How is the scientific method derived from philosophy?
Philosophical truths necessarily must preceed (have priority or come before) the rules of science. In fact, the act of creating rules (for categorization, testing, evaluation, validations, meaning, purpose, consistency of interpretation, falsification, etc. etc.) all must exist before there can be any empirical science.
The scientific method is a collection of rules that scientists follow. Science cannot create itself – nor can mathematics create itself. Philosophy creates the rules which are based on reason, logic – and what we call “meaning” or “purpose”.
Metaphysics is the study of the higher laws of being and reason. Science is dependent on philosophy - necessarily. The rules of logic are developed by philosophy – not through scientific experiments in test tubes or biology labs.
The rules of logic and mathematics are not traced to any molecular activity (thus, materialism is refuted on that point alone).
Permitting this assumption, how does that make philosophy a science?
I can’t see how that question is going to help you much since it doesn’t follow from anything that has been said so far. Empirical science is derived from philosophy. Science cannot exist without philosophy.
In simpler terms, you are not arguing with anyone here using science at all – you’re using philosophical terms.
The reason philosophy is generally not considered a science is because science requires observations, hypotheses, testing and predictions.
Those are all philosophical constructs. Science cannot explain what a hypothesis is. Science can only deal with material reality. If a hypothesis can be found in a collection of molecules somewhere – and then measured and analyzed, then it would be something scientific.
Instead, however, a hypothesis is a philosophical construct. It follows rules created by philosophy, not science.
Which areas of study in philosophy produce this?
Again, the challenge is for you – which scientific papers show the origin and physical composition of a thing called a “hypothesis”?
Science is completely powerless to even explain its own rules and findings – it must rely on philosophy.