Currently i'm trying to understand what Distributed Morphology (DM, as introduced by Halle&Marantz 1993) is about.
One of the basic operations belonging to this framework is fission.
However, i'm not sure if i understand the idea of fission. Let me demonstrate this by presenting the following made up paradigm for a personal pronoun:
I also alreay decomposed the features into binary features (there might be more sophistcated ways to do this):
Assuming that we only have one morphem initially available for insertion, one could introduce the following rule of fission to explain the syncretisms:
[±Obj, ±1, ±2, ±Sg] -> [[±1, ±2][±Obj, ±Sg]]
Note that this rule is not supposed to have any restrictions, so the fission applies to every form of the pronoun. By applying this fission, the features are seemingly rearranged in a certain order which will determine the order later when we insert the vocabulary items, at least that's the idea. What bothers me is that this whole process seems rather arbitrary. To me it looks like the order of the brackets after fission could easily be reversed. But let's proceed.
We also need rules for the insertion of the vocabulary items:
- /fa/ <-> [+1]
- /sa/ <-> [+2]
- /ta/ <-> [ ]
- /re/ <-> [+Sg, -Obj]
- /si/ <-> [+Sg]
- /ro/ <-> [ ]
Is this a proper analysis?
On first sight, it looks like it could be. For example, for the first slot in case of 1st Pers Sg. Nom. ([+1][-Obj, +Sg]), /fa/ is the most specific item which would fit. And since the features reflecting Person are in the first slot exclusively, /fa/ would be inserted at this spot correctly. But again, this looks a bit "too easy" to me.
Anoter irritating aspect to me is, that we have two vocabulary items here without any context (/ta/ and /ro/). One is only supposed to be inserted in the first slot, the other one into the second slot obviously. Again i'm not sure if this is a valid approach.
Note that actually i'm currently trying to analyze a much more complex paradigm coming from a real language. But to ask my question in a more straightforward way, i decided to make up an example for the sake of simplicity. I'm also reading the original papers by Halle, Marantz etc. but i'm having a hard time understanding them.
TL,DR: In Distributed Morphology, can fission determine the order of morphems?