From the Polyani quote in the text of Part I:
‘The recognition of certain basic impossibilities has laid the foundations of some major principles of physics and chemistry; similarly, recognition of the impossibility of understanding living things in terms of physics and chemistry, far from setting limits to our understanding of life, will guide it in the right direction.’7
Williams then extends Polanyi’s insight to label each “level of the autopoietic heirarchy” as being impossible to be explained by the one below it (Part I and II). Therefore, Williams believes that each level of the autopoietic hierarchy cannot be naturalistically explained by the level below, and thus each level (from a materialistic point of view) represents a “Polanyi impossibility.”
The attributes of water cannot be derived from the attributes of hydrogen and oxygen taken separately.
Therefore water is impossible.
I thought that Williams' resort to the language of "Polanyi impossibility" was a tad unfortunate. But I can understand his basic motivation for putting the problem that way. (I.e., it makes the concept easier for laymen to grasp.)
I imagine that what Polanyi was speaking of is more correctly given in the language of "Polanyi plateaus", which are not "convergent." Each "plateau" has its own level of description adequate to its function in the overall scheme of life. The point is, the "lower level" plateau(s) don't (can't) explain the "plateaus" of higher hierarchical order.