It is difficult to define terms like rationality (rational, rationalism) and reason (reasonable, reasonableness, reasoning) without ending up in a circular definition, as we do not yet have a good understanding of how intelligence – i.e. that quality which allows entities to reason – functions. It is much easier to identify specific examples that are not rational (and to explain why they are not) than it is to give a set of rules by which rationality can be identified.
Obtaining this understanding is one of the major goals of the study of artificial intelligence, since the best way to recreate something artificially is to understand how it works.
The words "rational" and "rationality" are often misused to advocate solutions which serve some specific pragmatic goal at the expense of larger ideals, e.g. "rational economic theory says that the minimum wage [or pollution laws, or safety inspections, etc.] harms businesses and reduces profits". If your goal is to improve conditions for a community, however, it is not rational to accept a solution which maximizes local benefits (e.g. corporate profits) at the expense of that community's well-being.
The concept of rationalization is often conflated with "rationality".
- The rule of succession is a rational, mathematical way of estimating the odds of something which has never been observed to occur.