Despite its recent popularity, Emergence is still a field where philosophers and physicists often talk past each other. In fact, while philosophical discussions focus mostly on ontological emergence, physical theory is inherently limited to the epistemological level and the impossibility of its conclusions to provide direct evidence for ontological claims is often underestimated. Nevertheless, the emergentist philosopher’s case against reductionist theories of how the different levels of reality are related to each other can still gain from the assessment of paradigmatic (...) examples of discontinuity between models in physics, even though their implications must be handled with care. (shrink)