Physicists have been dealing with a tricky duality for some time: is an electron (or some other baryon) a wave or a particle? In some situations it is easier to think of it as a wave, in others as a particle. Ultimately, though, it is both–especially if some variation of super-string theory turns out to be accurate.
In the same way, you could say that we humans are both matter and spirit, and you can no more cleave the 2 aspects asunder than you could cleave an electron’s waveness and particleness apart. (Don’t do a spell check on those words, I just invented them.) Of course we don’t have a mathematics-based set of equations that unites soul and body, unlike the physicists…but then why does all reality have to be explained in terms of math?