I have been considering what differences or similarities in any properties at all could be found between:
- a language where whatever the supposed “deep structure” of a language truly is (like, the ultimate logical/semantic form, I guess) is fully explicit in strings of a language - therefore, it is deterministically parsible (and this means, it is guaranteed to obtain a parse: there is never incompleteness or insufficient information to parse totally - and only one parse: there is never ambiguity or multiple possible parses.)
- The opposite, in some way. This means, however the language is used, there is a degree of non-determinism in it. That could mean that there are approximation techniques which people use to guess what deep structure element some surface structure element has (like resolving a pronoun to its referent), and they may be effective in 90% of cases, but 10% of the time, it is necessary to ask for clarification.
The question can be contextualized by looking at some similar, interesting phenomena.
- I read that sign languages may have anaphora mechanisms that are quite different from spoken language, like “tethering” a referent to a particular area or object in the room.
- I do not know any programming language that permits implicit anaphora, but it’s an interesting question if it could be useful. That means, the computer should statistically guess what the referent of an expression, based on how recent it was.
- A non-deterministic language can be more extreme than just having a few statistically resolved elements in the parse. Perhaps it is an inherently stochastic or aleatoric language, in which the use has something to do with the language’s ability to generate an unexpected meaning, each time the same sentence is said (or anything more out of the box like that, for its conceptual value).
- Possibly, the factors at play include: a. How many possible parses are there? b. What is the probability for each one? c. What elements of sentence creation and parsing have a relationship to those questions?
Maybe it is a simple formula, but I would like to see it developed. Maybe we can consider a single global metric for the amount of steps required to produce a message in its final form, and to parse it.
Then, it may be something like this:
-> let us abstractly imagine S is the set of all possible statements in the language of thought (LoT). We choose to ignore their internal structure or relationship to one another and simply list each with a unique identifier, a, b, c, d, etc.
-> For some reason, there is a transformation system that symbolically changes the LoT into a “transport form”, for it to arrive at the recipient of the message. The recipient is able to parse the incoming message and restore it to its original form, thereby obtaining the true message.
Consider the transformations/mappings/rules/programs necessary to transform a message into transport form, and the reverse. Mathematically, it may be the case that they are not true inverses of one another.
I think there might be a formula between the size of the generator program, the size of the message, the size of the parser program, and the mathematical goal of the communication system (to transport messages with perfect one-to-one fidelity, or not, and why?). For the last one, we should decide a criteria on the system to be fulfilled, and it could be many different things. Whatever criteria are selected becomes an optimization metric on the system. We could have a system that was selected to optimize for message brevity. It’s an open question, but maybe this would imply that the generator is trivial: it maps one element from LoT to one element in a transport medium. There is a lot of thinking to be done, but the point is, you can notice how different systems achieve different things, and not claim all human languages share an identical optimization explanation.
It reminds me of something you hear nowadays that all languages are equivalent in their expressive capability, but it’s not clear what argument was given to demonstrate that. I recently felt that Chinese is easier to use on a smartphone because you type a few letters, and the keyboard suggests various characters. I’m not sure, but I wonder if you use your fingers less in Chinese, on smartphones.
We might ask:
Assuming we have some good mathematical data on situations of ambiguity, do we know, say, the average accuracy, speed, and even brain energy consumption, with which, say, English speakers resolve ambiguities, in language? (I now realize that ambiguities goes far behind anaphora, but even includes homophones or similar-sounding words.)