Bayesian approaches are gaining momentum in cognitive sciences. See for instance "The Bayesian brain" article by Knoll and Pouget.

There is also Cox's theorem, that essentially states that probability theory is the only sound system that extends logic in the presence of uncertainty, to continuous values (between 0 and 1) instead of the two values 0 and 1.

Fair point, the beginning section does seem to suggest that. I have a note in the middle explaining this is not the case.

I make the connection to demonstrate that Bayes is not some arcane statistical artifact, but qualitatively in line with intuition, albeit miscalibrated. This opens up avenues to then move towards ideal bayesian-ness.

Ah, hey, didn't see you were also the submitter. I enjoyed your writing; it is interesting to run across systems thinkers.

And just to fill up the word count; if you haven't read up on the major statistical paradoxes it is possible you'll enjoy them. https://en.wikipedia.org/wiki/Category:Statistical_paradoxes for your attention. If you are playing with stats for the framework then the other half of the fun is delving into the paradoxes; knowing them by heart is a great trick for interpreting evidence. Simpson's, Berkson's and the Elevator Paradox explain a lot of life.

Ah, yes indeed! Thank you.

I really enjoyed this explanation of Simpson's Paradox: http://michaelnielsen.org/reinventing_explanation/

A better, more satisfying explanation for Simpson's Paradox comes from Pearl et al.'s work in modern causation theory, in which they point out that the paradox exists only because we fail to consider the causal structure that generated the apparently paradoxical data. If we take that structure into account and are clear about the causal question we are trying to answer, the paradox disappears. For a recent example involving COVID-19, check out this blog post:

http://causality.cs.ucla.edu/blog/index.php/2020/07/06/race-...

Hi Tom I used to enjoy your blog a lot and your posts on G+ pray continue blogging.

I thought it was abundantly obvious that the author meant it in a qualitative way, i.e. we update our certainty as evidence comes in. Not necessarily in the quantitatively correct amount.

Exactly. You can witness that happen in real time during conversations.

Though we don't always work that way. Consider all the cognitive bias we're susceptible to. You have to account for that.