Treatise Chapter 1, Paragraphs 6-8

1.6 – The First Division of essential order is the division of this ambiguous order into the more concrete orders that constitute it: those of “eminence” and “dependence.”

1.7 – In the order of eminence, what is more perfect is prior to that which is less perfect. To illustrate this, Scotus cites Aristotle's proof (Metaphysics, Book IX, Part 8) that action itself is more perfect than the potential for action. A contemporary example: a computer programmer has the potential to write code. But the programmer is not fulfilling her function as “computer programmer” unless she is actually coding. A computer programmer is someone who programs computers, not someone who just has the capacity for programming them. She is thus more perfectly a programmer when she is actually coding, because she is exercising her function, rather than merely having the potential to do so. This sort of order (and any others that involve varying scales of perfection) is an order of eminence.

1.8 – The order of dependence places that which is dependent posterior to that upon which it depends. It should be noted that the prior in this order can exist without the posterior, but the reverse is not true, even if the posterior proceeds necessarily from the prior (so that there are no possible instances of it without the posterior). This is because the existence of the posterior without the prior is contradictory - to go back to an example from earlier, it is a contradiction to have a child without a parent. The existence of the prior without the posterior is bound by no such restrictions, and is not a contradiction, even if the two are necessarily paired. There is no law of nature that prevents a parent from existing without a child; the child needs the parent for existence, but the same does not work in reverse. This requirement is what Scotus calls dependence.

Note: In my attempt to make Scotus's definition of essential order more plain in section 1.5, I used the terms 'causer' and 'caused'. These terms do not fully reflect what is meant by "essential order", in fact, they only reflect one possible view of the term - in the form of the "order of dependence" - as (hopefully) demonstrated in this post. Though for precision's sake, I probably should have just maintained Scotus's use of 'prior' and 'posterior', I believe that 'causer' and 'caused' do help to make the definition more vivid and perhaps a little bit easier to understand. So I'm not editing it out - a bit of imprecision in the beginning for the sake of a little bit of ease of understanding on a difficult work seems to be the proper sacrifice to make, especially since the imprecision is noted (and hopefully eliminated) here.