PhyloCode is a controversial proposal for a new system of biological nomenclature
Where it diverges from Linnaeus is in recognising explicitly that there are no taxa in nature except species. All other levels, genus and kingdom, family and order and phylum, are arbitrary creations existing only by virtue of having a name. Nature does not branch into phyla or families, nature just branches. The only real kind of taxonomic group for species is a clade, a lineage consisting of an ancestral species together with every single one of its descendant species. Every time speciation occurs, a new clade is created. Potentially every single one of these might be important enough for classificatory purposes to need a name.
Clades are defined by ancestry and descent, not by features. A synapomorphy or common feature of a taxon is no longer to be a defining feature, merely a diagnostic one, making it probable that the creatures that have the synapomorphy are really descendants of the ancestor that innovated it. There can never be a paraphyletic or polyphyletic group.
The PhyloCode name would allow binomial names just like the Linnaean one, and as far as possible all existing Linnaean names would be preserved: we would still be Homo sapiens, thale cress would be Arabidopsis thaliana, and so on, except that of course the bureaucratic process of registry under PhyloCode would be an opportunity to pin down once and for all which of alternative names are to be used, where there are rival claims.
So the first element of a PhyloCode binomial designation is a clade name, not a genus. There is no longer a hierarchy of kingdom to order to genus, but clade to clade to clade indefinitely. This also means that once a species is assigned a PhyloCode name, it will virtually never be reassigned. Under the present system if you discover by DNA testing that the three-spined stickleback is actually more closely related to whelks or robins than to other sticklebacks, you're in trouble. You have to dismember the taxon they formerly both belonged to, and probably rename at least one of them (depending on whether it's a genus or something higher up that is being split).
But PhyloCode is not actually binomial. With genera no longer important, we could be called Homo sapiens but we would also be Hominidae sapiens, Australopithecus sapiens, Primates sapiens, and so on back to the top. The species name is the identifier and any rankless taxon name is a claim about history.
Under the new proposal, there is only inclusion of one clade within another. This is a theoretical claim about a particular fact of evolution: that, say, Aves descended from Dinosauria. If this turns out not to be true, the clade Aves is still a valid clade, but evolved from some other reptilian clade. No change of names is needed when beliefs about evolutionary history change. By the way, under this system birds aren't just descended from dinosaurs, they are dinosaurs, or rather they are Dinosauria, and human beings "are" reptiles, fish, and bacteria.
This phylogenetic naming system was originated in the 1980s by Kevin de Quiroz and Jacques Gauthier, and they have made rather grand claims about it, calling it a Darwinian revolution. A full draft of the proposed code was put on the Web in 2000 and can be read at www.ohiou.edu/phylocode.
Critics have piled scorn on it, saying that as well as being confusing it multiplies entities unnecessarily. You could take any group of creatures, such as all the plants in your garden, and assign a name to the clade consisting of their most recent common ancestor plus all its descendants. Unless you know exactly the evolutionary relationships of all those plants, you have no idea what this common ancestor actually was and might therefore have no way of telling whether some other plant was in the same clade. But against this, although they had a common ancestor, there is no need to name it unless it becomes significant in the course of science.
It is controversial to a significant degree because of the urgency of cataloguing all living creatures faster than the Sixth Great Extinction wipes them out. Opponents say there aren't enough scientists trained in taxonomy to do the job even under the existing system, and switching to a new one would compromise and confuse this job.