I'm going through a logic textbook and there is an exercise of assessing truth or falsity of following claim: You can make a valid argument invalid by adding extra premisses
At first, I had reasoning similar to the one included in the answers: the claim is false, because adding premiss to already valid argument will be redundant. My made-up example:
All mermaids are mysterious. Ariel is a mermaid. So Ariel is mysterious.
And added premiss: Elsa is a blonde haired girl, either true or false, won't change a thing in valid argument. But then I thought about premiss:
Ariel is not a mermaid.
Will adding it won't change above argument into invalid? Adding contradiction seems to make things broken, but since the answer is "false" I guess this "counterexample" isn't a good one.
I have the same problem with the opposite: apparently, making any invalid argument into valid one is trivial: just add conclusion to the premisses. But is invalid argument
Ariel is a mermaid. So Ariel is not a mermaid.
will be "fixed" by including conclusion in premisses?
Can anybody explain how to deal with these contradictions and how this doesn't change the conclusions that you can't make valid argument invalid and that you absolutely can make invalid one valid.