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In effect, what the General seems to be saying is that, if something cannot be demonstrated by means of the scientific method, then that something cannot be real. This strikes me as being a "pre-analytical notion" that has been smuggled in as a first principle without any kind of prior critical analysis. The "principle" is simply assumed to be true....

The "principle" is not only too far up the ladder to be a first principle, but it is ignored when inconvenient. Lots of evo stuff can't be demonstrated by the scientific method:

A FEW of the MATERIALIST'S MIRACLES	When the process was observed/ repeated
Matter has always existed/ matter is eternal.
Matter existed before (!) time began. Matter takes up space, space is impossible w/o time.
All the matter was compressed into the size of a point (some say "infinitely small").
The point exploded (The universe created itself).
Time began.
The universe was 100 trillion degrees celsius (some say "infinitely high").
Only quarks and photons existed which gave rise to hydrogen.
Hydrogen gave rise to all the other elements.
Some particles accelerated beyond the speed of light. (requires infinite energy)
Particles departing from each other at the speed of light formed planets and stars
Rain on rocks gave rise to life (spontaneous generation)
Rocks gave rise to intelligence.
1-celled structures invented their own genetic info.
Frogs gave rise to princes.