That doesn't state that bears have green toes, it's just a combination of random words.
Well then your example's a little flawed in its own right -- the question "What if math was solved?" is't a combination of random words, it's a question that even has a clear answer: "There is no such thing as solving mathematics." -- the answer you provided.
I did not say that nonsense coming from the mouth of a fool conveys information intended by the speaker, but to a trained listener it conveys information nonetheless. Even nonsense sometimes adheres to a pattern.
Even nonsensical sentences convey information.
Incorrect. The meaning of a sentence and the information it conveys are identical. Therefore, a sentence without meaning doesn't convey information.
This is rarely the case. Many people have quite a bit if difficulty conveying exactly what they mean (the meaing of a sentence), but can usually come to a pretty good approximation (the information it conveys). This is also often done intentionally by writers who know exactly what they're doing (unwritten subtexts, metaphore and allegory, symbolism etc.).
A combination of words that doesn't make sense isn't any different from a random sequence of letters.
Sure it does, there is are at least some clues as to context when words are discernable.
Solving chess....far too many combinations and variations of moves that could be played, it would be fair to say it is beyond human capability.
It's beyond computational capability.
What someone wants to write is not nessecarily the meaning of the sentence they write. The meaning of the sentence they write is the combined meaning of the words they use.
It's a part of randomness that there isn't any context and if you happen to read one from the words, that's coincidence rather than an actual context.
That's a very literalist viewpoint, and quite constraining especially as it pertains to many literary devices.
Also, randomness, may well convey meaning. But this is really besides the point since the original hypothetical question in this case was not a random sequence of words, just an uninformed one.
In the immortal words of e e cummings:
The meaning of the sentence they write is the combined meaning of the words they use.
Not very often and only in the simplest of sentences. Ya' gotta' read between the lines, brother.
The poem does indeed have meaning, and, you're right, is far from random.
The problem here, I think, is that meaning is subjective, whereas information is less so (yet still has an element of subjectivity). Even considering just the information side of the equation, the sum of the information available is also not just limited to the words, but also to the context, to the literary devices being used, even down to typeface, word order and arrangement as in the poem above.
As for the comparison, the comparison of the question that was posed to a random sequence of words is really where this all falls apart. Everything after that is just academic and not really relevant to the discussion at hand.
The meaning of the sentence they write is the combined meaning of the words they use.
Not very often and only in the simplest of sentences. Ya' gotta' read between the lines, brother.
For example, the meaning of those two sentences is the same as the comvined meaning as the words. These two sentences too.
Actually, I think bigpoison was trying (subtly) to tell you something.
Starting with the comparison (because I have the answer for that immediately without any significant thinking), I wasn't comparing the question. I was comparing your sentence of "even if mathematics were to be solved." That assumption doesn't have a meaning.
Aha, here's the crux of our initial misunderstanding.
I never said "even if mathematics were to be solved". You said "There is no such thing as solving mathematics" and I said, in response, "Even if there were...," (such a thing as solving mathematics).
As for your first paragraph (it seems I didn't need any significant thinking for this either, so I could had done it in the other order), it's decided that each word have one or several definitions and when you use the word, it means one of those definitions. You are right about that the context does matter for which definition it means (the convention is to use the definition that makes the sentence meaningful), but that's only down to what other words are in the sentence and not about the context that the sentence is used in.
The context the sentence is used in is often the overriding factor in determining meaning.
For example, if the sentence above had in response to a claim by you that 50% of the context was in the overall discussion and 50% was in the words, then the meaning of the above sentence would be that I agree with you in principle, but disagree on proportion.
However, the sentence above was in response to the claim that none of the meaning could be derived from the context of the overall discussion, and we must look only to the other words in the sentence. In this case, the meaning of the first sentence in my response is that I believe you are completely wrong in this regard and need to re-evaluate this belief.
It's all about the context.
Now you're confusing meaning with the information conveyed.
Now you're confusing meaning with the information conveyed.
There's a fine example of a sentence saying something other than what the words tell the reader.
Now you're confusing meaning with the information conveyed.
But they are the same. That's the basis of a language, that the words have defined definitions and that the convention is that they mean those definitions.
Words yes, sentences however have can emergent meanings that transcend their purely literal interpretations.
Now you're confusing meaning with the information conveyed.
There's a fine example of a sentence saying something other than what the words tell the reader.
my guess for the casual player who just enjoys playing the game and doesn't spend alot of time reading and studying chess, it wouldn't a bit of difference.
When have words ever been static?
What's decadent mean?
OK, another example:
Inflection in spoken language can have a huge impact on the meaning of a question. Consider the following sentence I've often been asked in restaurants with the inflection in two different places:
Would you like soup or salad?
Would you like soup or salad?
To the first question, I'll probably answer "soup" (depending on my mood). To the second, I may well answer "yes please". It's the inflection, in this case, that changes the meaning of the question.
Nevermind the times I think I'm being offered a super-salad....
Even nonsensical sentences convey information.