People who think they are having a scientific argument online try to throw up supporting facts for their theory or falsifying facts against their opponents. This is what is happening with the anti-vaccination movement. Celebrities have bought some story about vaccinations causing autism, and are taking up the noble cause of terrifying parents into foregoing all vaccinations. As a result, preventable illnesses and deaths are on the rise in America, and autism ... well, autism is still doing its own thing exactly as before.
It would seem to be a simple cut-and-dry case of "What The Hell Were You Thinking?", but no matter the facts being shown, the scare-mongers are not backing down. It is therefore clear that this is not a fight about facts. It is a fight about mindset, about worldview, about basic scientific literacy. It is a fight about the interpretation of facts. If you start with the wrong axioms, you will view facts in a distorted way, but it is also the case that starting with the right axioms gives you a bias. Facts do not speak for themselves. They never have, and they never will, because your audience will always have a worldview ready to apply their own interpretation. Facts don't cut through delusion automatically. When you present facts about the number of preventable illnesses and deaths, compared to the number of autism diagnoses scientifically linked to vaccinations, someone with the "vaccination = autism" viewpoint will assume that not enough scientists are looking for the link, so they need to scream louder until the world wakes up. The same facts, wildly different interpretations.
Question the axioms. It's your only hope of winning an argument like that. Also, you can't change someone's mind for them. You need to ask the right questions to make them examine their assumptions.
Mokalus of Borg
PS - Knowing what your opponent is assuming is always a good step in an argument.
PPS - At least for understanding them.