All I can say is, kudos to John Duns Scotus.  He has me thoroughly befuddled.  I don’t remember spending this long trying to figure out a philosopher since reading Husserl as an undergraduate.

The question is:  When Duns Scotus tries to argue that the “nature” of a thing (its species or form) is “less than numerical unity,” what in the world does he mean?  I could understand it if Scotus drew an analogy with the geometric point so beloved by mathematicians.  A point (commonly referred to as a “unity,” since Euclid defined it as “that which has no part”) has no length or breadth or height.  That is to say, it has 0 spatial extension.  So, even though it involves a concept of unity equal to 1 (a single thing), its numerical value would be 0.  This, of course, creates problems for how to talk about points… you can say, for example, “Here’s point A and there’s point B, so that means we have two points total in our diagram.”  But two times zero is still zero; so even if you have two points, you really don’t have anything.  And whatever you do have, numerically speaking, is going to be less than the number one. 

This is really the only case I can get my brain around for a sort of “unity” that has a numerical value less than one.  Too bad Scotus does not use this illustration.  Too bad that I have a dark suspicion that he is not talking about geometry when referring to natures and forms.  Too bad that it’s been more than 500 years since anyone last used his philosophical lingo, and that I might have to resort to using mediums to bring him up for extended questioning.  (That is an advantage to knowing Latin… with a universal language, Scotus’s ghost and I could probably keep up a decent conversation.)  It is all too, too bad.