I'm a little late to Paul Graham's essay on How To Disagree.
Apparently lots of people have seen it before me, but if you haven't seen it, check it out. A useful thing to have in mind when you are thinking about what to say to the Person Being Wrong on The Internet.
Graham's level 0 for disagreement is name-calling. And I think we can all agree that "you're an asshole" doesn't really move an argument forward. Perhaps it is the lowest level at which we can still call this interchange a discussion. But there are two other patterns of responses, neither of them positive, that might qualify for negative numbers on the Graham hierarchy.
The one I've heard too much of recently is "argument by intimidation". Call it Level -1, but unfortunately we can't avoid thinking about how to respond to it when it happens. Name-calling is ugly and hurtful, but responses that threaten and explicitly bully are outside the realm of "let's try to talk about this". Rape threats and death threats, wishes for physical harm to the speaker, defacing of images, are all not-uncommon responses to internet conflict, and it seems particularly common as a response to women standing up against harassment . I don't actually recommend clicking on this link of the responses to Lindy West's assertion that the field of comedy is hostile to women; it's stomach-turning. Suffice to say they prove the point..
The other response that might be just sideways to the hierarchy of disagreement is "silencing". "Oh, shut up" is not an argument. [comment deleted] is not an argument either. It might be an appropriate refusal to engage with Level -1 and maybe even Level 0 comments. But deleting arguments because you disagree with them or they put you in a bad light means that there's no chance for examining our differences and maybe learning a thing or two about each other. If it's your blog you can discuss what you want to, how you want to, and remove all the comments you like, but there's a difference between a soapbox and a discussion. So I don't know what to call this one. Level square-root-of-negative-1 perhaps, because now the discussion has to move to the inside of our heads.