Treatise Chapter 1, Paragraphs 9-12

1.9 – The Second Division of essential order divides the order of dependence based on the cause of the dependent. The dependent can rely exclusively upon that which it depends for its existence, or both the dependent and that upon which it depends can both rely on some other thing for their existence - the latter merely closer on the “chain” of causes to this other, prior cause, while the former is further away.

1.10 – That the first part of the second division falls under the order of dependence is rather obvious: in such a case, both the dependent and that on which it depends are clearly known, and it is also clear that the two are necessarily related through the relation of dependence, as defined in 1.8.

For example, if I throw a brick and it breaks a window (assuming those are the only events), my throw is the cause of the effect of the broken window. It is clear that the breaking of the window depends on my throw – without it, the window would never have been broken.

1.11 – The second part of the second division could use some further clarification. If one cause produces multiple effects (for simplicity's sake, we'll consider two effects, though the concept could easily work with more), and one of those effects could be caused before the other (by the nature of the two causes, rather than mere chance), while the second can only be caused if the first effect has already occurred, then the second is posterior to the first on the order of essential dependence.

For example, imagine I am enthusiastically debating about the existence of free will, and my arm hits my cup of coffee. The cup falls, and the coffee then spills all over the floor. One cause (my arm hitting the cup) causes two effects (the cup falling, and the coffee spilling). The coffee could not spill without the cup first falling, and so the spilling depends upon the fall – even though both are effects of the same cause. If the spilling depends on the fall in this way, then it is posterior in the order of essential dependence.

1.12 – That the second part resides within the order of dependence is demonstrated in three ways:

1. The second effect cannot exist without the first. To return to the previous example, if the cup did not fall, the coffee would not spill.

2. The causality* possessed by the initial cause affects both of the effects according to their order. These effects, then, are ordered essentially through their separate relations to the initial cause.

3. The first effect can be discussed as the immediate cause of the following effect. Without the first effect, the initial cause can only be regarded as “remotely” responsible (as there is no direct connection between the cause and its effects) for the rest of the effects that result from it. With the first effect in place, the initial cause can be regarded as the “proximate” cause of the later effects, as the connection between the cause and its effects is, if not obvious, at least available for discussion. Obviously, no effect can result from a remote cause alone, so the second effect depends on the initial cause's giving existence to the first effect – thus the second effect essentially depends on the first.

*This is the word Scotus uses to argue for the second demonstration, and its meaning is not very clear to me. Apparently there is some debate among the scholarly community about what exactly Scotus means by 'causality', and his lack of definition is a strike against him here. However, it is not a critical strike, as the gist of the second demonstration seems rather clear, and even if the second demonstration fails, there are still two others for Scotus's argument to fall back on.