Expanding on the Relationship Between Unity and Number

Cusa's principled distinction between the "absolute maximum" and "number" comes within our reach with a pedagogical exercise involving the creation of a "circle of two". The reader is invited to create a circle of two.

With some effort, the reader might conclude that they may not create a "circle of two" without first defining unity. After having established that "one" necessarily must precede "two", the incredulous reader will often retort that quantitatively this proves nothing. The small is a component of the large. "Of course you need one in order to make two! One is LESS than two!"

At this point the trap snaps shut and the error in this manner of thinking is demonstrated, as the second challenge is leveled. Create a circle of one-half. Is one also "less" than one half? Not quantitatively. But you cannot create a circle of one half without first defining a unit of measurement. From this it is shown that the concept of unity differs from the concept of number, and must exist, metaphysically, prior to that of number.

"More" and "less" are quantitative notions, which have no bearing on the relationship between numbers and unity. What matters is priority. Not temporal priority in the causal sense, but metaphysical prioricity, which creates the possibility of a certain state of relations. For example, if the existence of a thing is made possible only by the existence of another thing, as is the case for falsehood and truth, respectively, it is said that the latter has prioricity. Unity establishes the possibility for a state of relations we call number. Unity must necessarily exist prior to the existence of number. Again, not temporily, but metaphysically.

Cusa developed this concept fully in his "De Docta Ignorantia", which Professor Jasper Hopkins here at the University of Minnesota has graciously published for all to read.