"language is not a logical system" -_communication_ is not a logical system, but language is.
Care to explain this?
From most NLP classes I have taken and work I have done, I have always understood that languages are logical only in a very loose sense of that word. It is pretty hard to express grammar systems in formal logic for most practical human languages as far as I know.
Maybe I am missing something?
I'm not sure what you mean. More specifically, what logical underpinnings does language have that communication doesn't? For me, communication is the transfer of ideas from one brain to another, and I would define language as the means of doing so. So you can't have one without the other.
"The method must be logical in its formation because otherwise it can't be sure it is understood by both parties."
Isn't true in any description of language. You can't be 0/1 sure that language will be understood by both parties. You can only make a guess that probably the way I'm producing communication symbols will probably be understood by the receiver. If the probabilities align, then communication has succeeded...but a 1:1 production-to-understanding ratio almost never happens.
Receivers of communication understand some percentage less than 100% every time. But it's their own internal models of the language that let's them fill in the gaps. You as a communication producer hope that they are filling in the gaps with a model that's close enough to your model that everything works. And for the most part it does, we're pretty good at it, but miscommunication occurs dozens of times a day, every day for every daily set of communication events.
> The method must be logical in its formation because otherwise it can't be sure it is understood by both parties.
Again I don't know what you mean by "logical". Logic is universal and absolute and doesn't change. But while languages each have an internal consistency, they're all very different from each other, and each of them evolves quite drastically given enough time.
How could language have ever developed if it needed to be logical for it to be understood? Seems to me all you need is a bit of empathy and some dexterous body parts (fingers/arms, vocal cords/tongue) to build a real language starting from pointing and gesturing and grunting, none of which is at all systematic.
Over time, I think modern languages developed that internal consistency because their users needed to express more and more complicated ideas. If the idea I'm conveying to you has lots of actors and actions and nuanced imagery in it, things have to be orderly and highly patterned-based or else I know that you will not understand. So we all mutually agreed on an arbitrary system for these things.