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You use terminology very differently from the way I understand it. Here are my definitions.
Phonetics is the properties of the information channel.
Phonology is the manner in which the channel is used to encode information.
Lexicon is the information encoded in the identity of the words.
Morphology is the information contained in the internal structure of the words.
Syntax is the information contained in the order of the words.
Pragmatics is the information contained in the context of the utterance.

Pete Bleackley
The Fantastical Devices of Pete The Mad Scientist - http://fantasticaldevices.blogspot.com
Emily Semantic Recommendation - https://emily-petebleackley.rhcloud.com

-----Original Message-----
From: And Rosta <[log in to unmask]>
To: [log in to unmask]
Sent: Tue, 11 Aug 2015 7:35 pm
Subject: Re: DLM (dependency length minimization)

On 11 Aug 2015 18:53, "Pete Bleackley" <[log in to unmask]>
wrote:
>
> Suppose I pick a word at random from a book, and challenge you to
identify its grammatical role by asking a series of polar questions. Thanks
to your expert knowledge of English grammar, you can get it in five
questions.
>
> Now I'm going to make it easier for you by telling you what the
grammatical role of the previous word was. Now you can get it in two
questions. The syntax has given you three bits of information.
>
> Now let's play the game with Latin. Without knowing the role of the
previous word, you can work it out in 5 questions. But Latin's word order
is more variable than English, so when I tell you the role of the previous
word, it still takes you 4 questions to work it out. Latin syntax has only
given you one bit of information. Latin doesn't need to put as much
information into its syntax because more is contained in its morphology.

Thanks.

In my terms:
Word order, which is a syntax-driven characteristic of phonological
structure, gives more clues to syntactic structure in English than in Latin.
Inflection, which is also a syntax-driven characteristic of phonological
structure, gives more clues to syntactic structure in Latin than in English.

And mixing my terms and yours:
Word order carries more information in English than in Latin.
Inflection carries more information in Latin than in English.

Even tho I don't think word order is part of syntactic structure, I do
think that the processing difficulty of dependency distance is based on the
number of nodes in phonological structure that correspond to nodes in
syntactic structure; and much so-called syntactic processing difficulty has
to do with the difficulty of recovering the syntactic structure from the
phonological.

--And.