When is a connective truth functional?What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?Conditional statements truth tableWhat is the difference between a statement and a proposition?Truth functional propositional logic for “If” in Hunter's MetalogicWhat is the truth value of a unevaluated truth functional?Does the individual meaning of two propositions determine or constrain what kind of logical connectives can be formed between them?syllogism, truth-functional, or neither?Basic Logic: Presuming TruthWhat's the difference between XY=F and XY=0 in Jeffrey's Logic of Decision?Truth-functional connectives - functions of what exactly?What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?

How do I gain back my faith in my PhD degree?

Are there any examples of a variable being normally distributed that is *not* due to the Central Limit Theorem?

Can a virus destroy the BIOS of a modern computer?

Why can't we play rap on piano?

Would Slavery Reparations be considered Bills of Attainder and hence Illegal?

Assassin's bullet with mercury

Can compressed videos be decoded back to their uncompresed original format?

How can I determine if the org that I'm currently connected to is a scratch org?

How badly should I try to prevent a user from XSSing themselves?

How do I deal with an unproductive colleague in a small company?

Could the museum Saturn V's be refitted for one more flight?

Is it inappropriate for a student to attend their mentor's dissertation defense?

How can saying a song's name be a copyright violation?

Why didn't Miles's spider sense work before?

Examples of smooth manifolds admitting inbetween one and a continuum of complex structures

Why is this clock signal connected to a capacitor to gnd?

Plagiarism or not?

Which is the best way to check return result?

Why doesn't using multiple commands with a || or && conditional work?

Do scales need to be in alphabetical order?

Bullying boss launched a smear campaign and made me unemployable

What about the virus in 12 Monkeys?

How writing a dominant 7 sus4 chord in RNA ( Vsus7 chord in the 1st inversion)

How could indestructible materials be used in power generation?



When is a connective truth functional?


What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?Conditional statements truth tableWhat is the difference between a statement and a proposition?Truth functional propositional logic for “If” in Hunter's MetalogicWhat is the truth value of a unevaluated truth functional?Does the individual meaning of two propositions determine or constrain what kind of logical connectives can be formed between them?syllogism, truth-functional, or neither?Basic Logic: Presuming TruthWhat's the difference between XY=F and XY=0 in Jeffrey's Logic of Decision?Truth-functional connectives - functions of what exactly?What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?













4















I got this question from Logic, laws of truth, by Nicholas J.J Smith.



He says (page 24) :




"A connective is truth functional if it has the property that the truth or falsity of a compound proposition formed from the connective and some other propositions is completely determined by the truth or falsity of those component propositions."




I don't really seem to be able to appreciate the usefulness of truth-functional connectives.



Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.



Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?










share|improve this question









New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 1





    When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

    – Conifold
    6 hours ago















4















I got this question from Logic, laws of truth, by Nicholas J.J Smith.



He says (page 24) :




"A connective is truth functional if it has the property that the truth or falsity of a compound proposition formed from the connective and some other propositions is completely determined by the truth or falsity of those component propositions."




I don't really seem to be able to appreciate the usefulness of truth-functional connectives.



Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.



Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?










share|improve this question









New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 1





    When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

    – Conifold
    6 hours ago













4












4








4








I got this question from Logic, laws of truth, by Nicholas J.J Smith.



He says (page 24) :




"A connective is truth functional if it has the property that the truth or falsity of a compound proposition formed from the connective and some other propositions is completely determined by the truth or falsity of those component propositions."




I don't really seem to be able to appreciate the usefulness of truth-functional connectives.



Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.



Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?










share|improve this question









New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












I got this question from Logic, laws of truth, by Nicholas J.J Smith.



He says (page 24) :




"A connective is truth functional if it has the property that the truth or falsity of a compound proposition formed from the connective and some other propositions is completely determined by the truth or falsity of those component propositions."




I don't really seem to be able to appreciate the usefulness of truth-functional connectives.



Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.



Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?







logic






share|improve this question









New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 3 hours ago









Frank Hubeny

9,68051553




9,68051553






New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 11 hours ago









MinigameZ moreMinigameZ more

464




464




New contributor




MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






MinigameZ more is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 1





    When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

    – Conifold
    6 hours ago












  • 1





    When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

    – Conifold
    6 hours ago







1




1





When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

– Conifold
6 hours ago





When its truth value only depends on truth values of its components, and not their meaning. For example, natural disjunction is not truth functional: "it will rain tomorrow or it will not rain tomorrow" holds today even though neither "it will rain tomorrow" nor "it will not rain tomorrow" have definitive truth values today.

– Conifold
6 hours ago










2 Answers
2






active

oldest

votes


















5















When is a connective truth functional?




Short answer : when it is defined by a truth table.




Classical propositional logic is a truth-functional logic in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the contrary, modal logic is non-truth-functional.





See an example in Truth Functionality and non-Truth Functional Connectives, comparing :




Agnes will attend law school and so will Bob,




where the truth-value of the compound sentence depends only on the truth-value of the two atomic sentences, with :




Agnes will attend law school and then she will make millions,




where the "and then" connective express a time-dependency between the two atomic sentences.



For different examples, see 6.3.1 Indicative and Counterfactual Conditionals (page 110) of Smith's book.





An example (motivated by your previous question) dealing with the concept of "internal structure" of a statement will be the following.



The statement




"Jim is a bachelor and Jim (the same Jim) is married"




is not a contradiction in propositional logic, because the sentence has the logical form B ∧ M, and this formula is not a contradiction.



In order to discover the contradicition, we need a deeper level of analysis that consider also the semantics of the expressions "is a bachelor" and "is married", in addition to the logical connective "and".



This level of analysis will be available with predicate logic where we can analyze the atomic sentences with a subject-predicate logical form :




Bachelor(Jim) and Married(Jim).




In this case, privided the axiom :




Bachelor(x) iff not Married(x),




we may derive the contradiction not expressible in propositional logic.






share|improve this answer
































    2














    Nicholas Smith defines the internal structure of arguments as propositions (page 23-4). He then breaks propositions, the internal structure of arguments, into two kinds.




    1. Basic propositions which have no parts that are themselves propositions.


    2. Compound propositions which are composed of other propositions and connectives between them.

    Propositional logic studies the internal structure of compound propositions, but it does not concern itself with the internal structure of basic propositions, that is, it is not interested in the internal structure of basic propositions.



    Predicate logic looks at the internal structure of basic propositions.



    Here are the questions:




    I don't really seem to be able to appreciate the usefulness of truth-functional connectives.




    Truth-functional connectives allow one to study compound propositions in propositional logic. These connectives are part of the internal structure that breaks the compound proposition into component propositions and connectives. This is why they are useful.




    Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.




    The truth or falsity of the compound proposition can be determined by examining the truth or falsity of its component propositions and by studying how they are related by the connectives joining those component propositions.



    Instead of trying to determine the truth or falsity of a compound proposition, which might be complicated, there is a way to break that compound proposition into simpler component propositions by looking at how the connectives join them together into the compound proposition. That is what makes truth-functional connectives useful. They simplify the problem of determining the truth value of compound propositions.




    Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?




    Smith discussed three levels of internal structure.



    1. An argument has an internal structure made up of propositions.

    2. A compound proposition has an internal structure made up of other propositions and connectives studied in propositional logic.

    3. A basic proposition has an internal structure as well which is studied in predicate logic.

    From the perspective of propositional logic the basic propositions can be viewed as having no internal structure that propositional logic studies.




    Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.






    share|improve this answer

























      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
      );



      );






      MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.









      draft saved

      draft discarded


















      StackExchange.ready(
      function ()
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f61586%2fwhen-is-a-connective-truth-functional%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









      5















      When is a connective truth functional?




      Short answer : when it is defined by a truth table.




      Classical propositional logic is a truth-functional logic in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the contrary, modal logic is non-truth-functional.





      See an example in Truth Functionality and non-Truth Functional Connectives, comparing :




      Agnes will attend law school and so will Bob,




      where the truth-value of the compound sentence depends only on the truth-value of the two atomic sentences, with :




      Agnes will attend law school and then she will make millions,




      where the "and then" connective express a time-dependency between the two atomic sentences.



      For different examples, see 6.3.1 Indicative and Counterfactual Conditionals (page 110) of Smith's book.





      An example (motivated by your previous question) dealing with the concept of "internal structure" of a statement will be the following.



      The statement




      "Jim is a bachelor and Jim (the same Jim) is married"




      is not a contradiction in propositional logic, because the sentence has the logical form B ∧ M, and this formula is not a contradiction.



      In order to discover the contradicition, we need a deeper level of analysis that consider also the semantics of the expressions "is a bachelor" and "is married", in addition to the logical connective "and".



      This level of analysis will be available with predicate logic where we can analyze the atomic sentences with a subject-predicate logical form :




      Bachelor(Jim) and Married(Jim).




      In this case, privided the axiom :




      Bachelor(x) iff not Married(x),




      we may derive the contradiction not expressible in propositional logic.






      share|improve this answer





























        5















        When is a connective truth functional?




        Short answer : when it is defined by a truth table.




        Classical propositional logic is a truth-functional logic in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the contrary, modal logic is non-truth-functional.





        See an example in Truth Functionality and non-Truth Functional Connectives, comparing :




        Agnes will attend law school and so will Bob,




        where the truth-value of the compound sentence depends only on the truth-value of the two atomic sentences, with :




        Agnes will attend law school and then she will make millions,




        where the "and then" connective express a time-dependency between the two atomic sentences.



        For different examples, see 6.3.1 Indicative and Counterfactual Conditionals (page 110) of Smith's book.





        An example (motivated by your previous question) dealing with the concept of "internal structure" of a statement will be the following.



        The statement




        "Jim is a bachelor and Jim (the same Jim) is married"




        is not a contradiction in propositional logic, because the sentence has the logical form B ∧ M, and this formula is not a contradiction.



        In order to discover the contradicition, we need a deeper level of analysis that consider also the semantics of the expressions "is a bachelor" and "is married", in addition to the logical connective "and".



        This level of analysis will be available with predicate logic where we can analyze the atomic sentences with a subject-predicate logical form :




        Bachelor(Jim) and Married(Jim).




        In this case, privided the axiom :




        Bachelor(x) iff not Married(x),




        we may derive the contradiction not expressible in propositional logic.






        share|improve this answer



























          5












          5








          5








          When is a connective truth functional?




          Short answer : when it is defined by a truth table.




          Classical propositional logic is a truth-functional logic in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the contrary, modal logic is non-truth-functional.





          See an example in Truth Functionality and non-Truth Functional Connectives, comparing :




          Agnes will attend law school and so will Bob,




          where the truth-value of the compound sentence depends only on the truth-value of the two atomic sentences, with :




          Agnes will attend law school and then she will make millions,




          where the "and then" connective express a time-dependency between the two atomic sentences.



          For different examples, see 6.3.1 Indicative and Counterfactual Conditionals (page 110) of Smith's book.





          An example (motivated by your previous question) dealing with the concept of "internal structure" of a statement will be the following.



          The statement




          "Jim is a bachelor and Jim (the same Jim) is married"




          is not a contradiction in propositional logic, because the sentence has the logical form B ∧ M, and this formula is not a contradiction.



          In order to discover the contradicition, we need a deeper level of analysis that consider also the semantics of the expressions "is a bachelor" and "is married", in addition to the logical connective "and".



          This level of analysis will be available with predicate logic where we can analyze the atomic sentences with a subject-predicate logical form :




          Bachelor(Jim) and Married(Jim).




          In this case, privided the axiom :




          Bachelor(x) iff not Married(x),




          we may derive the contradiction not expressible in propositional logic.






          share|improve this answer
















          When is a connective truth functional?




          Short answer : when it is defined by a truth table.




          Classical propositional logic is a truth-functional logic in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the contrary, modal logic is non-truth-functional.





          See an example in Truth Functionality and non-Truth Functional Connectives, comparing :




          Agnes will attend law school and so will Bob,




          where the truth-value of the compound sentence depends only on the truth-value of the two atomic sentences, with :




          Agnes will attend law school and then she will make millions,




          where the "and then" connective express a time-dependency between the two atomic sentences.



          For different examples, see 6.3.1 Indicative and Counterfactual Conditionals (page 110) of Smith's book.





          An example (motivated by your previous question) dealing with the concept of "internal structure" of a statement will be the following.



          The statement




          "Jim is a bachelor and Jim (the same Jim) is married"




          is not a contradiction in propositional logic, because the sentence has the logical form B ∧ M, and this formula is not a contradiction.



          In order to discover the contradicition, we need a deeper level of analysis that consider also the semantics of the expressions "is a bachelor" and "is married", in addition to the logical connective "and".



          This level of analysis will be available with predicate logic where we can analyze the atomic sentences with a subject-predicate logical form :




          Bachelor(Jim) and Married(Jim).




          In this case, privided the axiom :




          Bachelor(x) iff not Married(x),




          we may derive the contradiction not expressible in propositional logic.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 10 hours ago

























          answered 11 hours ago









          Mauro ALLEGRANZAMauro ALLEGRANZA

          29.4k22065




          29.4k22065





















              2














              Nicholas Smith defines the internal structure of arguments as propositions (page 23-4). He then breaks propositions, the internal structure of arguments, into two kinds.




              1. Basic propositions which have no parts that are themselves propositions.


              2. Compound propositions which are composed of other propositions and connectives between them.

              Propositional logic studies the internal structure of compound propositions, but it does not concern itself with the internal structure of basic propositions, that is, it is not interested in the internal structure of basic propositions.



              Predicate logic looks at the internal structure of basic propositions.



              Here are the questions:




              I don't really seem to be able to appreciate the usefulness of truth-functional connectives.




              Truth-functional connectives allow one to study compound propositions in propositional logic. These connectives are part of the internal structure that breaks the compound proposition into component propositions and connectives. This is why they are useful.




              Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.




              The truth or falsity of the compound proposition can be determined by examining the truth or falsity of its component propositions and by studying how they are related by the connectives joining those component propositions.



              Instead of trying to determine the truth or falsity of a compound proposition, which might be complicated, there is a way to break that compound proposition into simpler component propositions by looking at how the connectives join them together into the compound proposition. That is what makes truth-functional connectives useful. They simplify the problem of determining the truth value of compound propositions.




              Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?




              Smith discussed three levels of internal structure.



              1. An argument has an internal structure made up of propositions.

              2. A compound proposition has an internal structure made up of other propositions and connectives studied in propositional logic.

              3. A basic proposition has an internal structure as well which is studied in predicate logic.

              From the perspective of propositional logic the basic propositions can be viewed as having no internal structure that propositional logic studies.




              Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.






              share|improve this answer





























                2














                Nicholas Smith defines the internal structure of arguments as propositions (page 23-4). He then breaks propositions, the internal structure of arguments, into two kinds.




                1. Basic propositions which have no parts that are themselves propositions.


                2. Compound propositions which are composed of other propositions and connectives between them.

                Propositional logic studies the internal structure of compound propositions, but it does not concern itself with the internal structure of basic propositions, that is, it is not interested in the internal structure of basic propositions.



                Predicate logic looks at the internal structure of basic propositions.



                Here are the questions:




                I don't really seem to be able to appreciate the usefulness of truth-functional connectives.




                Truth-functional connectives allow one to study compound propositions in propositional logic. These connectives are part of the internal structure that breaks the compound proposition into component propositions and connectives. This is why they are useful.




                Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.




                The truth or falsity of the compound proposition can be determined by examining the truth or falsity of its component propositions and by studying how they are related by the connectives joining those component propositions.



                Instead of trying to determine the truth or falsity of a compound proposition, which might be complicated, there is a way to break that compound proposition into simpler component propositions by looking at how the connectives join them together into the compound proposition. That is what makes truth-functional connectives useful. They simplify the problem of determining the truth value of compound propositions.




                Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?




                Smith discussed three levels of internal structure.



                1. An argument has an internal structure made up of propositions.

                2. A compound proposition has an internal structure made up of other propositions and connectives studied in propositional logic.

                3. A basic proposition has an internal structure as well which is studied in predicate logic.

                From the perspective of propositional logic the basic propositions can be viewed as having no internal structure that propositional logic studies.




                Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.






                share|improve this answer



























                  2












                  2








                  2







                  Nicholas Smith defines the internal structure of arguments as propositions (page 23-4). He then breaks propositions, the internal structure of arguments, into two kinds.




                  1. Basic propositions which have no parts that are themselves propositions.


                  2. Compound propositions which are composed of other propositions and connectives between them.

                  Propositional logic studies the internal structure of compound propositions, but it does not concern itself with the internal structure of basic propositions, that is, it is not interested in the internal structure of basic propositions.



                  Predicate logic looks at the internal structure of basic propositions.



                  Here are the questions:




                  I don't really seem to be able to appreciate the usefulness of truth-functional connectives.




                  Truth-functional connectives allow one to study compound propositions in propositional logic. These connectives are part of the internal structure that breaks the compound proposition into component propositions and connectives. This is why they are useful.




                  Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.




                  The truth or falsity of the compound proposition can be determined by examining the truth or falsity of its component propositions and by studying how they are related by the connectives joining those component propositions.



                  Instead of trying to determine the truth or falsity of a compound proposition, which might be complicated, there is a way to break that compound proposition into simpler component propositions by looking at how the connectives join them together into the compound proposition. That is what makes truth-functional connectives useful. They simplify the problem of determining the truth value of compound propositions.




                  Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?




                  Smith discussed three levels of internal structure.



                  1. An argument has an internal structure made up of propositions.

                  2. A compound proposition has an internal structure made up of other propositions and connectives studied in propositional logic.

                  3. A basic proposition has an internal structure as well which is studied in predicate logic.

                  From the perspective of propositional logic the basic propositions can be viewed as having no internal structure that propositional logic studies.




                  Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.






                  share|improve this answer















                  Nicholas Smith defines the internal structure of arguments as propositions (page 23-4). He then breaks propositions, the internal structure of arguments, into two kinds.




                  1. Basic propositions which have no parts that are themselves propositions.


                  2. Compound propositions which are composed of other propositions and connectives between them.

                  Propositional logic studies the internal structure of compound propositions, but it does not concern itself with the internal structure of basic propositions, that is, it is not interested in the internal structure of basic propositions.



                  Predicate logic looks at the internal structure of basic propositions.



                  Here are the questions:




                  I don't really seem to be able to appreciate the usefulness of truth-functional connectives.




                  Truth-functional connectives allow one to study compound propositions in propositional logic. These connectives are part of the internal structure that breaks the compound proposition into component propositions and connectives. This is why they are useful.




                  Perhaps, I don't understand what he is saying in that paragraph, so I would appreciate any explanation of what he is trying to say and why truth-functional connectives are useful.




                  The truth or falsity of the compound proposition can be determined by examining the truth or falsity of its component propositions and by studying how they are related by the connectives joining those component propositions.



                  Instead of trying to determine the truth or falsity of a compound proposition, which might be complicated, there is a way to break that compound proposition into simpler component propositions by looking at how the connectives join them together into the compound proposition. That is what makes truth-functional connectives useful. They simplify the problem of determining the truth value of compound propositions.




                  Also (if you want to) can you guys explain what Nicholas means when he says "...this proposition has no internal structure..."?




                  Smith discussed three levels of internal structure.



                  1. An argument has an internal structure made up of propositions.

                  2. A compound proposition has an internal structure made up of other propositions and connectives studied in propositional logic.

                  3. A basic proposition has an internal structure as well which is studied in predicate logic.

                  From the perspective of propositional logic the basic propositions can be viewed as having no internal structure that propositional logic studies.




                  Smith, N. J. (2012). Logic: The laws of truth. Princeton University Press.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 3 hours ago

























                  answered 3 hours ago









                  Frank HubenyFrank Hubeny

                  9,68051553




                  9,68051553




















                      MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.









                      draft saved

                      draft discarded


















                      MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.












                      MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.











                      MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.














                      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%2f61586%2fwhen-is-a-connective-truth-functional%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

                      Are there any AGPL-style licences that require source code modifications to be public? Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?Force derivative works to be publicAre there any GPL like licenses for Apple App Store?Do you violate the GPL if you provide source code that cannot be compiled?GPL - is it distribution to use libraries in an appliance loaned to customers?Distributing App for free which uses GPL'ed codeModifications of server software under GPL, with web/CLI interfaceDoes using an AGPLv3-licensed library prevent me from dual-licensing my own source code?Can I publish only select code under GPLv3 from a private project?Is there published precedent regarding the scope of covered work that uses AGPL software?If MIT licensed code links to GPL licensed code what should be the license of the resulting binary program?If I use a public API endpoint that has its source code licensed under AGPL in my app, do I need to disclose my source?

                      2013 GY136 Descoberta | Órbita | Referências Menu de navegação«List Of Centaurs and Scattered-Disk Objects»«List of Known Trans-Neptunian Objects»

                      Mortes em março de 2019 Referências Menu de navegação«Zhores Alferov, Nobel de Física bielorrusso, morre aos 88 anos - Ciência»«Fallece Rafael Torija, o bispo emérito de Ciudad Real»«Peter Hurford dies at 88»«Keith Flint, vocalista do The Prodigy, morre aos 49 anos»«Luke Perry, ator de 'Barrados no baile' e 'Riverdale', morre aos 52 anos»«Former Rangers and Scotland captain Eric Caldow dies, aged 84»«Morreu, aos 61 anos, a antiga lenda do wrestling King Kong Bundy»«Fallece el actor y director teatral Abraham Stavans»«In Memoriam Guillaume Faye»«Sidney Sheinberg, a Force Behind Universal and Spielberg, Is Dead at 84»«Carmine Persico, Colombo Crime Family Boss, Is Dead at 85»«Dirigent Michael Gielen gestorben»«Ciclista tricampeã mundial e prata na Rio 2016 é encontrada morta em casa aos 23 anos»«Pagan Community Notes: Raven Grimassi dies, Indianapolis pop-up event cancelled, Circle Sanctuary announces new podcast, and more!»«Hal Blaine, Wrecking Crew Drummer, Dies at 90»«Morre Coutinho, que editou dupla lendária com Pelé no Santos»«Cantor Demétrius, ídolo da Jovem Guarda, morre em SP»«Ex-presidente do Vasco, Eurico Miranda morre no Rio de Janeiro»«Bronze no Mundial de basquete de 1971, Laís Elena morre aos 76 anos»«Diretor de Corridas da F1, Charlie Whiting morre aos 66 anos às vésperas do GP da Austrália»«Morreu o cardeal Danneels, da Bélgica»«Morreu o cartoonista Augusto Cid»«Morreu a atriz Maria Isabel de Lizandra, de "Vale Tudo" e novelas da Tupi»«WS Merwin, prize-winning poet of nature, dies at 91»«Atriz Márcia Real morre em São Paulo aos 88 anos»«Mauritanie: décès de l'ancien président Mohamed Mahmoud ould Louly»«Morreu Dick Dale, o rei da surf guitar e de "Pulp Fiction"»«Falleció Víctor Genes»«João Carlos Marinho, autor de 'O Gênio do Crime', morre em SP»«Legendary Horror Director and SFX Artist John Carl Buechler Dies at 66»«Morre em Salvador a religiosa Makota Valdina»«مرگ بازیکن‌ سابق نساجی بر اثر سقوط سنگ در مازندران»«Domingos Oliveira morre no Rio»«Morre Airton Ravagniani, ex-São Paulo, Fla, Vasco, Grêmio e Sport - Notícias»«Morre o escritor Flavio Moreira da Costa»«Larry Cohen, Writer-Director of 'It's Alive' and 'Hell Up in Harlem,' Dies at 77»«Scott Walker, experimental singer-songwriter, dead at 76»«Joseph Pilato, Day of the Dead Star and Horror Favorite, Dies at 70»«Sheffield United set to pay tribute to legendary goalkeeper Ted Burgin who has died at 91»«Morre Rafael Henzel, sobrevivente de acidente aéreo da Chapecoense»«Morre Valery Bykovsky, um dos primeiros cosmonautas da União Soviética»«Agnès Varda, cineasta da Nouvelle Vague, morre aos 90 anos»«Agnès Varda, cineasta francesa, morre aos 90 anos»«Tania Mallet, James Bond Actress and Helen Mirren's Cousin, Dies at 77»e