I'm not sure I follow. Godel's incompleteness theorems referred to first order logical languages being unable to completely and consistently symbolise basic arithmetic - this doesn't mean the universe at large doesn't operate according laws and rules than can be described by a single grand unified theory, and I really don't see what it has to do with reductionism
Reality dies not operate according to laws and rules, we just perceive it as such. Reality just is. A scientific hypothesis is a map of reality it is not reality. We formulate the actions of reality into
logical understandings. Which was I think Godel's point.
Godel's theorem basically says that a some statements cannot be proved or disproved from a set of axioms. If those axioms are consistent. Therefore what Godel suggest (if we apply his reasoning to science) is that if we are to understand reality in its entirely we may need to make inconsistent theories*.
Why can't we, in principle, derive biological theories from their biochemical, chemical, or even physical underpinnings?
That's not the important question. The question is
can we, in principle, derive biological theories from their biochemical, chemical, or even physical underpinnings?
I am not saying that it is not possible in this specific case however it is possible that some "actions" of reality cannot be explained by a strict reductionist approach. They may be computationally derivable but not analytically derivable.
Err... no. The inconsistency between GR and QM means that either one, the other, or both, are false.Physicists, myself included, tend to err on the side of QM; unforuntately for Einstein, GR is not as good as QM.
The inconsistency between GR and QM does not mean one is false.
A thing containing things that behave according to mathematically describable laws.
This is a terrible definition. My cup of coffee consists of a thing (the cup) that contains a thing (coffee) that behave according to mathematically describable laws. Does Starbucks have multiple universes within its premises?
*His position was actually more extreme in the sense that he thought attempts to find a "Grand Unified Theory" were fundamentally "misguided".