Life is one of those things that we can recognize in the extremes but gets difficult as we get into the grey.
It is clear that by whatever definition that would work for most people you are alive and your desk isn't. The challenge rears up as you get down to simpler and simpler things. A good example is viruses (viri). There are those who would argue they are alive and those who would argue they are not. So your definition has to decide what is it about them that makes them alive or not.
One suggested definition is something which is an imperfect replicator. In this case, some chemicals can fall into the living category. To exclude them you would have to add the idea of it maintaining a thermodynamic disequilibium. However, I think you then have to argue over "for how long? ". You can mess around a lot and still have trouble getting a really good definition.
BTW and off the official topic of this thread:
If the big bang produced zero carbon (and I think it did, in fact, produce very little if any at all) there is no problem for carbon based life. Close enough to ALL of the non hydrogen or helium elements were formed after the big bang.
It is not improable at all. We (the universal we more than I) understand the steller phyics of supernovae which is where the heavier elements came from. Stars are hydrogen "burning" engines and big ones end their lives by a sudden production of heavier elements in a supernova; both producing them and spewing them out into space.
All stars "burn" hydrogen into carbon.
I'd say if that is an example of the book in general you should get rid of it at a rummage sale.