> Handling uncertainty is difficult regardless; attaching probabilities to judgements did not ensure the social sciences avoided the replication crisis.

Indeed! I'd say that using probabilities is necessary (or at least very useful), but not sufficient for handling uncertainty.

> I'm not sure what you mean by "low flexibility of interpretation": purely logical proofs are supposed to assume nothing about interpretation.

Yes. I found this part hard to phrase. What you are saying is correct.

I meant it in the sense that there are some assumptions made in logic which do not necessarily hold in normal reasoning. As a simple example, classical logic requires no contradictions whereas the average person may hold several contradictory beliefs without going insane (human compartmentalization is there for a reason, after all!). Paraconsistent logics aim to address this. Classical logic also does not take into account the passage of time.

But by "flexibility of interpretation" I meant something like in logic to derive the truth or falsehood of a statement P(X) about some element X, we can only use known facts about X (i.e., previous statements Q, R, S). We pin down a very specific definition which we can interpret any way we want, but we pick axioms Q, R, S to match our interpretation. This is what I meant by the "interpretation of X is inflexible" (poor phrasing). I mean that the properties / axioms are decided at the beginning and do not shift.

However, when we reason in every day life about e.g. chairs, you and I don't start by pinning down an exact definition of what a "chair" is - we assume some shared knowledge and then debate despite starting from different worldviews. During the debate, we might decide to start pinning down a definition of a chair for the purpose of the debate (is it "something that has been created with the explicit purpose of being sat on"? What is "created"? What if I come across a log that I use to sit on every day? What if I take a dining room chair and stick it to the roof so no-one can sit on it?). If you are convincing enough, the way I use the word "chair" in every day life might change. This is what I mean by the "interpretation of the word chair is flexible".

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My own background is in mathematics and programming, with interest in mathematical logic. I'm afraid my philosophical background is rather lacking. I'm sure such concepts have been described in some depth by various philosophers, but I'm not sure which, or I would just reference the relevant concepts by their common name / link the relevant Wikipedia / Standford Encyclopedia of Philosophy articles.