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If the advice is “don’t rule out what is merely uncertain to be true”, how can we distinguish this from arguments brought forward by, say, those who believe in homeopathy in the face of studies showing that there is no measurable effect beyond the placebo?

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This is about the precautionary principle. We need to act when outcomes are uncertain and stakes are high, to prevent harm. In the case of homeopathy, the outcome if you take a sugar pill that works as well as the placebo is -- who cares? But in the case of climate change, the outcome if you're not sure how bad it's gonna get, how fast, is -- world on fire? Get in your time machine and hail Sagan.

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