Theoremata Scoti, Pars III A

Part three of the Theoremata is divided into subsections, labeled by the editors "A" and "B". These appear to be two versions or two drafts of the same train of thought: Scotus gives some definitions, draws some corollaries, and makes some conclusions, all about conceptual analysis. Then he starts over with the same material, but takes it in another direction. This post looks at the first subsection.

Definition 1: I call that which terminates the act of understanding a concept.

"A concept is called either "object" or "intelligible" or "intellected" [intellectum] or "intention". The first is most common, because [it pertains] to all [intelligible] potencies. The second is common, because [it pertains] to the object understood either in potency or in act. The third is proper [i.e. is properly a concept]. The fourth is how the Arabs Avicenna and Averroes understand it. But just as "intention" is said equivocally of the object and of the act, so also is "concept". But here I take it to be the object."

Definition 2: That is said to be conceived first which is adequated to the intellect.

Scotus explains that by adequation he means that in the "first" concept what is understood is the whole object, not some part of the object.

Definition 3: Whatever is essentially included in the first concept is conceived per se.

For instance, whenever a species is conceived its genus is automatically conceived per se, and so for similar cases. When I conceived of "triangle" I also ipso facto conceive of "figure".

Definition 4: That and only that is perfectly conceived, of which nothing is concealed which is essentially included in it.

"'Perfect' is here understood [to mean] the act, not insofar as it is elicited from its potency, but insofar as it is compared to its object, namely so that nothing intrinsic to the object is unknown, in whatever mode it is being known."

Definition 5: A concept which cannot be analyzed into [simpler] concepts is simply simple.

Definition 6: A concept which is per se one, yet is analyzable into [simpler] concepts, is not simply simple.

For example: "triangle" can be analyzed into simpler concepts, namely "figure", "side", "three", etc. It is a simple concept--it can be grasped as a per se whole--but it isn't simple simpliciter.

Corollary: Therefore "essentially" belongs to more than is said "in quid".

Scotus next offers two premises establishing or assuming that his definitions have actual counterparts. There is something which can be conceived first and perfectly, and there are some concepts which are distinct.

From all the foregoing Scotus now draws several conclusions and corollaries:

Conclusion 1: The analysis of concepts has a stopping-point [status].

Here Scotus inserts a brief discussion of the inability of a finite power, such as the human mind, either to grasp infinites all at once or to be able to run through an infinite series. This is relevant to the following conclusions.

Conclusion 2: No concept [which is] one "in quid" can be predicated of all others.

There is no concept--call it a--which designates "what" something is as a whole which can be predicated of every other such concept. There is no common "what" under which every such concept can be subsumed. This is because, if there were, no other concept other than this hypothetical one a would be simply simple as defined above, since every other concept would include a as a factor or constituent. Therefore one and the same concept--every concept except for a--would include a concept of an infinite in itself, or rather would include actual infinities. For any concept other than a would include both a and something else, and that something else would include a and something else, and so on to infinity.

In addition to this argument Scotus offers two more for the same point.

Corollary: There is nothing in common between the concept of a genus and a difference, nor does one include the other; similarly with matter and form.

"Figure" does not include "Three Sides", when the difference "Three Sides" is added to "Figure" to produce "Triangle". We can't define "Triangle" as "Three-sided Figure with three sides". And so forth.

Another Corollary: Nor is a superior difference, which is included in a genus, included in an inferior difference. Otherwise definition would be pointless [nugatio] and there would be a progression to infinity with difference, because they would differ by their own differences.

This point is similar to the last one. "Animal" cannot include "Rational" and "Rational" cannot include "Animal", since the one is determinable by the other and vice versa.

Conclusion 3: The analysis of concepts will come to a stop at some first [concepts].

Definitions, etc., must be in terms of things which are themselves not reducible to something.

Corollary: a determining and a determinable never include one concept, nor does one of them include the concept of the other per se.

As though it follows from the foregoing, Scotus finishes this subsection, without further explanation or argument, with a conclusion which seems to contradict the theory of conceptual univocity which he holds elsewhere:

Conclusion 5: No identical concept is per se common to the created and the uncreated.

What to make of all this? Stay tuned for more!