Let me give an analogy and then a solution to your paradox. Temperature. Sometimes you read that it's a measure of warmth; sometimes cold. Aren't hot and cold

Let me give an analogy and then a solution to your paradox. Temperature. Sometimes you read that it's a measure of warmth; sometimes cold. Aren't hot and cold opposites? Yes, hot and cold are opposites, but in a way they give the same kind of information. That's also true for information and randomness. Specifically, little randomness means more (certain) information.