I think the answers above are excellent, but I'd like to point out a related issue.
During the early 20th century we developed two entirely new types of physics, GR and QM. Its difficult to imagine two theories that were more different from each other. GR is essentially classical mechanics in a non-Euclidean geometry, QM is, well, still being debated.
So for much of the middle of the 20th century you saw the QM people trying to quantize GR, and the GR people trying to "geometrize" QM. So we had the idea of gravitons, the quanta of gravity, as well as twistors, the geometry of particles. Neither worked, and we're still largely where we started off in spite of much effort (and strings, supergravity, etc.).
The parallel is important. Classical mechanics remains spectacularly successful. So when you start thinking about something like "heat", the first thing you do is try to re-use your existing models, and presto, you get a formula for heat transfer that actually works... mostly. But as time went on we saw that some things simply didn't work that way no matter how hard we tried, like radioactivity, and eventually we stopped trying to apply mechanics to absolutely every problem.
And thus the quote. We no longer try to apply some version of Newton's original axioms to every problem because we know they aren't universal.