Thursday, July 3, 2014

The One and the Many


1.  Taking up one of the concerns of the previous article, Thomas next asks in what way the one and the many are opposed to each other.  This article is rich and those with an appreciation for logic will find it quite beautiful.  He proposes four objections.

2.  The first is from the solution to the second objection of the previous article: every multitude is in some way one.  But if this is the case, then “one” and “many” cannot be opposed, since every instance of “many” is also an instance of “one”.  Second, he observes that a multitude is composed of individuals, and it is absurd to say that a thing is composed of its opposite.  Third, he says that “few” is the opposite of “many”, and therefore “one” cannot be its opposite.  Fourth, he says that if “one” and “many” are opposites, then they are opposed to each other as the whole (the multitude) is opposed to the parts into which it is divided (the one), but a whole is logically prior to its parts, and parts are defined relative to their whole.  A multitude, however, is defined relative to one, so that we would end up with a circular definition.

3.  For the Sed Contra he remarks that one and many differ in their definitions (rationes), and therefore differ as such: the notion of one includes lack of division, the notion of many includes division.  Thus they are opposed to each other.

4.  For the Corpus he explains how “one” and “many” are opposed for both the numerical one and the one convertible with being.  One as quantity is opposed to many because the quantitative multitude is judged to be a multitude relative to whatever measures it, which is the unit.  If we were to take some multitude as the unit of measure, it would cease logically to be a multitude (e.g. “one gross”).  On the other hand, the “one” convertible with being, it is opposed to “many” as what is divided in its being is opposed to what is perfect and undivided in its being.  More will be said on this point as we proceed.

5.  The replies to the objections contain the brunt of the substance of this question, and are extremely noteworthy.  He begins his reply to the first by noting a principle of the nature of privations: Nulla privatio tollit totaliter esse.  No privation removes the existence of a thing completely.  Privations always exist in beings, because they have only relative existence: they only exist as the lack of something in something actual.  He draws a comparison then between the privations of the terms convertible with being: the privation of goodness (i.e. evil) is in an otherwise good thing, and is founded on that thing’s goodness; the privation of unity (i.e. multitude) is in some one thing, and founded the unity of that thing, such as it is; the privation of being is also in something actual, or it is not actual at all.  “Et exinde contingit quod multitudo est quoddam unum, et malum est quoddam bonum, et non ens est quoddam ens.”

6.  However, he replies to the objection, one opposite is never predicated of the other in the same way at the same time: thus what is a multitude simpliciter though it is in some way one, cannot be one simpliciter, but only secundum quid.  Likewise what is evil simpliciter (e.g. sin) cannot be good simpliciter but only secundum quid.  And so on.

7.  He follows up this wonderful analysis with another.  In response to the second objection, he distinguishes between two sorts of wholes: homogeneous wholes and heterogeneous wholes.  A homogeneous whole is such that every part has in itself the form of the whole.  Thus a shaving of iron cut from an iron bar is just as much iron as the bar from which it was cut.  A drop of water is as much water as a lake, etc.  Heterogeneous wholes are such that none of their parts have in themselves the form of the whole: a wall is not a house, nor is an arm a man, nor is a plank a ship.  

8.  Having established this distinction, he observes that multitude is, as such, a heterogeneous whole, so that “one” makes up the being of a multitude only inasmuch as the being of the multitude depends on the being of the parts that compose it, not as though the not-multitude were the cause of the multitude of the whole.  For example, the not-house-ness of the lumber and concrete that make up a house are not the cause of the house: rather, the substance of the parts is the cause of the substance of the whole.

9.  To the third objection he distinguishes two senses of “many”: in its strict sense, “many” is opposed to one, but insofar as “many” refers to an excess or surfeit, its opposite is a few, or a paucity.

10.  He replies to the fourth objection by explaining that the order of notions in a definition depends on the order in which we come to know things.  So he lays out the order of discovery for the relevant concepts: first we are aware of a thing as being, then we we notice a lack of identity in being (“hoc ens non est illud ens”), then we conceive of division as the cause of the distinction of things, and from this we conceive of what is un-divided, i.e. the one, and finally we consider the collection of individuals as a multitude.  So the order of definition, which follows the order of discovery, would be: being, distinction, division, unity, multitude.


- Every multitude is somehow one.
- No opposite is composed of its opposites.
- The opposite of many is few.
- Circularity would result in the definition of multitude.

- “One” as the basis of number is opposed to “many” as the measure to the measured.
- “One” as convertible with “being” is opposed to “many” as the undivided to what is divided, and as perfection to privation.

- Nulla privatio tollit totaliter esse.
- Multitude is a hetereogeneous whole, and thus is composed of its parts by their being, not by their lack of multitude.
- Many is only opposed to few when taken in the sense of “plenty” or “excess”.
- The order of definition follows the order of discovery.  The order of discovery here is: being, distinction, division, unity, multitude.

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