The Conjunction Principle says, roughly, that if the truth of a conjunction can be brought about, then the truth of each conjunct can be brought about. The current essay argues that this principle is not valid. After a clarification of the principle, it is shown how a proper understanding of the involved notions falsify the principle. As a corollary, a recent attack on van Inwagen’s Consequence Argument will be rebutted, because it relies on the invalid conjunction principle.