Finally, here is the rest of "the insight".
I would like to clarify two terms before I begin.
1) Demonstration is the name of the art of true reasoning (which includes deduction and induction).
2) Dialectic, or argumentation, is the art of reasoning from reputable opinions.
Places For Dialecticians
Why are the schemes used in argumentation called places more than any other thinking skills that one commits to memory? Think of the difference between the shopping list and the characteristics of dogs. The shopping list is unordered by nature and must artificially be given an order through the 'place' technique. The characteristics of dogs are naturally ordered - as the mind grasps the abstract nature of the dog each characteristic finds its place in the mind and is, consequently, remembered.
The Topics is concerned with reasoning from "reputable opinions". One is not naturally investigating an object of thought - one is arguing the merits of reputable opinions. By and large, those engaged in argumentation are not 'natural thinkers'. Thought is still artificial - the best that the arguer can hope for is to train himself to follow proper technique as given by a master (Aristotle, Ralbag or Ramchal) - a well ordered shopping list of argumentation, if you will.
In other words, the dialectician - not being a 'natural thinker' is in need of guidance. The purpose of the topoi and m'komot is to provide that guidance. The master provides his student with a topology of mind, a map, to guide him along the path to truth.
Topics and M'komot
In this post, I wrote what my first thoughts were after the scholar told me that makom is the translation of topos:
Ralbag's m'komot were topoi - argumentative schemes enabling the reader (who is in a sense a dialectician, building his arguments out of authoritative statements) to construe an argument for the conclusion that a specific mitzvah or shoresh can be placed on (or emerge from) a specific text.
I believe this was in essence true though lacking. What was I missing? The fundamental role of m'komot in the development of a talmid being guided by his Rav - in this case the Ralbag. Just as the topoi were the schemes by which Aristotle, as expert reasoner, guided his students to become better reasoners, so too, the m'komot are an expression of the chesed of the Ralbag, as master m'pharaish, to his talmidim guiding them through the process of peirush.
Please forgive me if I go back and make some changes. I have been a bit harried as of late which is not the best state to engage in the reflection necessary to write a good post. However, I did want to get this post up already. As usual, all critiques are welcome and greatly appreciated.