An archaic or rare form meaning opposed to or opposed to aristocracy and aristocratic systems.
From anti- (against) + aristocratical (Greek aristos best + kratia rule, plus -ical forming an archaic adjective). The -ical ending was common in older English but is rarely used this way in modern language.
The -ical suffix appears in older texts like 18th-century political writings, where you'd find phrases about antiaristocratical sentiments—it's a window into how English speakers emphasized abstract political concepts!
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