I am reading How to prove it by Velleman, and something is bothering me. On page 74, he states that "all unicorns are green" is vacuously true and so is "all unicorns are purple." He goes on to state that this two statements do not contradict each other and does not give any reasons why. This does not make sense to me. If both statements are considered to be true, the conclusion is that they contradict each other.
I understand the mathematical reasoning behind the conclusion, but that still does not explain why we should accept that both of the statements that are supposedly true do not contradict each other. Does this signal to a problem in the theory of quantificational logic mainly in how the conditional connector is defined?