Is “This sentence is true” true or false (or both); is it a proposition?












5












$begingroup$


From what I understand, a proposition is either true or false, but not both. "This sentence is false" can be neither true nor false and is thus not a proposition.



However, is "This sentence is true" true or false (or both)? And hence, is "This sentence is true" a proposition?






logic philosophy







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$endgroup$












  • $begingroup$
    I think is a paradox :O... Look at here for a philosophical answer.
    $endgroup$
    – manooooh
    Mar 1 '18 at 2:26










  • $begingroup$
    Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
    $endgroup$
    – Dan Christensen
    Mar 1 '18 at 6:07










  • $begingroup$
    See Liar Paradox: some solutions.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:49










  • $begingroup$
    Already discussed here with links to more posts.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:51
















5












$begingroup$


From what I understand, a proposition is either true or false, but not both. "This sentence is false" can be neither true nor false and is thus not a proposition.



However, is "This sentence is true" true or false (or both)? And hence, is "This sentence is true" a proposition?






logic philosophy







share|cite|improve this question











$endgroup$












  • $begingroup$
    I think is a paradox :O... Look at here for a philosophical answer.
    $endgroup$
    – manooooh
    Mar 1 '18 at 2:26










  • $begingroup$
    Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
    $endgroup$
    – Dan Christensen
    Mar 1 '18 at 6:07










  • $begingroup$
    See Liar Paradox: some solutions.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:49










  • $begingroup$
    Already discussed here with links to more posts.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:51














5












5








5


1



$begingroup$


From what I understand, a proposition is either true or false, but not both. "This sentence is false" can be neither true nor false and is thus not a proposition.



However, is "This sentence is true" true or false (or both)? And hence, is "This sentence is true" a proposition?






logic philosophy







share|cite|improve this question











$endgroup$




From what I understand, a proposition is either true or false, but not both. "This sentence is false" can be neither true nor false and is thus not a proposition.



However, is "This sentence is true" true or false (or both)? And hence, is "This sentence is true" a proposition?






logic philosophy




logic philosophy






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 1 '18 at 2:10









Git Gud

28.8k1050100




28.8k1050100










asked Mar 1 '18 at 2:07









Kenny LJKenny LJ

1,51811632




1,51811632












  • $begingroup$
    I think is a paradox :O... Look at here for a philosophical answer.
    $endgroup$
    – manooooh
    Mar 1 '18 at 2:26










  • $begingroup$
    Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
    $endgroup$
    – Dan Christensen
    Mar 1 '18 at 6:07










  • $begingroup$
    See Liar Paradox: some solutions.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:49










  • $begingroup$
    Already discussed here with links to more posts.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:51


















  • $begingroup$
    I think is a paradox :O... Look at here for a philosophical answer.
    $endgroup$
    – manooooh
    Mar 1 '18 at 2:26










  • $begingroup$
    Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
    $endgroup$
    – Dan Christensen
    Mar 1 '18 at 6:07










  • $begingroup$
    See Liar Paradox: some solutions.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:49










  • $begingroup$
    Already discussed here with links to more posts.
    $endgroup$
    – Mauro ALLEGRANZA
    Mar 1 '18 at 8:51
















$begingroup$
I think is a paradox :O... Look at here for a philosophical answer.
$endgroup$
– manooooh
Mar 1 '18 at 2:26




$begingroup$
I think is a paradox :O... Look at here for a philosophical answer.
$endgroup$
– manooooh
Mar 1 '18 at 2:26












$begingroup$
Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
$endgroup$
– Dan Christensen
Mar 1 '18 at 6:07




$begingroup$
Whether it is true, false, a proposition, not a proposition or just pure nonsense doesn't seem to matter much in mathematics. Maybe it does in philosophy, I couldn't say.
$endgroup$
– Dan Christensen
Mar 1 '18 at 6:07












$begingroup$
See Liar Paradox: some solutions.
$endgroup$
– Mauro ALLEGRANZA
Mar 1 '18 at 8:49




$begingroup$
See Liar Paradox: some solutions.
$endgroup$
– Mauro ALLEGRANZA
Mar 1 '18 at 8:49












$begingroup$
Already discussed here with links to more posts.
$endgroup$
– Mauro ALLEGRANZA
Mar 1 '18 at 8:51




$begingroup$
Already discussed here with links to more posts.
$endgroup$
– Mauro ALLEGRANZA
Mar 1 '18 at 8:51










3 Answers
3






active

oldest

votes


















2












$begingroup$

It's an "anti-paradox", the true or false outcome is totally the choice of the reader, not the statement itself, unlike "This sentence is false", which is self contradicting, and independent of the reader.
The reader could themselves can be considered self contradicting, but not the statement, and the statement is self consistent on either choice.



This could explain the apparent contradiction which physicist's have in the "Double slit experiment",where there is an particle/wave duality observed. The observer has the choice of whether a photon, electron, etc, is observed as a particle or wave, by the choice of detection device. The outcome of the experiment is dependent on the observers choice.



The result is explainable if our apparent reality is not material but just pure information ("energy", movement) on a true material reality (the aether).
The phenomena of time would be just the sequence of the information.



In electronic circuits, "This statement is false" equivalent is an inverter with feedback (output goes back into the input). If the input is "0" the output is "1", and visa versa. The circuit would become self contradictory, the output oscillating at "0" and "1".

"This statement is true", electronic equivalent is a flip-flop (bistable, one bit memory) with feedback. If the input is "0" the output is "0", and the same with "1". The circuit is self affirming, a stable output, no oscillating.






share|cite|improve this answer











$endgroup$





















    0












    $begingroup$

    The dichotomy sentence/proposition is quite complex to manage, due to its philosophical implications.



    See e.g. Nik Weaver,Truth and Assertibility, World Scientific PC (2015), page 4:




    Many philosophers consider truth to be fundamentally an attribute
    not of sentences but of some more abstract correlate of sentences called
    “propositions”. The idea is that sentences function by referring to or expressing abstract propositions, and it is these propositions which are the
    “primary bearers of truth”. This seems to be a common opinion, but it is
    controversial, with some dissenters denying that there even are such things
    as propositions.




    Thus, if we want to stay in the realm of propositional logic, we can say that the basic entities are sentences, i.e. linguistic entities, that have a definite truth value.



    If so, a sentence like: "This sentence is false", that can be neither true nor false, is not a meaningful sentence to be used in the context of propositional logic.



    What about:




    "This sentence is true" ?




    Is it paradoxical ? I think so.



    Assume that the sentence is true; then its negation: "This sentence is not true" must be false.



    But the negated sentence is equivalent to "This sentence is false".



    But if "This sentence is false" is false, then the sentence (asserting something about a sentence, i.e. a linguistic entity) "agrees" with the way the things are, and this means that it is true.



    Again, we have reached a contradiction.






    share|cite|improve this answer









    $endgroup$









    • 1




      $begingroup$
      I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
      $endgroup$
      – Peter
      Mar 1 '18 at 15:39










    • $begingroup$
      @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
      $endgroup$
      – Mauro ALLEGRANZA
      Mar 1 '18 at 15:47



















    -2












    $begingroup$

    "This sentence is true" - call this sentence TT - is not paradoxical. It can be assigned either of the truthvalues T or F. The negation of TT is not the paradoxical Liar sentence "This sentence is false", since the 'this' in these two sentences refer to different sentences. The negation of TT might be rendered as "The sentence 'This sentence is true' is false" - call this sentence NT - which is awkward but quite self-consistent, since TT can indeed consistently be false; in fact, NT can also be true or false: as one would expect, its truthvalue must be the opposite of the truthvalue of TT.
    It might be worth emphasizing that being a sentence which can be true or false is nothing particularly remarkable. Most sentences of logic are in this category. None of this has anything at all to do with the double-slit experiment, Quantum theory or the nature of physical reality.






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      3 Answers
      3






      active

      oldest

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      3 Answers
      3






      active

      oldest

      votes









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      oldest

      votes






      active

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      2












      $begingroup$

      It's an "anti-paradox", the true or false outcome is totally the choice of the reader, not the statement itself, unlike "This sentence is false", which is self contradicting, and independent of the reader.
      The reader could themselves can be considered self contradicting, but not the statement, and the statement is self consistent on either choice.



      This could explain the apparent contradiction which physicist's have in the "Double slit experiment",where there is an particle/wave duality observed. The observer has the choice of whether a photon, electron, etc, is observed as a particle or wave, by the choice of detection device. The outcome of the experiment is dependent on the observers choice.



      The result is explainable if our apparent reality is not material but just pure information ("energy", movement) on a true material reality (the aether).
      The phenomena of time would be just the sequence of the information.



      In electronic circuits, "This statement is false" equivalent is an inverter with feedback (output goes back into the input). If the input is "0" the output is "1", and visa versa. The circuit would become self contradictory, the output oscillating at "0" and "1".

      "This statement is true", electronic equivalent is a flip-flop (bistable, one bit memory) with feedback. If the input is "0" the output is "0", and the same with "1". The circuit is self affirming, a stable output, no oscillating.






      share|cite|improve this answer











      $endgroup$


















        2












        $begingroup$

        It's an "anti-paradox", the true or false outcome is totally the choice of the reader, not the statement itself, unlike "This sentence is false", which is self contradicting, and independent of the reader.
        The reader could themselves can be considered self contradicting, but not the statement, and the statement is self consistent on either choice.



        This could explain the apparent contradiction which physicist's have in the "Double slit experiment",where there is an particle/wave duality observed. The observer has the choice of whether a photon, electron, etc, is observed as a particle or wave, by the choice of detection device. The outcome of the experiment is dependent on the observers choice.



        The result is explainable if our apparent reality is not material but just pure information ("energy", movement) on a true material reality (the aether).
        The phenomena of time would be just the sequence of the information.



        In electronic circuits, "This statement is false" equivalent is an inverter with feedback (output goes back into the input). If the input is "0" the output is "1", and visa versa. The circuit would become self contradictory, the output oscillating at "0" and "1".

        "This statement is true", electronic equivalent is a flip-flop (bistable, one bit memory) with feedback. If the input is "0" the output is "0", and the same with "1". The circuit is self affirming, a stable output, no oscillating.






        share|cite|improve this answer











        $endgroup$
















          2












          2








          2





          $begingroup$

          It's an "anti-paradox", the true or false outcome is totally the choice of the reader, not the statement itself, unlike "This sentence is false", which is self contradicting, and independent of the reader.
          The reader could themselves can be considered self contradicting, but not the statement, and the statement is self consistent on either choice.



          This could explain the apparent contradiction which physicist's have in the "Double slit experiment",where there is an particle/wave duality observed. The observer has the choice of whether a photon, electron, etc, is observed as a particle or wave, by the choice of detection device. The outcome of the experiment is dependent on the observers choice.



          The result is explainable if our apparent reality is not material but just pure information ("energy", movement) on a true material reality (the aether).
          The phenomena of time would be just the sequence of the information.



          In electronic circuits, "This statement is false" equivalent is an inverter with feedback (output goes back into the input). If the input is "0" the output is "1", and visa versa. The circuit would become self contradictory, the output oscillating at "0" and "1".

          "This statement is true", electronic equivalent is a flip-flop (bistable, one bit memory) with feedback. If the input is "0" the output is "0", and the same with "1". The circuit is self affirming, a stable output, no oscillating.






          share|cite|improve this answer











          $endgroup$



          It's an "anti-paradox", the true or false outcome is totally the choice of the reader, not the statement itself, unlike "This sentence is false", which is self contradicting, and independent of the reader.
          The reader could themselves can be considered self contradicting, but not the statement, and the statement is self consistent on either choice.



          This could explain the apparent contradiction which physicist's have in the "Double slit experiment",where there is an particle/wave duality observed. The observer has the choice of whether a photon, electron, etc, is observed as a particle or wave, by the choice of detection device. The outcome of the experiment is dependent on the observers choice.



          The result is explainable if our apparent reality is not material but just pure information ("energy", movement) on a true material reality (the aether).
          The phenomena of time would be just the sequence of the information.



          In electronic circuits, "This statement is false" equivalent is an inverter with feedback (output goes back into the input). If the input is "0" the output is "1", and visa versa. The circuit would become self contradictory, the output oscillating at "0" and "1".

          "This statement is true", electronic equivalent is a flip-flop (bistable, one bit memory) with feedback. If the input is "0" the output is "0", and the same with "1". The circuit is self affirming, a stable output, no oscillating.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 8 '18 at 6:40

























          answered Dec 6 '18 at 8:44









          Simon RuszczakSimon Ruszczak

          213




          213























              0












              $begingroup$

              The dichotomy sentence/proposition is quite complex to manage, due to its philosophical implications.



              See e.g. Nik Weaver,Truth and Assertibility, World Scientific PC (2015), page 4:




              Many philosophers consider truth to be fundamentally an attribute
              not of sentences but of some more abstract correlate of sentences called
              “propositions”. The idea is that sentences function by referring to or expressing abstract propositions, and it is these propositions which are the
              “primary bearers of truth”. This seems to be a common opinion, but it is
              controversial, with some dissenters denying that there even are such things
              as propositions.




              Thus, if we want to stay in the realm of propositional logic, we can say that the basic entities are sentences, i.e. linguistic entities, that have a definite truth value.



              If so, a sentence like: "This sentence is false", that can be neither true nor false, is not a meaningful sentence to be used in the context of propositional logic.



              What about:




              "This sentence is true" ?




              Is it paradoxical ? I think so.



              Assume that the sentence is true; then its negation: "This sentence is not true" must be false.



              But the negated sentence is equivalent to "This sentence is false".



              But if "This sentence is false" is false, then the sentence (asserting something about a sentence, i.e. a linguistic entity) "agrees" with the way the things are, and this means that it is true.



              Again, we have reached a contradiction.






              share|cite|improve this answer









              $endgroup$









              • 1




                $begingroup$
                I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
                $endgroup$
                – Peter
                Mar 1 '18 at 15:39










              • $begingroup$
                @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
                $endgroup$
                – Mauro ALLEGRANZA
                Mar 1 '18 at 15:47
















              0












              $begingroup$

              The dichotomy sentence/proposition is quite complex to manage, due to its philosophical implications.



              See e.g. Nik Weaver,Truth and Assertibility, World Scientific PC (2015), page 4:




              Many philosophers consider truth to be fundamentally an attribute
              not of sentences but of some more abstract correlate of sentences called
              “propositions”. The idea is that sentences function by referring to or expressing abstract propositions, and it is these propositions which are the
              “primary bearers of truth”. This seems to be a common opinion, but it is
              controversial, with some dissenters denying that there even are such things
              as propositions.




              Thus, if we want to stay in the realm of propositional logic, we can say that the basic entities are sentences, i.e. linguistic entities, that have a definite truth value.



              If so, a sentence like: "This sentence is false", that can be neither true nor false, is not a meaningful sentence to be used in the context of propositional logic.



              What about:




              "This sentence is true" ?




              Is it paradoxical ? I think so.



              Assume that the sentence is true; then its negation: "This sentence is not true" must be false.



              But the negated sentence is equivalent to "This sentence is false".



              But if "This sentence is false" is false, then the sentence (asserting something about a sentence, i.e. a linguistic entity) "agrees" with the way the things are, and this means that it is true.



              Again, we have reached a contradiction.






              share|cite|improve this answer









              $endgroup$









              • 1




                $begingroup$
                I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
                $endgroup$
                – Peter
                Mar 1 '18 at 15:39










              • $begingroup$
                @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
                $endgroup$
                – Mauro ALLEGRANZA
                Mar 1 '18 at 15:47














              0












              0








              0





              $begingroup$

              The dichotomy sentence/proposition is quite complex to manage, due to its philosophical implications.



              See e.g. Nik Weaver,Truth and Assertibility, World Scientific PC (2015), page 4:




              Many philosophers consider truth to be fundamentally an attribute
              not of sentences but of some more abstract correlate of sentences called
              “propositions”. The idea is that sentences function by referring to or expressing abstract propositions, and it is these propositions which are the
              “primary bearers of truth”. This seems to be a common opinion, but it is
              controversial, with some dissenters denying that there even are such things
              as propositions.




              Thus, if we want to stay in the realm of propositional logic, we can say that the basic entities are sentences, i.e. linguistic entities, that have a definite truth value.



              If so, a sentence like: "This sentence is false", that can be neither true nor false, is not a meaningful sentence to be used in the context of propositional logic.



              What about:




              "This sentence is true" ?




              Is it paradoxical ? I think so.



              Assume that the sentence is true; then its negation: "This sentence is not true" must be false.



              But the negated sentence is equivalent to "This sentence is false".



              But if "This sentence is false" is false, then the sentence (asserting something about a sentence, i.e. a linguistic entity) "agrees" with the way the things are, and this means that it is true.



              Again, we have reached a contradiction.






              share|cite|improve this answer









              $endgroup$



              The dichotomy sentence/proposition is quite complex to manage, due to its philosophical implications.



              See e.g. Nik Weaver,Truth and Assertibility, World Scientific PC (2015), page 4:




              Many philosophers consider truth to be fundamentally an attribute
              not of sentences but of some more abstract correlate of sentences called
              “propositions”. The idea is that sentences function by referring to or expressing abstract propositions, and it is these propositions which are the
              “primary bearers of truth”. This seems to be a common opinion, but it is
              controversial, with some dissenters denying that there even are such things
              as propositions.




              Thus, if we want to stay in the realm of propositional logic, we can say that the basic entities are sentences, i.e. linguistic entities, that have a definite truth value.



              If so, a sentence like: "This sentence is false", that can be neither true nor false, is not a meaningful sentence to be used in the context of propositional logic.



              What about:




              "This sentence is true" ?




              Is it paradoxical ? I think so.



              Assume that the sentence is true; then its negation: "This sentence is not true" must be false.



              But the negated sentence is equivalent to "This sentence is false".



              But if "This sentence is false" is false, then the sentence (asserting something about a sentence, i.e. a linguistic entity) "agrees" with the way the things are, and this means that it is true.



              Again, we have reached a contradiction.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Mar 1 '18 at 14:49









              Mauro ALLEGRANZAMauro ALLEGRANZA

              65.8k449114




              65.8k449114








              • 1




                $begingroup$
                I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
                $endgroup$
                – Peter
                Mar 1 '18 at 15:39










              • $begingroup$
                @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
                $endgroup$
                – Mauro ALLEGRANZA
                Mar 1 '18 at 15:47














              • 1




                $begingroup$
                I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
                $endgroup$
                – Peter
                Mar 1 '18 at 15:39










              • $begingroup$
                @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
                $endgroup$
                – Mauro ALLEGRANZA
                Mar 1 '18 at 15:47








              1




              1




              $begingroup$
              I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
              $endgroup$
              – Peter
              Mar 1 '18 at 15:39




              $begingroup$
              I am not very well versed in these kinds of things, so I have an honest question. Isn't the negation of "This sentence is true" not the sentence: "The sentence 'This sentense is true' is false"? After all, in the sentence "This sentence is true" the phrase 'this sentence' refers to another sentence than the same phrase does in the sentence "This sentence is not true".
              $endgroup$
              – Peter
              Mar 1 '18 at 15:39












              $begingroup$
              @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
              $endgroup$
              – Mauro ALLEGRANZA
              Mar 1 '18 at 15:47




              $begingroup$
              @Peter - the issue of managing self-refernce is not easy :-). See the Liar Paradox discussion. We can "name" LIAR the sentence "LIAR is false"; thus, its negation will be "LIAR is not false", i.e. "LIAR is true".
              $endgroup$
              – Mauro ALLEGRANZA
              Mar 1 '18 at 15:47











              -2












              $begingroup$

              "This sentence is true" - call this sentence TT - is not paradoxical. It can be assigned either of the truthvalues T or F. The negation of TT is not the paradoxical Liar sentence "This sentence is false", since the 'this' in these two sentences refer to different sentences. The negation of TT might be rendered as "The sentence 'This sentence is true' is false" - call this sentence NT - which is awkward but quite self-consistent, since TT can indeed consistently be false; in fact, NT can also be true or false: as one would expect, its truthvalue must be the opposite of the truthvalue of TT.
              It might be worth emphasizing that being a sentence which can be true or false is nothing particularly remarkable. Most sentences of logic are in this category. None of this has anything at all to do with the double-slit experiment, Quantum theory or the nature of physical reality.






              share|cite|improve this answer









              $endgroup$


















                -2












                $begingroup$

                "This sentence is true" - call this sentence TT - is not paradoxical. It can be assigned either of the truthvalues T or F. The negation of TT is not the paradoxical Liar sentence "This sentence is false", since the 'this' in these two sentences refer to different sentences. The negation of TT might be rendered as "The sentence 'This sentence is true' is false" - call this sentence NT - which is awkward but quite self-consistent, since TT can indeed consistently be false; in fact, NT can also be true or false: as one would expect, its truthvalue must be the opposite of the truthvalue of TT.
                It might be worth emphasizing that being a sentence which can be true or false is nothing particularly remarkable. Most sentences of logic are in this category. None of this has anything at all to do with the double-slit experiment, Quantum theory or the nature of physical reality.






                share|cite|improve this answer









                $endgroup$
















                  -2












                  -2








                  -2





                  $begingroup$

                  "This sentence is true" - call this sentence TT - is not paradoxical. It can be assigned either of the truthvalues T or F. The negation of TT is not the paradoxical Liar sentence "This sentence is false", since the 'this' in these two sentences refer to different sentences. The negation of TT might be rendered as "The sentence 'This sentence is true' is false" - call this sentence NT - which is awkward but quite self-consistent, since TT can indeed consistently be false; in fact, NT can also be true or false: as one would expect, its truthvalue must be the opposite of the truthvalue of TT.
                  It might be worth emphasizing that being a sentence which can be true or false is nothing particularly remarkable. Most sentences of logic are in this category. None of this has anything at all to do with the double-slit experiment, Quantum theory or the nature of physical reality.






                  share|cite|improve this answer









                  $endgroup$



                  "This sentence is true" - call this sentence TT - is not paradoxical. It can be assigned either of the truthvalues T or F. The negation of TT is not the paradoxical Liar sentence "This sentence is false", since the 'this' in these two sentences refer to different sentences. The negation of TT might be rendered as "The sentence 'This sentence is true' is false" - call this sentence NT - which is awkward but quite self-consistent, since TT can indeed consistently be false; in fact, NT can also be true or false: as one would expect, its truthvalue must be the opposite of the truthvalue of TT.
                  It might be worth emphasizing that being a sentence which can be true or false is nothing particularly remarkable. Most sentences of logic are in this category. None of this has anything at all to do with the double-slit experiment, Quantum theory or the nature of physical reality.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 8 '18 at 7:06









                  Pat HayesPat Hayes

                  1




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