Why isn’t ‘because’ a logical connective in propositional logic?











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In simple terms, could someone explain why there is not a logical connective for ‘because’ in propositional logic like there is for ‘and’ and ‘or’?



Is this because the equivalent of ‘because’ is the argument of the form ‘if p, then q’, or am I missing something?



Please illustrate your answer with example(s) if possible.










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  • 15




    "because" is about causality, not implication
    – Hagen von Eitzen
    2 days ago








  • 1




    Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
    – Barry Cipra
    2 days ago








  • 1




    I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
    – Joshua
    yesterday










  • @Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
    – Derek Elkins
    15 hours ago










  • $(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
    – Henry
    13 hours ago

















up vote
34
down vote

favorite
7












In simple terms, could someone explain why there is not a logical connective for ‘because’ in propositional logic like there is for ‘and’ and ‘or’?



Is this because the equivalent of ‘because’ is the argument of the form ‘if p, then q’, or am I missing something?



Please illustrate your answer with example(s) if possible.










share|cite|improve this question


















  • 15




    "because" is about causality, not implication
    – Hagen von Eitzen
    2 days ago








  • 1




    Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
    – Barry Cipra
    2 days ago








  • 1




    I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
    – Joshua
    yesterday










  • @Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
    – Derek Elkins
    15 hours ago










  • $(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
    – Henry
    13 hours ago















up vote
34
down vote

favorite
7









up vote
34
down vote

favorite
7






7





In simple terms, could someone explain why there is not a logical connective for ‘because’ in propositional logic like there is for ‘and’ and ‘or’?



Is this because the equivalent of ‘because’ is the argument of the form ‘if p, then q’, or am I missing something?



Please illustrate your answer with example(s) if possible.










share|cite|improve this question













In simple terms, could someone explain why there is not a logical connective for ‘because’ in propositional logic like there is for ‘and’ and ‘or’?



Is this because the equivalent of ‘because’ is the argument of the form ‘if p, then q’, or am I missing something?



Please illustrate your answer with example(s) if possible.







logic propositional-calculus






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 2 days ago









seeker

2,68855184




2,68855184








  • 15




    "because" is about causality, not implication
    – Hagen von Eitzen
    2 days ago








  • 1




    Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
    – Barry Cipra
    2 days ago








  • 1




    I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
    – Joshua
    yesterday










  • @Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
    – Derek Elkins
    15 hours ago










  • $(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
    – Henry
    13 hours ago
















  • 15




    "because" is about causality, not implication
    – Hagen von Eitzen
    2 days ago








  • 1




    Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
    – Barry Cipra
    2 days ago








  • 1




    I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
    – Joshua
    yesterday










  • @Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
    – Derek Elkins
    15 hours ago










  • $(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
    – Henry
    13 hours ago










15




15




"because" is about causality, not implication
– Hagen von Eitzen
2 days ago






"because" is about causality, not implication
– Hagen von Eitzen
2 days ago






1




1




Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
– Barry Cipra
2 days ago






Folks might find basicbooks.com/titles/judea-pearl/the-book-of-why/9780465097609 of interest.
– Barry Cipra
2 days ago






1




1




I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
– Joshua
yesterday




I would love to see a complete prepositional logic theory where P→Q is not equivalent to ¬P∨Q but I haven't yet. :(
– Joshua
yesterday












@Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
– Derek Elkins
15 hours ago




@Joshua Maybe I'm misunderstanding what you mean, but that equivalence typically fails in non-classical logics. It definitely fails in constructive/intuitionistic logic. So Intuitionistic Propositional Logic would be a propositional logic where $Pto Q$ is not equivalent to $neg Plor Q$.
– Derek Elkins
15 hours ago












$(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
– Henry
13 hours ago






$(Pto Q) lor (Qto P)$ is a tautology in classical logic, so presumably $(Qleftarrow P) lor (Pleftarrow Q)$ is too. You would not want to read "$leftarrow$" as because here
– Henry
13 hours ago












4 Answers
4






active

oldest

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up vote
99
down vote



accepted










It is because 'because' is not truth-functional.



That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$'



For example, the two statements 'Grass is green' and 'Snow is white' are both true, but 'Grass is green because snow is white' is an invalid argument, and hence, as a statement as to the validity of that argument, a false statement.



On the other hand,'Grass is green because grass is green' is a true statement as to the validity of this as an argument, but yet again it involves two true statements.



This shows that with $P$ and $Q$ both being true, the statement '$P$ because of $Q$' can either be true or false, and hence it is not truth-functional.






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  • 12




    This is an exceedingly better answer than I expected possible. Kudos!
    – Daniel R. Collins
    2 days ago






  • 3




    Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
    – Vaelus
    yesterday






  • 4




    @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
    – David Z
    yesterday








  • 5




    @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
    – Bram28
    yesterday






  • 1




    @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
    – kutschkem
    7 hours ago




















up vote
12
down vote














Why isn’t ‘because’ a logical connective in propositional logic?



Is this because the equivalent of ‘because’ is the argument of the form ‘if $p$, then $q$’ ?




Exactly.



Either the connective "because" is truth-functional, in which case it is the same as "if..., then...", or it is not truth-functional, in which case we need a different way of modelling it.



See e.g. Counterfactual Theories of Causation.



See also Arthur Burks, The Logic of Causal Proposition, Mind (1951).






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  • I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
    – Henry
    13 hours ago












  • @Henry - reverse ?
    – Mauro ALLEGRANZA
    12 hours ago






  • 1




    What does the first word (exactly) refer to?
    – Carsten S
    11 hours ago


















up vote
6
down vote













I agree with the other answers, however I want to add that the closest thing might be the turnstyle symbol $vdash$, although this is usually read as "yields", and thus points the other way. If I write



$$A vdash B$$
this is read as "A yields B", or "knowing A, I can prove B". If you wanted to encode because, you could probably read it backwards as "B because of A".



Note however that this is not used as part of a logical formula, but as a shorthand between formulas when writing down a proof. So $A vdash B$ is no longer a formula, but rather a statement on how to prove $B$. (In most of the rest of mathematics, you would write $Rightarrow$ in your proof instead, however in logic this is of course easily confused with the implication inside formulas)






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  • 2




    Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
    – Bram28
    yesterday


















up vote
1
down vote













You can define things however you want. (Be careful; you may accidentally be inconsistent.)



Either:




  • "because" is logically equivalent to a binary operator

  • or it's not


If it is, it's probably the same as "only if" (Or take your pick of the other 15 operators). Adding a "because" overload would create an additional word to remember: unneeded complexity. We like simplicity.



If it isn't, you can define a binary function because(a, b) however you want.






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    4 Answers
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    4 Answers
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    up vote
    99
    down vote



    accepted










    It is because 'because' is not truth-functional.



    That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$'



    For example, the two statements 'Grass is green' and 'Snow is white' are both true, but 'Grass is green because snow is white' is an invalid argument, and hence, as a statement as to the validity of that argument, a false statement.



    On the other hand,'Grass is green because grass is green' is a true statement as to the validity of this as an argument, but yet again it involves two true statements.



    This shows that with $P$ and $Q$ both being true, the statement '$P$ because of $Q$' can either be true or false, and hence it is not truth-functional.






    share|cite|improve this answer

















    • 12




      This is an exceedingly better answer than I expected possible. Kudos!
      – Daniel R. Collins
      2 days ago






    • 3




      Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
      – Vaelus
      yesterday






    • 4




      @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
      – David Z
      yesterday








    • 5




      @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
      – Bram28
      yesterday






    • 1




      @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
      – kutschkem
      7 hours ago

















    up vote
    99
    down vote



    accepted










    It is because 'because' is not truth-functional.



    That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$'



    For example, the two statements 'Grass is green' and 'Snow is white' are both true, but 'Grass is green because snow is white' is an invalid argument, and hence, as a statement as to the validity of that argument, a false statement.



    On the other hand,'Grass is green because grass is green' is a true statement as to the validity of this as an argument, but yet again it involves two true statements.



    This shows that with $P$ and $Q$ both being true, the statement '$P$ because of $Q$' can either be true or false, and hence it is not truth-functional.






    share|cite|improve this answer

















    • 12




      This is an exceedingly better answer than I expected possible. Kudos!
      – Daniel R. Collins
      2 days ago






    • 3




      Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
      – Vaelus
      yesterday






    • 4




      @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
      – David Z
      yesterday








    • 5




      @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
      – Bram28
      yesterday






    • 1




      @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
      – kutschkem
      7 hours ago















    up vote
    99
    down vote



    accepted







    up vote
    99
    down vote



    accepted






    It is because 'because' is not truth-functional.



    That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$'



    For example, the two statements 'Grass is green' and 'Snow is white' are both true, but 'Grass is green because snow is white' is an invalid argument, and hence, as a statement as to the validity of that argument, a false statement.



    On the other hand,'Grass is green because grass is green' is a true statement as to the validity of this as an argument, but yet again it involves two true statements.



    This shows that with $P$ and $Q$ both being true, the statement '$P$ because of $Q$' can either be true or false, and hence it is not truth-functional.






    share|cite|improve this answer












    It is because 'because' is not truth-functional.



    That is, knowing the truth-values of $P$ and $Q$ does not tell you the truth-value of '$P$ because of $Q$'



    For example, the two statements 'Grass is green' and 'Snow is white' are both true, but 'Grass is green because snow is white' is an invalid argument, and hence, as a statement as to the validity of that argument, a false statement.



    On the other hand,'Grass is green because grass is green' is a true statement as to the validity of this as an argument, but yet again it involves two true statements.



    This shows that with $P$ and $Q$ both being true, the statement '$P$ because of $Q$' can either be true or false, and hence it is not truth-functional.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 days ago









    Bram28

    57.7k34185




    57.7k34185








    • 12




      This is an exceedingly better answer than I expected possible. Kudos!
      – Daniel R. Collins
      2 days ago






    • 3




      Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
      – Vaelus
      yesterday






    • 4




      @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
      – David Z
      yesterday








    • 5




      @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
      – Bram28
      yesterday






    • 1




      @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
      – kutschkem
      7 hours ago
















    • 12




      This is an exceedingly better answer than I expected possible. Kudos!
      – Daniel R. Collins
      2 days ago






    • 3




      Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
      – Vaelus
      yesterday






    • 4




      @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
      – David Z
      yesterday








    • 5




      @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
      – Bram28
      yesterday






    • 1




      @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
      – kutschkem
      7 hours ago










    12




    12




    This is an exceedingly better answer than I expected possible. Kudos!
    – Daniel R. Collins
    2 days ago




    This is an exceedingly better answer than I expected possible. Kudos!
    – Daniel R. Collins
    2 days ago




    3




    3




    Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
    – Vaelus
    yesterday




    Wouldn't this reaoning also apply to if statements? "If snow is white, then grass is green" happens to be true, despite not making much sense in common English.
    – Vaelus
    yesterday




    4




    4




    @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
    – David Z
    yesterday






    @Vaelus If I've understood the answer correctly, the point is that the truth of "if P then Q" is uniquely determined by the truth values of P and Q, whereas the truth of "P because Q" is not determined by the truth values of P and Q. That is, there are cases where "[true statement] because [true statement]" is true, and also cases where "[true statement] because [true statement]" is false, which is not the case for logical if statements.
    – David Z
    yesterday






    5




    5




    @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
    – Bram28
    yesterday




    @Vaelus Yes, the English 'if ... then ...' does not seem to be teuth-functional either .... so why do logicians define a truth-functional operator (called the material implication) to try and capture it? There is a long standing debate about this. Please look up 'Paradox of Material Implication' if you want to know more.
    – Bram28
    yesterday




    1




    1




    @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
    – kutschkem
    7 hours ago






    @Ooker No, "Q happens because P happens" is not what he is saying, he is saying "(I know Q is true) because (I know P is true)". This is not stating anything about causality. For example, in a simple world it may be true that "If it is wet outside today, it rained last night." (and also "If it rained last night, it is wet outside today"). But only one of "It is wet outside today because it rained last night" and "It rained last night because it is wet outside today" is true, namely rain => wet. It is however true that I know it rained because I know it is wet.
    – kutschkem
    7 hours ago












    up vote
    12
    down vote














    Why isn’t ‘because’ a logical connective in propositional logic?



    Is this because the equivalent of ‘because’ is the argument of the form ‘if $p$, then $q$’ ?




    Exactly.



    Either the connective "because" is truth-functional, in which case it is the same as "if..., then...", or it is not truth-functional, in which case we need a different way of modelling it.



    See e.g. Counterfactual Theories of Causation.



    See also Arthur Burks, The Logic of Causal Proposition, Mind (1951).






    share|cite|improve this answer























    • I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
      – Henry
      13 hours ago












    • @Henry - reverse ?
      – Mauro ALLEGRANZA
      12 hours ago






    • 1




      What does the first word (exactly) refer to?
      – Carsten S
      11 hours ago















    up vote
    12
    down vote














    Why isn’t ‘because’ a logical connective in propositional logic?



    Is this because the equivalent of ‘because’ is the argument of the form ‘if $p$, then $q$’ ?




    Exactly.



    Either the connective "because" is truth-functional, in which case it is the same as "if..., then...", or it is not truth-functional, in which case we need a different way of modelling it.



    See e.g. Counterfactual Theories of Causation.



    See also Arthur Burks, The Logic of Causal Proposition, Mind (1951).






    share|cite|improve this answer























    • I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
      – Henry
      13 hours ago












    • @Henry - reverse ?
      – Mauro ALLEGRANZA
      12 hours ago






    • 1




      What does the first word (exactly) refer to?
      – Carsten S
      11 hours ago













    up vote
    12
    down vote










    up vote
    12
    down vote










    Why isn’t ‘because’ a logical connective in propositional logic?



    Is this because the equivalent of ‘because’ is the argument of the form ‘if $p$, then $q$’ ?




    Exactly.



    Either the connective "because" is truth-functional, in which case it is the same as "if..., then...", or it is not truth-functional, in which case we need a different way of modelling it.



    See e.g. Counterfactual Theories of Causation.



    See also Arthur Burks, The Logic of Causal Proposition, Mind (1951).






    share|cite|improve this answer















    Why isn’t ‘because’ a logical connective in propositional logic?



    Is this because the equivalent of ‘because’ is the argument of the form ‘if $p$, then $q$’ ?




    Exactly.



    Either the connective "because" is truth-functional, in which case it is the same as "if..., then...", or it is not truth-functional, in which case we need a different way of modelling it.



    See e.g. Counterfactual Theories of Causation.



    See also Arthur Burks, The Logic of Causal Proposition, Mind (1951).







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited 11 hours ago

























    answered 2 days ago









    Mauro ALLEGRANZA

    63.2k448110




    63.2k448110












    • I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
      – Henry
      13 hours ago












    • @Henry - reverse ?
      – Mauro ALLEGRANZA
      12 hours ago






    • 1




      What does the first word (exactly) refer to?
      – Carsten S
      11 hours ago


















    • I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
      – Henry
      13 hours ago












    • @Henry - reverse ?
      – Mauro ALLEGRANZA
      12 hours ago






    • 1




      What does the first word (exactly) refer to?
      – Carsten S
      11 hours ago
















    I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
    – Henry
    13 hours ago






    I would have thought a truth-functional because might be considered the reverse of if..., then... rather than the same
    – Henry
    13 hours ago














    @Henry - reverse ?
    – Mauro ALLEGRANZA
    12 hours ago




    @Henry - reverse ?
    – Mauro ALLEGRANZA
    12 hours ago




    1




    1




    What does the first word (exactly) refer to?
    – Carsten S
    11 hours ago




    What does the first word (exactly) refer to?
    – Carsten S
    11 hours ago










    up vote
    6
    down vote













    I agree with the other answers, however I want to add that the closest thing might be the turnstyle symbol $vdash$, although this is usually read as "yields", and thus points the other way. If I write



    $$A vdash B$$
    this is read as "A yields B", or "knowing A, I can prove B". If you wanted to encode because, you could probably read it backwards as "B because of A".



    Note however that this is not used as part of a logical formula, but as a shorthand between formulas when writing down a proof. So $A vdash B$ is no longer a formula, but rather a statement on how to prove $B$. (In most of the rest of mathematics, you would write $Rightarrow$ in your proof instead, however in logic this is of course easily confused with the implication inside formulas)






    share|cite|improve this answer

















    • 2




      Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
      – Bram28
      yesterday















    up vote
    6
    down vote













    I agree with the other answers, however I want to add that the closest thing might be the turnstyle symbol $vdash$, although this is usually read as "yields", and thus points the other way. If I write



    $$A vdash B$$
    this is read as "A yields B", or "knowing A, I can prove B". If you wanted to encode because, you could probably read it backwards as "B because of A".



    Note however that this is not used as part of a logical formula, but as a shorthand between formulas when writing down a proof. So $A vdash B$ is no longer a formula, but rather a statement on how to prove $B$. (In most of the rest of mathematics, you would write $Rightarrow$ in your proof instead, however in logic this is of course easily confused with the implication inside formulas)






    share|cite|improve this answer

















    • 2




      Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
      – Bram28
      yesterday













    up vote
    6
    down vote










    up vote
    6
    down vote









    I agree with the other answers, however I want to add that the closest thing might be the turnstyle symbol $vdash$, although this is usually read as "yields", and thus points the other way. If I write



    $$A vdash B$$
    this is read as "A yields B", or "knowing A, I can prove B". If you wanted to encode because, you could probably read it backwards as "B because of A".



    Note however that this is not used as part of a logical formula, but as a shorthand between formulas when writing down a proof. So $A vdash B$ is no longer a formula, but rather a statement on how to prove $B$. (In most of the rest of mathematics, you would write $Rightarrow$ in your proof instead, however in logic this is of course easily confused with the implication inside formulas)






    share|cite|improve this answer












    I agree with the other answers, however I want to add that the closest thing might be the turnstyle symbol $vdash$, although this is usually read as "yields", and thus points the other way. If I write



    $$A vdash B$$
    this is read as "A yields B", or "knowing A, I can prove B". If you wanted to encode because, you could probably read it backwards as "B because of A".



    Note however that this is not used as part of a logical formula, but as a shorthand between formulas when writing down a proof. So $A vdash B$ is no longer a formula, but rather a statement on how to prove $B$. (In most of the rest of mathematics, you would write $Rightarrow$ in your proof instead, however in logic this is of course easily confused with the implication inside formulas)







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 days ago









    mlk

    2,865915




    2,865915








    • 2




      Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
      – Bram28
      yesterday














    • 2




      Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
      – Bram28
      yesterday








    2




    2




    Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
    – Bram28
    yesterday




    Yes, this would therefore be a 'meta-logical' symbol;: a symbol used to say something about logic exprssion .. but it is not a logical connective or operator.
    – Bram28
    yesterday










    up vote
    1
    down vote













    You can define things however you want. (Be careful; you may accidentally be inconsistent.)



    Either:




    • "because" is logically equivalent to a binary operator

    • or it's not


    If it is, it's probably the same as "only if" (Or take your pick of the other 15 operators). Adding a "because" overload would create an additional word to remember: unneeded complexity. We like simplicity.



    If it isn't, you can define a binary function because(a, b) however you want.






    share|cite|improve this answer

























      up vote
      1
      down vote













      You can define things however you want. (Be careful; you may accidentally be inconsistent.)



      Either:




      • "because" is logically equivalent to a binary operator

      • or it's not


      If it is, it's probably the same as "only if" (Or take your pick of the other 15 operators). Adding a "because" overload would create an additional word to remember: unneeded complexity. We like simplicity.



      If it isn't, you can define a binary function because(a, b) however you want.






      share|cite|improve this answer























        up vote
        1
        down vote










        up vote
        1
        down vote









        You can define things however you want. (Be careful; you may accidentally be inconsistent.)



        Either:




        • "because" is logically equivalent to a binary operator

        • or it's not


        If it is, it's probably the same as "only if" (Or take your pick of the other 15 operators). Adding a "because" overload would create an additional word to remember: unneeded complexity. We like simplicity.



        If it isn't, you can define a binary function because(a, b) however you want.






        share|cite|improve this answer












        You can define things however you want. (Be careful; you may accidentally be inconsistent.)



        Either:




        • "because" is logically equivalent to a binary operator

        • or it's not


        If it is, it's probably the same as "only if" (Or take your pick of the other 15 operators). Adding a "because" overload would create an additional word to remember: unneeded complexity. We like simplicity.



        If it isn't, you can define a binary function because(a, b) however you want.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 16 hours ago









        Words Like Jared

        1337




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