Can you experimentally prove that you are doing an experiment?
Also, can you experimentally prove the person doing the science (the scientist) exists or is real?
This is a refutational question on scientism, as my friend believes science is everything.
Experimental technique is a skill that can be taught, and a key part of the scientific method. While it is possible to design and execute an experiment according to these rules and then convince a scientist that you are performing an experiment, the level of proof depends on the skepticism of the beholder. If the beholder is not a scientist, no level of proof might suffice.
Prove in its most strict linguistic sense usually only fits in deductive systems like a formal logic system or mathematics. In addition. we need necessary premises (axioms, definitions) to prove any non-tautological non-trivial proposition with truth value of your interest to possibly and hopefully prove or disprove.
Other than above theoretical realms, most our real life is dealing with inductive practical knowledge. Here we don't strictly say knowledge proves, while actually say knowledge reliably demonstrates such and such concluding statement. And empiricist Hume famously proposed his firm doubt about the analytic provability of such synthetic knowledge as the Problem of induction. Later many philosophers including critical rationalist Kant and polymath Russell labored hard to try to resolve this problem to make knowledge certain but without complete success...
Under this context, your above question may not be ever answered in certainty in your hoped analytically philosophical way. Philosophers with various views throughout history created numerous arguments or paradox to argue against seemingly obvious reality of some phenomena. Similar to your case to try to "prove" another person's existence, modern philosophers proposed Brain in a vat argument to challenge whether we can know ourselves' real physical existence or merely an illusory simulation. As Karl Popper pointed out, scientific knowledge can only be criticized and negated, but never can be affirmed.
Dig a little deeper in a metaphysical way, your friend's Scientism sounds very similar to modern philosopher Quine's Naturalized epistemology which seems popular due to obvious technology proliferation in modern society everywhere, also partly as a response to some intrinsic failure of all kinds of traditional epistemologies. It argues no need for philosophical discourse and labor since studying science is naturally all there is to discard any arbitrary or falsely conceived theory. But a major counter argument against scientism lies in the same above reasoning, since science is mainly founded on inductive reasoning, it's purely descriptive without normative justification from traditional philosophy. It's like a man wandering with lots of facts but without any normative or justified true belief (JTB) to light him ahead. No wonder many people nowadays just act like machines with less and less humor or wisdom...
You could verify if scientific experiments follow the scientific method. Also, in general, belief systems about sciences do not have metaphysical grounds within the greatest metaphysical issues. The sciences have systems of reference and it is in that sense that sciences have metaphysical ground.
To ask a scientist to prove the existence of their system of references or even of their scientific community is to ask a scientist to do a philosopher's job. Science deals with questions that do not deal like this with matters of existence.
You do not need to follow Descartes and prove your own existence to prove everything else (granted the existence of god).
