The meaning of ‘hierarchy’

The meaning of ‘hierarchy’

The passage below is from A History of the Index by Dennis Duncan

If any of that rings true, then it may give us a sense of why alphabetical order, though not unknown, was extremely rare during the early part of the Middle Ages. As the medieval historians Mary and Richard Rouse put it, ‘The Middle Ages did not like alphabetical order, which it considered to be the antithesis of reason.’ That same repugnance we feel at an exhibition whose hanging is arbitrary, outsourced to an unrelated ordering, was felt too by medieval scholars considering the way that ideas were organized in their books:

God had created a harmonious universe, its parts all linked to each other; it lay with the scholar to discern these rational connections – those of hierarchy, of chronology, of similarity and difference, etc. – and to reflect these in the structure of their writing. Alphabetical order implied the abdication of this responsibility.

I have two questions from the underlined phrase.

First, what does those represent in this context. I think it stands for ‘connections’. (Am I right?)

Last, the meaning of hierarchy.

Free Dictionary suggests five meanings of the word as follows:

https://www.thefreedictionary.com/hierarchy

1. any system of persons or things ranked one above another.
2. government by ecclesiastical rulers.
3. the power or dominion of a hierarch.
4. an organized body of ecclesiastical officials in successive ranks or orders: the Roman Catholic hierarchy.
5. one of the threedivisions of the angels, each made up of three orders, conceived as constituting a graded body.

I think #3 meaning doesn’t fit in this context, so I rule it out.

(Am I right?)

Now I have four meanings from which I can choose. But I cannot decide the best answer. I think #1 is better than the other three, but I cannot tell why the other three cannot be the answer.

Thanks in advance.