Table Of Theorems
TABLE OF THEOREMS
Scotus structures Chapters 2-4 of the Treatise around forty-six theorems (conclusiones). He frequently invokes prior theorems as premises in proofs of later theorems. In the commentary I adopt a similar practice. Those readers who, like me, cannot hold all the theorems in mind, will benefit from the following table.
Theorems of Chapter 2 Describing Essential Order Theorem 2.1
Nothing whatsoever is essentially ordered to itself.
Theorem 2.2
In any essential order a circle is impossible.
Theorem 2.3
What is not posterior to the prior, is not posterior to the posterior.
4th Division of Essential Order: Causal Dependence Theorem 2.4
What is not ordered to an end, is not an effect.
Theorem 2.5
What is not an effect, is not ordered to an end.
Theorem 2.6
What is not an effect, is not made of matter.
Theorem 2.7
What is not composed of matter, is not composed of form; and what is not composed of form, is not composed of matter.
Theorem 2.8
What is not caused by extrinsic causes, is not caused by intrinsic causes.
Theorem 2.9
The four types of causes are essentially ordered in their caus ing of one and the same thing.
3rd Division of Essential Order: Non-Causal Dependence Theorem 2.10 When two things are related to the same cause, that cause is either proximate or remote. xi
xii Table of Theorems 2nd Division of Essential Order: Causal and Non-Causal Dependence
Theorem 2.11 It is not the case that each thing [B] more proximately caused by a cause [C] is itself a cause of a more remote thing
[A] caused by that same cause [C]. Therefore, it [B] is some thing caused prior [to A], but it is not causally prior [to A].
Theorem 2.12 A thing essentially depends only on a cause or on something caused that is more proximate to some cause.
1st Division of Essential Order: Eminence and Dependence Theorem 2.13 Not everything that is excelled essentially depends on that which is more eminent than it. Therefore the first member of the first division does not entail the second member.
Theorem 2.14 Not every dependent thing is excelled by that on which it depends.
Theorem 2.15 Plurality is never to be posited without necessity.
Theorem 2.16 Everything ordered to an end is excelled.
Theorems of Chapter 3 Primacy of Efficiency Theorem 3.1
Among beings, some nature can produce an effect.
Theorem 3.2
Something able to produce an effect is simply first—that is, it cannot be produced, and it can produce its effect without the power of anything else.
Theorem 3.3
That which can produce an effect in a way that is simply first is uncausable, because it cannot be the effect of anything else and it can produce an effect independent of anything else.
Theorem 3.4
Something able to produce an effect in a way that is simply first exists in actuality, and some actually existing nature can produce an effect in this way.
Theorem 3.5
What is uncausable exists necessarily from itself.
Theorem 3.6
Existing necessarily from itself pertains to only one nature.
xiii Table of Theorems Primacy of Finality Theorem 3.7
There is some nature among beings such that it can be an end.
Theorem 3.8
Something that can be an end is simply first, that is, it can not be ordered to some other end, and not by anything else's power is it the end of other things.
Theorem 3.9
The first among beings that can be an end, is itself uncausable.
Theorem 3.10 The first among beings that can be an end, actually exists, and this primacy belongs to some actually existing nature.
Primacy of Eminence Theorem 3.11 Among the natures of beings there is something that excels.
Theorem 3.12 Some eminent nature is simply first in perfection.
Theorem 3.13 The Supreme Nature is uncausable.
Theorem 3.14 The Supreme Nature is something actually existing.
Triple Primacy Theorem 3.15 To one and the same unique and actually existing nature belongs the triple primacy within the three types of essential orders discussed in this chapter, namely, efficiency, finality, and eminence.
Theorem 3.16 It is impossible for one and the same thing to depend essen tially on two things in such a way that its dependence termi nates wholly in each.
The Uniqueness of the First Nature Theorem 3.17 To only one nature belongs each primacy of any type of extrinsic cause.
Theorem 3.18 The First Nature that can produce an effect is most actual because it virtually contains every possible actuality. The first in finality is the best, virtually containing every possible good. The first in eminence is most perfect, eminently con taining every possible perfection.
xiv Table of Theorems Everything Is Ordered Theorem 3.19
One actually existing nature is first in the three aforementioned orders with respect to any other nature, such that any other nature is posterior to that First Nature in these three ways.
Theorems of Chapter 4 Simplicity Theorem 4.1
The First Nature in itself is simple.
Pure Perfection Theorem 4.2
Whatever is intrinsic to the highest nature is the highest such thing.
Theorem 4.3
Every pure perfection belongs to the highest nature neces sarily and in the highest degree.
Intellect and Will Theorem 4.4
The first efficient cause understands and wills.
Theorem 4.5
The first cause causes contingently whatever it causes.
Theorem 4.6
The First Nature is the same as its love for itself.
Theorem 4.7
No act of understanding can be an accident of the First Nature.
Theorem 4.8
(i) The intellect of the First Nature actually understands— always, necessarily, and distinctly—all intelligible things, and (ii) its understanding of these is naturally prior to their actual existence.
Infinity Theorem 4.9
You are infinite existence and are incomprehensible by what is finite.
Simplicity Theorem 4.10 Every kind of simplicity follows from infinity.
Uniqueness Theorem 4.11 You are one God, besides whom there is no other, as you have said through the Prophet.