That's a really hard belief to justify. And what implications would that position have? Should biologists give up?
The largest of the finite simple groups (themselves objects of study as a means of classifying other, finite but non-simple groups, which can always be broken down into simple groups) is the Monster Group -- it has order 808017424794512875886459904961710757005754368000000000, and cannot be reduced to simpler "factors". It has a whole bunch of very interesting properties which thus can only be understood by analyzing the whole object in itself.
Now whether this applies to biology, I doubt, but it's good to know that limits do exist, even if we don't know exactly where they'll show up in practice.
Biologists stand out because they have already given up on that idea. They may still seek to simplify complex things by refining principles of some kind, but it's a "whatever stories work best" approach. More Feyerabend, less Popper. Instead of axioms they have these patterns that one notices after failing to find axioms for a while.
Actually, neither do Rationalists, but instead they cosplay at being rational.
What do you mean? The biologists I've had the privilege of working with absolutely do try to. Obviously some work at a higher level of abstraction than others, but I've not met any who apply any magical thinking to the actual biological investigation. In particular (at least in my milieu), I have found that the typical biologist is more likely to consider quantum effects than the typical physicist. On the other hand (again, from my limited experience), biologists do tend to have some magical thinking about how statistics (and particularly hypothesis testing) works, but no one is perfect.
Reasoning from first principles cannot span very far in reality, as for starters the complexity of the argument quickly overwhelms our capacity for it. Its numerous other limits have been well-documented.
Logicomix, Gödel Escher Bach are some common entry points.
I'm kinda new here but am surprised I haven't seen this book mentioned more. Maybe I just haven't seen it or it's old news but it seems right up HNs alley.