Science is defined by two methodological ideals.
- Honesty - it seeks to test hypotheses rather than prove them.
- Objectivity - it gives results as written procedures anyone can follow to get the same result no matter what they want or believe.
The only restriction on subject is the applicability of these methodological ideals. They are not, for example, applicable to claims which are not falsifiable. This restricts it to the mathematical space-time structure of the universe because this is where there are things capable of measurement.
Yes, according to the above explanation the “natural” is measurable because of its mathematical space-time structure.
And the methodological restriction is necessary to science because as @beaglelady said, “We don’t find natural explanations unless we look for them.”
I think my two methodological ideas covers these 5 things described.
No. Metaphysics is the philosophical study of the nature of reality.
I am not such a one. I only believe in the spiritual because I find it impossible to believe that the mathematical description (which as a physicist I identify with physical reality) is the limit of reality itself. At least… that is the first of my reasons for belief.