The phrase 'contradictions exist' is correct and usable in written English.
You can use this phrase when you want to express the idea that two or more ideas, facts, beliefs, or opinions are opposed to each other. For example, "The teacher's lectures often contain contradictions, as he sometimes states two opposing beliefs in the same sentence."
"The same divisions and contradictions exist in my family," he says, "even within individuals.
However, some contradictions exist parallel to this trend.
Strauss infers from this that the contradictions exist to show the attentive reader that Locke does not really believe in natural law at all.
Apparently, contradictions exist between public support for renewable energy innovation on the one hand, and obstruction or even resistance against the realization of specific projects in the neighbourhood, on the other hand.
Moreover, by examining the interactions between ordinary people and legal procedures, this work carefully analyzes the whole case-filing procedure and finds that contradictions exist between systematic legal logics and living logics, as well as between legal practice and daily actions.
Glaring contradictions exist within each policy sphere and among them.
Russell's discovery of a hidden contradiction in Frege's attempt to formalize set theory, with the help of his simple comprehension scheme, caused some mathematicians to wonder how one could make sure that no other contradictions existed.
The selective institutionalizations of these key boundary objects helped the participants overcome various contradictions existed in the systems development.
The selective institutionalizations of these key boundary objects helped the participants to overcome various contradictions existed in the socio-technical system of collaborative cross-border disaster management.
All of these contradictions existed before Trump came along.
Several contradictions existed towards the use of medical interventions and the associated risk of caesarean section for obese women, as these were viewed as either prohibitive to or facilitative of normal birth.
