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The definition must be reasonably close to popular usage, yet precise enough to distinguish fascism as a twentieth century phenomenon.
Here is my suggestion - alternatives are invited:
Fascism is a form of government characterized by explicit anti-egalitarian ideals, and with a non-monarchical head of state.
or
A fascist state is an anti-egalitarian republic.
(Where republic denotes that the head of state is not a monarch, and that the state is not intrinsically religious.)
Thus fascism is a reaction - defined more by what it is not, than what it is - a reaction 1. against the egalitarianism of the mainstream left; and a reaction 2. against the divinely-ordained monarchy and/or 'theocracy' (rule by priests) of the traditional (religious) Right.
The Nationalism, which has been a very obvious feature of some fascisms, is therefore regarded as a second-order phenomenon - essentially a means for creating social cohesion: replacing on the one hand religious cohesion, and on the other hand the egalitarian ideology of Leftism.
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