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>Outside of vaccines

Will you allow an argument against this?

I mean, I want to show an example where it is only a problem when someone else is not as convinced as yourself, one way or the other.

>so the way to refute is to ask for proof..

No use. The same proof will not be convincing for everyone. Let us take vaccine. The proof for a Vaccine for X saving Y lives is often the following.

"Before the vaccine there was Y deaths per year from X. But after vaccines there is zero deaths from X".

The implication is that vaccines saved X lives. This could convince most of the people. But someone can ask. Are those kids who are not dying of X (thanks to the vaccine), are dying of something else?

Now the picture is not so clear.

See, same data, different results depending on how deep you want to probe,