Ratio and Reason

The main connection of the notion 'Ratio' with common connotations of 'reasonability' and 'rationality', is the concept of Balance. Since a given ratio, per se, would seem to be neither balanced nor unbalanced, while it is, more accurately, the derivative notion, 'Proportion', i. e. equality of ratios, that is entailed by Balance. Still, Ratio is a relation between two numbers that transcends their particularity, e. g. a relation between 5 and 3 is not a ratio until it is equated with, e. g. that between 10 and 6. So, Proportion is fundamentally Ratio. Now, the concept of Balance is plainly central to many Philosophical topics, primarily Justice, but the relevance of Ratio to the cognitive power Reason is not so clear, e. g. even 'unbalanced' people seem to have 'reasons' for what they do. On the other hand, like a ratio, a reason transcends particularity, but the 'reasons' of the unbalanced lack generalizability. In other words, both Ratio and Reason can be expressed as a universal formula, i. e. just as the latter can be defined as a function which, given an argument, e. g. a cause, yields a value, e. g. an effect, the former can be defined as a function, which, taking one number as an argument, yields another, i. e. the 'Rule of Three' in Mathematics. So, Rational Balance consists not in the comparison of magnitude peculiar to Ratio, but in the uniformity of instantiation, of either Ratio or Reason.