Essentially a valid argument is an argument where it would be impossible for the conclusion to be false if all of the premises are true.

So ponder this syllogism:

P1) Premise 2 is false.

P2) Premise 1 is false.

C) Pigs can fly.

This syllogism apparently satisfies the conditions for a valid argument because since both of the premises contradict each other there is no possible condition where both of the premises are true. It apparently doesn't matter what the conclusion is. Since the premises contradict each other there is no condition in which both of the premises are true and the conclusion is false; therefore the argument is valid.

I discussed this the other day with someone and I felt like we didn't really come to any conclusions. Personally I don't really understand how these arguments are valid because the conclusion does not deductively follow from the premises. I would like to hear other peoples thoughts on this apparent paradox because I'm not sure I have fully wrapped my head around it.