Is EAO third figure valid in all cases?

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3
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EAO third figure has the form :

M-P

M-S

S-P




As an example :



No men are roses

All men are cabbages

Some cabbages are not roses



I'm new to logic and I'm wondering how above syllogism is valid.



Suppose there are $2$ men, $500$ roses, and $100$ cabbages;

then the second premise does imply there exist 2 cabbages that are not roses. No issues so far.



But what if I choose $0$ men ? The first two premises seem to not care about this ?




logic




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    up vote
    3
    down vote

    favorite













    EAO third figure has the form :

    M-P

    M-S

    S-P




    As an example :



    No men are roses

    All men are cabbages

    Some cabbages are not roses



    I'm new to logic and I'm wondering how above syllogism is valid.



    Suppose there are $2$ men, $500$ roses, and $100$ cabbages;

    then the second premise does imply there exist 2 cabbages that are not roses. No issues so far.



    But what if I choose $0$ men ? The first two premises seem to not care about this ?




    logic




    share|cite|improve this question





















      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite












      EAO third figure has the form :

      M-P

      M-S

      S-P




      As an example :



      No men are roses

      All men are cabbages

      Some cabbages are not roses



      I'm new to logic and I'm wondering how above syllogism is valid.



      Suppose there are $2$ men, $500$ roses, and $100$ cabbages;

      then the second premise does imply there exist 2 cabbages that are not roses. No issues so far.



      But what if I choose $0$ men ? The first two premises seem to not care about this ?




      logic




      share|cite|improve this question












      EAO third figure has the form :

      M-P

      M-S

      S-P




      As an example :



      No men are roses

      All men are cabbages

      Some cabbages are not roses



      I'm new to logic and I'm wondering how above syllogism is valid.



      Suppose there are $2$ men, $500$ roses, and $100$ cabbages;

      then the second premise does imply there exist 2 cabbages that are not roses. No issues so far.



      But what if I choose $0$ men ? The first two premises seem to not care about this ?





      logic





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      share|cite|improve this question




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      asked 2 days ago









      rsadhvika

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          1 Answer
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          There is a well-known distinction between unconditionally valid categorical syllogisms and conditionally valid categorical syllogisms.



          EAO-3 is an example of a conditionally valid syllogism: if you assume that every class (category) of objects is non-empty (this assumption is sometimes called the Assumption of Categorical Import), then the syllogism is valid. But if you do not make that assumption, then you can indeed get a counterexample by using an empty category, as you found.



          Indeed, any syllogism where both premises are universal statements, but the conclusion is an existential statement, can at best be conditionally valid.






          share|cite|improve this answer























          • Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
            – rsadhvika
            2 days ago










          • @rsadhvika You're welcome! :)
            – Bram28
            2 days ago










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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          4
          down vote













          There is a well-known distinction between unconditionally valid categorical syllogisms and conditionally valid categorical syllogisms.



          EAO-3 is an example of a conditionally valid syllogism: if you assume that every class (category) of objects is non-empty (this assumption is sometimes called the Assumption of Categorical Import), then the syllogism is valid. But if you do not make that assumption, then you can indeed get a counterexample by using an empty category, as you found.



          Indeed, any syllogism where both premises are universal statements, but the conclusion is an existential statement, can at best be conditionally valid.






          share|cite|improve this answer























          • Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
            – rsadhvika
            2 days ago










          • @rsadhvika You're welcome! :)
            – Bram28
            2 days ago














          up vote
          4
          down vote













          There is a well-known distinction between unconditionally valid categorical syllogisms and conditionally valid categorical syllogisms.



          EAO-3 is an example of a conditionally valid syllogism: if you assume that every class (category) of objects is non-empty (this assumption is sometimes called the Assumption of Categorical Import), then the syllogism is valid. But if you do not make that assumption, then you can indeed get a counterexample by using an empty category, as you found.



          Indeed, any syllogism where both premises are universal statements, but the conclusion is an existential statement, can at best be conditionally valid.






          share|cite|improve this answer























          • Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
            – rsadhvika
            2 days ago










          • @rsadhvika You're welcome! :)
            – Bram28
            2 days ago












          up vote
          4
          down vote










          up vote
          4
          down vote









          There is a well-known distinction between unconditionally valid categorical syllogisms and conditionally valid categorical syllogisms.



          EAO-3 is an example of a conditionally valid syllogism: if you assume that every class (category) of objects is non-empty (this assumption is sometimes called the Assumption of Categorical Import), then the syllogism is valid. But if you do not make that assumption, then you can indeed get a counterexample by using an empty category, as you found.



          Indeed, any syllogism where both premises are universal statements, but the conclusion is an existential statement, can at best be conditionally valid.






          share|cite|improve this answer















          There is a well-known distinction between unconditionally valid categorical syllogisms and conditionally valid categorical syllogisms.



          EAO-3 is an example of a conditionally valid syllogism: if you assume that every class (category) of objects is non-empty (this assumption is sometimes called the Assumption of Categorical Import), then the syllogism is valid. But if you do not make that assumption, then you can indeed get a counterexample by using an empty category, as you found.



          Indeed, any syllogism where both premises are universal statements, but the conclusion is an existential statement, can at best be conditionally valid.







          share|cite|improve this answer















          share|cite|improve this answer



          share|cite|improve this answer








          edited 2 days ago


























          answered 2 days ago









          Bram28

          54.5k33778




          54.5k33778











          • Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
            – rsadhvika
            2 days ago










          • @rsadhvika You're welcome! :)
            – Bram28
            2 days ago
















          • Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
            – rsadhvika
            2 days ago










          • @rsadhvika You're welcome! :)
            – Bram28
            2 days ago















          Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
          – rsadhvika
          2 days ago




          Good to know that some valid forms require non-empty sets. I think I get this... Thank you so much :)
          – rsadhvika
          2 days ago












          @rsadhvika You're welcome! :)
          – Bram28
          2 days ago




          @rsadhvika You're welcome! :)
          – Bram28
          2 days ago












           

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