[1] http://people.math.harvard.edu/~ctm/home/text/others/shannon...
[1] http://people.math.harvard.edu/~ctm/home/text/others/shannon...
[1] https://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.35...
It's surprisingly difficult to motivate complex- (rather than real-) valued quantum mechanics. See eg https://www.scottaaronson.com/blog/?p=4021, for example.
(As they point out, though, motivating "not quaternions" is pretty easy at least.)
Eh, this can be said about a lot of foundational disciplines/studies/theories. Philosophy of science (or philosophy of mathematics), logic, category theory, model theory etc would all fit the description. I'm not saying you're wrong, it's just that information theory isn't unique in this respect.
Even the distinction between that most vaunted science, physics, and it's far more fluid, subjective sibling, metaphysics is squarely settled in the philosopher's forum rather than the scientist's academy. To the scientist, the epistemic question is settled by your choice of field by necessity.
Another way to think of it: The Art to good Philosophy is to learn to cope with and identify those patterns of reasoning that degenerate down to navel gazing.
It is why the very tool by which we interlocute and communicate is in and of itself a matter of great philosophical concern. The ability to elicit a shared understanding of a purportedly common world phenomema is still hotly debated within philosophical circles. The question of what the essence of meaning is and what it means to be all happen far outside the borders of any science's capability to operate or even exist as standalone rational framework.
A science is a rational workshop, which is what is because of the collection tools and products of philosophically established ground states that render the space conducive to ongoing thought and reasoning.
Seriously. If yoy think philosophy is all deductive, crack open some books. Enrich thyself, and marvel.