Rational, Irrational, and Arational.
Here is how I'm defining these terms in relation to each other.
Rational means not irrational.
Irrational means not rational.
Arational means not rational AND not irrational.
Thus, only things within the class of reason can be classified as being rational or irrational. Everything outside of that class (i.e. things not based on reason) would be arational, so saying, for example, "football is rational", or this "cup is irrational" would be category errors.
"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan