That's the terminology we use when talking about statistics and science though. I know it's lacking in the world in general, but we can use our common sense to draw conclusions on whether two events were linked.
So, so, SO many things have 'not proven to be related'. 99.999% of these have not been proven because there is no value in spending time and resources definitively proving something which is either already common sense, or so obviously not related.
Like, did you know that it's never been proven that consuming over 6 tonnes of car rubber in a sitting is bad for your health? Because how and why would you prove that?
And, an estimated 16% of the Americans will die after semi-consciously wrapping themselves in polyester or cotton. Despite that being an 8th of the population, there has been no study into why this happens. What causes this!? That's a worse death rate than covid!
But that's figure comes from the fact that 1 in 8 people will die in their sleep. Bedding materials themselves are judged to be safe for human contact, so there's no reason to study a relation between tucking ourselves to bed, because we know those people are actually dying from heart attacks, strokes, etc.
I know it's kind of hard to grasp with medical stuff, but the same kind of thing is happening here. 0.0018% of people died after having the vaccine, just like 16% of people died after encasing themselves in bedsheets. Are they related? Finding out takes time and effort, and people are working on it.
Remember the fuss that kicked off when the anomalous blood clots started with the AZ jab? That kind of thing will happen for anything else where a potential pattern pops up too.
How can we trust that this is happening? I'll tell you why I trust it.
'The Scientists" or "The Medical Community" aren't a unified group of people. They are 10s, maybe 100s of millions of individuals, who are human beings just like you and me. They've trained for years to get where they are, and know a lot more about medicine or science than we do, and all of them have slightly different opinions and views.
Many are where they are for ethical beliefs and because they want to do the right thing and contribute to humanity. Many are there because they want to get rich or like power. For every person who wants to get rich inventing a vaccine, there is a dozen suspicious professionals who wants to catch them out, either to get rich themselves or for their own ethics.
You can also bet there is a shit ton of corporate espionage between the vaccine providers. For example, J&J will be spying on their competitors, looking for a weakness, and when that weakness appears they will publicize the shit out of it in the hopes of strengthening their own market share by weakening their competitors. This is one of the double-edged-sword strengths of freedom of speech and capitalism as a model for societies.
I would be way less trusting if I was getting the Russian or Chinese vaccine, knowing there was a culture of punishing whistleblowers and that the vaccine I was taking may been the result of a dubious decision from the higher ranks. I'd also be less trusting if I was in a third world country, where corruption is rife and the "Pfizer" vaccine I was getting might actually just be a vial of saline solution provided by criminals with government connections to make bank.
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Anyway, sorry I went off on a tangent. You seem like an inquisitive person so I would recommend you learn more about statistics, how to use them, and how they are used! I can recommend this book: https://www.amazon.co.uk/Data-Detective-Rules-Sense-Statistics/dp/0593084594. It's by a british economist/journalist called Tim Harford. He also does a great free podcast called "Cautionary Tales" which I'd highly recommend if you like learning about the psychological traps people fall in to!
You should check out this book.
https://www.amazon.com/Data-Detective-Rules-Sense-Statistics/dp/0593084594