torekp comments on How to provide a simple example to the requirement of falsifiability in the scientific method to a novice audience? - Less Wrong Discussion
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Go through a Venn diagram explanation of Bayes's Theorem. Not necessarily the formula, but just a graphical representation of updating on evidence. Draw attention to the distribution of probability of H between E and not-E. Point out that if the probability of H doesn't go down upon the discovery of not E, it can't possibly go up upon the discovery of E.
This has the advantage of showing the requirement of falsifiability to be an extreme case of a more powerful general principle.
This could be supplemental to some of the great suggestions by your other commenters.
Most lay audiences can't simply generalize an abstract mathematical model to the real world. They need actual examples to learn in a way that impacts their day-to-day reasoning.