User blog comment:Reximus55/Government Series - Introduction/@comment-29118948-20131024053317/@comment-1375165-20131026041210

Although there are many definitions of republic and democratic state, the ones I presented are (two of the many) legitimate definitions used by political scientists (although I was wrong not to clarify that by elector I meant "citizen with voting rights" and by monarch I meant "hereditary leader"). Since the terms can be defined to be identical I have no interest in arguing over which definitions should be accepted, or if a republic can be run as a dictatorship. My main concern was to correct the improper logic of sets and improper geometry (in saying that squares are not comparable to rectangles when they are a type of rectangle). Like I said, my point was mainly pedantic since my intentions had little to do with the content of the discussion :p

To clarify my pedantry:

A square is defined as an "equilateral rectangle" or "rectangle with equal sides". Rectangle is the species, equilateral or having equal sides is the differentia. Their relationship is the same as that between electromagnetic force and force (square and rectangle) insofar as the former is a less general class (subset) of the latter.

My third point can also be clarified. Sameness is a transitive and non-unitary relation between classes or between elements. For example, two classes are the same (or equal) if and only if they contain the same members. The classes dog and animal contain different elements and so are not the same. A dog is a type of animal (i.e. it would be defined as "Animal with X", where X is some differentia, but "being a dog" is not the same as "being an animal" insofar as being a dog entails its differentia.

One way in which saying that "being a dog" is the same as "being an animal" becomes awkward is that since sameness is transitive: if "being a cat" is the same as "being an animal" and "being an animal" is the same as "being a dog", then "being a cat" is the same as "being a dog". An obviously wrong argument like this is avoided by stating that there is some difference in "being a dog" from "being an animal" (i.e. in being a member of some class from being a member of its higher class). This difference is the aptly named differentia of the subclass/subset/species.