C. Ewing asks,
"how do we reconcile conservation of mass with singularities?"Short answer, we don't.
Longer answer: Einstein's theory of general relativity accounts for gravitation in terms of a curvature of space with a fraction x/y. Under certain concentrations of mass and energy, the y in that fraction goes to zero. As we all remember from elementary school, you can't divide by zero, it is not defined, it has no meaning.
So, what happens when our equations in physics give us nonsense results? Three possibilities: First is ignore it. When we are figuring out a length and the answer is the square root of four, we may realize that the square root of four is either positive or negative two, but since we cannot have negative lengths, we just ignore the negative possibility because it is "not physical."
Second, is we say that we need an alternative interpretation of the trouble spots, that is, we come up with some story about what happens there that is consistent with the rest of the theory so that we can keep it. Physicists talk of "smoothing out" the singularities, that is, tinkering slightly with the math so that we keep the spirit of the approach, but patch up the problems. The problem is when we have multiple possible patches, how do we decide which one we want to accept?
Third, you point at that spot as a weakness in the theory. You say that theory works well as far as it goes, but the next theory that replaces it will have to improve on this. Science gives us insight, but always opens more questions to be answered and what happens in this sort of situation would just be one of the ones we need a new theory to deal with.
This gives us a nice segue to Gwydion's question,
"What are the critiques of scientism that do not resort to or invoke supernaturalism, and what (if any) merit do you give them? Layman's terms, please."If we take scientism to be the view that the set of all justified beliefs is equivalent to the set of all legitimate scientific results, we have several problems. The first obvious one is determining what counts as a legitimate scientific result. Is it a matter of consensus among scientists? That then turns it into a sociological matter influenced by all sorts of economic, political, and race, gender, and class-based factors -- certainly not the rock solid basis that was advertised. Is it the set of conclusions that derive with certainty or high probability from that mythical logical beast "the scientific method"? There is no unique logic underlying all scientific practice and inference.
Further, tying one's beliefs to a literal interpretation of scientific theories comes with serious risk since our best theory at any given time is at least provisional. The great philosopher of science, Imre Lakatos, famously said that every theory is born refuted, in other words, scientists know that our best theories, strictly speaking are always wrong. They are useful, but they will be replaced by new theories after a time, new theories that come with different concepts. Newton's theory of mechanics and gravitation stood for 300 years, but when replaced by Einstein's theory of relativity, it required a radical revision of the basic notions of space, time, motion, mass, and energy. If we tie our cart to horses we know will die, we should not attach them in a way that doesn't allow them to be unhitched.
Finally, we come to the question of interpretation itself. The concerns with scientism are not in appeals to supernaturalism, but to metaphysics. If there was a half-way house for abused words, metaphysics is one of the poor lexicographic souls that would have to reside there. When philosophers say metaphysics (or "ontology" if we are trying to impress someone), is not pyramid power, ESP, and chaneling, but rather the study of reality. What really exists?
We want to say things about the world, for example, that there are electrons and gravitational fields, but this goes beyond the theory. Scientific theories are what an old physics prof of mine called "a bunch of squiggles." Some of those squiggles connect to observable quantities like distance or mass, things we can measure, often things we can experience. We seem to have good reason to believe these are real (although here Descartes' worry about bridging the gap between our perceptions and that which caused the perception). Other squiggles are mathematical formalism, mere grammar that is not meant to be world pointing. An equal sign or a negative sign, for example, are part of the language we use to express our equations, but not held to represent part of the system whose behavior is being described. But then there is a third group of squiggles, what we call "theoretical terms," things like potentials, affine connections, field values. these are terms we use to connect the observable terms into something we can use to make predictions about observations to come.
But are they real? The best our scientific theories will give us is that they are useful, or useful in certain contexts of modeling. The hard-core scientistic folks, for example Ernst Mach, held that because they are unobservable, they cannot be given a metaphysical status. They are mere tools, not real things. And thus Mach derided anyone who thought atoms were real. And therein lies the problem with scientism, it gets rid of God, but with him goes metaphysical entities that even the hard core lover of science would want.