Suppose you have an argument with false premises and a false conclusion. Given this information, what do you...












2















The argument is almost valid.

The argument is neither valid nor invalid.

The argument must be valid.

The argument must be invalid.

The argument may be either valid or invalid.





logic







share|improve this question


















  • 2





    The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

    – Christian Dean
    Feb 2 at 5:28






  • 1





    There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

    – christo183
    Feb 2 at 11:03
















2















The argument is almost valid.

The argument is neither valid nor invalid.

The argument must be valid.

The argument must be invalid.

The argument may be either valid or invalid.





logic







share|improve this question


















  • 2





    The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

    – Christian Dean
    Feb 2 at 5:28






  • 1





    There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

    – christo183
    Feb 2 at 11:03














2












2








2








The argument is almost valid.

The argument is neither valid nor invalid.

The argument must be valid.

The argument must be invalid.

The argument may be either valid or invalid.





logic







share|improve this question














The argument is almost valid.

The argument is neither valid nor invalid.

The argument must be valid.

The argument must be invalid.

The argument may be either valid or invalid.





logic




logic






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Feb 2 at 5:17









Krystal GarciaKrystal Garcia

191




191








  • 2





    The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

    – Christian Dean
    Feb 2 at 5:28






  • 1





    There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

    – christo183
    Feb 2 at 11:03














  • 2





    The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

    – Christian Dean
    Feb 2 at 5:28






  • 1





    There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

    – christo183
    Feb 2 at 11:03








2




2





The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

– Christian Dean
Feb 2 at 5:28





The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

– Christian Dean
Feb 2 at 5:28




1




1





There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

– christo183
Feb 2 at 11:03





There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion".

– christo183
Feb 2 at 11:03










2 Answers
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active

oldest

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6














First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.




Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.



Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must
be true.



Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness




Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.



Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).



From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.





  • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]

  • Premise 2 : Unicorns exist [false, probably by induction]

  • Conclusion : Therefore, Unicorns have 2 horns [false]




As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)



You can change the first premise to obtain :





  • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]

  • Premise 2 : Unicorns exist [false, probably by induction]

  • Conclusion : Therefore, Unicorns have 2 horns [false]




It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.



Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.



So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.



So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.



So, your answer is the last option: 



The argument may be either valid or invalid.





share|improve this answer


























  • I edited the answer to include the case where the argument is invalid.

    – SmootQ
    Feb 3 at 15:26



















3














The argument may be either valid or invalid.



Logic deals with forms of reasoning or logical form. For example :




  1. No A is B


  2. Some C is B





  1. Some C is not A


This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.



It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.



Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :




  1. All cats are purple animals (F)


  2. All purple animals have four eyes (F)





  1. All cats have four eyes (F)


Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.



By contrast :




  1. New York is the capital of the USA (F)


  2. The San Andreas Fault is in Tennessee (F)





  1. The 16th President of the United States was born in 1811 (F)


is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.



Moral of all this :



FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.






share|improve this answer


























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    2 Answers
    2






    active

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    2 Answers
    2






    active

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    active

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    active

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    6














    First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.




    Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.



    Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must
    be true.



    Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness




    Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.



    Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).



    From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.





    • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)



    You can change the first premise to obtain :





    • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.



    Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.



    So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.



    So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.



    So, your answer is the last option: 



    The argument may be either valid or invalid.





    share|improve this answer


























    • I edited the answer to include the case where the argument is invalid.

      – SmootQ
      Feb 3 at 15:26
















    6














    First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.




    Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.



    Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must
    be true.



    Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness




    Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.



    Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).



    From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.





    • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)



    You can change the first premise to obtain :





    • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.



    Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.



    So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.



    So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.



    So, your answer is the last option: 



    The argument may be either valid or invalid.





    share|improve this answer


























    • I edited the answer to include the case where the argument is invalid.

      – SmootQ
      Feb 3 at 15:26














    6












    6








    6







    First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.




    Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.



    Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must
    be true.



    Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness




    Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.



    Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).



    From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.





    • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)



    You can change the first premise to obtain :





    • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.



    Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.



    So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.



    So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.



    So, your answer is the last option: 



    The argument may be either valid or invalid.





    share|improve this answer















    First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.




    Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.



    Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must
    be true.



    Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness




    Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.



    Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).



    From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.





    • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)



    You can change the first premise to obtain :





    • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]

    • Premise 2 : Unicorns exist [false, probably by induction]

    • Conclusion : Therefore, Unicorns have 2 horns [false]




    It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.



    Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.



    So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.



    So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.



    So, your answer is the last option: 



    The argument may be either valid or invalid.






    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited Feb 3 at 15:25

























    answered Feb 2 at 10:37









    SmootQSmootQ

    1,651214




    1,651214













    • I edited the answer to include the case where the argument is invalid.

      – SmootQ
      Feb 3 at 15:26



















    • I edited the answer to include the case where the argument is invalid.

      – SmootQ
      Feb 3 at 15:26

















    I edited the answer to include the case where the argument is invalid.

    – SmootQ
    Feb 3 at 15:26





    I edited the answer to include the case where the argument is invalid.

    – SmootQ
    Feb 3 at 15:26











    3














    The argument may be either valid or invalid.



    Logic deals with forms of reasoning or logical form. For example :




    1. No A is B


    2. Some C is B





    1. Some C is not A


    This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.



    It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.



    Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :




    1. All cats are purple animals (F)


    2. All purple animals have four eyes (F)





    1. All cats have four eyes (F)


    Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.



    By contrast :




    1. New York is the capital of the USA (F)


    2. The San Andreas Fault is in Tennessee (F)





    1. The 16th President of the United States was born in 1811 (F)


    is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.



    Moral of all this :



    FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.






    share|improve this answer






























      3














      The argument may be either valid or invalid.



      Logic deals with forms of reasoning or logical form. For example :




      1. No A is B


      2. Some C is B





      1. Some C is not A


      This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.



      It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.



      Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :




      1. All cats are purple animals (F)


      2. All purple animals have four eyes (F)





      1. All cats have four eyes (F)


      Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.



      By contrast :




      1. New York is the capital of the USA (F)


      2. The San Andreas Fault is in Tennessee (F)





      1. The 16th President of the United States was born in 1811 (F)


      is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.



      Moral of all this :



      FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.






      share|improve this answer




























        3












        3








        3







        The argument may be either valid or invalid.



        Logic deals with forms of reasoning or logical form. For example :




        1. No A is B


        2. Some C is B





        1. Some C is not A


        This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.



        It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.



        Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :




        1. All cats are purple animals (F)


        2. All purple animals have four eyes (F)





        1. All cats have four eyes (F)


        Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.



        By contrast :




        1. New York is the capital of the USA (F)


        2. The San Andreas Fault is in Tennessee (F)





        1. The 16th President of the United States was born in 1811 (F)


        is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.



        Moral of all this :



        FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.






        share|improve this answer















        The argument may be either valid or invalid.



        Logic deals with forms of reasoning or logical form. For example :




        1. No A is B


        2. Some C is B





        1. Some C is not A


        This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.



        It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.



        Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :




        1. All cats are purple animals (F)


        2. All purple animals have four eyes (F)





        1. All cats have four eyes (F)


        Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.



        By contrast :




        1. New York is the capital of the USA (F)


        2. The San Andreas Fault is in Tennessee (F)





        1. The 16th President of the United States was born in 1811 (F)


        is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.



        Moral of all this :



        FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited Feb 2 at 19:35

























        answered Feb 2 at 18:03









        Geoffrey Thomas♦Geoffrey Thomas

        27.3k222105




        27.3k222105






























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            in spring boot 2.1 many test slices are not allowed anymore due to multiple @BootstrapWith

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            1 I tried to upgrade a yummy sandwich made of two test slices (@JsonTest and @JdbcTest in my case, crunchy test code in between) adding spring boot 2.1 flavour to it. But it seems it was not much of a success. I cannot annotate my tests with many @...Test since they are now each bringing their own XxxTestContextBootstrapper. It used to work when they all used same SpringBootTestContextBootstrapper. @RunWith(SpringRunner.class) @JdbcTest @JsonTest public class Test { @Test public void test() { System.out.printn("Hello, World !"); } } The error I get from BootstrapUtils is illegalStateException : Configuration error: found multiple declarations of @BootstrapWith for test class I understand I might be doing something wrong here but is there an easy way I could load both Json and Jdbc contex...
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            How to fix TextFormField cause rebuild widget in Flutter

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            .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I've got the same issue at #9280. I tried all solutions from that topic with/without GlobalKey for Scaffold and Form but the problem wasn't fixed. I tried to build a authentication form with login and signup. But the keyboard doesn't show when I tap the TextFormField at the first time. Then I try to input some letter from physical keyboard, the widget is rebuilt. Like this: login screen Nothing to be log when I run flutter run --verbose, so I logged manually. Every tapping on field, the widget called dispose -> init -> build. [√] Flutter (Channel beta, v1.0.0, on Microsoft Windows [Version 10.0.17763.195], ...
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