Is it okay that vacuously true statements can contradict each other? 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?

To get a contradiction, you must have a pair of sentences which are the negations of one another. You seem to believe that "all unicorns are green" and "all unicorns are not-green" are negations of one another, but this is not true. For comparison, consider "all numbers are even" and "all numbers are odd." Both of these sentences are obviously false, which means they can't be negations of one another, because the negation of a false statement should be a true statement.
Instead, the negation of "all numbers are even" is "at least one number is odd," which is a true statement, as we would expect from negating a false statement. Similarly, the negation of "all unicorns are green" is "at least one unicorn is not green," but that can't be true unless at least one non-green unicorn actually exists.
