Principle of charity? http://en.wikipedia.org/wiki/Principle_of_charity

I took "mutual understanding" to be an alternative to "search for the truth" - and a very carefully chosen one at that. Although I don't agree, I can see a number of potential arguments for the idea (given some of his other premises) that in math we find the search for truth, whereas in human conversations we find increased mutual understanding (under the best conditions), but no hope of a search for truth.

I'm insisting myself because the debate is on a topic I care about and one that's inherently interesting.

"Find the search for truth"? Either you search for truth or you don't. In the process, you may (or may not) find the truth, and you may (or may not) be closer to it. What did you actually mean by "hope of a search for truth"?

Now, trying to "find some agreeable progress in mutual understanding" sounds like a damn good substitute to "searching for truth". Mutual understanding is the best approximation of truth I know of, when truth actually has something to do with the conversation.

Now that I think of it, mutual understanding may not be such a good substitute, but merely a prerequisite. Meaning, until the different parties understand where they agree, and where they disagree (and maybe even why they do), search for the truth is hopeless.

I meant that (per the argument under discussion), in some areas there is no (real) possibility of searching for the truth. So, in those areas you don't "find the search for truth." When the OP talks about math vs. human language (all other contexts?), he appears to imply that in math it is possible to search for truth, but in "human language", there is no possibility of finding truth. So, what I meant was roughly this (the following is a reconstruction of the OP's argument, as I understand it, not my views):

1. In math, where there is "a fixed set of consistent rules" (his words), you can meaningfully search for truth.

2. In "human language", which "is not a formal system with complete rules and non-contradictions" (his words), you cannot meaningfully search for truth.

3. The phrase "mutual understanding" indicates a second-best option (since the search for truth is ruled out) for "human language". As you and I talk - now for instance - we cannot usefully search for truth, but we can at least try to figure out what the other person intends to say. That's "mutual understanding," and I think you can see why it's only a consolation prize compared with the search for truth.

The whole thing reminds me a bit of a certain kind of logical positivism. Only some statements are even potentially truth-evaluable. (For example 'x = x' is truth evaluable.) All the rest is simply an expression of personal belief, attitude, disposition or emotion. Under that view, if I say "action x is always wrong" and someone else says "under some circumstances action x is not wrong", the best we can do is figure out what the other person means by their statement. But there is no possibility of saying whether either of those statements is true or false, since such statements are (by definition) not truth-evaluable. That's the kind of thing I thought the OP was saying.