Comment by joe_the_user

Why do you think these are so different?

Because "reality" doesn't have "atomic", certain, etc operations? Also, it's notable that since most reasonings about the real world are approximate, the law of excluded middle is much less likely to apply.

If you want to talk about the bus always being late you just do this distributionally. Probabilities are our formalization around uncertainty.

Ah, but you can't be certain that you're dealing with a given distribution, not outside the quantum realm. You can talk about, you can roughly model, real world phenomena with second order or higher kind of statements. But you can't just use axioms

We're talking about "rationalist" cults, axioms, logic, and "from first principles", I don't think using a formal language around this stuff is that much of a leap, if any.

Sure, this group used (improperly) all sorts of logical reasoning and so one might well formal language to describe their (less than useful) beliefs. But this discussion began with the point some made that their use of axiomatic reasoning indeed lead to less than useful outcomes.