Bertrand Russell's mathematical logic. — Banno
Not to make too fine a point of philosophical history, but the Principia Mathematica, to which your quotes certainly refer, were authored by Whitehead and Russel, in that order on the cover. Russel was Whitehead's student. They both authored it, and Whitehead was in the lead.
If the analytic tradition exists, and if it has any claim to fame, it is because of PM. And mind you, you will find no mention of French kings
anywhere in its three volumes.
PM break down logic into it's fundamental bits and in turn, describe arithmetics into purely formal logic. In doing so, it indeed made it possible for machines to understand, or rather perform, logical and arithmetic operations. Hence the information revolution, computers etc. The price to pay is that they needed dozen of pages to define the addition. Something a kid can grasp in less than 10 seconds was painstakingly broken down in myriads of elementary statements covering dozens of pages. In other words, machine language. Code.
Why is it then that Whitehead, the lead author of this seminal work, is rarely mentioned or even remembered? That has a lot to see with what he wrote AFTER, which was at a brutal variance with AP.
By then, AP had become "the reigning tradition" (aka a dominant force in the halls of English-speaking academia). A host of AP professors disliked Whitehead's quasi mysticism with all the passion they could summon. Granted that was not very much, but that's why you never hear of him. He's been ghosted.
So in my understanding of what historically happened, AP, based on the success of PM in making arithmetics understandable by machines, proceeded to make philosophy understandable by machines... Whitehead saw that this was going too far. I guess he figured that his 'code' needed dozens of pages to describe what a kid could grasp in 10 second, so translating Kant in formal logic seemed undoable... There's only so much formal logic can do. In any case, he went another way. The AP's just fossilized progressively into philosophy for computers. A few of them woke up a bit late to the idea that language always has a human
context, a locutor, interlocutors, intentions and the likes, and therefore (gasp!) that
ambiguity exists. Irreducible, central to the philosophical pursuit.
At a fundamental level, philosophy is about the ambiguities of the human condition, which we try to clarify and disambiguate. So precision is indeed necessary, to the extent possible, and I appreciate that care. But human language is fundamentally ambiguous, and that's also a strength, not just a weakness. It's about being flexible.