I think “probabilistic reasoning” doesn’t quite point at the thing; it’s about what type signature knowledge should have, and what functions you can call on it. (This is a short version of Viliam’s reply, I think.)
To elaborate, it’s different to say “sometimes you should do X” and “this is the ideal”. Like, sometimes I do proofs by contradiction, but not every proof is a proof by contradiction, and so it’s just a methodology; but the idea of ‘doing proofs’ is foundational to mathematics / could be seen as one definition of ‘what mathematical knowledge is.’
I think “probabilistic reasoning” doesn’t quite point at the thing; it’s about what type signature knowledge should have, and what functions you can call on it. (This is a short version of Viliam’s reply, I think.)
To elaborate, it’s different to say “sometimes you should do X” and “this is the ideal”. Like, sometimes I do proofs by contradiction, but not every proof is a proof by contradiction, and so it’s just a methodology; but the idea of ‘doing proofs’ is foundational to mathematics / could be seen as one definition of ‘what mathematical knowledge is.’