My gut reaction to these arguments has always been to disagree, however I think that I have been missing the more nuanced interpretation, with which I actually

My gut reaction to these arguments has always been to disagree, however I think that I have been missing the more nuanced interpretation, with which I actually agree. Of _course_ biology won't be explainable using just the mathematics for basic physics. Quantum physics and classical physics are able to account for an enormous amount of the complexity of in the universe. However, their representation is so compressed, and has been developed and tested on such 'low dimensional' system, that there are surely mathematical laws that they simply cannot encode, nor should we expect them to. The number of stable combinations of fundamental particles and the number of different orbital configurations etc. etc. are a set of rules with which everything 'must' be consistent (unless there is a major shift in our understanding of the fundamental laws of the universe). However, they give us little to no insight into what other constraints might be imposed on systems where the phenomena they describe are merely parts (yes I know that I have a wave function). All this to say that it seems to me that there must be other mathematical laws that do not follow directly from 'basic' physics, that also constrain the behavior of more complex physical systems. The answer is not therefore that biology irreducible to some mathematical description, which is how I usually interpreted these arguments, but rather that there are additional mathematical laws that are needed. Perhaps that rather than despairing at the 'irreducibility' of biology to physics, we merely need to extend our notion of 'physics' to include the mathematical laws that constrain biology.