I would say it differently: natural sciences, abstract sciences and philosophy are all parts of human endeavors… In a temporal setting, philosophy was probably the first, it included the natural sciences, due to the lack of knowledge “how” things work…
…natural sciences also ask a “why”, but in a different manner than philosophy… Unfortunately we are confronted with a lack of phrases, we only have one word: “why”? Some usual questions of philosophy are “why are we are here?”, or "what is the purpose of our existence?, “what came first, the hen or the egg?”…These are irrelevant questions and they cannot be answered…
…epistemology: “how do we gain knowledge”? What are the proper methods of obtaining information?
…Natural sciences do not deal with these questions. They are only interested in pragmatic problems. “How does electricity work?” is a valid scientific question. On the other hand the question: “why is it that on the innermost electron path there can be only 2 electrons?” is not relevant. We observe that this is how it is, and do not seek a higher level of “why”? And most importantly, we never ask (in science) “who arranged that only 2 electrons can reside on the innermost electron path?”.
I say that there some things which we both accept as basic, which cannot be answered because they are basic. They are assumptions. They simply are what they are.
It’s good that you were a mathematician because you would have made a lousy scientist, conceptually.
Philosophy did not just proceed natural science temporally but precedes it necessarily at all times. I am a researcher in the field of biology. As a researcher, the first questions which I must ask myself are always metaphysical or philosophical. I observe a supposed reality (natural phenomenon), think about how to interpret what I have observed, generate a hypothesis relating the observation to others I have made, then use whatever tools I have available that are applicable to test that hypothesis. Of course, I first must ascertain whether the tools I have are up to the task, and for that I (or hopefully someone before me) must also generate and test a hypothesis, and so on. The assumptions we make when dealing with the physical world are metaphysical. In this way metaphysics and philosophy necessarily precedes natural science.
When a philosopher asks “which came first, hen or egg?”, the natural scientist asks, “how is each caused?” The philosopher retorts, “Do all things in reality have a cause?”, and the scientist realizes he cannot prove this is so but must assume it.
Assumption #1: all material things (nature) have a cause.
The philosopher may drag this question back so that science investigates the origins of the universe and discovers evidence to support a theory, the Big Bang, while also discovering evidence to discount a literal interpretation of Genesis. What caused the Big Bang? Science has yet to discover this, but it is not assumed, it is an open question…
Now the philosopher asks, “How do you know your methods of scientific deduction are useful? How do you know what tools are appropriate for determining how hens and eggs are caused or how old the universe is?” Epistomology - of the utmost importance to science. Note, this is not the question of “How do I know this isn’t all just an illusion?” but rather “How do I know I am collecting relevant information and interpreting it correctly with regard to my experiment?”
Science contributes to ethics by means of observing “natural laws”. Suicide, by all observations, is a behavior limited to humanity; altruism is not. Art, math, language, civilization are all phenomena associated exclusively with humanity, family-structure and the passing on of knowledge is not. These observations can tell us about ourselves and inform, though certainly not fully establish, codes of ethics.
Finally, asking “why is it that on the innermost electron path there can be only 2 electrons?” is the domain of philosophy but of the utmost relevance to science because questions like this are what drive scientific discovery! It’s like asking “Why don’t oil and water dissolve into one another?” It isn’t “just that way” - we do NOT assume it as a basic property and unanswerable question. The scientific question becomes “How do oil and water resist dissolution?” and “How does the presence of 2 electrons on the innermost path prevent the addition of more? Can there be less?” We then use our intellect to develop tools to test hypotheses that teach us more about the properties of “atoms”, but we don’t stop there! We develop tools to investigate
sub-atomic particles and the spaces between! Why does light show behavior related both to particles and waves? The scientific question: “How does it show each behavior? Can we alter this behavior?”
Natural science and philosophy are intrinsically intertwined. The “basic assumptions” of science are all philosophical, namely “All material things have a cause”; and the “laws” of thermodynamics are really only scientific theories based on philosophical assumptions. But the essence of science is to never stop at a basic assumption, to never
assume that a question cannot be answered.
What if humans evolved from another species? What if all life evolved from a single organism? - metaphysical questions with scientific relevance.
What if some entity
did create the universe? (metaphysical question) “Who” might be beyond the field due to lack of the appropriate tools for discovery, but it is not irrelevant to science, for discovering “who” might help us discover “how” if we know something about the “who”.
To summarize, scientists only
assume a thing to be true for practical purposes when attempting to discover something else, but that basic assumption should never be dogmatic - “that’s just how it is” has no place in science unless accompanied by “we don’t know why”. In science we ask “Why is this the case? How do we go about investigating it? Is what we have learned relevant? Now what?”
I don’t think so. Supernatural is something totally and completely beyond the physical (read natural) existence, and it is forever closed to us.
Look up “supernatural”. Your definition is too restrictive for it implies full knowledge of what is “natural”, which is silly. If the “supernatural” were forever closed to us, we would have no experience of it for that would be impossible, yet we use the term to describe observed phenomena and experiences beyond normal natural description - miracles, spirits, that for which we have to physical explanation. The natural and the “super”-natural interact.
shrug