How is the argument “I love all logic, but I don’t love deductive reasoning. Therefore, the moon is made of green cheese.” valid?

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This example came up in class:




I love all logic, but I don’t love deductive reasoning.
Therefore, the moon is made of green cheese.




I understand the premise is contradictory and the conclusion is false, but the prof said the argument is valid, which I don't understand.



The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



Isn't the premise false?






logic







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  • I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
    – Frank Hubeny
    yesterday










  • validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
    – Mr. Kennedy
    yesterday






  • 3




    Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
    – Ben Voigt
    yesterday










  • There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
    – T. Sar
    23 hours ago







  • 1




    One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
    – Ben
    20 hours ago















up vote
18
down vote

favorite
7












This example came up in class:




I love all logic, but I don’t love deductive reasoning.
Therefore, the moon is made of green cheese.




I understand the premise is contradictory and the conclusion is false, but the prof said the argument is valid, which I don't understand.



The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



Isn't the premise false?






logic







share|improve this question









New contributor




user34930 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.



















  • I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
    – Frank Hubeny
    yesterday










  • validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
    – Mr. Kennedy
    yesterday






  • 3




    Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
    – Ben Voigt
    yesterday










  • There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
    – T. Sar
    23 hours ago







  • 1




    One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
    – Ben
    20 hours ago













up vote
18
down vote

favorite
7









up vote
18
down vote

favorite
7






7





This example came up in class:




I love all logic, but I don’t love deductive reasoning.
Therefore, the moon is made of green cheese.




I understand the premise is contradictory and the conclusion is false, but the prof said the argument is valid, which I don't understand.



The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



Isn't the premise false?






logic







share|improve this question









New contributor




user34930 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











This example came up in class:




I love all logic, but I don’t love deductive reasoning.
Therefore, the moon is made of green cheese.




I understand the premise is contradictory and the conclusion is false, but the prof said the argument is valid, which I don't understand.



The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



Isn't the premise false?






logic




logic






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user34930 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|improve this question









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edited yesterday









virmaior

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  • I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
    – Frank Hubeny
    yesterday










  • validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
    – Mr. Kennedy
    yesterday






  • 3




    Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
    – Ben Voigt
    yesterday










  • There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
    – T. Sar
    23 hours ago







  • 1




    One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
    – Ben
    20 hours ago

















  • I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
    – Frank Hubeny
    yesterday










  • validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
    – Mr. Kennedy
    yesterday






  • 3




    Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
    – Ben Voigt
    yesterday










  • There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
    – T. Sar
    23 hours ago







  • 1




    One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
    – Ben
    20 hours ago
















I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
– Frank Hubeny
yesterday




I made an edit to put the statement in a box for clarity. You may roll this back or continue editing. You can see the versions by clicking on "edited" above. If the premise is false the logical conditional would be considered valid no matter what the conclusion was. It is only when the premise is true and the conclusion is false that the conditional is invalid.
– Frank Hubeny
yesterday












validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
– Mr. Kennedy
yesterday




validity pertains to the form of the argument and soundness the truth value. iep.utm.edu/val-snd
– Mr. Kennedy
yesterday




3




3




Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
– Ben Voigt
yesterday




Possible duplicate of If the premises of an argument CANNOT all be true, then said argument is valid
– Ben Voigt
yesterday












There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
– T. Sar
23 hours ago





There is a difference between the logical argument being valid and the logical argument being "correct" in the usual sense of the word. You have to abstract away what the words actually say when playing with formal logic.
– T. Sar
23 hours ago





1




1




One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
– Ben
20 hours ago





One way to think about it is: Is there any possible universe, where you love all logic, yet don't love deductive logic, in which the moon might possibly not be made of green cheese? There are no such universes, therefore there are no universes where the moon is not green cheese, therefore the implication is valid.... "All my cars are red" and "all my cars are black" can both be true, if, and only if, I have no cars.
– Ben
20 hours ago











4 Answers
4






active

oldest

votes

















up vote
26
down vote



accepted










This is an example of the principle of explosion or ex falso quodlibet. This is a property of some logical systems (including classical logic) where a false premise, or, equivalently, inconsistent premises, make the inference valid regardless of what the conclusion is.



We can see from the truth table definition of the → connective in classical logic that if the left argument is false, then the whole expression is true.



Classical implication P → Q is equivalent to ¬P ∨ Q



 [P → Q] P ¬P
 Q 1 1
 ¬Q 0 1


and equivalently



[¬P ∨ Q] P ¬P
 Q 1 1
 ¬Q 0 1


Just looking at the definition of the connective doesn't prove that the inference is valid on its own. It does suggest why this might be the case. → only inspects the truth values of its arguments, not the content.



For that, let's look at a skeleton inference rule with primitive propositions P and Q.



P ∧ ¬P
------
Q


Since P and Q are independent of each other, this potential inference rule being valid would show that the system we are working in satisfies the principle of explosion.



To justify the rule we can translate it into a formula involving just the primitive connectives by replacing ----- with → and determining whether the statement is an unconditional tautology.



(P ∧ ¬P) → Q

[(P ∧ ¬P) → Q] P ¬P
 Q 1 1
 ¬Q 1 1


It is one, therefore classical logic satisfies the principle of explosion because the given rule is admissible / a theorem.



The premise in the statement given I love all logic, but I don't love deductive reasoning is intended to be manifestly a contradiction (false) and also a joke. The moon is made of green cheese is also commonly used as an example of an irrelevant conclusion. The example is supposed to highlight the disconnect between everyday reasoning with natural language and classical logic.



Paraphrased using disjunction instead of negation, the sentence would read, roughly




Either it is not the case that I love all logic but hate deductive reasoning,
or the moon is made of green cheese.




This sentence, to me at least, simply seems to be true since it boils down to Either TRUE or FALSE.






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    up vote
    9
    down vote














    The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



    Isn't the premise false?




    The premises are contradictory.



    So it is impossible for the premises to all be true.



    Thus it is impossible for the premises to all be true and the conclusion false.



    Therefore the argument is valid.






    share|improve this answer
















    • 1




      Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
      – Battle
      yesterday










    • This "answer" doesn't explain anything. I would -1 it if I had the rep.
      – Pod
      yesterday

















    up vote
    8
    down vote













    It's not perfectly clear, but my best guess is that the instructor intends:




    I love all logic, but I don’t love deductive reasoning.




    to contain two incompossible premises.



    meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.



    and conversely if "I don't love deductive reasoning", then "I love all logic is false".



    Ergo, this argument can never have both of its premises true.



    If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).



    Where the argument suffers a bit is on clarity. There's three issues here.



    First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are cannot both be true. To understand that we need to use "all" and other concepts you may not have learned. We can formalize the argument as :



    1. ∀x (Lx -> Vx) [for any x if x is a logic, then love x]

    2. La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]

    These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.



    Second, the argument uses "I". This gets a bit dicey due to two issues:



    1. Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)

    2. "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.

    Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, but this example is not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.






    share|improve this answer


















    • 1




      I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
      – virmaior
      yesterday






    • 2




      The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
      – virmaior
      yesterday






    • 3




      @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
      – Eliran H
      yesterday






    • 1




      @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
      – virmaior
      yesterday






    • 2




      @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
      – Mike Scott
      20 hours ago

















    up vote
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    down vote













    The way I think of this is similar to how Ben describes it in the comments to the question i.e. it's similar to a vacuous truth. Formally, I guess it's not exact the same but it might be easier to understand coming from that direction.



    In a nutshell you can make any assertion about the properties of members of an empty set and it's true. For example, if I say "all flying elephants have gossamer wings", the statement is true. How so? Well if it's not true, then there need be one flying elephant whose wings are not gossamer. It's also true that no flying elephants have gossamer wings for the same reason.



    The most common way you might encounter such a construction is when someone says somoething like "if he's a doctor then I'm Santa Claus" which is ultimately a fancy way of saying the premise (i.e. he is a doctor) must be false.



    It's a little arbitrary but if logic wasn't defined this way, I recall that it creates issues in more complex situations, the details of which I can't remember.






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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      26
      down vote



      accepted










      This is an example of the principle of explosion or ex falso quodlibet. This is a property of some logical systems (including classical logic) where a false premise, or, equivalently, inconsistent premises, make the inference valid regardless of what the conclusion is.



      We can see from the truth table definition of the → connective in classical logic that if the left argument is false, then the whole expression is true.



      Classical implication P → Q is equivalent to ¬P ∨ Q



       [P → Q] P ¬P
       Q 1 1
       ¬Q 0 1


      and equivalently



      [¬P ∨ Q] P ¬P
       Q 1 1
       ¬Q 0 1


      Just looking at the definition of the connective doesn't prove that the inference is valid on its own. It does suggest why this might be the case. → only inspects the truth values of its arguments, not the content.



      For that, let's look at a skeleton inference rule with primitive propositions P and Q.



      P ∧ ¬P
      ------
      Q


      Since P and Q are independent of each other, this potential inference rule being valid would show that the system we are working in satisfies the principle of explosion.



      To justify the rule we can translate it into a formula involving just the primitive connectives by replacing ----- with → and determining whether the statement is an unconditional tautology.



      (P ∧ ¬P) → Q

      [(P ∧ ¬P) → Q] P ¬P
       Q 1 1
       ¬Q 1 1


      It is one, therefore classical logic satisfies the principle of explosion because the given rule is admissible / a theorem.



      The premise in the statement given I love all logic, but I don't love deductive reasoning is intended to be manifestly a contradiction (false) and also a joke. The moon is made of green cheese is also commonly used as an example of an irrelevant conclusion. The example is supposed to highlight the disconnect between everyday reasoning with natural language and classical logic.



      Paraphrased using disjunction instead of negation, the sentence would read, roughly




      Either it is not the case that I love all logic but hate deductive reasoning,
      or the moon is made of green cheese.




      This sentence, to me at least, simply seems to be true since it boils down to Either TRUE or FALSE.






      share|improve this answer
























        up vote
        26
        down vote



        accepted










        This is an example of the principle of explosion or ex falso quodlibet. This is a property of some logical systems (including classical logic) where a false premise, or, equivalently, inconsistent premises, make the inference valid regardless of what the conclusion is.



        We can see from the truth table definition of the → connective in classical logic that if the left argument is false, then the whole expression is true.



        Classical implication P → Q is equivalent to ¬P ∨ Q



         [P → Q] P ¬P
         Q 1 1
         ¬Q 0 1


        and equivalently



        [¬P ∨ Q] P ¬P
         Q 1 1
         ¬Q 0 1


        Just looking at the definition of the connective doesn't prove that the inference is valid on its own. It does suggest why this might be the case. → only inspects the truth values of its arguments, not the content.



        For that, let's look at a skeleton inference rule with primitive propositions P and Q.



        P ∧ ¬P
        ------
        Q


        Since P and Q are independent of each other, this potential inference rule being valid would show that the system we are working in satisfies the principle of explosion.



        To justify the rule we can translate it into a formula involving just the primitive connectives by replacing ----- with → and determining whether the statement is an unconditional tautology.



        (P ∧ ¬P) → Q

        [(P ∧ ¬P) → Q] P ¬P
         Q 1 1
         ¬Q 1 1


        It is one, therefore classical logic satisfies the principle of explosion because the given rule is admissible / a theorem.



        The premise in the statement given I love all logic, but I don't love deductive reasoning is intended to be manifestly a contradiction (false) and also a joke. The moon is made of green cheese is also commonly used as an example of an irrelevant conclusion. The example is supposed to highlight the disconnect between everyday reasoning with natural language and classical logic.



        Paraphrased using disjunction instead of negation, the sentence would read, roughly




        Either it is not the case that I love all logic but hate deductive reasoning,
        or the moon is made of green cheese.




        This sentence, to me at least, simply seems to be true since it boils down to Either TRUE or FALSE.






        share|improve this answer






















          up vote
          26
          down vote



          accepted







          up vote
          26
          down vote



          accepted






          This is an example of the principle of explosion or ex falso quodlibet. This is a property of some logical systems (including classical logic) where a false premise, or, equivalently, inconsistent premises, make the inference valid regardless of what the conclusion is.



          We can see from the truth table definition of the → connective in classical logic that if the left argument is false, then the whole expression is true.



          Classical implication P → Q is equivalent to ¬P ∨ Q



           [P → Q] P ¬P
           Q 1 1
           ¬Q 0 1


          and equivalently



          [¬P ∨ Q] P ¬P
           Q 1 1
           ¬Q 0 1


          Just looking at the definition of the connective doesn't prove that the inference is valid on its own. It does suggest why this might be the case. → only inspects the truth values of its arguments, not the content.



          For that, let's look at a skeleton inference rule with primitive propositions P and Q.



          P ∧ ¬P
          ------
          Q


          Since P and Q are independent of each other, this potential inference rule being valid would show that the system we are working in satisfies the principle of explosion.



          To justify the rule we can translate it into a formula involving just the primitive connectives by replacing ----- with → and determining whether the statement is an unconditional tautology.



          (P ∧ ¬P) → Q

          [(P ∧ ¬P) → Q] P ¬P
           Q 1 1
           ¬Q 1 1


          It is one, therefore classical logic satisfies the principle of explosion because the given rule is admissible / a theorem.



          The premise in the statement given I love all logic, but I don't love deductive reasoning is intended to be manifestly a contradiction (false) and also a joke. The moon is made of green cheese is also commonly used as an example of an irrelevant conclusion. The example is supposed to highlight the disconnect between everyday reasoning with natural language and classical logic.



          Paraphrased using disjunction instead of negation, the sentence would read, roughly




          Either it is not the case that I love all logic but hate deductive reasoning,
          or the moon is made of green cheese.




          This sentence, to me at least, simply seems to be true since it boils down to Either TRUE or FALSE.






          share|improve this answer












          This is an example of the principle of explosion or ex falso quodlibet. This is a property of some logical systems (including classical logic) where a false premise, or, equivalently, inconsistent premises, make the inference valid regardless of what the conclusion is.



          We can see from the truth table definition of the → connective in classical logic that if the left argument is false, then the whole expression is true.



          Classical implication P → Q is equivalent to ¬P ∨ Q



           [P → Q] P ¬P
           Q 1 1
           ¬Q 0 1


          and equivalently



          [¬P ∨ Q] P ¬P
           Q 1 1
           ¬Q 0 1


          Just looking at the definition of the connective doesn't prove that the inference is valid on its own. It does suggest why this might be the case. → only inspects the truth values of its arguments, not the content.



          For that, let's look at a skeleton inference rule with primitive propositions P and Q.



          P ∧ ¬P
          ------
          Q


          Since P and Q are independent of each other, this potential inference rule being valid would show that the system we are working in satisfies the principle of explosion.



          To justify the rule we can translate it into a formula involving just the primitive connectives by replacing ----- with → and determining whether the statement is an unconditional tautology.



          (P ∧ ¬P) → Q

          [(P ∧ ¬P) → Q] P ¬P
           Q 1 1
           ¬Q 1 1


          It is one, therefore classical logic satisfies the principle of explosion because the given rule is admissible / a theorem.



          The premise in the statement given I love all logic, but I don't love deductive reasoning is intended to be manifestly a contradiction (false) and also a joke. The moon is made of green cheese is also commonly used as an example of an irrelevant conclusion. The example is supposed to highlight the disconnect between everyday reasoning with natural language and classical logic.



          Paraphrased using disjunction instead of negation, the sentence would read, roughly




          Either it is not the case that I love all logic but hate deductive reasoning,
          or the moon is made of green cheese.




          This sentence, to me at least, simply seems to be true since it boils down to Either TRUE or FALSE.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered yesterday









          Gregory Nisbet

          39626




          39626




















              up vote
              9
              down vote














              The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



              Isn't the premise false?




              The premises are contradictory.



              So it is impossible for the premises to all be true.



              Thus it is impossible for the premises to all be true and the conclusion false.



              Therefore the argument is valid.






              share|improve this answer
















              • 1




                Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
                – Battle
                yesterday










              • This "answer" doesn't explain anything. I would -1 it if I had the rep.
                – Pod
                yesterday














              up vote
              9
              down vote














              The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



              Isn't the premise false?




              The premises are contradictory.



              So it is impossible for the premises to all be true.



              Thus it is impossible for the premises to all be true and the conclusion false.



              Therefore the argument is valid.






              share|improve this answer
















              • 1




                Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
                – Battle
                yesterday










              • This "answer" doesn't explain anything. I would -1 it if I had the rep.
                – Pod
                yesterday












              up vote
              9
              down vote










              up vote
              9
              down vote










              The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



              Isn't the premise false?




              The premises are contradictory.



              So it is impossible for the premises to all be true.



              Thus it is impossible for the premises to all be true and the conclusion false.



              Therefore the argument is valid.






              share|improve this answer













              The definition of validity was taught as: if premises are true, the conclusion must be true or it is impossible for the premises to be true and the conclusion to be false.



              Isn't the premise false?




              The premises are contradictory.



              So it is impossible for the premises to all be true.



              Thus it is impossible for the premises to all be true and the conclusion false.



              Therefore the argument is valid.







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered yesterday









              Graham Kemp

              32417




              32417







              • 1




                Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
                – Battle
                yesterday










              • This "answer" doesn't explain anything. I would -1 it if I had the rep.
                – Pod
                yesterday












              • 1




                Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
                – Battle
                yesterday










              • This "answer" doesn't explain anything. I would -1 it if I had the rep.
                – Pod
                yesterday







              1




              1




              Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
              – Battle
              yesterday




              Is that merely because it is a logical implication p ⇒ q where it's only false if p is true and q is false? Is "therefore" what indicates that it is an implication? And would 'p' stand for both premises here?
              – Battle
              yesterday












              This "answer" doesn't explain anything. I would -1 it if I had the rep.
              – Pod
              yesterday




              This "answer" doesn't explain anything. I would -1 it if I had the rep.
              – Pod
              yesterday










              up vote
              8
              down vote













              It's not perfectly clear, but my best guess is that the instructor intends:




              I love all logic, but I don’t love deductive reasoning.




              to contain two incompossible premises.



              meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.



              and conversely if "I don't love deductive reasoning", then "I love all logic is false".



              Ergo, this argument can never have both of its premises true.



              If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).



              Where the argument suffers a bit is on clarity. There's three issues here.



              First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are cannot both be true. To understand that we need to use "all" and other concepts you may not have learned. We can formalize the argument as :



              1. ∀x (Lx -> Vx) [for any x if x is a logic, then love x]

              2. La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]

              These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.



              Second, the argument uses "I". This gets a bit dicey due to two issues:



              1. Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)

              2. "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.

              Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, but this example is not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.






              share|improve this answer


















              • 1




                I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
                – virmaior
                yesterday






              • 2




                The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
                – virmaior
                yesterday






              • 3




                @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
                – Eliran H
                yesterday






              • 1




                @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
                – virmaior
                yesterday






              • 2




                @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
                – Mike Scott
                20 hours ago














              up vote
              8
              down vote













              It's not perfectly clear, but my best guess is that the instructor intends:




              I love all logic, but I don’t love deductive reasoning.




              to contain two incompossible premises.



              meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.



              and conversely if "I don't love deductive reasoning", then "I love all logic is false".



              Ergo, this argument can never have both of its premises true.



              If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).



              Where the argument suffers a bit is on clarity. There's three issues here.



              First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are cannot both be true. To understand that we need to use "all" and other concepts you may not have learned. We can formalize the argument as :



              1. ∀x (Lx -> Vx) [for any x if x is a logic, then love x]

              2. La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]

              These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.



              Second, the argument uses "I". This gets a bit dicey due to two issues:



              1. Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)

              2. "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.

              Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, but this example is not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.






              share|improve this answer


















              • 1




                I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
                – virmaior
                yesterday






              • 2




                The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
                – virmaior
                yesterday






              • 3




                @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
                – Eliran H
                yesterday






              • 1




                @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
                – virmaior
                yesterday






              • 2




                @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
                – Mike Scott
                20 hours ago












              up vote
              8
              down vote










              up vote
              8
              down vote









              It's not perfectly clear, but my best guess is that the instructor intends:




              I love all logic, but I don’t love deductive reasoning.




              to contain two incompossible premises.



              meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.



              and conversely if "I don't love deductive reasoning", then "I love all logic is false".



              Ergo, this argument can never have both of its premises true.



              If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).



              Where the argument suffers a bit is on clarity. There's three issues here.



              First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are cannot both be true. To understand that we need to use "all" and other concepts you may not have learned. We can formalize the argument as :



              1. ∀x (Lx -> Vx) [for any x if x is a logic, then love x]

              2. La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]

              These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.



              Second, the argument uses "I". This gets a bit dicey due to two issues:



              1. Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)

              2. "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.

              Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, but this example is not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.






              share|improve this answer














              It's not perfectly clear, but my best guess is that the instructor intends:




              I love all logic, but I don’t love deductive reasoning.




              to contain two incompossible premises.



              meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.



              and conversely if "I don't love deductive reasoning", then "I love all logic is false".



              Ergo, this argument can never have both of its premises true.



              If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).



              Where the argument suffers a bit is on clarity. There's three issues here.



              First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are cannot both be true. To understand that we need to use "all" and other concepts you may not have learned. We can formalize the argument as :



              1. ∀x (Lx -> Vx) [for any x if x is a logic, then love x]

              2. La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]

              These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.



              Second, the argument uses "I". This gets a bit dicey due to two issues:



              1. Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)

              2. "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.

              Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, but this example is not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited yesterday

























              answered yesterday









              virmaior

              23.8k33791




              23.8k33791







              • 1




                I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
                – virmaior
                yesterday






              • 2




                The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
                – virmaior
                yesterday






              • 3




                @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
                – Eliran H
                yesterday






              • 1




                @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
                – virmaior
                yesterday






              • 2




                @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
                – Mike Scott
                20 hours ago












              • 1




                I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
                – virmaior
                yesterday






              • 2




                The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
                – virmaior
                yesterday






              • 3




                @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
                – Eliran H
                yesterday






              • 1




                @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
                – virmaior
                yesterday






              • 2




                @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
                – Mike Scott
                20 hours ago







              1




              1




              I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
              – virmaior
              yesterday




              I'm not sure if my wording was confusing or if you don't understand validity. The standard go to definition of validity is: "if all of the premises are true, then the conclusion must be true." Ergo, if it is never the case that all premises can be true, then an argument is valid -- because it can never produce a situation where the premises are true but the conclusion is false.
              – virmaior
              yesterday




              2




              2




              The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
              – virmaior
              yesterday




              The composition of the moon has dependency on someone's opinion of logic therefore this argument is invalid. many statements depend on facts about the world (or people's opinions about them), but an argument can be valid even if it deals in things we know to be false -- because validity looks at the forms -- not the truth or falsity of the statements with respect to the world.
              – virmaior
              yesterday




              3




              3




              @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
              – Eliran H
              yesterday




              @Cell What virmaior is saying is standard textbook logic. It's also known as the principle of explosion: en.wikipedia.org/wiki/Principle_of_explosion
              – Eliran H
              yesterday




              1




              1




              @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
              – virmaior
              yesterday




              @Cell I'm doing my best to make sense of the problem the OP was given. The OP was told by their professor that the argument is valid. The way to make sense of this is not P & Q. Therefore, R. Instead, it's ∀x (Bx) & ~Ba. Therefore, R.
              – virmaior
              yesterday




              2




              2




              @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
              – Mike Scott
              20 hours ago




              @Cell you're confusing "the argument is valid" with "the conclusion is true". They aren't the same thing. A valid argument only implies a true conclusion if the premises are true, which they aren't in this case. Saying that "the Moon is made of green cheese" is a valid conclusion here is not saying anything at all about the composition of the Moon.
              – Mike Scott
              20 hours ago










              up vote
              0
              down vote













              The way I think of this is similar to how Ben describes it in the comments to the question i.e. it's similar to a vacuous truth. Formally, I guess it's not exact the same but it might be easier to understand coming from that direction.



              In a nutshell you can make any assertion about the properties of members of an empty set and it's true. For example, if I say "all flying elephants have gossamer wings", the statement is true. How so? Well if it's not true, then there need be one flying elephant whose wings are not gossamer. It's also true that no flying elephants have gossamer wings for the same reason.



              The most common way you might encounter such a construction is when someone says somoething like "if he's a doctor then I'm Santa Claus" which is ultimately a fancy way of saying the premise (i.e. he is a doctor) must be false.



              It's a little arbitrary but if logic wasn't defined this way, I recall that it creates issues in more complex situations, the details of which I can't remember.






              share|improve this answer
























                up vote
                0
                down vote













                The way I think of this is similar to how Ben describes it in the comments to the question i.e. it's similar to a vacuous truth. Formally, I guess it's not exact the same but it might be easier to understand coming from that direction.



                In a nutshell you can make any assertion about the properties of members of an empty set and it's true. For example, if I say "all flying elephants have gossamer wings", the statement is true. How so? Well if it's not true, then there need be one flying elephant whose wings are not gossamer. It's also true that no flying elephants have gossamer wings for the same reason.



                The most common way you might encounter such a construction is when someone says somoething like "if he's a doctor then I'm Santa Claus" which is ultimately a fancy way of saying the premise (i.e. he is a doctor) must be false.



                It's a little arbitrary but if logic wasn't defined this way, I recall that it creates issues in more complex situations, the details of which I can't remember.






                share|improve this answer






















                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  The way I think of this is similar to how Ben describes it in the comments to the question i.e. it's similar to a vacuous truth. Formally, I guess it's not exact the same but it might be easier to understand coming from that direction.



                  In a nutshell you can make any assertion about the properties of members of an empty set and it's true. For example, if I say "all flying elephants have gossamer wings", the statement is true. How so? Well if it's not true, then there need be one flying elephant whose wings are not gossamer. It's also true that no flying elephants have gossamer wings for the same reason.



                  The most common way you might encounter such a construction is when someone says somoething like "if he's a doctor then I'm Santa Claus" which is ultimately a fancy way of saying the premise (i.e. he is a doctor) must be false.



                  It's a little arbitrary but if logic wasn't defined this way, I recall that it creates issues in more complex situations, the details of which I can't remember.






                  share|improve this answer












                  The way I think of this is similar to how Ben describes it in the comments to the question i.e. it's similar to a vacuous truth. Formally, I guess it's not exact the same but it might be easier to understand coming from that direction.



                  In a nutshell you can make any assertion about the properties of members of an empty set and it's true. For example, if I say "all flying elephants have gossamer wings", the statement is true. How so? Well if it's not true, then there need be one flying elephant whose wings are not gossamer. It's also true that no flying elephants have gossamer wings for the same reason.



                  The most common way you might encounter such a construction is when someone says somoething like "if he's a doctor then I'm Santa Claus" which is ultimately a fancy way of saying the premise (i.e. he is a doctor) must be false.



                  It's a little arbitrary but if logic wasn't defined this way, I recall that it creates issues in more complex situations, the details of which I can't remember.







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 15 hours ago









                  JimmyJames

                  35927




                  35927




















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                      List of Gilmore Girls characters

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                      The season three cast—(Back row): Lane, Michel, Paris, Emily, Richard, Sookie, Miss Patty, Kirk; Front row: Jess, Luke, Lorelai, Rory, Dean This is a list of characters for the comedy-drama television series Gilmore Girls . Contents 1 Main characters 1.1 Lorelai Gilmore 1.2 Rory Gilmore 1.3 Sookie St. James 1.4 Lane Kim 1.5 Michel Gerard 1.6 Luke Danes 1.7 Emily Gilmore 1.8 Richard Gilmore 1.9 Paris Geller 1.10 Dean Forester 1.11 Jess Mariano 1.12 Kirk Gleason 1.13 Jason Stiles 1.14 Logan Huntzberger 2 Major recurring characters 2.1 Christopher Hayden 2.2 Jackson Belleville 2.3 Mrs. Kim 2.4 Tristin DuGray 2.5 Max Medina 2.6 Taylor Doose 2.7 Dave Rygalski 2.8 Marty 3 Recurring characters 3.1 Stars Hollow 3.2 Chilton 3.3 Yale 3.4 Other 4 Notable guest stars 5 Unseen characters 6 Notes 7 References Main characters Actor Character Appearances Season 1 Season 2 Season 3 Season 4 Season 5 Season 6 Season 7 A Year in the Life Lauren Graham Lorelai Gilmore...
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                      Confectionery

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                      Prepared foods made with a lot of sugar or other cabohydrates "Sweetmeat" redirects here. For the racehorse, see Sweetmeat (horse). Not to be confused with Sweetbread. This Kransekake is a traditional Scandinavian baker's confection. Confectionery is the art of making confections , which are food items that are rich in sugar and carbohydrates. Exact definitions are difficult. [1] In general, though, confectionery is divided into two broad and somewhat overlapping categories, bakers' confections and sugar confections. [2] Bakers' confectionery, also called flour confections , includes principally sweet pastries, cakes, and similar baked goods. Sugar confectionery includes candies ( sweets in British English), candied nuts, chocolates, chewing gum, bubble gum, pastillage, and other confections that are made primarily of sugar. In some cases, chocolate confections (confections made of chocolate) are treated as a separate category, as are sugar-free versions of ...
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