A definition of rationality (from tle Latin ratio, faculty of reason), useful also because it contains a gradation:
the subtler the differences and similarities one can see, the more one is rational;
the more one puts all eggs in one basket, the more one is irrational.
The terms reason and rationality have an ambiguity because in Italian the term reason implies that the purpose of the reasoning is being right in the sense of prevailing over: hence, prevailing over whom or what?
One thing is prevailing over problems in the sense of solving them to the benefit of all, quite another thing is prevailing over one's fellows in the sense of defeating and harming them to one's supposed benefit.
The definition of ethics as an objective in the Solutions & Proposals section solves this ambiguity conclusively: the ethical reason and rationality are those to the benefit of all. Actual benefit, not fake. Therefore non-ethical absence of reason and irrationality are those to the actual detriment of all.
From this definition of rationality derive increasing degrees of rationality in logic:
Single-valued logic: there exists only one value, fixated, and any fact must correspond to it. Example: "Wear your woollens!" "But it's one hundred degrees!" "Just put it on!"
Two-valued logic: there exist only two values, true or false, black or white, and any fact must correspond to either one of them. Example: "Either you are with us, or against us!" "Wait a moment, ..." "Then you're against us!"
Infinitely-valued logic: there exist infinite values, just like points in geometry, so that it is the values that correspond to facts as precisely as possible (and not the other way round as claimed by those who are either plain dumb or playing dumb). Example: "How much is the value of pi?" "3.14159265358979..." "Thank you; is it beween 3.1415 and 3.1416?" "Yes." "Good."