artificial intelligence and more generally any situation where a machine is "making decisions" based on data about the world around it, and we're modeling that process (either in implementing it or in analyzing it after-the-fact) with a logical system.



          Of course, what's true and what's currently believed are different (duh!), and so this isn't really an example of the phenomenon you're interested in. But implicitly invoked in our bringing this up is the principle that there are no true contradictions, and this is not universally held; the rejection of this principle is called dialetheism.




          • And on the formal logic side, you may be interested in paraconsistent logic and relevant/relevance logic; note that this is very different from intuitionistic logic, which rejects the law of the excluded middle but nonetheless does not permit contradictons.


          Now we get into a very interesting mess: how should a dialetheist think of possibility? I don't know of anyone who's argued - within the dialetheist context - that possibility entails consistency, and hence that there are true impossible facts as well as true contradictions, but I can sort of see how an argument for this might go. Since I think producing "original research" here isn't really appropriate (you asked "is there any argument" not "can there be any argument," after all) I won't go into this, but I do think it's worth mentioning in this context: that dialetheism puts us in a situation where the question becomes at the very least not trivially trivial.






          share|improve this answer













          Obviously truth implies possibility. So let me make a case for truth not implying possibility.



          Let's start with an "applied logic" example. Suppose I'm trying to reason about the world using imperfect information (i.e. my senses and informal induction). At any given moment, I'll have some idea of what the world is, but that idea will probably be contradictory in subtle ways. For example, I may "accept" - for some meaning of the word - two physical theories which each work extremely well in their appropriate contexts but which as currently posed contradict each other (think about general relativity versus quantum mechanics). I believe each of a set of statements the conjunction of which is not possible. This is a situation in which I might want a formal system in which <> is interpreted as "is possible" but I don't have the rule "from p, infer <>p." And this issue also arises, with somewhat more urgency, in the context of artificial intelligence and more generally any situation where a machine is "making decisions" based on data about the world around it, and we're modeling that process (either in implementing it or in analyzing it after-the-fact) with a logical system.



          Of course, what's true and what's currently believed are different (duh!), and so this isn't really an example of the phenomenon you're interested in. But implicitly invoked in our bringing this up is the principle that there are no true contradictions, and this is not universally held; the rejection of this principle is called dialetheism.




          • And on the formal logic side, you may be interested in paraconsistent logic and relevant/relevance logic; note that this is very different from intuitionistic logic, which rejects the law of the excluded middle but nonetheless does not permit contradictons.


          Now we get into a very interesting mess: how should a dialetheist think of possibility? I don't know of anyone who's argued - within the dialetheist context - that possibility entails consistency, and hence that there are true impossible facts as well as true contradictions, but I can sort of see how an argument for this might go. Since I think producing "original research" here isn't really appropriate (you asked "is there any argument" not "can there be any argument," after all) I won't go into this, but I do think it's worth mentioning in this context: that dialetheism puts us in a situation where the question becomes at the very least not trivially trivial.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 1 hour ago









          Noah SchweberNoah Schweber

          25418




          25418













          • Incidentally, this answer of mine may be of tangential interest.

            – Noah Schweber
            1 hour ago



















          • Incidentally, this answer of mine may be of tangential interest.

            – Noah Schweber
            1 hour ago

















          Incidentally, this answer of mine may be of tangential interest.

          – Noah Schweber
          1 hour ago





          Incidentally, this answer of mine may be of tangential interest.

          – Noah Schweber
          1 hour ago


















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Philosophy Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f61776%2fshould-truth-entail-possible-truth%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          “%fieldName is a required field.”, in Magento2 REST API Call for GET Method Type The Next...

          How to change City field to a dropdown in Checkout step Magento 2Magento 2 : How to change UI field(s)...

          變成蝙蝠會怎樣? 參考資料 外部連結 导航菜单Thomas Nagel, "What is it like to be a...