The following once happened: I posted a link to some article on an IRC channel. A friend of mine read the article in question and brought up several criticisms. I felt that her criticisms were mostly correct though not very serious, so I indicated agreement with them.
Later on the same link was posted again. My friend commented something along the lines of "that was already posted before, we discussed this with Kaj and we found that the article was complete rubbish". I was surprised - I had thought that I had only agreed to some minor criticisms that didn't affect the main point of the article. But my friend had clearly thought that the criticisms were decisive and had made the article impossible to salvage.
Every argument actually has two parts, even if people often only state the first part. There's the argument itself, and an implied claim of why the argument would matter if it were true. Call this implied part the relevance claim.
Suppose that I say "Martians are green". Someone else says, "I have seen a blue Martian", and means "I have seen a blue Martian (argument), therefore your claim of all Martians being green is false (relevance claim)". But I might interpret this as them saying, "I have seen a blue Martian (argument), therefore your claim of most Martians being green is less likely (relevance claim)". I then indicate agreement. Now I will be left with the impression that the other person made a true-but-not-very-powerful claim that left my argument mostly intact, whereas the other person is left with the impression that they made a very powerful claim that I agreed with, and therefore I admitted that I was wrong.
We could also say that the relevance claim is a claim of how much the probability of the original statement would be affected if the argument in question were true. So, for example "I have seen a blue martian (argument), therefore the probability of 'Martians are green' is less than .01 (relevance claim)", or equivalently, "I have seen a blue martian" & "P(martians are green|I have seen a blue martian) < .01".
If someone says something that I feel is entirely irrelevant to the whole topic, inferential silence may follow.
Therefore, if someone makes an argument that I agree with, but I suspect that we might disagree about its relevance, I now try to explicitly comment on what my view of the relevance is. Example.
Notice that people who are treating arguments as soldiers are more likely to do this automatically, without needing to explicitly remind themselves of it. In fact, for every argument that their opponent makes that they're forced to concede, they're likely to immediately say "but that doesn't matter because X!". Because we like to think that we're not treating arguments as soldiers, we also try to avoid automatically objecting "but that doesn't matter because X" whenever our favored position gets weakened. This is a good thing, but it also means that we're probably less likely than average to comment about an argument's relevance even in cases where we should comment on it.
(Cross-posted from my blog.)