Is this an unsound argument?

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I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise:




Premise 1: All humans are mortal.



Premise 2: Socrates is mortal.



Conclusion: Socrates is human.




It is asked to find if this argument is sound or not.



From the definition of soundness of an argument, it needs to be valid and the premises need to be true. Hence, I think this one is a sound sentence. (Though intuitively it seems the argument is not correct. Here, I am not talking about validity. By not being correct I mean this is not a good argument.)



But, the answer is - "This argument has all true premises (and a true conclusion) but it it is invalid. So it is not sound."



I am not getting how this is invalid (and hence, not getting how it is an unsound argument). Can anyone explain to me how this argument is invalid?






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I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise:




Premise 1: All humans are mortal.



Premise 2: Socrates is mortal.



Conclusion: Socrates is human.




It is asked to find if this argument is sound or not.



From the definition of soundness of an argument, it needs to be valid and the premises need to be true. Hence, I think this one is a sound sentence. (Though intuitively it seems the argument is not correct. Here, I am not talking about validity. By not being correct I mean this is not a good argument.)



But, the answer is - "This argument has all true premises (and a true conclusion) but it it is invalid. So it is not sound."



I am not getting how this is invalid (and hence, not getting how it is an unsound argument). Can anyone explain to me how this argument is invalid?






logic validity soundness







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tarit goswami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE!
    – Frank Hubeny
    3 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise:




Premise 1: All humans are mortal.



Premise 2: Socrates is mortal.



Conclusion: Socrates is human.




It is asked to find if this argument is sound or not.



From the definition of soundness of an argument, it needs to be valid and the premises need to be true. Hence, I think this one is a sound sentence. (Though intuitively it seems the argument is not correct. Here, I am not talking about validity. By not being correct I mean this is not a good argument.)



But, the answer is - "This argument has all true premises (and a true conclusion) but it it is invalid. So it is not sound."



I am not getting how this is invalid (and hence, not getting how it is an unsound argument). Can anyone explain to me how this argument is invalid?






logic validity soundness







share|improve this question









New contributor




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











I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise:




Premise 1: All humans are mortal.



Premise 2: Socrates is mortal.



Conclusion: Socrates is human.




It is asked to find if this argument is sound or not.



From the definition of soundness of an argument, it needs to be valid and the premises need to be true. Hence, I think this one is a sound sentence. (Though intuitively it seems the argument is not correct. Here, I am not talking about validity. By not being correct I mean this is not a good argument.)



But, the answer is - "This argument has all true premises (and a true conclusion) but it it is invalid. So it is not sound."



I am not getting how this is invalid (and hence, not getting how it is an unsound argument). Can anyone explain to me how this argument is invalid?






logic validity soundness




logic validity soundness






share|improve this question









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











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Check out our Code of Conduct.











  • I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE!
    – Frank Hubeny
    3 hours ago
















  • I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE!
    – Frank Hubeny
    3 hours ago















I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE!
– Frank Hubeny
3 hours ago




I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE!
– Frank Hubeny
3 hours ago










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Hence, I think this one is a sound sentence.




Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.



The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:




  1. If human, then mortal.

  2. S is mortal.

Therefore, S is human.




More abstractly:




  1. If P then Q.

  2. s is Q.

Therefore, s is P.




This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:




  1. If human, then mortal.

  2. My friend's dog is mortal.

Therefore, my friend's dog is human.




You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).



More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).






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    Hence, I think this one is a sound sentence.




    Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.



    The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:




    1. If human, then mortal.

    2. S is mortal.

    Therefore, S is human.




    More abstractly:




    1. If P then Q.

    2. s is Q.

    Therefore, s is P.




    This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:




    1. If human, then mortal.

    2. My friend's dog is mortal.

    Therefore, my friend's dog is human.




    You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).



    More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).






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      Hence, I think this one is a sound sentence.




      Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.



      The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:




      1. If human, then mortal.

      2. S is mortal.

      Therefore, S is human.




      More abstractly:




      1. If P then Q.

      2. s is Q.

      Therefore, s is P.




      This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:




      1. If human, then mortal.

      2. My friend's dog is mortal.

      Therefore, my friend's dog is human.




      You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).



      More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).






      share|improve this answer






















        up vote
        3
        down vote










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        Hence, I think this one is a sound sentence.




        Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.



        The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:




        1. If human, then mortal.

        2. S is mortal.

        Therefore, S is human.




        More abstractly:




        1. If P then Q.

        2. s is Q.

        Therefore, s is P.




        This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:




        1. If human, then mortal.

        2. My friend's dog is mortal.

        Therefore, my friend's dog is human.




        You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).



        More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).






        share|improve this answer













        Hence, I think this one is a sound sentence.




        Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.



        The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:




        1. If human, then mortal.

        2. S is mortal.

        Therefore, S is human.




        More abstractly:




        1. If P then Q.

        2. s is Q.

        Therefore, s is P.




        This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:




        1. If human, then mortal.

        2. My friend's dog is mortal.

        Therefore, my friend's dog is human.




        You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).



        More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).







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