Rationalism and Incommensurability

The term 'irrational number' is a misnomer.  For, no less than a 'rational number', an 'irrational number' can be expressed as a Ratio.  Instead, as the later Pythagorean Eudoxus observes, the distinction is between the commensurability and the incommensurability of the terms of a Ratio.  A terminological adjustment is also relevant to Modern Rationalism.  That variety, the basic operation of which is Inference, seems to have little to do with a Ratio.  However, the concept that is the basis of its fundamental principle--Contradiction--is derived from Incommensurability.  For, Contradiction is a special case of Incommensurability.  Others are not opposites, just radically different in some respect.  Likewise, there is a more comprehensive system of which what is generally conceived as Modern Rationalism is a special case.  Since that system is governed by correspondingly more comprehensive concept of Incommensurability, and Incommensurability is a characteristic of a Ratio, this more comprehensive system is a variety of Rationalism, perhaps identifiable as Super-Rationalism.