Exactly, and if you keep going, you'd notice you need each time a longer, more precise description, which at the same time, paradoxically, opens the door for more ambiguity.
In that example, the first context is English language, then knowing who I is, then what a mile is, and a treadmill and today. All of those are contextual. Even mile. How long is a mile? Like any physical measure, it actually varies, because it is defined relative to something else which varies. The meaning of English language has also varied over time, that sentence might not make any sense to someone reading it in 20 years. And then when is today? May 7, 2019 - which is also a relative measure of time and not even that precise.
And then finally, what if you were lying? Did you really walk a mile today? How can I be sure? And how can you be sure I understand the same meaning from the words you say or write?
I understand where you are coming from, but a lot of what you just presented isn't actually relevant to the topic of ambiguity from lack of context in language. Some of it just doesn't apply. Allow me to explain...
> the first context is English language
Let's ignore this context. If you don't understand English then you shouldn't be expected to understand an English statement regardless of context.
> How long is a mile?
That depends on what time and space you are in. But that's ok. All such measurements are relative and defined by non-natural constructs. But we can be realistic and assume a mile is whatever our government has decided.
When I tell you "I ran a mile", I'm not telling someone in Australia I ran a mile. I"m telling you that. If we are speaking over the internet it might complicate things, but we only have to resolve the meaning of mile once for our relationship, and all proceeding discussions will use this meaning.
I would argue that this makes the word mile unambiguous in the sense that you are saying. If we had to assert each time what I meant by a mile, then that would be ambiguous.
> that sentence might not make any sense to someone reading it in 20 years
Evolution of language is a separate phenomenon. We don't need to consider that. Only what the language means today right now as I use it. That's the utility of language. For older English texts, we have literature which matches our common vernacular to the vernacular of the time. Foreign translations are out of scope for the same reason listed above. Since we have mappings between today's English and yesterday's English, I would again argue that this is not a source of ambiguity.
> And then when is today? May 7, 2019
That doesn't have anything to do with language. That is a chronospacial coordinate. It represents a certain degree of completion of our orbit around the sun. It isn't a measurement of time at all. It's only relative in the sense that all time and space measurements are relative to the spacetime coordinate of the Big Bang.
Time is inherently a relative concept. We don't have time unless we are comparing (relating) two different frames. We define one in terms relative to the other (motion, state, etc). In a single, non-relative frame of reference time just doesn't exist.
> And then finally, what if you were lying?
Again, this has nothing to do with language. You aren't trying to guess what I'm thinking, you're trying to understand what I'm saying. That's what language parsing is about. Discussion of motivations, misdirection, etc. is irrelevant.
Interesting. All of the above rebuttals are basically: ignore this because it's context and should be obvious.
Well, that's the problem. It might seem obvious to you now, but it is not obvious to everyone all the time, which is what makes any statement ambiguous.
Additionally, I don't know the purpose of what you are saying. For example, you might say you ran a mile because you wanted to express you were tired, or because you wanted to imply you are healthy, or who knows why, it is definitely not clear from the statement alone what you wanted to convey, which is the main problem.
We feel something internally and then we try to express that in words, hoping that those words will mean the same to the person perceiving them. That process is highly suceptible to noise in many forms, like the other person not hearing you correctly, being distracted, being stressed out, or maybe they speak a slightly different version of your language and some of the words or expressions mean something a bit different to them than to you.
In the end, any statement doesn't have meaning by itself, it only acquires meaning when someone interprets it and understands it in a certain way. That is always a subjective process.
Honestly I feel like we could have a very deep conversation about this because I certainly agree with a lot of what you're saying.
Language is certainly subjective, but I would argue that we can make certain concessions on what context truly is "obvious" and what isn't. And I think the matter of what level of precision is acceptable enough to consider a statement or idea "understood" is up for debate and is also contextual.
At some point, any extra information is just that, extra information. The core idea may have been expressed fully, even if there are certain small ambiguities or if the listener wishes to draw insight from the statement beyond the basic sentiment expressed.
In that example, the first context is English language, then knowing who I is, then what a mile is, and a treadmill and today. All of those are contextual. Even mile. How long is a mile? Like any physical measure, it actually varies, because it is defined relative to something else which varies. The meaning of English language has also varied over time, that sentence might not make any sense to someone reading it in 20 years. And then when is today? May 7, 2019 - which is also a relative measure of time and not even that precise.
And then finally, what if you were lying? Did you really walk a mile today? How can I be sure? And how can you be sure I understand the same meaning from the words you say or write?