I understand your point and I agree with the sentiment of your paraphrase. By adhering to that maxim, courageous thinkers sparked the Scientific Revolution and freed the world from a long period of superstition and blind submission to authority. Whether professionally trained as scientists or not, people who formulate hypotheses, gather data, and use those data to try to falsify their hypotheses will always provide humanity a great service as they help to slowly render objective reality. This thought tradition has redistributed power and wealth from despotic rulers more reliably than all the political revolutions in history. Tesla and SpaceX are testament to it and Elon should have his place among the historical figures who best exemplify the tradition.
However, this is not the thought tradition that Elon has chosen to amplify with his commentary on covid.
Instead, he has chosen to amplify the voices of those who scream "question everything" from atop Mount Stupid:
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This is the mob who read a headline about an ER doctor saying COVID-19 isn't as bad as "the doctors and scientists" claim, and wield it as
proof that the experts are lying. That only counts as "questioning" in the laziest possible sense. It is certainly not an intellectually honest or rigorous attempt to arrive at a clearer understanding of reality, and it is worse than useless when trying to craft a policy response that balances our best scientific understanding with the need to reopen the economy.
The moment strong enough policy was adopted to successfully mitigate the spread of this virus (i.e. to prevent our healthcare system from collapsing) it was inevitable that a chorus of people would emerge to denounce that policy as an over-reaction and unnecessary.
If Elon were approaching this issue from the perspective of the Slope of Enlightenment (as he does so laudably in his many areas of expertise) I think his commentary would acknowledge the possibility that a hasty mistake now could worsen the problem later. Instead, he seems to treat inconvenient projections with disdain and instead chooses to believe rosier forecasts (e.g. his now infamous tweet about close to zero new cases by the end of April) that are viewed with skepticism by those nasty, unreliable experts.
So,
“Question everything. Don’t just believe something because of the person who said it. Believe it when it is demonstrated to be true”? He should follow his own advice. Elon's commentary about COVID-19 makes me sad precisely because it encourages people to believe something because of the person who said it, not because of the preponderance of evidence.