The book I got this question from is "logic, the laws of truth" by Nicholas j.j smith.
"Necessary truth preserving" (NTP in the book) is defined as the property that an argument has when it is impossible for the premises to be true and the conclusion false.
Now an argument is valid if and only if
- The premises cannot be true while the conclusion false (it is NTP).
- The form or structure of the argument guarantees that it is NTP.
the 2nd criterion for judging ( whether and argument is valid or not) does not make sense to me.
and the answers of the exercises ( on determining validity), imply that an argument being NTP is enough for being valid and I don't really see 2nd criterion for judging ( whether and argument is valid or not) being needed to get the correct answers.
1)All dogs are mammals. All mammals are animals.
All dogs are animals.
2)All dogs are mammals All dogs are animals.
All mammals are animals.
the first one is valid and second one isn't, but we can find the answers without knowing what validity is/ equating validity with NTP.
I hope I'm clear enough, I just read this from the book, so i couldn't articulate my thoughts very clearly.