Perhaps the genus should not be Socialism.Perhaps Collectivism should be the genus and that Socialism,Communism,Facism and Nazism are the species.The other contrast would be Individualism as the genus with Libertarianism,Classic Liberalism etc as the species.
I think you've nailed it here. The genus/species device is great. It captures with a bit more elegance the point I was trying to make in my #167 -- which is that there are two variables to consider, but that they are not of equal importance and their rank must be considered.
The first variable is whether or not the government is going to force some kind of social/economic idealogy down the throats of its citizens.
The second variable is which ideology that's going to be.
And the first is clearly ranked higher since the importance of the second is predicated upon the condition of the first. The first variable is primary; the second is a modifier.
So with regards to socialists and fascists, they could be quantified like this (forgive my ham-fisted latinizations here):
either...
collectivus socialistus and collectivus fascistus
or perhaps...
socialistus progressivus and socialistus nationalistus
With regard to the original article, it appears Piekoff would lean towards the second grouping, with "socialist" as the genus designation.
LOL, zoology and politics...
Seriously though, perhaps the politics in not the primary.Maybe all totalitarian/authoritarian politics are a branch of Platonic collectivism which then would be the true genus.Plus we would also have to give thanks for Hegel's contribution to insaneapoliticus.