>Category theory reduces all of mathematics to the study of arrows. The only mistake you can make with an arrow is to get it pointing the wrong way. Thus, in category theory, this is the mistake you will make.

So for example if one would define an implication by \$$A \rightarrow B :\iff A \land B \$$ instead of \$$A \rightarrow B \iff \neg (A \land \neg B) \$$ then it seems that one can't define an order by \$$false \leq true \$$.